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Determination of coefficient of storageby use of gravity measurements.
Item Type Dissertation-Reproduction (electronic); text
Authors Montgomery, Errol Lee,1939-
Publisher The University of Arizona.
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Link to Item http://hdl.handle.net/10150/190978
DETERMINATION OF COEFFICIENT OF STORAGE
BY USE OF GRAVITY MEASUREMENTS
by
Errol Lee Montgomery
A Dissertation Submitted to the Faculty of the
DEPARTMENT OF GEOSCIENCES
In Partial Fulfillment of the RequirementsFor the Degree of
DOCTOR OF PHILOSOPHYWITH A MAJOR IN GEOLOGY
In the Graduate College
THE UNIVERSITY OF ARIZONA
1971
THE UNIVERSITY OF ARIZONA
GRADUATE COLLEGE
I hereby recommend that this dissertation prepared under my
direction by Errol Lee Montgomery
entitled
DETERMINATION OF COEFFICIENT OF STORAGE BY
USE OF GRAVITY MEASUREMENTS
be accepted as fulfilling the dissertation requirement of the
degree of DOCTOR OF PHILOSOPHY
Notles..Ltr- /9 7ODate
// .
//11/ 3 / 7(-,) s atign Co- irecto Date
Affér inspection of the final copy of the dissertation, the(....--
following members of the Final Examination Committee concur in
its approval and recommend its acceptance:*
s approval and acceptance is contingent on the candidate'sa quate performance and defense of this dissertation at thefinal oral examination. The inclusion of this sheet bound intothe library copy of the dissertation is evidence of satisfactoryperformance at the final examination.
STATEMENT BY AUTHOR
This dissertation has been submitted in partial fulfillment of
requirements for an advanced degree at The University of Arizona and
is deposited in the University Library to be made available to borrow-ers under rules of the library.
Brief quotations from this dissertation are allowable withoutspecial permission, provided that accurate aknowledgment of source
is made. Requests for permission for extended quotation from or re-
production of this manuscript in whole or in part may be granted by
the head of the major department of the Dean of the Graduate College
when in his judgment the propsed use of the material is in the inter-
ests of scholarship. In all other instances, however, permission
must be obtained from the author.
SIGNED: A) _
ACKNOWLEDGMENTS
Grateful acknowledgment is given to Dr. John W. Harshbarger
and Dr. John S. Sumner, Department of Geosciences . , The University of
Arizona, who jointly supervised this study and reviewed the disserta-
tion. The advice and assistance of Drs. Willard C. Lacy, Willard D.
Pye, Joseph F. Schreiber, Jr., and Jerome J. Wright, who served on my
doctoral committee, are sincerely appreciated.
Financial support through the 1968-1969 and 1969-1970 aca-
demic years was provided by a National Defense Education Act Fellow-
ship. Field equipment and back-up facilities were furnished by the
Water Resources Research Center Allotment Grant A-017.
The staff members of the Department of Agricultural Engineer-
ing, The University of Arizona, were especially helpful in providing
basic hydrologic data in the field area. Many of my fellow students
are acknowledged for their assistance with field work and data reduc-
tion. Special acknowledgment is made to my wife, Ann, whose en-
couragement and help were instrumental in making this dissertation
possible.
iii
TABLE OF CONTENTS
Page
LIST OF ILLUSTRATIONS vii
LIST OF TABLES xi
ABSTRACT
INTRODUCTION 1
Statement of Problem 1Location and Drainage 2Source and Periods of Data 4Previous Work 4
COEFFICIENT OF STORAGE 7
Specific Yield 7Saturated-zone Effects 7
GEOMETRIC EFFECTS 10
The Bouguer Slab 11Modification of the Bouguer Slab Equation
for Groundwater Use 11
ANALYSIS OF THE INTERPRETATIONAL MODEL 13
Model Errors Due to Water-table Gradient andFinite Area of Water-level Change 13Gravity Effect of a First-order Tilted Slab 14Gravity Effect of a Second-order Tilted Slab 16Errors Due to Slab Tilt 18Errors Due to Limited Slab Size 19
Corrections of Errors Due to Inexact BouguerSlab Assumptions 20
Errors Due to Spatial Changes in Coefficient of Storage • • 20Vertical Changes in Coefficient of Storage 21Lateral Changes in Coefficient of Storage 21
Other Interpretational Models 21Composite Geometric Models 22Graticule Analysis of Irregular Models 22Analysis of Irregular Models by Integration 23
iv
TABLE OF CONTENTS--Continued
UNSATURATED-ZONE EFFECTS
Page
26
Vadose Water 27Soil Water 27Intermediate Water 27The Capillary Fringe 28
The Gravity Effect of Water in the Unsaturated Zone • • • • 29Changes in the Amount of Vadose Water
Due to Irrigation and Precipitation 29Changes in the Amount of Vadose Water
Due to Infiltration from Surface-water Bodies • • • 30
COLLECTION AND REDUCTION OF GRAVITY DATA 32
The Gravity Meter 32Instrument Errors 33
Procedure for Gravity Surveys 35Base Stations 36Field Stations 36
Corrections for Time and Position 36Correction for Time Variations 38Correction for Position Variations 41
The Reduction Procedure Used in This Study 44Relative Gravity 45
Methods of Increasing the Accuracy of Future Studies . • • 45Reducing the Error Due to Variation in Vertical Position 45Reducing the Tidal Correction Error . . . . .. 47Reducing the Error Due to Temperature Tilt 47
FIELD TEST AREA 48
Geologic Features of the Tucson Basin 48Rillito Beds 49Basin-fill Deposits 50Terrace Deposits 51Flood-plain Alluvium 51
Geohydrology of the Ewing Farm Area 52Geology 52Hydrology 56
Storage Estimates by Others 62Ewing Farm Studies 62Water Resources Research Center Studies 63Tucson Basin Studis 65
Movement of Water in Unsaturated Zone 66Extent of Lateral Movement 66Time Span of Excess Unsaturated-zone Water 68Conclusions 69
vi
TABLE OF CONTENTS--Continued
Page
COEFFICIENTS OF STORAGE COMPUTED BY THEGRAVITY METHOD 71
Relative Gravity versus Time 72Relative Gravity versus Water-level Decline 75Computation of the Coefficient of Storage Using
the Bouguer Slab Interpretation Model 75Modification of the Coefficient of Storage Values 76
Corrections Due to Water-table Slope 77Corrections Due to the Areal Extent of
the Water-table Decline 77Corrections Due to Other Inexact Model Assumptions 78
Corrections Due to Unsaturated-zone Effects 81The Unsaturated-zone Effect Due to
Infiltration from Precipitation 81The Unsaturated-zone Effect Due to
Infiltration from Irrigation. 82The Unsaturated-zone Effect Due to
Infiltration from Ephemeral Stream Flow 83Corrections Applied to Coefficient of Storage
Values Computed in the Ewing Farm Area 101Statistical Measures of Ewing Farm
Coefficient of Storage Values 104Analysis 104Conclusions 109
EVALUATION OF THE GRAVITY METHOD 111
Conditions under Which the Gravity Method May Be Used 112Geohydrologic Conditions 112Geographic Conditions 113
Comparison of the Gravity Method with OtherConventional Methods of Determiningthe Coefficient of Storage 114
-Advantages of the Gravity Method 114Disadvantages of the Gravity Method 115Conventional Methods of Determining
the Coefficient of Storage 115
SUMMARY OF CONCLUSIONS 120
APPENDIX: PLOTS OF RELATIVE GRAVITY VERSUS WATER-LEVEL DECLINE AT GRAVITY STATIONS 124
REFERENCES 142
LIST OF ILLUSTRATIONS
Figure Page
1. Index Map of the Ewing Farm Area 3
2. Schematic Drawing and Hydraulic Data of aPortion of a Water-table Aquifer 9
3. Terminology of the Tilted Slab 15
4. Index Map of Gravity Stations andWells on the Ewing Farm 37
5. Comparison of Computed and Observed Tide Corrections 39
6. Geologic Map of the Ewing Farm Area,Pima County, Arizona 53
7. Driller's Log and Drilling Sample SizeAnalysis of Ewing Farm Well E-2R 54
8. Groundwater Table Contours, 1970, Ewing Farm Area . 57
9. Hydrographs of Wells on the Ewing Farm and Vicinity. . in pocket
10. North-south Cross Section through theWest Boundary of the Ewing Farm 61
11. Hydrograph of Observation Well E-2 andRelative Gravity at EW-1 73
12. Hydrograph of Observation Well D-2 andRelative Gravity at NE-6 74
13. Dates of Gravitational Field Intensity Measurements . 84
14. Distribution and Uncertainty of ComputedCoefficient of Storage Values 105
15. Relative Gravity versus Water-level Declineat Station EW-1 125
16. Relative Gravity versus Water-level Declineat Station EW-2 126
vii
viii
LIST OF ILLUSTRATIONS- -Continued
Fig re Page
17. Relative Gravity versus Water-level Declineat Station EW-7
18. Relative Gravity versus Water-level Declineat Station NW-2
19. Relative Gravity versus Water-level Declineat Station NW-3
20. Relative Gravity versus Water-level Declineat Station NW-4
21. Relative Gravity versus Water-level Declineat Station.EW-13
22. Relative Gravity versus Water-level Declineat Station N-1
23. Relative Gravity versus Water-level Declineat Station N-2
24. Relative Gravity versus Water-level Declineat Station N-3
25. Relative Gravity versus Water-level Declineat Station N-S
26. Relative Gravity versus Water-level Declineat Station EW-16
27. Relative Gravity versus Water-level Declineat Station NE-4
28. Relative Gravity versus Water-level Declineat Station NE-5
29. Relative Gravity versus Water-level Declineat Station NE-6
30. Relative Gravity versus Water-level Declineat Station NT-7
31. Relative Gravity versus Water-level Declineat Station ENE-1
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
LIST OF TABLES
Table Page
1. Slab Coefficients (K) and Half Slab Coefficients(K/2) Relating Tilted Finite First-order andSecond-order Slabs to Equation (1) 17
2. Summary of Errors Due to Imprecise Gravity Surveyand Data Reduction Methods 46
3. Coefficients of Storage at Selected Field Stationson the Ewing Farm 76
4. Statistical Data and Coefficients of Storage 103
ix
ABSTRACT
The purpose of the study was to develop a method to determine
the coefficient of storage of a water-table aquifer by correlating change
in gravitational field intensity with change in groundwater storage. In
theory, this purpose may be accomplished by modifying the Bouguer slab
equation to coefficient of storage equals 78.3 times the ratio of change
in gravity in milligals to change in water-table elevation in feet. Errors
which result from the Bouguer slab assumptions may be corrected through
analysis of tilted finite slabs.
Field investigations were made to test the theory. The study
area is located in the northern Tucson basin, Pima County, Arizona, and
lies on unconfined basin-fill deposits and flood-plain alluvium aquifers.
The basin-fill aquifer overlies less permeable Rillito beds and is over-
lain by the flood-plain alluvium. The two upper aquifers are flat-bedded
heterogeneous deposits of sand and gravel. The water table through
these aquifers slopes westward at a rate of approximately 0.5 degree.
Estimates of the coefficient of storage for the basin-fill deposits and
the flood-plain alluvium have been previously made by others from lab-
oratory and field tests and by model analyses. The most reliable deter-
minations of the coefficient of storage range from 0.15. to 0.30.
The significance of the gravity method lies in determination of
the coefficient of storage by measuring the quantities which define it:
rise or decline in head and weight of water placed into or removed from
storage. Change in gravity was determined by repeated gravity surveys
xi
using the same set of field stations through the period, October 1968 to
June 1970. Water levels in wells were recorded for the same period. The
relationship between change in gravitational field intensity and change in
head was determined using a straight line solution method, and the coef-
ficient of storage was computed from the slope of the straight line.
At the conclusion of the field investigations, coefficients of
storage were computed for 17 field stations. After correction for limited
area of water-level decline and for water-table slope, the values of the
coefficients ranged from 0.11 to 0.41. An error analysis indicates a
maximum probable error in gravity data of + 26 microgals. This error may
be reduced by modifying the survey and reduction procedures and by
using a more sensitive gravimeter.
Analysis of changes in gravitational field intensity resulting
from change of amounts of water in the unsaturated zone indicates that
the coefficient of storage computed for field stations near Rillito Creek,
the source of the unsaturated-zone water, are too low. Using data from
stations least affected by gravity increases after stream recharge, a
probable range of 0.25 to 0.29 was determined for the coefficient of
storage in the study area. The range for values of the coefficient of
storage using the gravity method confirms the larger coefficient of stor-
age estimation made by others for the same area.
The study indicates that the gravity method may be used with
success over aquifers which have high coefficients of storage and in
which the water table rises or declines 20 feet or more. However, large
changes in the water content of the unsaturated zone cause gravity data
to show large scatter with respect to water-level data. For this reason
the gravity method is more suitable for analysis of those portions of a
water-table aquifer which are recharged by underflow than for the por-
tions recharged by infiltration from surface sources.
xii
INTRODUCTION
Statement of Problem
The problem treated in this dissertation is an evaluation of the
usefulness of gravity meter measurements in defining mass changes cor-
responding to change of groundwater levels and relating these changes
to the coefficient of storage. A change in gravitational field intensity
over an unconfined aquifer may be caused by a combination of several
effects.
An unsaturated-zone effect results from changes in the amount
or position of water in the unsaturated zone. Such changes may be
caused by infiltration and subsequent movement of water derived from
precipitation, irrigation, and stream flow. The amount of water in the
unsaturated zone is not a direct function of the coefficient of storage;
therefore, the unsaturated-zone effects must be quantified to permit
analysis of changes due to other effects.
A geometric effect is due to the shape and dimensions of the
solid defined by successive positions of the water table together with
the aquifer boundaries. This solid represents the portion of the aquifer
that undergoes drainage or resaturation with a decline or rise in the
water table and therefore undergoes a change in mass. An interpreta-
tional model must be developed to analyze the change in gravitational
field intensity due to the change in mass of such a solid.
A saturated-zone effect results from the change in density of
the portion of a water-table aquifer which is resaturated or drained due
1
2
to an increase or decrease in groundwater storage. The change in gravi-
tational field intensity due to the saturated-zone effect is related to the
quantity of water which moves into or drains from the portion of the
water-bearing media through which the water table moves. The change
in density associated with water-table movement is thus controlled by
the coefficient of storage
The precise numerical value of the coefficient of storage is dif-
ficult to determine by conventional techniques. The gravity method may
provide a collaborative technique for determining the numerical value of
this aquifer property.
Location and Drainage
The University of Arizona Ewing farm was chosen for this study
as a locality in which to test the application of this gravity method. The
Ewing farm lies in the SW1/4 sec. 20, T. 13 S. , R. 14 E. , which is
near the northern edge of the Tucson basin in the Basin and Range physi-
ographic province of southern Arizona. The northern part of the Tucson
basin is bounded on the west by the Tucson Mountains, on the north by
the Santa Catalina Mountains, and on the east by the Tanque Verde and
Rincon Mountains. Figure 1 is an index map of the Ewing" farm area.
The northward-flowing Santa Cruz River together with its tribu-
taries drains the basin. Rillito Creek, a major tributary of the Santa
Cruz River, trends westward through the Ewing farm draining the north-
ernmost portions of the Tucson basin. The Santa Cruz River in the
Tucson area, as well as Rillito Creek in the vicinity of the Ewing farm,
are ephemeral streams.
R. 14 E.
T. 13 S,
,,..,
20
Ewing //7
W %4Farm z,30 29
/Phoenix \ /
\ /\ /
0Tucson
N
3
Figure 1. Index Map of the Ewing Farm Area
4
Source and Periods of Data
Gravity data were collected in the field from October 1968 to
June 1970. Water-level measurements during the same period were made
in observation wells on the Ewing farm property. Additional water-level
measurements made by the Agricultural Engineering bepartment, The
University of Arizona, prior to and during the same period were used as
supplementary basic data.
Previous Work
Gravimetry has been applied to geohydrologic problems in the
past, but its use has been largely restricted to investigating geologic
structures which control the occurrence and movement of ground water.
When the investigations which led to this dissertation were started,
there were no published reports of surface gravity methods which could
be used to compute the coefficient of storage of an aquifer. Therefore,
both the development of the theory of this gravity method and the field
testing of the method were believed to be original work. Prior to the
completion of this dissertation, Eaton and Watkins (1970) reported on
gravity methods which may provide a means of estimating the specific
yield of an aquifer. They show four interpretative models and curves
representing various Bouguer gravity profiles associated with several
water-level positions and specific retention values. These investigators
suggest that "if precise gravity measurements were made periodically in
an area where annual fluctuation of the water-table was around 100 feet,
or where, over a period of years, water levels declined by this amount
as a result of inadequate recharge, they would provide a means of
5
estimating the specific yield of the materials drained." No field experi-
ments were reported.
The geology and hydrology of the northern portion of the Tucson
basin have been described by many authors. The most recent works are
given below.
Schwalen and Shaw (1957 and 1961) and Heindl and White (1965)
have reported on Tucson basin hydrology. Davidson (1970) has prepared
a comprehensive work on the hydrology and geology of the Tucson basin
in which many new facts and interpretations are presented. Wilson and
DeCook (1968), Wilson (1969), and Matlock (1970) have reported on
hydrologic field experiments along Rillito Creek and the Santa Cruz
River in the Tucson area. The Tucson office of the United States Geo-
logical Survey, Water Resources Division, and The University of
Arizona, Agricultural Engineering Department, have gathered hydrologic
data in the Tucson basin for many years. These data, together with
open-file maps, are available.
Several University of Arizona students have written theses and
dissertations on the geology and hydrology of the Tucson basin. In-
cluded among these are Coulson (1950)--Tertiary stratigraphy; Blissen-
bach (1951)--alluvial fans; Brennan (1957)--Tertiary straftigraphy;
Kidwai (1957)--groundwater and stratigraphy; Voelger (1953)--Cenozoic
stratigraphy; Maddox (1960)--Tertiary and Cenozoic sedimentology;
Streitz (1962)--stratigraphy and hydrology; Ganus (1965)--groundwater
hydrology; and Pashley (1966)--stratigraphy and structure. Geophysical
and hydrologic theses and dissertations pertinent to the Tucson basin
have been written by Bhuyan (1965)--gravity; Abuajamieh (1966)--Ter -
tiary structure; and Davis (1967)--gravity, hydrology, and structure.
6
COEFFICIENT OF STORAGE
Theis (1935) brought about a major advancement in groundwater
hydraulics with the development of the non-equilibrium formula which
introduced the coefficient of storage. The coefficient of storage, S, of
an aquifer is defined as the volume of water released or taken into stor-
age per unit surface area of the aquifer per unit change in the component
of head normal to that surface. The coefficient of storage is a dimen-
sionless term; its nurnerical value ranges from a maximum of approximate-
ly 0.30 under water-table conditions to a minimum of about 0.00001 under
artesian conditions. In the present work attention is given to only the
larger values, those found under water-table or non-artesian conditions.
Specific Yield
The quantity of water yielded by gravity drainage from saturated
water-bearing material is termed the specific yield and is expressed as
a percentage of the total volume of the material drained. In theory the
value of the coefficient of storage of an unconfined aquifer and the spe-
cific yield of the aquifer are equal (Ferris, 1949, p. 233).
Saturated-zone Effects
The change in gravitational field intensity over an unconfined
aquifer which undergoes a change in storage is attributed in part to the
quantity of the water which is added to or lost from storage. The gravity
effect due only to the change in density in the saturated zone is here
informally termed the saturated-zone effect. The saturated-zone
7
8
effect is controlled both by the density of water and by the amount of
water that will drain from a unit volume of representative aquifer material.
Figure 2 is a schematic drawing of a portion of a water-table
aquifer. Here the density of the saturated sample is 2.40 gm/cc, and
the gravity-drained density is 2.20 gm/cc. Thus, the change in density,
or the density contrast, is 0.20 gm/cc.
The coefficient of storage, or the specific yield of the aquifer
sample, may be related to the density contrast by the equation:
S = Saturated Density - Gravity-drained Density
Fluid Density
Density Contrast Fluid Density
The density of water under normal temperatures and concentrations of
dissolved solids is very nearly equal to one. Therefore, the coefficient
of storage of a water-table aquifer and the density contrast due to grav-
ity drainage may be equated.
The saturated-zone effect is demonstrated to be determined by
the density contrast of the aquifer materials under saturated and gravity-
drained conditions. It is also equivalent to the coefficient of storage.
The density contrast S of a water-table aquifer may be estimated by
weighing in the laboratory an aquifer sample under both saturated and
gravity-drained conditions. The coefficient of storage may also be de-
termined by "weighing" large portions of an aquifer with a gravimeter
by determining the change in gravitational field intensity corresponding
to a change in depth to ground water.
Specific Yield orCoefficient of Storage (S) = 0.20
Specific Retention = 0.10
Porosity = 0.30
Saturated Density = 2.40 gm/cc
Gravity-drained Density = 2.20gm/cc
Density Contrast = 0.20 gm/cc
Figure 2. Schematic Drawing and Hydraulic Data of a Portionof a Water-table Aquifer
9
GEOMETRIC EFFECTS
The saturated-zone effect discussed in the preceding section is
equated to the change in density of the portion of a water-table aquifer
which is resaturated or drained due to an increase or decrease in ground-
water storage. The change in field intensity due to the size and shape
of the volume undergoing a change in mass is here informally termed the
geometric effect.
The shape and dimensions of the portion of the aquifer undergo-
ing a change in mass may be described by successive positions of the
water table together with the aquifer boundaries. In many areas the
slope of the water table does not exceed a few degrees from horizontal.
The smoothed slope over a square mile area is often less than one de-
gree. Thus, successive positions of the water table may be approximated
by horizontal planes. Any pair of these planes describes a horizontal
slab whose thickness is equal to the rise or decline of the water table.
The areal extent of the horizontal slab is limited to the area
under which the water-table rise or decline is relatively constant.
Therefore, the boundaries of the slab may be represented by aquifer
boundaries or by other portions of the aquifer in which the water-level
change was significantly different than that represented by the slab
thickness. Although the areal extent of a uniform water-level change is
finite, the horizontal slab used to approximate the water-level change
is assumed to be infinite.
10
11
Geometric effects may be approximated by the gravitational
field intensity due to the infinite horizontal slab interpretational model
introduced above. Saturated-zone effects may be incorporated in the
model as the density contrast.
The Bouquer Slab
The infinite horizontal slab is used as an interpretational model
in gravimetry when the body under investigation exhibits large horizontal
and small vertical dimensions and small deviations from a horizontal at-
titude. The density of the slab is assumed to be constant. The infinite
slab geometry is common and is termed the Bouguer slab.
The gravitational field intensity due to a Bouguer slab is given
as:
g = 0.012770t milligals per foot (Garland, 1965, p. 68)
where g is gravitational field intensity in cm/sec 2 , (5 is the density
contrast of the slab with the surrounding material, and t is the slab
thickness in feet. Note that the gravitational attraction of the slab
varies only with its thickness and density contrast and not with depth
of burial.
Modification of the Bouquer SlabEquation for Groundwater Use
It has been concluded that the density contrast of aquifer mater-
ials undergoing drainage or resaturation was equivalent to the storage
coefficient S. Therefore, S may be substituted for C5 in the Bouguer
slab equation. The thickness of the slab t is the distance in feet that
the groundwater levels have risen or declined since the initial gravity
observation. Because the thickness of the slab is defined as a change
12
in water- level elevation, t is replaced in the equation with nt. Gravi-
tational field intensity g, due to the rise or decline of water levels, is
found by subtracting subsequent values of field intensity from the initial
value. Therefore, g is replaced in the equation with Pg reflecting the
difference in gravitational field strength. Substituting these modifica-
tions into the Bouguer slab equation gives:
Pg = 0.01277S Lt
Lg or S = 78.3 .
(1)Pt
Equation (1) expresses the coefficient of storage uniquely as
a linear function of differences in gravitational field intensity and cor-
responding differences in water-table elevation. A straight line solution
of this equation may be made using an arithmetic plot consisting of
simultaneous water-level and gravity measurement data pairs. The
slope (
ng ) of the line of best fit through these data points may beLt
measured and used directly to compute an uncorrected coefficient of
storage.
It may be anticipated that the plot of data pairs just described
may exhibit some degree of scatter. The degree of scatter is a function
of errors in the gravity survey and the reduction method, of errors due to
short-term or long-term deviations from the Bouguer slab assumptions,
and of the magnitude of unsaturated-zone effects. If the scatter due to
these causes is random, no correction may be necessary to the coeffi-
cient of storage computed using equation (1). However, some or all of
the causes of scatter may be systematic and give rise to errors in the
slope of the line of best fit through the data pairs.
ANALYSIS OF THE INTERPRETATIONAL MODEL
The Bouguer slab interpretational model is used in this disser-
tation because of its unique linear relationship to slab thickness which
permits a straight line solution using several data pairs. Other interpre-
tational models yield equations which are not linear with model dimen-
sions; they vary also with depth and lateral displacement of the mass
change from the point of measurement. If a model other than the Bouguer
slab is used, a separate solution for coefficient of storage would be
required for each measured change in water-level elevation and the cor-
responding change in gravitational field intensity.
The most serious defects in using the Bouguer slab model are
the required assumptions that the water table is horizontal both before
and after the rise or decline and that the water-table movement is equal
at every point throughout an infinite aquifer. In most unconfined aqui-
fers, the water table slopes regionally and locally. The areal extent of
a rise or decline of a water table is variable with time. The significance
of these defects may be assessed more precisely by developing finite
tilted models and comparing their gravitational field strengths with that
of the Bouguer slab.
Model Errors Due to Water-table Gradient and Finite Area of Water-level Change
Several models are developed in this chapter. A model having
a single constant slope and finite lateral dimensions is termed a first-
order slab. A model consisting of two half slabs, each having a unique
13
14
constant slope, is termed a second-order slab. The gravity effects of
the first- and second-order slabs are computed in this chapter, and the
results of several examples are given as coefficients (K) to equation (1)
in the form:
ng S = 78.3 (K) nt
where (K) modifies equation (1) to give the gravitational field intensity
due to a tilted slab or a slab with a finite areal extent at a specific
depth of burial.
Gravity Effect of a First-order Tilted Slab
The gravity effect of a uniform vertical movement of the water
table may be approximated by a slab having a constant slope equal to
the smoothed water-table gradient, a thickness equal to the uniform rise
or decline, and an areal extent equal to a square or rectangle approxi-
mating the area of uniform rise or decline. The gravitational field inten-
sity due to a first-order tilted finite slab at a point above its center was
computed using the equation given by Grant and West (1965, p. 274),
g = 2GC5t[1/2sind (ln A - Y _ B - Y
+ cos d (tan -1 Y (1 + sin d - x cos d) B (x sin d = h cos d)
Y (h sin d- tan-1 - x cos d) (2)B (x sin d + h cos d)
using the nomenclature of Figure 3 and where
A =i(x - 1 cos d) 2 = (h + 1 sin d) 2 + y2
and
B =ix 2 + h 2 + Y2
A+Y B+Y
15
16
If equation (2) is solved for a horizontal (d = 0) slab whose
lateral dimensions approach infinity, the expression simplifies to:
g = 27(bdt,
which is the equation giving the gravitational field intensity of a Bouguer
slab.
For slab configurations other than horizontal, the Grant and
West equation requires a value for Z which is the depth to the slab from
the point of measurement and is used to compute h. Z and h are related
by the equation h = Z - xtand. For example, if Z = 50 feet and a
square slab is selected which has side lengths of 8,000 feet, it follows
that this slab extends 4,000 feet beyond the point of measurement in
each of four directions. Using the terminology of Figure 3, this first-
order slab has Y dimensions of 4,000 and an 1 dimension of 8,000 feet.
To determine the gravitational acceleration at a point above the center
of the slab, x is set equal to lcos d. The value of the coefficients to
equation (1) computed using equation (2) and the dimensions given above
range from 1.0114 to 1.0151 for slopes of zero to five degrees from hori-
zontal. The coefficients computed at one-degree intervals of slope are
shown in Table 1, which summarizes coefficients for the first-order
slab which has been described, and for second-order slabs which are
discussed below.
Gravity Effect of a Second-order Tilted Slab
The second-order slab consists of two half slabs meeting be-
neath the gravity station. For this example, each slab has Y and 1
dimensions of 4,000 feet and x = 0. Under the second-order configura-
tion, Z is equal to h and is the vertical dimension from the land surface
17
Table 1. Slab Coefficients (K) and Half Slab Coefficients (K/2) RelatingTilted Finite First-order and Second-order Slabs to Equation (1)
Slab Angle(Degrees fromHorizontal)
First-orderSlab
Coefficients* (K)
Second-order Half Slab Coefficients**
Angles belowHorizontal (K/2)
Angles AboveHorizontal (K/2)
0 1.0114 0.5057 0.5057
1 1.0115 0.4880 0.5234
2 1.0119 0.4704 0.5414
3 1.0128 0.4532 0.5596
4 1.0138 0.4359 0.5779
5 1.0151 0.4189 0.5962
the form:* Use of first-order slab coefficients modifies equation (1) to
S = 78.3 (K) .
** Use of second-order slab coefficients modifies equation (1)to the form:
S = 78.3 (K1/2 + K2/2) .
18
to the edge of the slab below the gravity station. Through the use of the
second-order slabs, the gravity effect of a uniform vertical movement of
a "groundwater valley, ridge, or monocline" can be computed. In prac-
tice, the smoothed groundwater gradient on opposite sides of the station
are determined, the appropriate dimensions are selec' ted, and the gravity
effect is evaluated using equation (2).
It should be noted that the coefficients shown in Table 1 are
appropriate for an 8,000-foot square slab, 50 feet below the observation
point. The values shown may change if different dimensions are used;
however, some generalized conclusions may be derived from these data
and from further relationships expressed by equation (2).
Errors Due to Slab Tilt
The effect of tilt is a nonlinear function of slab size and depth
to the slab; however, the numerical value of the coefficients are rela-
tively insensitive to a change in lateral dimensions of several thousand
feet from those used in this example and to increases in depth of a few
tens of feet. If the depth to water decreases, the coefficients also
change slowly for a few tens of feet unless the tilted water table ap-
proaches the surface, in which case K increases rapidly:
The coefficients derived from the example slab indicate that
the change in gravitational field intensity due to water-table gradients
up to five degrees which may be modeled by a first-order slab is less
than one percent different from the field intensity expressed by equation
(1). The coefficients do not change appreciably if this slab is lowered a
few tens of feet.
19
The effect of tilt using the second-order slab model is more
serious if the dips of the half slabs oppose one another. An error of ap-
proximately 10 percent is reached when the half slabs dip toward each
other or away from each other at an angle of three degrees or when one
half slab is horizontal and the other dips at 5 degrees. Greater opposing
dips yield larger errors.
Errors Due to Limited Slab Size
The gravity effect of an 8,000-foot horizontal slab buried at 50
feet is shown to differ. from that of the Bouguer slab by slightly more
than one percent. The difference changes to approximately 10 percent if
the slab dimension is reduced to 1,000 feet with the depth remaining
constant. This proportionate change is also approximately true for the
corresponding tilted slabs. Therefore, an error of several thousand feet
could be made in estimating slab dimensions without seriously altering
the computed value of the coefficient of storage if it was recognized
that the slab length exceeded 1,000 feet and the depth to the slab was
approximately 50 feet.
The relative significance of local water-table deviations from
the approximating tilted plane may also be evaluated by reducing the
slab size. Assuming the depth to the slab is held constant at 50 feet,
the gravity effect is reduced to approximately 33 percent of that of the
Bouguer slab if the first- and second-order slab side length is reduced
to 100 feet. It follows that a computed coefficient of storage would be
in error by approximately 33 percent if the water table in a 100-foot
square centered below a gravity station changes twice as much as the
average observed water-level change. The error in S would be reduced
20
rapidly if the anomalous change in water level were displaced laterally
from the gravity station.
The gravitational field intensity due to a finite horizontal slab
becomes less if the depth to the slab is increased and becomes greater
if the slab is raised. The change in field intensity May be negligible if
the change in elevation is small with respect to the lateral dimensions
of the slab. For the example slab, K decreases by approximately one
percent when the depth of the slab is changed from 50 feet to 25 feet
and increases by approximately one percent if the depth is increased to
100 feet.
Corrections of Errors Due to Inexact Bouquer Slab Assumptions
The errors introduced by the inexact Bouguer slab assumption
of horizontality and infinite areal extent may be evaluated for a water-
table change through the use of equation (2). If the errors are signifi-
cant, correction factors (K) may be computed and used with equation (1),
which determines the coefficient of storage through the linear plot of
gravity and water-level data pairs. K should be computed for average
water-level depths as well as high and low water-level elevations be-
neath the gravity stations to determine the range of K.
Errors Due to Spatial Changes in Coefficient of Storage
A further assumption in the Bouguer slab model is that the den-
sity contrast and hence the coefficient of storage is constant throughout
the slab. However, in many water-table aquifers the coefficient of
storage changes laterally as well as with depth.
21
Vertical Changes in Coefficient of Storage
A change in S occurring with depth in an aquifer will be mani-
ng fested by a change in slope of the line plotted through the data
pairs derived from measurements at an overlying station. Due to compu-
tation of the coefficient of storage from the slope of a single line through
these data pairs, no loss of accuracy occurs in the average value of S.
Lateral Changes in Coefficient of Storage
A lateral change in S is not apparent at a single station. This
change may be discovered by observing an increasing or decreasing
trend of computed coefficients of storage at the various field stations
in a direction corresponding to the direction of change in S within the
aquifer. Errors may be introduced by a lateral change in S due to an
effect similar to that of changing the thickness of the slab. These er-
rors may be corrected by appropriate changes in the areal extent of the
finite slab.
Other Interpretational Models
All water-level changes have been treated as being "slab-like"
to this point. Some water-level changes may not be reasonably approxi-
mated by a single slab. If sufficient detail is proved by water-level
data from many observation wells, the shape of the zone through which
the water table moves may be approximated either by a combination of
regular geometric solids or by an irregular-shaped body whose gravity
22
effect may be determined either by graticule analysis or by integration.
Solution of these interpretational models must be done using
the difference in gravitational field intensity noted at two water-table
positions. For accurate results the water-table positions must be des-
cribed in detail and the gravitational field intensity at each water-table
position be established by several gravity measurements at each field
station.
Composite Geometric Models
Equations giving the gravitational field intensity of many
simple geometric solids are available in most gravimetry texts. A com-
posite model consisting of two or more such shapes may be constructed
and used as an interpretational model. For example, a dewatered zone
approximating the shape of a truncate cone could be described by a
series of horizontal discs whose radii may be defined by the diameter
of the cone at various depths.
The gravity effect of a composite model is the sum of the ef-
fects of the individual models. The measured change in gravitational
field intensity over the aquifer is assumed to be g, and the interpre-
tational model equations are solved for a common density contrast to
compute S.
Graticule Analysis of Irregular Models
If the aquifer zone undergoing a change in mass is sufficiently
irregular, the use of geometric model approximations may be
23
inappropriate. The gravitational field intensity of an irregular shape may
be evaluated through the use of a gravity graticule . Hubbert (1948)
gives the theory of a common graticule design and illustrates its use.
Graticule analysis is made using a vertical cross section which
shows the boundaries of the zone which changed mass. The analysis
assumes that the zone extends to infinity in the dimension not described
by the cross section. Therefore, the graticule analysis may be appro-
priate for studying the gravity effect of changes in mass of an aquifer
which has two short dimensions (width and height) and one long dimen-
sion (length). It is not appropriate to use this method if the length and
width of the zone which changes mass are approximately equal unless
these dimensions exceed several thousand feet.
Analysis of Irregular Models by Integration
Analysis of gravitational field intensity due to subsurface
masses, including the models described in this paper, are based on the
relationships expressed by Newton's law:
g = G M, •rz
This expression may be modified to the volume integral form,
g _ Gof cost , vr 2 u
(3)
where gS is the angle from vertical to dv, an element of the mass being
considered, r is the radial distance from the gravimeter to dv, and the
remaining symbols are as previously defined. The equation also con-
siders only vertical components of field intensity which are the
24
components measured by a gravimeter. Equation (3) can be used to eval-
uate the field intensity due to an aquifer mass change if the shape of the
volume undergoing the change in mass can be described by mathematical
relationships.
Field applications have been made of the integration method by
establishing a three-dimensional grid and relating the incremental vol-
umes defined by the grid to dv, the elemental volume of equation (3).
The total field intensity is computed by summing the effects of the many
elements, usually with the assistance of a digital computer.
The coefficient of storage could be computed using the integra-
tion method by approximating the volume of the aquifer undergoing a
change in storage with elemental volumes of a three-dimensional grid
similar to that described above. The shape being analyzed could be
most easily described from water-table contour maps constructed from
water-level data collected at times of gravity measurements.
All methods of computing the coefficient of storage described
in this dissertation rely on a comparison of measured change in gravita-
tional field intensity with that computed through the use of an interpre-
tational model. The simplest and most convenient model is the Bouguer
slab; the most complex is that described by the integration method.
Each model has the defect of assuming constant density contrast, hence
a constant S. If a change in storage occurs in two or more zones having
different coefficients of storage, the computed value of S will be a com-
posite value, representative of the composite zones, and the location of
these zones with respect to the location of the gravity observations.
25
The appropriate model used for a specific aquifer analysis may
be determined by the shape of the solid defined by successive water-
table positions and by the magnitude of acceptable error in modeling this
solid.
UNSATURATED-ZONE EFFECTS
Methods of computing the coefficient of storage have been
developed in the preceding chapters which relate the change in gravita-
tional field intensity to saturated-zone effects and to geometric effects.
The measured change in gravitational field intensity is also a function
of what is here informally termed unsaturated-zone effects which are
gravity changes due to changes in the quantity and position of water in
the unsaturated zone.
The value of the coefficient of storage is not easily determined
by studies of water in the unsaturated zone. Therefore, gravity changes
arising from the unsaturated zone are not useful and tend to obscure the
pattern of gravity changes due to saturated-zone effects and geometric
effects. Due to the obscuring nature of unsaturated-zone effects, at-
tempts must be made to quantify changes in the volume and location of
water above the water table so the gravity effect of these changes may
be evaluated and removed from total change in field intensity.
The term unsaturated zone refers to the portion of an unconfined
aquifer which extends from the land surface to the temporary position of
the water table. The term is equivalent to the terms vadose zone and
zone of aeration. Meinzer (1923, p. 21) defines the zbne of aeration as
the zone in which the interstices of permeable rocks are not filled with
water under hydrostatic pressure. Water in the zone of aeration is called
vadose water and is divided into three belts of water by Meinzer (1923,
p. 23) which are soil water, intermediate water, and capillary water.
26
27
Vadose Water
Water in the zone of aeration is called vadose water and is
divided into three belts of water by Meinzer (1923, P. 23) which are
soil water, intermediate water, and capillary water.
Soil Water
The land surface above most unconfined aquifers is occupied by
crops or natural vegetation. The zone of soil water available to these
plants extends into the subsurface for various distances depending on
the root depth of the vegetation type. The depth of the zone is a few
feet for most crops but may extend to greater than 20 feet for some veg-
etation types.
Most of the water in the soil zone is supplied from precipita-
tion and irrigation. The amounts of soil-zone water derived from precip-
itation changes with geographic location and climate. Irrigation
augmentation is absent in some areas and is variable in quantity and
time in other areas. The quantity and distribution in time of precipita-
tion and irrigation may be estimated by use of weather records and irri-
gation records together with pertinent observations in the area of interest.
A significant portion of the soil water is depleted through trans-
piration by plants and through evaporation. A second variable and often
indeterminable portion percolates downward beyond the root zone into
the intermediate unsaturated zone.
Intermediate Water
Water in the intermediate unsaturated zone lies below the belt
of soil water and above the capillary fringe. In many areas the vertical
28
dimension of this zone far exceeds the dimensions of the zone of soil
water and the capillary fringe.
The most continuous source of intermediate water is from down-
ward percolation of excess soil water. A second source is infiltration
from surface-water sources. Infiltrated water moves both laterally and
vertically in the intermediate zone from areas of recharge. Stratification
of the sediments in this zone promotes lateral spreading of the interme-
diate water. Occasionally portions of the intermediate zone may become
saturated, and a temporary mo. und of recharge water may exist above the
water table.
A portion of the intermediate water may move upward if a mois-
ture deficit exists in the soil zone. Another portion may be removed from
the subsurface through evaporation, although evaportion is less signifi-
cant in the intermediate zone than in the belt of soil water because of
the decreased opportunity for air circulation at the greater depth. Much
of the intermediate water in excess of the specific retention drains down-
ward under the influence of gravity to the capillary fringe and into the
saturated zone below the water table.
The Capillary Fringe
The capillary fringe is the lowermost belt of vadose water. The
vertical extent of the capillary fringe ranges from a few inches to several
feet depending on the size of the openings in the rock lying immediately
above the water table. In very fine grained sediments the thickness of
the fringe may exceed 5 feet (Tolman, 1937, p. 155) and may be less
than an inch in well-rounded gravel deposits having large intergranular
openings.
29
If the water table rises or falls in response to a gain or loss in
groundwater storage, the capillary fringe undergoes a proportional verti-
cal movement, although a short time lag may accompany the fringe ad-
justment.
The Gravity Effect of Water in the Unsaturated Zone
The change in gravitational field intensity due to unsaturated-
zone effects may be modeled in much the same manner as were geometric
effects. A density contrast must be assumed, but guidelines to its value
may be derived from preliminary estimates of the coefficient of storage in
the saturated zone. For example, if preliminary analysis indicates that
the coefficient of storage may be approximately 0.20, a density contrast
of 0.15 to 0.20 for the unsaturated-zone model may be appropriate. The
shape of the unsaturated-zone model is less easily defined than that of
the saturated-zone model because water levels in observation wells
yield no information from the unsaturated zone. The shape of the model
must be approximated indirectly through analysis of the areal distribution
of sources of water to the unsaturated zone and by analysis of geologic
factors controlling the movement of infiltrated water in the unsaturated
zone.
Changes in the Amount of Vadose WaterDue to Irrigation and Precipitation
The change in the amount and position of water in the unsatu-
rated zone derived from irrigation and precipitation may be approximated
by a Bouguer slab. The slab would be located at the land surface initial-
ly but may move downward if excess soil moisture drains. The thickness
30
of the slab would be a function of the rate and quantity of water applica-
tion at the surface and on the rate of vertical drainage.
The slab approximation may be nearly exact for a short period
after the water is applied to the land surface. At this time, the depth to
the slab below the point of observation is small with respect to the lat-
eral extent of the slab. This water in the near-surface slab begins to
dissipate soon after its application due to moisture loss through evapo-
transpiration and through drainage of excess soil moisture. The down-
ward movement of the water which is in excess of the field capacity of
the soil zone may be approximated by a second slab. The second slab
will give a smaller gravity effect due to its lower volume of contained
water, and if derived from excess irrigation water, due to the increase
in depth with respect to the lateral extent of the slab.
The influence of the surface slab on measured change in gravi-
tational field intensity may be minimized by preventing infiltration of
water in the immediate vicinity of the gravity station or in irrigated areas
by placing gravity station at the margins of irrigated fields or at unirri-
gated areas between fields. The effect of the slab due to drainage of
excess soil moisture would not be significantly reduced by selective
gravity station placement due to lateral spreading which may accompany
the downward movement.
Changes in the Amount of Vadose Water Due toInfiltration from Surface-water Bodies
A substantial amount of recharge to unconfined aquifers is de-
rived from stream flow or from other bodies of surface water. Wilson
and De Cook (1968) have shown that the quantity of water in storage in
31
the unsaturated zone may rise significantly due to infiltration of ephem-
eral stream flow. This change in volume of vadose water may not be
reflected by an immediate rise of the water table.
The shape of the zone of excess water above the water table
may be approximated at ground level by the shape of the source of infil-
tration. The degree of subsurface lateral spreading of the body of
infiltrated water may be unknown but is controlled chiefly by the vertical
permeability of the sediments between the recharge source and the water
table and by the rate of infiltration. If the vertical permeability is low
and the rate of infiltration is high, significant lateral movement of vadose
water may occur and the increase in gravitational field intensity due to
this water may be widespread. If the vertical permeability is much great-
er than the rate of infiltration, the gravity effect may be localized near
the source of infiltration.
Modeling of the unsaturated-zone effect resulting from surface-
water infiltration may be inappropriate due to the inability to describe
closely the limits of lateral percolation in the unsaturated zone. Rather
than modeling, it may be more feasible to attempt to determine which
measurements of gravitational field intensity may be in error due to un-
saturated-zone effects and to remove these data points from the analysis.
The coefficient of storage may then be determined using those gravity
data which are not significantly affected by recharge effects.
COLLECTION AND REDUCTION OF GRAVITY DATA
The procedure of the gravity survey and reduction method used
for this dissertation differs from that of conventional gravity surveys.
The purpose of conventional gravity surveys is to determine the areal
distribution and magnitude of gravitational field intensities. Results of
such a survey are usually plotted on a gravity map which shows the
change in gravity with respect to position.
The results of the surveys made for this study show the change
in gravity with respect to time. The change in gravitational field inten-
sity was determined by repeating gravity surveys periodically and com-
paring the results of the initial survey with those of subsequent surveys.
The same set of field stations were used for each survey to eliminate
variations in gravitational field intensity other than those caused by a
change in mass.
The Gravity Meter
The instrument used in this study is the LaCoste and Romberg
Model G Geodetic Gravity Meter, No. 174. The meter was manufactured
by LaCoste and Romberg, Inc., 6606 North Lamar, Austin, Texas 78752.
The makers claim the meter possesses a range of over 700 milligals , a
reading sensitivity of + 0.01 milligal, and a drift rate of less than one
milligal per month. Use of the meter in this study has indicated that
the reading sensitivity is greater and drift rate is less than that speci-
fied by the manufacturers.
32
33
Instrument Errors
Errors due to variation in reading the gravimeter, linearity of
meter response, repeatability, and reaction of the meter to being slightly
tilted are considered to be instrument errors, although they may be attri-
buted in part to the fallibility of the observer.
Reading. The maximum probable reading error is believed to
be two microgals, the sum of the uncertainties in the index line place-
ment and the dial interpolation. In practice, the reading error may be
less than two microgals due to repetition and averaging of measurements
at each station or may be large if the dial reading is incorrectly recorded.
Linearity. In the present study it is assumed that the spring
constants do not vary and that the threads on the micrometer screw
cause a linear axial progression when the screw is turned. The non-
linearity problem is minimized in the present study because a limited
range of values is encountered. The largest dial unit change occurred
between the gravity base and the field stations and was approximately
eight turns of the micrometer dial. The range of the field station values
were encompassed by one turn of the meter dial. This small range of
values limits the variability of the spring constants and tends to im-
prove the reliability of the data. The nonlinearity of the micrometer
screw, if due to a cyclic error in cutting of the threads, may not be
affected by the limited range. The magnitude of errors of linearity in
the present work appears to be small and is considered to be negligible.
Levels. The gravimeter is very sensitive to deviations from
precise level. A leveling error of one minute of arc causes the meter to
read erroneously low by approximately 50 microgals (Bhuyan, 1965, p. 62).
34
In the present work great care was taken to examine both level-
ing vials before and after each gravity measurement. If after a measure-
ment the meter Was found to be out of level, the reading was discarded
and a new reading made. Because of the care exercised in the field to
level the meter properly, it is believed that errors due to unobserved tilt
are small, probably less than one microgal.
Another cause of mis leveling is the effect of heating on the
spirit level vial. The radius of curvature of a sensitive vial may exceed
100 feet. This radius is so great that it can seldom be made absolutely
constant throughout the length of the vial. If the radius is greater at one
end of the vial, temperature expansion may cause the bubble to lengthen
more at the opposite end. This unequal expansion may cause a leveling
error.
The greatest error in bubble leveling is probably due to temper-
ature gradients along the axis of the leveling vial. A temperature grad-
ient causes the bubble to move toward the warmer end where the spirit
is vaporizing more rapidly.
A change in temperature of the liquid in the tubes may be due
to a variation in outside air temperature or to sunlight penetrating the
leveling vials. Gravity surveys were done at night or on cloudy days
when possible to reduce error due to temperature tilt. However, it was
not possible to eliminate all temperature changes.
The error due to temperature tilt was not precisely established
but was noted to exceed 15 microgals under extreme conditions. The
probable maximum error due to temperature tilt is estimated to be 10
35
microgals . This error value is less than the maximum noted because
precautions were taken to minimize temperature effects.
Drift. These instrument errors contribute to a total error
which is compensated in part by the drift correction. Study of the long-
term drift rate appears to indicate that drift observed during a survey is
probably more closely related to position, time, and instrument errors
than to true drift. Therefore, an estimate of drift error would tend to
duplicate in large part the errors previously discussed. For this reason
no drift error estimation is made.
Procedure for Gravity Surveys
A gravity survey began at a base station which was a perma-
nent reference point where the gravitational field strength is known or
assumed. The gravimeter is read at the base station and then at field
stations where the gravitational field strength is to be determined. After
the field stations had been occupied, the meter was returned to the
gravity base station and a second reading made at that location. The
time of each observation was recorded.
The difference between the dial readings at the base station
and field stations was coniputed, as was the difference between the
two base-station observations. The dial unit differences were converted
to milligal differences. Observed gravity may be computed for each field
station by algebraically adding the milligal difference between the base
station and field station to the known or assumed gravity value at the
base station.
36
Base Stations
The gravity surveys for this study were tied both to a base
station located on gneissic bedrock in the foothills of the Santa Catalina
Mountains and to a station located in the basement of the Geology Build-
ing at The University of Arizona. The Catalina foothills station is lo-
cated in the NE1/4NW1/4 sec. 3, T. 13 S. , R. 14 E . Gravity at this
station is not believed to be affected by rise or decline of the water
table because of the location of the station on low-porosity rock. Water
levels in the vicinity of the Geology Building base declined approximately
3 feet through the study period. However, no decline in gravity with
respect to the Catalina base was noted. The lack of gravity response
at the Geology Building base is probably due to the small decline in
water level in that vicinity and the low coefficient of storage in the
underlying basin-fill deposits.
Field Stations
Monuments were placed at the selected locations on the Ewing
farm to provide stable points for subsequent gravity observations. The
monument at each field station consisted of a concrete pad approximately
14 inches in diameter with a footing which extended to a depth of approx-
imately one foot below ground surface. The locations of the field sta-
tions are shown on Figure 4.
Corrections for Time and Position
The earth's gravity varies both with time and with position.
Variations that are considered significant for the purposes of a specific
survey were computed and added to observed gravity as correction factors.
NE-7
0
- -
Property Boundary
37
A Gravity Station
0 Observation Well
0 Irrigation Well
NE-4NW-4
\ 7NW-3
VN-2
NW-2
EW- I
N-1
E-2
EW- 7
EW -2 E -2FN EW-I3 EW-16
SectionCorner
19 20
30 29
Figure 4. Index Map of Gravity Stations and Wells on the Ewing Farm
38
Correction for Time Variations
In this study two effects varying with time are computed and
used to correct observed gravity. These factors are termed tide correc-
tions and drift corrections. The time of each gravity measurement was
recorded and is believed to be correct within + two minutes.
Tide Corrections. The tidal attraction of the sun and moon
cause a measurable variation of gravity which is significant in this
study. Several methods are available to correct for the tidal effect.
The method selected for this Study is that given by Damrel (undated) .
This method requires the use of data published in the American Nautical
Almanac together with the tables published in Damrel's pamphlet. Damrel
computed the tidal effects assuming that the earth has a rigid body and
then used an earth-tide factor of 1.20 to adjust the tidal effects to re-
flect nonrigid conditions, It should be noted that the proper earth-tide
factor for a specific area may deviate significantly from the 1.20.
Figure 5, a comparison of computed and observed tidal effects,
shows a plot of computed tidal corrections and observed tide, both
plotted against time, through portions of March 20 and 21, 1970. The
tidal corrections were computed using both the Damrel method and the
method given by the European Association of Exploration Geophysicists
(1969). Observed tide values were computed from instrument readings
made on the concrete floor slab of my home in Tucson. Signs of the ob-
served tide were reversed so the two sets of data could be more easily
compared. The close match`of the amplitudes of the curves would indi-
cate that the 1.20 earth-tide factor used by Damrel and by the European
Association of Exploration Geophysicists may be appropriate for use in
100
80
60
40
20
o-o1-7
o
-20
-40
-60
-80
-100
O Observed Tide Correct ion
• Damrel Correction
O European Assoc. Exploration
Geophysicists Cor rection
J
IIIIII II I I I I I
0 0 00 0 0 0 00 0 00 0 00 0 0 00 00 0 00 . . 2
1-0 00 0 00 0 0 0 0 0 00 0
N- , 0 ro . to r-co - CO C:n _0 O.J tO tr — N.._ cu 0.1 N N N
39
Arizona Time
Figure 5. Comparison of Computed and Observed Tide Cor-rections
40
the Tucson area. Observations by others (Bhuyan, 1965) have indicated
that the value of the earth-tide factor should be modified for the Tucson
area; however, present data would indicate that this conclusions may be
premature.
The tidal correction is applied to observed gravity values de-
rived from field surveys in the same manner. A tidal correction curve is
plotted using the Damrel method for the time period of the survey. The
amplitude of the tidal curve is set equal to zero at the time of initial
base reading and later readings are corrected by the difference in ampli-
tude.
Tide Errors. The maximum rate of tidal change computed in this
study was approximately one microgal per minute. This rate of change
indicates that an error of two microgals may be associated with a time
uncertainty of two minutes.
Additional tide errors may result from the inability to describe
precisely the function relating the correction to the time of measurement.
An accuracy of + 3 microgals is given by Damrel (undated, p. 1) for the
tidal correction method. A further error of approximately + 3 microgals is
due to uncertainty in plotting the tidal correction curve through the inter-
vals between the computed points. This analysis indicates that the
maximum probable tide error may be as great as 8 microgals.
Drift Corrections. The magnitude of drift is determined by
by comparing the initial and final base readings which are usually not
equal even though tide effects have been removed. The residual differ-
ence between the base readings is assigned to instrument drift.
4 1
In the present study drift curves were constructed for each field
survey. The drift correction was computed by determining the microgal
differences in the base readings with time and assuming that the drift
rate was linear between base-station observations. A drift rate having
units of microgals per minute was then computed and applied as a cor-
rection to all observations made between the base readings.
Drift Errors. The maximum drift rate found in this study was
less than one microgal per 6 minutes. Therefore, the error associated
with an uncertainty in time of 2 minutes is less than 0.5 microgal and
is considered to be insignificant with respect to the magnitude of other
errors.
Correction for Position Variations
In most field surveys additional corrections are made for the
position of the field stations with respect to the location of the gravity
base station. Field gravity surveys are commonly corrected for latitude,
distance from the center of mass of the earth, density of crustal mater-
ials lying between the point of observation and a common datum, and
terrain. All the above corrections vary with the position of observation.
A gravity surveying technique described in this study required
periodic measurements at selected field stations. Ideally, the meter
would be placed at exactly the same location for each measurement.
This exactness in gravimeter location was not realized in the field,
although concrete monument p were used as field stations to minimize
both vertical and horizontal deviation from a specific location.
Latitude Correction. The numerical value of the latitude cor-
rection is closely approximated by the equation:
42
g -= 978.049 (1 - 0.0052884 sin 2 gS - 0.0000059 sin 2 24 gals (4)
where g3 is the latitude measured on the surface of the geoid. The equa-
tion is known as the "international gravity formula" and closely approxi-
mates the change in normal field strength from a low at the equator to a
high at the poles.
Magnitude of Errors Due to Variation in Horizontal Position.
The size of the concrete monuments used for field stations limits hori-
zontal differences in location to about 0.2 foot. The change in accelera-
tion due to a change in horizontal position of this dimension is a function
of direction of movement. The change in gravitational field strength due
to a horizontal movement in the north-south direction may be computed
using equation (4) and is 0.04 microgals.
Davis (1967, Plate 5) gives a residual gravity map of the Tuc-
son basin which shows a local gravity gradient increasing to the north
at a rate of approximately two milligals per mile in the Ewing farm area.
The maximum combined error due to local gradient and the latitude effect
is less than one microgal and is considered to be negligible.
Elevation Correction. Gravitational field strength decreases
with increase of distance from the center of mass of the earth. Gravity
data were adjusted for this effect by adding the elevation correction con-
sists of the resultant of two opposing effects.
1. Free air correction. It is noted from Newton's law that as the
separation between two masses increases, the gravitational
force between the two objects decreases. Over the surface of
the earth this relationship is nearly linear and is commonly
approximated by a gravity decrease with elevation of 0.09406
43
milligal per foot. The free air correction is added to observed
gravity to correct the observation to a lower common datum or
subtracted to correct to a higher datum
2. Bouguer correction. The Bouguer correction compensates for
the attraction of the material between the elevation of the field
station and the datum elevation. Because the attraction of the
material between the observation point and the datum is de-
pendent both on the density of the material and the difference
in elevation, the Bouguer correction must compensate for both.
The numerical value of the Bouguer correction is expressed as:
g = 0.012776h milligals per foot
where 6 is the density of the material in gm/cc and h is the
distance in feet between the point of observation and the com-
mon datum. The Bouguer correction is subtracted from observed
gravity to adjust to a lower datum.
The free air and the Bouguer corrections are often combined due
to their dependence on elevation. If the density of the material between
the elevation of the station and the datum is assumed to be 2.67, the
average density of crustal rocks, the total elevation correction very
nearly equals 0.06 milligals per foot. The elevation correction is added
to observed gravity to correct for the vertical displacement of the field
station above the common datum.
Magnitude of Errors Due to Variation in Vertical Position. It
is believed that the maximum range in variation of vertical position is
less than 0.05 feet. The change in acceleration corresponding to a 0.05
foot elevation change is
44
g = 0.09406 milligals (0.05 foot) = 0.0046 milligals •foot
Additional changes in field strength may be caused by vertical gradients
due to terrain effects and by regional gravity gradients. These effects
are believed to be insignificant with respect to the free air correction.
Therefore, the maximum difference between successive readings due to
variation in vertical position is probably less than 5 microgals.
The Reduction Procedure Used in This Study
The present study is directed toward observing long-term
changes in gravity at several selected field stations. Therefore, the
variation in field strength is of interest and absolute gravity values at
the field stations are of little concern. For this reason only corrections
varying with time are used to adjust the data. Although corrections due
to position variations were not used in the data reduction, they were
examined to evaluate the magnitude of errors in the data caused by small
variations of instrument position on the concrete monuments used as
field stations.
Other sources of error include reading errors by the observer,
nonexactness of the interpretational model, and lack of sensitivity in
the gravity survey and precision in the reduction of the data. Obvious
reading errors were noted in some computed gravity values. If the error
could not be identified and corrected, the gravity value was discarded.
A gravity datum deviation of more than 30 microgals from the trend of
the remainder of the data was assigned to this category of error.
The observed dial unit differences between the base station
and field stations were converted to milligals, and tide and drift correc-
tions were made. This procedure resulted in a corrected value giving a
45
measure of the gravitational field strength at a field station relative to
that measured at the base station.
Relative Gravity
The corrected gravity differences between a field station and
the gravity base are termed "relative gravity" in this study. Changes in
relative gravity with time are assumed to be due only to changes due to
saturated zone, unsaturated zone, and geometric effects.
Methods of Increasing the Accuracy of Future Studies
The field technique used in the present study was established
early in the data collection program. Subsequent analysis focused at-
tention to portions of the survey technique which yielded the largest
error potential.
Table 2, the summary of errors, indicates that the largest er-
rors are probably due to variation in vertical position, to tide errors,
and to temperature tilt. The sum of these errors is 88 percent of the
total computed error.
Reducing the Error Due to Variationin Vertical Position
The error due to variation in vertical position is + 5 microgals
corresponding to an uncertainty in vertical position of 0.05 foot. The
vertical variation may be reduced to 0.01 foot. This reduction could be
made in three steps: (I) by painting points on the concrete monuments
used as field stations on which the legs of the base plate of the meter
could be located, (2) by painting or grinding points on the base plate on
which the meter leveling screws could be located, and (3) by permanently
46
fixing the position of one leveling screw to limit adjustment to the re-
maining two leveling screws.
Table 2. Summary of Errors Due to Imprecise Gravity Survey and DataReduction Methods
Computed ErrorError Source (microgals)
Variation in position
Vertical -I- 5
Horizontal negligible
Time
Drift negligible
Tide +8_
Reading + 2_
Leveling
Unobserved tilt
Temperature tilt
Total
+ 26
If these modifications were made, the error due to uncertainty
in vertical position could be reduced to one microgal. This adjustment
of the field technique would be relatively simple and is recommended to
future investigators.
47
Reducing the Tidal Correction Error
More precise earth-tide corrections may be obtained by oper-
ating a high-precision tide meter in conjunction with the gravity survey.
Use of the tide meter would allow tide corrections to be made on data
from observed tidal effects rather than on computed tidal effects. If the
areal extent of the gravity survey is small with respect to the location
of the tide meter, the accuracy of the tide correction should be + one
microgal.
Reducing the Error Due to Temperature Tilt
The errors due to temperature tilt may be reduced by further
isolating the spirit levels from sources of heat. Isolation of the spirit
levels should include insulation to block heat conduction from the top
and sides of the meter and screening to minimize radiation heating.
The error reduction potential due to isolation of the spirit level
is not known, but a reduction of 50 percent appears to be reasonable.
If this reduction were realized, the error due to temperature tilt would
be lowered to ± 5 microgals.
The total computed error may be reduced from + 26 to approxi-
mately + 10 microgals if the above modifications were made in the equip-
ment and the surveying technique. The modifications are recommended
both to reduce data scatter and to allow observation of hydrologic phe-
nomena having a more subtle gravity effect.
FIELD TEST AREA
Preliminary analysis of the gravity method used in this disser-
tation indicated that the gravity surveys should be made over a water-
table aquifer in which fluctuations of the water table were great over
large areas and which was believed to have a relatively high coefficient
of storage. Theoretically these characteristics produce maximum change
in gravitational field intensity.
The University of Arizona Ewing farm overlies the flood-plain
alluvium and basin-fill aquifers of the Tucson basin. Geologic and
hydrologic data derived from studies by others indicate that the coeffi-
cient of storage in these aquifers probably lies in the range of 0.15 to
0.25. Water-level fluctuations greater than 30 feet in observation wells
on the Ewing farm have been documented. For these reasons the Ewing
farm vicinity was used as the field test area. Figure 4 is a map of the
Ewing farm showing the location of wells and gravity field stations.
Geologic Features of the Tucson Basin
The Tucson basin lies in one of a series of north-south trend-
ing structural depression of the Basin and Range physiographic province.
The basin owes its shape to faulting of the bedrock, subsequent erosion
of the uplifted areas, and deposition in the downfaulted trough. A com-
plex suite of igneous, metamorphic, and lithified sedimentary rocks of•
Cretaceous through Paleozoic age makes up the mountain blocks border-
ing the basin. The igneous rocks range in age from Precambrian to Cen-
ozoic. The rocks of the mountain blocks contain virtually no groundwater
48
49
resources. They form a hydrologic boundary to the basin, and for this
reason are grouped into one map unit for the purpose of this report.
The alluvial deposits underlie the basin floor and crop out on
the alluvial slopes adjoining the mountain blocks. The rock types in the
alluvial deposits range from claystone to sandstone and conglomerate.
In this report, the alluvial deposits are divided into four mappable units:
the Rillito beds, the basin-fill deposits, the terrace deposits, and the
flood-plain alluvium.
Rillito Beds
The Rillito beds were defined by Pashley (1966, p. 63) as
. . . the body of faulted, jointed, and tilted conglomerate, sandstone,
and mudstone units that crop out along the northern and eastern margins
of the Tucson basin." Pashley divided the Rillito beds into type I (old-
est), type II, and type III (youngest) on the basis of lithology. The first
two types are characterized by red conglomerates and pebble composi-
tions unlike the present rocks in the Santa Catalina and Rincon Mountain
source areas. The type III sequence is similar to the basin-fill deposits
in pebble types but is tilted and faulted in accordance with Pashley's
formation definition. The Rillito beds are recognized when penetrated in
the subsurface of the Tucson basin by the red color of the drilling
samples from the lower units and by the lower rate of penetration due
to their firm cementation.
No fossils have been found in the-Rillito beds. The beds are
tentatively dated as middle to late Tertiary on the basis of radioactive
dating and age of fossils in similar formations and by structural rela-
tionships to dated rock units.
50
An erosional surface was cut on the deformed Rillito beds, and
the basin-fill deposits were laid down on this surface. In the central
portions of the basin the recognition of this interface is important when
intercepted by the water well driller. The surface separates overlying
rocks of higher permeability from the underlying Rillito beds of lower
permeability (Pashley, 1966, P. 101).
Basin-fill Deposits
The basin-fill deposits consist of a sequence of heterogeneous
deposits of clay, silt, sand, and gravel which overlie the Rillito beds.
The pebble content of the sequence reflects generally the gneissic com-
position of the present Santa Catalina and Rincon Mountain source areas.
The deposits are lenticular but are essentially flat bedded and are not
deformed by other than minor post-depositional movement.
The origin of the basin-fill deposits is attributed to coalescing
alluvial fans which developed from the mountain fronts surrounding the
Tucson basin. The average sediment size in this unit decreases toward
the center of the basin. Layering may be indistinct in the peripheral
margins of the unit and may be prominent in the central portion due to
the change in environment of deposition.
The age of the basin-fill deposits in the Tucson basin has not
been identified by fossils or radioactive dating. The deposits have been
assigned a tentative age of upper Pliocene and Pleistocene on the basis
of structural relations and similar lithology and stratigraphy to dated
formations elsewhere in the state.
51
Many productive water wells have been drilled into the basin-
fill deposits. The upper 500 feet of this unit are generally coarse
grained and form an extensive aquifer in the Tucson basin.
Terrace Deposits
After the basin-fill deposits were laid down, the ancestral
Santa Cruz River and its tributaries, including Rillito Creek began to
down cut into the basin-fill unit and to deposit alluvial materials on
these cut surfaces. The ancient flood-plain surfaces together with their
alluvial sediments were preserved in part. The geomorphic unit is
termed a terrace and the underlying alluvial sediments denoted as terrace
deposits. Several terraces are found in the Tucson basin. The Jaynes
terrace is present south of but roughly paralleling the central reach of
Rillito Creek. The terrace deposits are an unconsolidated sequence of
silt, sand, and gravel. The thickness of the unit rarely exceeds 50 feet.
The terrace deposits are infrequently saturated because of their
limited thickness and near-surface position. Where the deposits are
found to be saturated, they form a highly permeable hydrogeological unit
similar to the alluvial deposits underlying the present flood plain of
Rillito Creek and the Santa Cruz River.
Flood-plain Alluvium
The flood plain of the Santa Cruz River and its major tributaries
is a geomorphic unit consisting of a shallow, nearly flat-bottomed "in-
ner" valley, roughly bisected lengthwise by the low-flow channel. The
geologic unit underlying the flood plain consists of unconsolidated sand
52
and gravels. The thickness of these alluvial deposits ranges approxi-
mately from 30 to 100 feet but probably averages about 60 feet.
The flood-plain deposits are an important geohydrologic unit.
They are frequently saturated in their basal part and form a highly per-
meable "shoestring" aquifer. The unsaturated portiOns provide a reser-
voir which is available for transient storage of infiltrated water from
occasional surface-water run off.
Geohydrology of the Ewing Farm Area
Only sufficient surface geologic work was done to verify the
mapping of Pashley (1966) and Davidson (1970). The geologic units dis-
cussed in this report are shown on Figure 6, a geologic map of a portion
of the Tucson basin which includes the Ewing farm. Drillers' logs and
their interpretations by various authors were studied to obtain an indica-
tion of the subsurface lithology, thickness, and location of the various
units. A typical driller's log and a sediment size analysis are shown
on Figure 7.
Geology
The surface outcrops of the mountain-block complex are mapped
to the north of the Ewing farm. This units is believed to occur beneath
the farm but at a greater depth than has been penetrated by drilling.
The Rillito beds also crop out to the north at a minimum dis-
tance of approximately 8,000 feet from the Ewing farm property. This
unit also underlies the area and is penetrated by the Ewing farm wells
at about 200 feet below land surface.
ts•oO O
R I 3 E
... ,i
(
4n
3-VÇ
Mil III
2 6A 2 . Otb
r
1010
Ilir01 b/Orb
r ilr
Qs -- 4
T
pT - Tif
52
LOs ir
II (s Ji
f 6)--'
Tr
at b0
Of b
7
‘2•---ff, F:(1 A r.IF
0 f b
TrowTS:
/ r ISO
,
nr9141.
.
0t b
iitr ,, 01 b
. . t /f f 1
0 t b
. ! 0-
:47----br
2409.---,,
T
i ,C) t b
------._
' •
r 1-2T,'
t)
1 24 I
// AblI/O':
reQtb
..,
i
1
CRE5.15„
: f i111 I -9---""—. •-. , I /
1)---• Q a 1 \----1•Os 11me
01 b
31 3e 33
__________._
34 35 36
Ot b
;IN 4
----\-/—'
3.e._(1-‘ ‘.13 ‘, '
n
00
I 6 5 4 3 21
i
Figure 6. Geologic Map of the Ewing Farm Area, Pima County, Arizona--Geology after Pashley (1966)
EXPLANATION
Oa!
Q)C 4-Q) c(..) 1:3 a)OC u <a Underlies strecm channels and flood17, 4)
Xco plains, unconsolidated sand, silt, andci gravel Thickness ranges from tens of
feet to 100 feet
Flood- plain Alluvium
I •5
Jaynes Terrace Deposits
Gravel and gravel ly sand Thicknessranges from a few feet to 50 feet.
t
Basin -fi Il Deposits
Gravel and gravelly sand to sandy silt.
Rillito Beds
Consolidated alluvion deposits of silt,sand, and gravel
P T - T
Mountai n Block Complex Undifferentiated
Cenozoic and pre-Cenozoic igneous, meta-morphic, and consolidated sedimentaryrocks
1 Scale
62,500
SYMBOLS
Contact
Ewing Farm
Campbell Well
2
Peck Well
3Mahoney Well
8
Q)
90 50 100 501111111
SoilSand
Sand, grovel, boulders
Fine sand
Coarse white sandSandy clayWhite sand 8 gravelRed sandy clay
Red cloy, sand, gravel
Fine white sand
Red clay a sand
Red clay eii coarse gravel
Red hard clay, sand, gravel
Red clay, lift ha sand - sticky
-
i i
I
'1, »LL _,-
-
d
-
-
-
-
54
Percent Fines Driller's Log
0
Flood -
plainAlluvium
50
--- -
-
100 -
BasinFi I IDeposits
150 -
-
200 -
-
RillitoBeds
250 -
-
300 -
-
350 -
Figure 7. Driller's Log and Drilling Sample Size Analysis of
Ewing Farm Well E-2R
55
The basin-fill deposits are mapped to the north and south of
Rillito Creek. This unit is penetrated by the Ewing farm wells at an
average depth of about 50 feet. Road cuts into the basin-fill deposits
in the Ewing farm vicinity expose the unit. Examination of these expo-
sures indicate that the unit is horizontally stratified, but it is difficult
to trace individual layers for more than a few tens of feet. Conglomerate
lenses and cut-and-fill structures are common. The sediments are weak-
ly cemented by calcium carbonate.
The sediments in the basin-fill deposit range in size from silt
to gravel. Pashley (1966, P. 121) shows results of seven size analyses
from a basin-fill outcrop in the NW1/4NW1/4NE1/4 sec. 27, T. 13 S.,
R. 14 E., which is approximately two miles east of the Ewing farm. The
average size distribution is 47 percent gravel, 47 percent sand, and 6
percent silt.
Size analysis of water-well drilling samples from the basin-fill
unit shows greater quantities of fine material. This reduction in grain
size is believed to be due to grinding by the drilling bit. The size dis-
tribution of basin-fill samples from the Ewing farm well E-2R is 57 per-
cent sand and gravel and 43 percent silt and clay. This distribution is
in agreement with drilling samples described by Pashley (1966, p. 184-
185) from the Ewing farm vicinity.
Deposits of the Jaynes terrace crop out to the south of the
Ewing farm and form a narrow belt parallel to the flood-plain alluvium.
The Ewing farm wells do not penetrate terrace deposits.
The Ewing farm lies entirely on the Quaternary flood-plain al-
luvium of Rillito Creek, which averages about one mile in width in this
56
area. Several sections of the alluvium exposed in the banks of Rillito
Creek were examined. The unit is stratified, but individual layers other
than minor lenses are not easily traced. The flood-plain alluvium is un-
consolidated to weakly cemented.
The sediments in the flood-plain alluvium range in size from
clay to boulders, although sand and gravel predominate. Sediment-size
analysis indicates similar distributions of silt, sand, and gravel as are
found in the basin-fill deposits in the Ewing farm area.
The contact between the basin-fill deposits and the flood-plain
alluvium is indistinct in the Ewing farm area when based on size analysis
and drillers' description. In the vicinity both units appear to be homo-
geneous on a large scale, although the appearance of each may be het-
erogeneous in a single outcrop. In other areas of the Tucson basin, the
basin-fill deposits contain greater amounts of silt and sand, and the
contact between the basin fill and and the flood-plain alluvium is more
distinct.
Hydrology
Ground water in an unconfined aquifer flows laterally in re-
sponse to the hydraulic gradient from areas of recharge to areas of dis-
charge. A water-level contour map shows graphically the shape of the
water table and hence the hydraulic gradient. Figure 8 is a water-table
contour map showing water levels in a portion of the Tucson basin in the
early spring of 1970. In the area surrounding the Ewing farm, the ground-.
water movement is in general southwestward, but locally the gradient
may be in other directions in response to recharge along the channel of
Rillito Creek and to pumping from individual wells.
T.
13
S.
57
R. 13 E. R. 14 E.
4 2 1
&V AI
•t
illJ 'A I,
"Md1111,Willy
6
7
5 4 2 ,
PrOr \12
illgirifilliti.
e , 8
3013,
,
1 32
2 2 ) 13,
1
1 33 1 .134 3
4 3 ,I 5 IFigure 8. Groundwater Table Contours, 1970, Ewing Farm Area--Modified from Groundwater Contours, Middle Santa Cruz
Valley, Univ. of Arizona, Dept. Ag. Engr., Open-File Map, 1970
58
Surface-water Runoff. The date and volume of surface flow in
Rillito Creek were determined in part from stream flow records from the
U.S. Geological Survey stream gaging station, Rillito Creek, near Tuc-
son, Arizona. This gage is located in the SE1/4NE1/4 sec. 24, T. 13 S.,
R. 13 E . , approximately 1 1/2 miles downstream from the Ewing farm.
Surface-water flows of one to three cubic feet per second may pass this
gage without being recorded; however, flows greater than three cubic
feet per second are registered. Due to the proximity of this gage to the
study area, it is assumed that the volume and time of flow recorded at
the gaging station are equal to those at the Ewing farm.
Records from this gaging station indicate that the last flow
prior to the study period was 20 acre feet on September 1, 1968. The
records show flow during the study period of 147 acre feet on November
14, 1968; a total of 275 acre feet on January 15 and 16, 1969; 16 acre
feet on January 22, 1969, 6 acre feet on August 1, 1969; a total of 246
acre feet on August 5, 6, 7, and 8, 1969; 18 acre feet on August 13,
1969; and 12 acre feet, 24 acre feet, and 7 acre feet on March 5, 11,
and 17, 1970, respectively. The quantity of flow recorded in March
1970 is believed to be in error due to problems with the water-stage
recorder. However, I noted flow through this period and on March 21,
1970 and estimate the quantity of flow through the period March 5 to
March 21, 1970 to be approximately 320 acre feet.
Groundwater Hydrographs . The Ewing farm lies in an area
which experienced a general water-level decline through the study
period. Hydrographs of four wells on the Ewing farm and three wells in
the Ewing farm vicinity are shown on Figure 9 (in pocket). The locations
59
of the Ewing farm observation wells are shown on Figure 5, and the lo-
cations of observation wells outside the farm are shown on Figure 6.
Ewing farm observation wells A-5, B-3, and D-2 lie within 300
feet of the center of the channel of Rillito Creek and show sharp rises
in response to surface-water flow. Measurements were made weekly in
these observation wells, hence the time of initial response to stream
flow is not precisely shown by the hydrographs.
The water-table rise which occurs in November 1968 is the re-
sult of flow in Rillito Creek on November 14. The water-level response
is nearly immediate. The hydrographs appear to peak within 3 to 5 days
after flow indicating that the drainage of the infiltrated water is rapid.
The hydrographs rise again in late January 1969 due to stream flow on
January 15, 16, and 22. The water table again rises immediately due to
recharge from the surface flow and peaks in approximately 6 days after
the final flow.
Following this recharge event, the hydrographs decline in
response to pumpage from the aquifer until August 1969 when they again
rise due to surface flow on August 1, 5, 6, 7, 8, and 13. The water-
table rise is delayed approximately 3 days after the initial flow, but the
hydrographs peak on about August 15, 2 days after the final flow and 7
days after the flow of August 8, 1969.
No runoff is believed to have occurred in Rillito Creek after
this flow until March 11, 1970. The small peaks in the hydrographs in
October, November, and December 1969 are probably due to temporary
halts in local pumping and to gains in storage due to groundwater inflow,
although the rises may be due to small unrecorded surface flows. The
60
hydrographs reacted nearly immediately to the surface-water flow which
occurred from March 5 through March 21, 1970. The hydrographs ap-
peared to peak approximately 7 days after flow.
The short time to initial response and to peak of the hydro-
graphs indicates that the vertical permeability of the flood-plain allu-
vium and the uppermost basin-fill deposits is large. Infiltration from
stream flow appears to move rapidly downward from the channel of
Rillito Creek to the water table.
The remaining observation wells lie at greater distances from
Rillito Creek. The hydrograph response at these wells is less precise
due to larger intervals of time between water-level measurements; how-
ever, they show rises after surface flow. The time lag to the peak of
these hydrographs is greater because of the greater distance to the
recharge source
In October 1968, the beginning of the period of field observa-
tions, the water table was above the flood-plain alluvium-basin fill
contact beneath the Ewing farm. To the north and south of the farm area,
the water table was located in basin-fill deposits. In June 1970, the
water table had lowered to a position which was probably entirely within
the basin-fill deposits. The zone dewatered through the period included
portions of both the basin fill and the flood-plain alluvium aquifer. As
a result the coefficients of storage computed in this work reflect a com-
posite of the coefficients of storage of both aquifers Figure 10 is a
geologic cross section showing the relationship of the water table in
October 1968 and in June 1970 to the flood-plain alluvium, the basin-
fill deposits, and the Rillito beds in the Ewing farm vicinity.
61
2-
o —
-o0rn
—00
oo
62
Storage Estimates by Others
Various authors have measured and estimated the value of the
coefficients of storage in the Tucson basin aquifers. Values ranging
from approximately 0.05 to 0.30 have been determined by several anal-
yses.
Ewing Farm Studies
Matlock (1970) reports the results of an investigation of math-
ematical simulation of recharge occurring along Rillito Creek. The Ewing
farm was used as his field test area. Porosity values ranging from 20 to
24 percent were measured in the subsurface on the Ewing farm using a
neutron logger, which gives an index of total water content in a spheri-
cal space surrounding the device. A precise moisture distribution profile
is not possible with this method as the radius of the sphere of detection
is a function of the water content. However, the profile derived from
the use of the logger is sufficiently accurate to derive generalized con-
clusions.
Porosity of alluvial materials collected at depths of 0.5, 2.0,
and 5.0 feet were reported to range from 26 to 36 percent. Several
values of specific yield, ranging from 0.15 to 0.30, were selected for
use in the simulation model. An optimum value of 20 percent was deter-
mined through comparison of the mathematical model results with his-
torical measurements. The analysis also indicated optimum values for
a stream bottom infiltration rate of 3.8 feet per day and a permeability
of 1,450 gallons per day per square foot (gallons per day per square foot
(gpd/ft 2) .
63
The flow system analyzed by Matlock is contained in both the
flood-plain alluvium and basin-fill aquifers. The specific yield value
of 20 percent reported by Matlock is probably representative of a com-
posite storage coefficient from these aquifers in the Ewing farm area.
Water Resources Research Center Studies
Wilson and DeCook (1968, P. 1223) report a storage coefficient
value of 0.0218 computed from the results of an aquifer test utilizing a
water well producing from the basin-fill deposits and the Rillito beds.
The test site was located at The University of Arizona Water Resources
Research Center on the flood plain of the Santa Cruz River approximately
5 miles west of the Ewing farm. The average sediment size of the basin-
fill deposits from which the test well produced water is finer than that in
the Ewing farm vicinity, and both units are highly stratified.
The aquifer test reported by Wilson and DeCook extended for a
period of two weeks. Water-level drawdown and recovery data were anal-
yzed through the use of the Theis equation to determine the value of the
coefficient of storage. Semi-confined conditions are indicated by a coef-
ficient of storage value of 0.0218, which may be due to widespread fine-
grained lenses in the basin-fill deposits and in the underlying Rillito
beds acting as confining layers. Although the test was of moderate dur-
ation, an error in the storage coefficient is possible due to delayed
drainage in the stratified aquifers.
In the same paper Wilson and DeCook (1968) report results of a
neutron probe study. The report contains several profiles showing vari-
ous levels of saturation in aquifer materials surrounding a cased test
hole. At depths ranging from 25 to 55 feet, moisture content
64
(volume/volume) under drained and later under essentially saturated
conditions ranges from approximately 20 percent to 45 percent, respec-
tively. These data would indicate that the specific yield may be equal
to the difference in water content or to about 25 percent. The authors of
the paper cite the 25 percent figure and term it "the average moisture
content change."
In a subsequent paper Wilson (1969, p. 34) reported additional
investigations at the Water Resources Research Center, again utilizing
the neutron probe. He concluded on the basis of differences in water
volume that the average porosity of the sediments was about 36 percent
and the specific yield was about 16 percent.
The results of the Wilson and DeCook (1968) study in the Water
Resources Research Center area also give information on the volume and
duration in time of water in the unsaturated zone after recharge events.
The authors include moisture logs made shortly before and after a 6-day
runoff event which reached a maximum discharge of 3,680 cfs. Ground-
water hydrographs were rising before this event due to infiltration from
two smaller events which occurred 6 and 12 days earlier. Although mois-
ture logs were not made until the largest runoff began, it may be assumed
that the volume of water in the unsaturated zone was high as a result of
the two preceding flows.
On the day the large flow began, a moisture log made in an
access tube located 330 feet from the low flow channel showed 32 feet
of essentially saturated sediments above the water table. On the third
day of the flow, the moisture log showed 33 feet of saturation above the
water table, and three days later, when the large flow ended, the
65
saturated thickness above the water table had increased to 44 feet. The
saturated thickness above the water table then changes to 45, 42, 39,
33, 32, and 30 feet on 3, 7, 11, 14, 18, and 23 days, respectively,
after flow ended. These data indicate that water content of the unsatur-
ated zone reached a maximum in 3 days after the flow and declined to
preflow levels within 18 days. No detailed data are shown, but the
authors indicate that further decrease in the water content in the un-
saturated zone was gradual. The groundwater hydrographs in nearby
observation wells peaked 9 days after the largest runoff event and then
slowly declined for several weeks. Water was noted to be cascading
into the observation wells both during hydrograph rise and for a period
of decline.
Tucson Basin Studies
Anderson (1968) analyzed the hydraulic system in the Tucson
basin through the use of an electric analog model. He estimated the
storage coefficient of the basin aquifer to be 0.15 (1968, p. 17), arriv-
ing at this value after a period of model adjustments required to repro-
duce historical water levels. He found it necessary to reduce the
coefficient of storage to 0.045 in a 5-square-mile area below the met-
ropolitan Tucson area. Anderson (1968, p. 22) also stated that the
drawdown indicated by the model was much greater than the actual
decline along Rillito Creek suggesting that the correct value of the
storage coefficient for that area is greater than 0.15.
66
Movement of Water in Unsaturated Zone
Geologic and hydrologic data collected in the Tucson basin
during this study and by others may be used to estimate the extent of
lateral movement of infiltration from runoff in Rillito Creek and the
length of time significant amounts of water may be present in the unsat-
urated zone subsequent to runoff.
Extent of Lateral Movement
The size distribution and the limited stratification shown in
outcrop and drilling samples of both the basin-fill deposits and the
flood-plain alluvium indicate that the vertical permeability of the sed-
iments in the unsaturated zone may be large. Studies by others on the
Ewing farm show an optimum stream-bottom infiltration rate of 3.8 feet
per day. This infiltrated water moves downward toward the water table
through an unsaturated environment. If this flow were under saturated
conditions and under a hydraulic gradient of unity, a vertical permea-
bility of 29 gpd/ft 2 would be required to limit the percolation path to
the sediments immediately below the Rillito Creek channel. Therefore,
a vertical permeability which is one-fiftieth of the reported horizontal
permeability of 1,450 gpd/ft 2 may allow water from Rillito Creek to
move nearly directly downward to the water table.
This simplified analysis indicates that lateral movement of
water in the unsaturated zone may be small after runoff in Rillito Creek.
Other factors which may terKi to increase the lateral movement are:
1. Because ground water movement above the water table takes
place under unsaturated conditions, the pore volume of the
rock through which flow may occur is more limited than for
67
saturated conditions and the effective permeability of the sed-
iments is lowered. Therefore, the areal extent of sediments
through which infiltration is occurring may increase.
2. The term hydraulic gradient is inappropriate when used to dis-
cuss flow above the water table. Because saturation does not
occur, or occurs infrequently, no head other than gravity is
available to cause water movement. Hence, the assumptions
of a hydraulic gradient of unity may give an erroneously high
rate of flow. If the 6ctual rate of flow is less than that com-
puted, the volume of sediments through which flow occurs may
be larger than the volume of sediments immediately below the
channel.
3. The rate of infiltration through the stream bed was given as
3.8 feet per day, the optimum value computed through mathe-
matical model analysis. The rate of stream-bed infiltration is
a function of permeability of the underlying sediments as well
as a direct function of the average depth of water in the stream.
Therefore, at high stream stages the infiltration rate may ex-
ceed 3.8 feet per day and may increase the areal extent of
sediments necessary to pass the greater flow.
4. Cascading water was noted in observation wells which are
approximately 300 feet from the Santa Cruz River in the Water
Resources Research Center area during the groundwater hydro-
graph rise and for â period during its decline. I have noted no
cascading water in any observation well in the Ewing farm area
and none was reported by the farm workers who were questioned.
68
The absence of cascading water in the Ewing farm area appears
to indicate that the lateral movement of large quantities of
vadose water in that vicinity is less than in the Water Re-
sources Research Center area.
It appears from the foregoing analysis that the water content,
and hence the mass of the unsaturated zone, probably increases not
only directly below the stream bed in the Ewing farm study area but
also laterally from the channel after runoff events. The magnitude of
the lateral movement is not indicated but appears to be less than that
which occurs in the Water Resources Research Center vicinity and may
be a few hundreds of feet.
Time Span of Excess Unsaturated-zone Water
The Water Resources Research Center study (Wilson and De-
Cook, 1968) using the neutron probe was done in sediments which are
more highly stratified than the sediments in the Ewing farm area. How-
ever, some correlation may be made between the results of that study
and observations on the Ewing farm.
The sequence of events after the end of flow at the Water
Resources Research Center was: at 3 days the water content of the
unsaturated zone reached a maximum, at 9 days the groundwater hydro-
graphs reached maximum stage, and at 18 days the water content of the
unsaturated zone had declined to preflow levels. In the Ewing farm area,
the groundwater hydrographs. appear to peak approximately 6 days after
flow, two-thirds the time required at the Water Resources Research Cen-
ter. The decrease in time to peak is believed to be chiefly due to the
coarser, less stratified nature of the sediments in the unsaturated zone
69
on the Ewing farm, but may also be due to smaller flows in Rillito Creek
and to the shorter distances between the observation wells and the
creek.
The time required to drain vadose water resulting from flow in
Rillito Creek is believed to be less than that required to drain vadose
water due to flow in the Santa Cruz River at the Water Resources Re-
search Center. Therefore, maximum water contents in the unsaturated•
zone may occur shortly after flow in Rillito Creek and the residual water
content after two or three weeks may be negligible.
Conclusions
The water-table decline which occurred in the Ewing farm
vicinity is a manifestation of a loss in storage both in the basin-fill and
the flood-plain alluvium aquifers. In the study area these aquifers con-
tain sediments of predominantly sand and gravel size. Both are indis-
tinctly bedded and may be considered relatively homogeneous.
Infiltration from surface-water flow percolates rapidly through these
units from the surface to the groundwater table.
Analysis of the studies cited indicates that the composite co-
efficient of storage in the Ewing farm area probably lies in the range of
0.15 to 0.25. Specific studies on the Ewing farm suggest that 0.20 may
be a representative average value.
At the Water Resources Research Center the high water content
of the unsaturated zone after runoff is a function of large flows in the
Santa Cruz River and of the highly stratified sediments above the water
table. On the Ewing farm the water content of the unsaturated zone is
believed to be much smaller because of the lower volume of flow in
70
Rillito Creek and the coarse, poorly stratified sediments above the water
table. The lateral extent of vadose water increases and attendant gravi-
tational field intensity increases on the Ewing farm are not known but
may be a few hundreds of feet. The time duration of large increases of
gravitational field intensity due to infiltrated water resulting from stream
flow is probably limited to less than three weeks after flow.
COEFFICIENTS OF STORAGE COMPUTED BY
THE GRAVITY METHOD
A method has been developed in the preceding sections which
theoretically may be used to compute the coefficient of storage of a
water-table aquifer from gravity survey data together with measurements
of water levels in observation wells. The Ewing farm was described as
a field area in which practical application of the gravity method may be
tested. The results of the Ewing farm tests are given in this section
and are used to compute a coefficient of storage at each field station.
A significant problem in the gravity method described is the
lack of precision in measuring gravitational field intensity. The re-
quired precision of many conventional gravity surveys is on the order
of 0.1 milligal. This precision is obtainable with many modern grav-
imeters and conventional data reduction techniques.
The theoretical gravitational field intensity due to an infinite
horizontal slab of aquifer material having an S of 0.25 and undergoing
a uniform decline of water level of one foot is 0.0032 milligals. The
computed error of the gravity survey and reduction technique reported
and analyzed earlier is + 0.026 milligals . Therefore, the gravity re-
sponse to small mass changes in the aquifer is not precisely described
by single measurements, and the straight line solution for S using an
arithmetic plot of several relative gravity and water-level decline data
pairs together with equation (1) is used. This procedure enables the
coefficient of storage to be determined by the trend of the data rather
71
72
than single values which may be individually in error due to imprecise
measurements of gravitational field intensity.
Relative Gravity versus Time
Plots of relative gravity against time at the various field sta-
tions were prepared to examine the trend of relative gravity. In the
Ewing farm area the trend at any station may not be apparent due to
scatter in relative gravity data until several months have elapsed and
the water-level decline has exceeded 10 feet.
Figure 11 shows relative gravity values measured at field
station EW-1 from October 1968 to June 1970. It may be observed that
a trend of relative gravity is visible although the scatter of the data
points is large. Figure 11 also shows the hydrograph of observation
well E-2 adjacent to gravity station EW-1 which indicates that the
water levels below the gravity station declined rather steadily through
the period of gravity measurements. Figure 12 shows similar data col-
lected at gravity station NE-6 and at observation well D-2. This grav-
ity station and observation well are near Rillito Creek and are therefore
influenced by unsaturated-zone effects resulting from surface-water
runoff. The general correspondence between decline in relative gravity
and decline in water level may be noted.
The scatter of the data points from a line similar to that des-
cribed by the water-level measurements is due chiefly to imprecision
in the gravity survey and in the gravity data reduction. A portion of the
scatter, however, must be attributed to random deviations in position of
the water table beyond that described by the observation wells and to
unsaturated-zone effects.
o
2280 8.870
o o
Jul OctJunOct FebNov Jan Mar AprAug JanFeb Mar Apr May DecDec NovSep May Jun .
1969 19701968
2300
8.960
8 950
2295
8.940
8.930
8.920
8,910
oo
2290
o
2285
0 Relative Gravity
- Water Level
o o
o
o
2275 L t
8.860
8.900
8.890
8.880
Figure 11. Hydrograph of Observation Well E-2 and Relative Gravity at EW-1
73
74
2315
o
10.020
231010.010
10.000
9.990
2305
9.9804-Q o
o
o>
oo
oo 9.970
2300
o
0 9.960 o
o
9 950 o
cr
9 940
2295 o
9.930
0 Relative Gravity
- Water Level
o9 920
2290 9.910
9.900
2285 Li
Oct
Nov
Dec
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May
Jun1968
1969 1970
Figure 12. Hydrograph of Observation Well D- 2 and Relative Gravity at NE - 6
75
The trend of the gravity data in Figures 11 and 12 is similar to
the trend of water levels. The degree of difference in these trends is
analyzed by plotting the change in gravitational field intensity against
water-level change and is related to the storage coefficient through
equation (1).
Relative Gravity Versus Water-level Decline
The correspondence between the trends of gravity data and
water-level decline was analyzed by constructing plots of relative grav-
ity data at each gravity station versus water level in nearby observation
wells. These plots are shown in the appendix (Figures 15 through 17).
The correspondence between average change in gravity and water-level
change was described by fitting a straight line through the data pairs
using the method of least squares and determining the slope of this line.
Lg The slope is equal to the average ratio of at the individual fieldnt
stations and has units of milligals per foot.
Computation of the Coefficient of Storage Using the Souquer Slab Interpretation Model
Equation (1) was developed to relate the coefficient of storage
to the change in relative gravity and to the corresponding change in
water levels through the use of the Bouguer slab interpretational model.
ng The expression was given as S = 78.3 where the ratio Lt
may be given as the slope of the line through the data pairs described
above and shown on the plots in the appendix. The coefficients of stor-
age computed in this manner for each of the field stations are shown in
Table 3.
76
Table 3. Coefficients of Storage at Selected Field Stations on theEwing Farm
Station Coefficient of Storage
EW-1 0.25
EW-2 .29
EW-7 .40
NW-2 .19
NW-3 .31
NW-4 .21
EW-13 .11
N-1 .19
N-2 .18
N-3 .25
N-5 .21
EW-16 .12
NE-4 .16
NE-5 .15
NE-6 .15
NE -7 .19
ENE-1 .27
Modification of the Coefficient of Storage Values
Use of equation (1) requires the assumption that the water-level
decline measured in each observation well could be approximated by a
horizontal slab throughout an infinite aquifer. The defects due to the
77
assumption of horizontality and to infinite lateral extent are corrected
using K factors derived from the tilted finite slab analysis.
Corrections Due to Water-table Slope
Figure 8 shows water-table contours in the Ewing farm vicinity
in the spring of 1970. The slope of the water table through the Ewing
farm area is southwestward at a rate of approximately 35 feet per mile
or about 0.5 degrees from horizontal. The slope of the water table in
the spring of 1968 and 1969 is comparable. Analysis of the tilted slabs
described earlier indicates that a correction factor, such as shown in
Table 1 due to a slope of 0.5 degree, has a value of approximately
1.0001 or less. This slope correction is insignificant, and the gravity
effect of the Bouguer slab model is assumed to be exact with respect
to assumptions of horizontality.
Corrections Due to the Areal Extent of the Water-table Decline
The groundwater decline which was recorded in the Ewing farm
vicinity was in general experienced on a reduced scale throughout the
northern portions of the Tucson basin. Through the early part of the
period of field measurements, the area of near maximum decline was
widespread with east-west and north-south dimensions of several miles.
Through the second half of the study period, the decline remained wide-
spread, but the rate of decline became intensified in a smaller area
roughly centered on the Ewing farm. The area of intense decline which
occurred late in the study period had east-west dimensions of approxi-
mately two miles and north-south dimensions of approximately one-half
mile.
78
The pattern of decline of the water table described above was
modeled by two horizontal finite slabs. The slab approximating the
early water-level decline was assigned equal side lengths of 10,000
feet. The slab used for the more limited area was given north-south
dimensions of 3,000 feet and east-west dimensions of 8,000 feet. The
gravity effects of reasonable modifications of these dimensions were
also examined. Correction coefficients similar to those shown in Table
1 were computed for each approximation. The results ranged from K
values of approximately 1.01 for early decline conditions to a maximum
of approximately 1.03 for late conditions. The variation between early
and late conditions would be theoretically manifested by a slight change
ng in slope of the plots shown in the appendix if the gravity measure-Lt
ments were exact. Due to the scatter of the gravity data, no change in
slope is apparent. The correction factor K to equation (1) due to limita-
tion of slab size is the average of those given above or 1.02.
Corrections Due to Other Inexact Model Assumptions
Throughout the analysis of water-table movements it has been
assumed that this movement is slab-like. Although water-table move-
ment may be largely slab-like, it may be anticipated that some amount
of undulatory movement of the water table may occur.
Local Slab Deviation. The gross effect of undulatory move-
ment, such as drawdown cones and recharge waves, is to cause gravity
data scatter similar to that encountered in this work. This effect is
ng minimized by determining the ratio using several gravity and water-Lt
level measurements and assuming that local unobserved positive and
negative water-table movements give rise to similar gravity variations
79
which cancel each other. Although these effects may grossly cancel,
the negative gravity effect due to drawdown cones may exceed sporadic
positive effects due to recharge and other causes.
The magnitude of the negative effect due to local mass deficits
may be estimated from the limited slab analysis where the gravitational
field intensity of a 100-foot-square slab was computed. The K correction
of such a slab is 1.33 assuming' that the slab was a mass deficit, unde-
tected by water-level measurements. The corresponding correction of a
drawdown cone would be less' due to the decreased thickness of the
cone with lateral extent and may be approximated by a K of 1.10. There-
fore, a correction of approximately 10 percent may be appropriate for
gravity stations very near to pumping wells, such as Ewing farm gravity
stations EW-7 and ENE-1. Although these stations are immediately ad-
jacent to pumping wells, the error described above is minimized because
gravity meter readings were not made at these stations while the wells
were pumping. Only residual drawdowns during non-pumping periods
were present to affect the measured gravitational field intensity. The
effect of drawdown cones on other gravity stations is further minimized
by lateral displacement of the cone from the point of measurement. Be-
cause of the intermittent nature of this effect and because measurements
were made only under non-pumping conditions, no corrections are be-
lieved to be necessary.
Variation in Coefficient of Storage. The coefficient of storage
of the portion of the aquifer Which changes mass is assumed to be con-
stant. This assumption may be valid when large portions of the aquifer
are considered; however, locally some deviations from average may be
80
anticipated. Matlock (1970, P. 5) assumed values of effective porosity
ranging from 0.15 to 0.30 for the flood-plain alluvium based on his
studies in the area and on results of reports from other areas. This range
may also be appropriate for the upper basin-fill deposits in the Ewing
farm vicinity. The gravity meter integrates large volumes of material
and therefore tends to average the value of the coefficient. However,
if the water table declines through a coarse gravel layer that extends for
several hundred feet horizontally, the change in gravitational field in-
tensity may be greater for dewatering in this zone with respect to under-
lying or overlying finer grained zones. This effect may also tend to
increase the scatter of relative data values, but this effect is believed
to be minimal because of the absence of through-going beds in outcrop
exposures of these sediments and the assumed similarity of the lithology
with depth.
The average coefficients of storage in the basin-fill and flood-
plain alluvium aquifers in the Ewing farm vicinity are believed to be
similar. If they are different by a few percent, it is improbable that the
difference may be determined or even indicated by the gravity method.
A degree of ambiguity in observing this possible change is due to the
data scatter, but it is also due to the geometry of the contact between
the two aquifers. At best, a large-scale change in the coefficient of
storage with depth in the aquifer system would be expressed by a slight
ng curvature in the line fitted to the data. Future measurements as-ntsuming continued drawdown in the Ewing farm vicinity may express a
difference in values of S by extension of the data.
81
Corrections Due to Unsaturated-zone Effects
Unsaturated-zone effects in the Ewing farm vicinity are due to
water moving from the land surface toward the water table. This water
is derived from three sources: precipitation, irrigation, and ephemeral
stream flow in Rillito Creek. The supply of water from these sources is
intermittent; therefore, changes in gravity due to unsaturated-zone ef-
fects are variable with time and with the quantity and position of infil-
trated water from the three sources.
The Unsaturated-zone Effect Due toInfiltration from Precipitation
The Ewing farm receives approximately 10 inches of precipita-
tion annually, nearly all in the form of rain. The greatest monthly pre-
cipitation during the study period was that of July and August 1969 when
nearly 4 inches of rainfall were recorded at the Ewing farm. The remain-
der of the months through the period of study show measurable precipi-
tation, but the monthly average was less than one inch as was the
maximum one-day rainfall.
The areal extent of soil water increases due to precipitation
may be approximated by a Bouguer slab. The mass of this slab assuming
one inch of rainfall prior to evapotranspiration losses would give a grav-
itational field intensity increase of approximately one microgal, an a-
mount which is insignificant with respect to the error of gravity meas-
urements. The occasional increase in gravitational field intensity due
to precipitation is probably less than that suggested above due to aver-
age rainfall amounts of less than one inch and evapotranspiration losses
which usually occur after rainfall and prior to time of gravity measure-
ments.
82
The Unsaturated-zone Effect Due toInfiltration from Irrigation
The crop lands on the Ewing farm are irrigated throughout the
year; however, the greatest quantity of irrigation water is applied during
the period extending from May through September. Irrigation water for
the Ewing farm is supplied from groundwater pumpage from wells and
through flood irrigation. Water is piped from the wells on the farm to
individual plots of several acres and is allowed to pond until the soils
appear saturated to a depth of several inches to a foot and until the en-
tire plot is covered with water. Maximum irrigation amounts are not be-
lieved to exceed 6 inches of water per individual application, although
the total water applied may be as much as 3 acre feet per acre per year.
The areal extent of the increases of vadose water from irriga-
tion may be approximated by a finite slab whose lateral dimensions may
be described by the dimensions of the irrigated plot. Gravity stations
near irrigated fields were located at the margins of the fields; therefore,
the change in gravitational field intensity due to irrigation may be ap-
proximated by a single half slab. The mass of the half slab, assuming
6 inches of irrigation water prior to evapotranspiration losses, would
give a gravitational field intensity increase of approximately 3 microgals.
However, the initial increase in field intensity is less than 3 microgals
due to lateral displacement of the near edge of the slab from directly be-
low the gravimeter. The magnitude of this displacement is equal to the
distance the gravity station is removed from the edge of the irrigated
field. This displacement reduces the effect of the initial slab to approx-
imately one microgal. The gravitational field intensity due to irrigation
water may change because of evapotranspiration losses which decrease
the mass and hence the gravity effect of the slab as well as lateral and
downward percolation of the irrigation water which may increase the
83
gravity effect. The decrease in the gravity effect due to lateral dis-
placement of the near edge of the slab may be partially eliminted by
horizontal movement of the soil water toward the unirrigated margins
of the plot. Therefore, the maximum unsaturated-zone effect due to
irrigation may be approximately two microgals.
The Unsaturated-zone Effect Due to Infiltrationfrom Ephemeral Stream Flow
This portion of the unsaturated-zone effect is not modeled be-
cause of the lack of acceptable data on the volume, lateral extent, and
duration of water in the unsaturated zone resulting from surface flow in
Rillito Creek. The errors due to the effects of recharge water in the un-
saturated zone are evaluated through examination of the gravity data col-
lected at each field station and attempting to correlate anomalous rises
in gravitational field intensity with time periods subsequent to surface-
water runoff. The dates of measurement of gravitational field intensities
at each station are shown on Figure 13.
A + 26 microgal survey error was computed earlier. This error
value was arbitrarily increased to + 30 microgals and was used to test
the validity of each gravity datum. Those data deviations more than 30
microgals from the line of best fit were assumed to be in error and were
discarded. The data which show negative deviations greater than 30
microgals are probably in error; however, the data which show positive
deviations greater than 30 microgals may be in error but may also indi-
cate an increase in gravitational field intensity due to unsaturated-zone
effects such as those resulting from surface-water runoff.
The gravity data at each field station are discussed below.
The deviation of the data points from the line of best fit for each sta-
tion is described and is assumed to be due to variation of gravity data,
although for some stations which are not near observation wells, some
EW-I o o o o o o 00 O© an) 0© oz 0 o 00 © 0 o o 0 0 0000 0 OGD
EW-2 O o o o 00 o o o 0 CID
EW-7 o o o o o o 00 0© aD 000 o o o o EID
NW-2 o o o o o 00 o © 000 o o o o o aD
NW-3 o o o o o 00 o o o o aD
NW-4 o o o o o o o o CD 000 0 o o o o ai)
EW-13 o o o 00 © o 00 o o o o 0 o a)
o N-1 o o o o o o 00 o o 0 Q o oaD
J-3
a)
N-2
N-3
o
o
o
o
o
o
o
o
0
CD
o
0
00 o
00 0
o
0
0
o
o
o
o
o
00D
o aD
N-5 o o o 0 o o 000 o o o 001D
EW-16 o o o o 00 o o 00 o o
NE-4 o o o o 00 o o o o o o 00 o o o o o o o aD
NE-5 o o o 0 00 co o o 0 aD
NE-6 o o o 0 00 o o 000 o o o co)
NE-7 Q o o 00 o o 000 o o o aD
ENE -I 0 o 00 o o o 0 o o o 0
Oct
Nov c
Jo n
Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jon Feb Mar Apr May Jun
1968
1969 1970
Figure 13. Dates of Gravitational Field Intensity Measurements
84
85
variation in data point position may be due to water-level variation. The
deviation of a gravity datum is described as negative if its plotted loca-
tion appears to indicate a decrease in gravity with respect to the line of
best fit, possibly indicating the presence of a mass deficit. The devia-
tion of a gravity datum is described as positive if its plotted location
may theoretically indicate an increase in mass with respect to the loca-
tion of the line of best fit. The gravity data having positive deviations
are those data which may indicate the presence of an unsaturated-zone
effect resulting from a temporary mass excess above the water table. A
positive deviation of 3.2 microgals is theoretically equal to the increase
in gravitational field intensity due to the presence of a one-foot Bouguer
slab of saturated sediments in the unsaturated zone. The sediments in
the slab are assumed to have a coefficient of storage of 0.25. Although
the above analogy is imprecise when applied to the unsaturated zone
and to the unsaturated-zone effects due to recharge resulting from run-
off, it may be used as an interpetative tool to visualize approximate
amounts of recharge water in the unsaturated zone below a gravity sta-
tion.
EW-1. This gravity field station is located 1,000 feet from
the channel of Rillito Creek and is immediately adjacent to observation
well E-2. The coefficient of storage computed for this station was done
using water-level data from E-2 and 41 gravity measurements at EW-1.
Forty-two measurements of gravity field intensity, ranging in
time from October 15, 1968 to June 2, 1970, were made at this station.
One measurement, that of October 15, 1968, was discarded due to a
positive apparent reading error of 50 microgals. This measurement was
86
made 6 weeks after the last preceding flow and is therefore not believed
to be due to infiltration from runoff.
Twelve gravity measurements were made at EW-1 within 30 days
after runoff in Rillito Creek. The data points on Figure 15 derived from
these 12 measurements are scattered randomly about the line of best fit.
There appears to be no correlation between changes in gravitational field
intensity at this station to runoff in Rillito Creek.
EW-2. Field station EW-2 is located 1,100 feet from Rillito
Creek and is approximately 120 feet from observation well E-2. Water-
level measurements in E-2 and 10 gravity measurements at EW-2 were
used to compute the storage coefficient`for this station.
Twelve measurements of gravitational field intensity ranging in
time from December 14, 1968 to June 2, 1970 were made at this station.
Two measurements, those of February 15 and April 12, 1969, were dis-
carded as due to apparent reading errors. The datum of February 15,
1969 deviates in the negative direction showing an apparent effect op-
posite to recharge. The April 12 datum deviates in the positive direction
indicating a possible mass surplus due to recharge, but the measurement
was taken over 80 days after flow and after several other measurements
which did not show a positive deviation due to this flow. Therefore,
both measurements were attributed to reading errors. There appears to
be no correlation of changes in gravitational field intensity at this sta-
tion to runoff in Rillito Creek.
EW-7. This field station is located 900 feet from Rillito Creek
and is approximately 475 feet from observation well E-2. The coefficient
of storage computed for this station was determined using water-level
87
data from observation well E-2 and 19 measurements of gravitational
field intensity at EW-7.
From October 15, 1968 to May 31, 1969, 22 gravity measure-
ments were made at this station. Three measurements were discarded
due to apparent reading errors. Two, which are dated February 1 and
February 15, 1969, deviate in the direction of negative mass; the third,
dated July 6, 1969, deviates more than 80 microgals in the positive di-
rection indicating possible recharge effects. The last gaged flow in
Rillito Creek preceding this measurement was January 22, 1969, several
months prior to the measurement. Therefore, this measurement is also
attributed to reading error. Unsaturated-zone effects due to runoff in
Rillito Creek are not indicated by the gravity data at this station.
NW-2. Gravity field station NW-2 is located 750 feet from
Rillito Creek and approximately 360 feet from observation well E-2. The
coefficient of storage at this station was computed using water-level
data from observation well E-2 and 19 measurements of gravitational
field intensity at NW-2.
Twenty gravity measurements were made at this station between
November 19, 1968 and June 2, 1970. The measurement dated November
19, 1968 was discarded; this measurement of gravitational field inten-
sity deviated from the line of best fit in the positive direction indicating
a possible recharge effect of approximately 35 microgals. The date of
the measurement coincides with the date of hydrograph peaks from ob-
servation wells near Rillito Creek due to runoff in mid-November 1968.
If this deviation is due to infiltration from recharge, it is equivalent to
88
the change in gravitational field intensity due to an infinite 11 - foot-
thick saturated zone in the sediments above the water table.
Eight other measurements which were made on July 5, 1969 to
September 24, 1969 and on January 10, 1970 have an average deviation
of approximately 15 microgals in the positive direction from the line of
best fit. Of these eight measurements, three were made in July 1969,
several months after the subsequent flow event and prior to the August
1969 flow events. The hydrographs of observation wells A-5 and B-3
show small rises, less than one foot, in July 1969, but no significant
flow events are indicated; therefore, the deviation is assumed to be
due to error.
The remaining five of these eight deviating measurements were
made on August 19 and 29, 1969, September 9 and 24, 1969, and January
10, 1970. The first measurement of this set, that of August 19, 1969,
coincides with the date of observation well hydrograph peaks due to run-
off in Rillito Creek through the first half of August 1969. This measure-
ment shows a positive deviation of 6 microgals indicating a possible
recharge effect equivalent to a 2-foot saturated slab in the unsaturated
zone. The subsequent measurement, dated August 29, 1969, was made
10 days after the groundwater-level hydrograph peak and shows a posi-
tive deviation of 3 microgals. Later measurements, taken September 9
and September 24 which were taken 21 and 36 days subsequent to flow,
show stronger positive deviations, averaging approximately 20 microgals.
If these measurements were precise, they would show an increase in
gravitational field intensity equivalent to that of a 6-foot saturated slab
in the unsaturated zone. The final measurement of the eight, which
89
show a positive deviation was made on January 10, 1970, 147 days after
the last surface flow. This gravity datum shows a positive 15 microgal
deviation.
Of these eight measurements only two, those of August 1969,
appear to be probably due to unsaturated-zone effects resulting from
runoff in Rillito Creek. The remainder occur during .periods in which
recharge effects should be small and certainly less than that possibly
indicated by the anomalous increase in gravitational field intensity. All
eight increases in field intenSity deviate less than 30 microgals from
the line of best fit through the data points and are therefore within the
computed survey error. It appears that increases of gravitational field
intensity at station NW-2 may correlate with runoff in November 1968
and August 1969 but not with that of January 1969 or March 1970.
NW-3. This field station is located 650 feet from Rillito
Creek and is approximately 380 feet from observation well E-2. The
coefficient of storage computed for this station was determined by using
water-level data from E-2 and nine gravity measurements at NW-3.
Thirteen measurements of gravitational field intensity ranging
from November 19, 1968 to June 2, 1970 were made at this station. Four
measurements were discarded due to large apparent reading errors. A
measurement dated November 19, 1968 coincides with the groundwater
hydrograph peaks resulting from the mid-November 1968 flow in Rillito
Creek. This measurement deviates in the positive direction and may
therefore indicate the preserice of a 10-foot-thick saturated zone above
the water table. The measurement made on December 14, 1968 deviates
in the negative direction as does the measurement made on March 31,
90
1969. The fourth discarded datum is that of February 15, 1969, which
deviates approximately 70 microgals in the positive direction indicating
a possible recharge effect equivalent to a 22-foot-thick slab above the
water table. This measurement occurs approximately 18 days after the
groundwater hydrograph peak due to runoff in mid-January 1969. An
earlier measurement made on February 1, 1969 during the time of the
groundwater hydrograph peak shows no recharge effect.
It appears that two of the deviating measurements, those of
November 19, 1968 and February 15, 1969, may be due to unsaturated-
zone effects resulting from surface water runoff in Rillito Creek. The
February 15, 1969 point is questionable because of its large deviation,
its delay in time after runoff, and because an earlier measurement flow-
ing the flow shows no recharge effect. The other two data points which
show negative deviations are probably due to reading errors.
The remaining gravity data appear to be randomly scattered
within the zone described by the computed survey error about the line
of best fit. No measurements were made in July, August, and September
of 1969 at this station; therefore, no conclusions may be drawn regard-
ing unsaturated-zone effects at this station due to runoff in August 1969
NW-4. Field station NW-4 is located 550 feet from Rillito
Creek and 460 feet from observation well E-2. The coefficient of storage
computation for this station was done using water-level data from E-2
and 19 gravity measurements at NW-4.
Twenty measuremerits of gravitational field intensity were made
at this station from November 19, 1968 to June 2, 1970. One measurement
was discarded due to a deviation greater than 30 microgals. This
91
measurement was made November 19, 1968 and shows a positive devia-
tion of 47 microgals indicating a possible recharge effect equivalent to
the presence of a 15-foot-thick saturated slab below the gravity station.
The time of this measurement coincides with the date of groundwater
hydrograph peaks due to runoff in Rillito Creek in mid-November 1968.
Therefore, this deviation may be due to unsaturated-zone effects result-
ing from infiltration of surface runoff.
At station NW-2 eight measurements which were made from
July 5, 1969 to September 24,. 1969 and on January 10, 1970 showed an
average positive deviation of 15 microgals . The measurements made at
NW-4 41so deviate in the positive direction averaging 15 microgals .
The analysis of these points is the same for both stations.
Correlation between changes in gravitational field intensity
and runoff in Rillito Creek appear to be possible at NW-4 for the runoff
events of November 1968 and August 1969. No correlation appears for
the runoff events of January 1969 and March 1970.
EW-13. This gravity field station is located 750 feet from
Rillito Creek, 925 feet from observation well E-2, and 900 feet from
observation well B-3. The coefficient of storage for this station was
computed using the averaged water-level data from observation wells
E-2 and B-3 and 17 gravity measurements at EW-13.
Eighteen measurements of gravitational field intensity were
made at EW-13. One measurement, that of November 19, 1968, was
discarded because of a positive deviation of approximately 70 microgals
from the line of best fit. The date of this measurement is the same as
the date of the groundwater hydrograph peak due to runoff in Rillito Creek
92
in November 1968. If the deviation is due to an unsaturated-zone effect,
it is equivalent to the presence of a 22-foot saturated zone above the
water table.
Seven gravity measurements made in March, July, August, and
September, 1969 and January 10, 1970 show a positive deviation averag-
ing approximately 20 microgals from the line of best fit. Several of these
deviations may be related to the flow in Rillito Creek of August 1969 and
are similar to the deviations shown for stations NW-2 and NW-4 at the
same time. Therefore, it appears that increases of gravitational field
intensity at station EW-13 may correlate with runoff in Rillito Creek dur-
ing November 1968 and August 1969 but not with that of January 1969 or
March 1970.
N-1. Gravity field station N-1 is located 600 feet from Rillito
Creek, 875 feet from observation well E-2, and 825 feet from observation
well B-3. The coefficient of storage was computed for this station using
water-level data from observation wells E-2 and B-3 and 14 gravity
measurements at station N-1.
Sixteen measurements of gravitational field intensity were made
at N-1 from November 19, 1968 to June 2, 1970. Two measurements,
those of November 19, 1968 and February 15, 1969, were discarded due
to deviations exceeding 30 microgals from the line of best fit. The datum
of November 19, 1968 deviates 37 microgals in the positive direction,
possibly indicating the presence of a 12-foot saturated zone above the
water table resulting from runoff in November 1968. The gravity datum
of February 15, 1969 deviates in the negative direction and is attributed
to error.
93
Again the measurements of field intensity made in July, August,
and September of 1969 and January 10, 1970 deviate in the positive direc-
tion, averaging approximately 15 microgals, similar to stations described
earlier. Increases of gravitational field intensity at station N-1 may cor-
relate with runoff in Rillito Creek during November 1968 and August 1969
but do not appear to correlate with runoff in January 1969 or March 1970.
N-2. This gravity field station is located 425 feet from Rillito
Creek, 900 feet from observation well E-2, and 725 feet from observation
well B-3. The storage coefficient for this station was computed using
water-level data from E-2 and B-2 and 15 gravity measurements at N-2.
Sixteen measurements of gravitational field intensity were made
at this station. One measurement, November 19, 1968, was discarded.
This discarded gravity datum deviates approximately 52 microgals in the
positive direction indicating an effect equivalent to the presence of an
18-foot-thick saturated zone above the water table.
Measurements of field intensity in July, August, and September
of 1969 and January 10, 1970 show an average positive deviation of ap-
proximately 15 microgals. Increases of gravitational field intensity at
station N-2 may correlate with runoff events in November 1968 and
August 1969 but not with flow events of January 1969 or March 1970.
N-3. Field station N-3 is located 200 feet from Rillito Creek,
1,000 feet from observation well E-2, and 675 feet from observation well
B-3. The coefficient of storage for this station was computed using
water-level data from E-2 and B-3 together with 16 gravity measurements
at N-3.
94
From November 19, 1968 to June 2, 1970, 17 measurements of
gravitational field intensity were made at N-3. One gravity datum, July
5, 1969, was discarded due to apparent large reading error. The measure-
ment of this date shows a negative deviation, an effect opposite to that
due to recharge.
The gravity datum of November 19, 1968, and the data of July
24, August 29, September 11 and 24, 1969 and January 10, 1970 show a
positive deviation averaging approximately 15 microgals. These data
indicate a possible correspondence between runoff in November 1968
and August 1969 and increased gravitational field intensity. No such
correspondence was associated with the runoff events of January 1969
and March 1970.
N-5. This station is located 150 feet from Rillito Creek,
1,225 feet from observation well E-2, and 700 feet from observation well
D-2. Water-level data from E-2 and D-2 and 13 gravity measurements
at N-5 were used to compute the coefficient of storage at this field sta-
tion.
Seventeen measurements of gravitational field intensity were
made at N-5; two of these measurements dated September 24, 1969 and
May 26, 1970 were discarded. The datum of September 24, 1969 shows
a positive deviation indicating possible recharge, while that of May 26,
1970 shows a negative deviation and is attributed to error.
The gravity measurements of July, August, and September 1969
show positive deviations averaging approximately 10 microgals. There-
fore, a correlation between runoff in November 1968 and August 1969
and increase in gravitational field intensity is indicated. No correlation
95
appears to be indicated at this station for the flow events of January
1969 and March 1970.
EW-16. This gravity station is located 750 feet from Rillito
Creek, 1,550 feet from observation well E-2, 625 feet from observation
well B-3, and 900 feet from observation well A-5. Water-level data
from E-2, B-3, and A-5 and eight gravity measurements at EW-16 were
used to compute the coefficient of storage for this station.
Twelve measurements of gravitational field intensity were made
at this station; three of these were discarded. The discarded data of
November 19, 1968, February 15, 1969, and March 9, 1969 show posi-
tive deviations which are greater than 50 microgals . The dates of these
measurements correspond to the dates of groundwater hydrograph rises
due to surface flow in Rillito Creek in November 1968 and January 1969.
The other discarded point, April 12, 1969, shows a negative deviation
which is attributed to error.
The gravity datum of July 6, 1969 shows a positive deviation
of approximately 20 microgals corresponding to a previously noted rise
in gravitational field intensity possibly associated with the runoff events
of August 1969. Therefore, an increase in gravitational field intensity
which may be correlated with three periods of surface-water flow in
Rillito Creek appears in the data from EW-16.
NE-4. Field station NE-4 is located 225 feet from Rillito
Creek, 100 feet from observation well B-3, 350 feet from observation
well D-2, and 675 feet from 'observation well A-5. The coefficient of
storage for this station was computed using water-level data from B-3,
D-2, and A-5 and 22 gravity measurements from NE-4.
96
From November 19, 1968 to June 2, 1970, 25 gravity measure-
ments were made at NE-4. Two of these measurements were discarded,
that of November 19, 1968 because of a large positive deviation and
that of April 8, 1969 because of a large negative deviation.
The gravitational field intensity datum of N -ovember 19, 1968
corresponds with the groundwater hydrograph peak due to surface-water
flow in November 1968 and indicates a possible recharge effect equiva-
lent to a 12-foot saturated slab above the water table. The data points
also indicate a less strong recharge effect, averaging approximately 10
microgals, due to runoff in August 1969 and March 1970. No recharge
effect is visible for the period of runoff in Rillito Creek during January
1969.
NE-5. This station is located 100 feet from Rillito Creek, 30
feet from observation well B-3, 225 feet from observation well D-2, and
675 feet from observation well A-5. The coefficient of storage was com-
puted for this station using water-level data from B-3, D-2, and A-5 and
10 measurements of gravitational field intensity at station NE-5.
Fourteen gravity measurements were made at this station be-
tween November 19, 1968 and June 2, 1970, and four of these measure-
ments were discarded. The gravity datum dated June 2, 1970 shows a
negative deviation and is attributed to reading error. The gravity datum
of November 19, 1968 shows a positive deviation of 62 microgals which
is equivalent to the gravitational field intensity of a 19-foot saturated
slab above the water table. This possible unsaturated-zone effect occurs
at the time of groundwater hydrograph peak due to the runoff in November
1968. The datum of February 15, 1969 shows a positive deviation of
97
several hundred microgals and is apparently due to a large reading error.
The gravity measurement dated Ppril 12, 1969 shows a positive devia-
tion of 51 microgals. This measurement occurs after approximately 82
days of no flow in Rillito Creek and after several other gravity meas-
urements which do not show excessive deviation, Therefore, the in-
crease shown by this datum may be due to unrecorded flow in Rillito
Creek or to error. Thus, two of the four discarded gravity data may in-
dicate large recharge effects due to Rillito Creek flows of November
1968 and possibly an unrecorded flow in early April 1969. The remainder
of the gravity data appear to be scattered randomly about the line of best
fit.
NE-6. Field station NE-6 is located in the channel of Rillito
Creek and is approximately 100 feet from observation well B-3, 160 feet
from observation well D-2, and 675 feet from observation well A-5. The
coefficient of storage was computed for this station using water-level
data from B-3, D-2, and A-5 and 14 gravity measurements at NE-6.
Sixteen measurements of gravitational field intensity were made
at this station between November 19, 1968 and June 2, 1970. Two meas-
urements, those of November 19, 1968 and February 15, 1969, were dis-
carded due to deviation in excess of 30 microgals from the line of best
fit. The gravity datum of November 19, 1968 shows a positive increase
in gravitational field intensity of approximately 47 microgals. The time
of this datum coincides with the date of groundwater hydrograph peak
due to the runoff in Rillito Creek in November 1968, and this increase
may be due to a mass surplus in the unsaturated zone. If this excess
gravitational field intensity were due to a slab of saturated material
98
above the water table, the thickness of the slab would be 15 feet. The
second deviating gravity datum is negative with respect to the line of
best fit and is attributed to error.
Increases in gravitational field intensity resulting from infil-
tration through the stream bed should be greatest at this station because
of its location. Although gravity measurements were made at NE-6 with-
ing 10 days after each of the four periods of flow, only the gravity datum
which was recorded 5 days after the November 1968 flow shows a large
positive deviation. Measurements were made 9 and 24 days after the
January 1969 flow, and both show negative deviations. Gravitational
field intensity measured 6 days and 16 days after the August 1969 runoff
event both deviate 15 microgals in the positive direction indicating an
increase in the field strength equivalent to the presence of a 5-foot
saturated slab. A measurement made 10 days after the March 1970 run-
off shows an 11-microgal positive deviation, equivalent to the effect of
a 3-foot saturated slab. Thus, three of the four flow events that oc-
curred during the study period are marked by subsequent increases in
gravitational field intensity which are apparently due to an unsaturated-
zone effect. Two of the increases are relatively small, 11 and 15 micro-
gals, and the other is large, 47 microgals.
NE-7. Field station NE-7 is located 150 feet from Rillito
Creek, 70 feet from observation well D-2, and 300 feet from observation
well B-3. The coefficient of storage was computed for this station using
water-level data from D-2 afid B-3 and 15 gravity measurements at NE-7.
From November 19, 1968 to June 2, 1970, sixteen measurements
of gravitational field intensity were made at field station NE-7. One of
99
these data, that of November 19, 1968, was discarded because of ex-
cessive deviation from the line of best fit. The gravity datum of that
date indicates a mass excess corresponding to groundwater hydrograph
peaks due to runoff in Rillito Creek during November 1969. The effect
was equivalent to an 11-foot saturated slab. The gravity datum of Arpil
1, 1970 deviates positively indicating the possible presence of a 3-foot
saturated slab. These data indicate that an increase in gravitational
field intensity may correlate with runoff in November 1968 and in March
1970 but not with that of Janu .ary 1969 or of August 1969.
ENE-1. This field station is located 150 feet from Rillito
Creek, 670 feet from observation well B"-3, and 150 feet from observa-
tion well A-5. The coefficient of storage was computed for this station
using water-level data from B-3 and A-5 and 13 measurements of gravi-
tational field intensity at ENE-1.
Fourteen gravity measurements were made at this station from
July 2, 1969 to May 31, 1970. One gravity datum, that of August 19,
1969, was discarded because of excessive deviation from the line of
best fit. This datum shows a positive deviation of approximately 95
microgals, equivalent to the gravitational field intensity due to a 30-
foot-thick saturated slab above the water table. The date of this datum
corresponds in time to the date of the groundwater hydrograph peak due
to surface flow in August 1969.
The remainder of the data falls within the + 30-microgal boun-
dary about the line of best fit. The gravity measurements of September
11 and 25, 1969 show an average positive deviation of 20 microgals
possibly as a result of flow during August 1969. The datum of March
100
10, 1970 shows a positive 25-microgal deviation possibly corresponding
to runoff in March 1970. Therefore, a possible recharge effect may be
correlated with the events of August 1969 and March 1970. No data were
collected at this station prior to July 1969.
Summary. Thirty-three measurements of gravitational field
intensity were discarded due to deviations greater than + 30 microgals
from the line of best fit. Twenty-one of these data show positive devia-
tions, possibly indicating mass excess due to a temporary recharge
mound in the unsaturated zone. Twelve data show negative deviation
and were attributed to error. If it is assumed that errors are random,
the number of positive and negative deviations should be nearly equal;
however, the positive deviations are nearly twice the negative.
Nearly all field stations show some gravity data deviations
which may be correlated with a groundwater hydrograph rise resulting
from stream flow in Rillito Creek. The seven field stations which are
250 feet or less from Rillito Creek, and thus should be those whose data
are most easily affected by recharge, do not consistently show positive
deviations following stream flow. All of the seven, except ENE-1 which
was not measured, show a positive deviation following stream flow in
November 1968 which was the flow of least volume; one of these sta-
tions, NE-5, shows a positive deviation after the January 1969 flow;
three of the seven show positive deviations after the flow of March 1970.
Each of the seven stations nearest the creek show positive deviations
occurring at times when no unsaturated-zone effect resulting from runoff
in Rillito Creek is indicated by stream-flow records or by groundwater
hydrographs.
101
Three gravity stations, EW-1, EW-2, and EW-7, lie farther
than 900 feet from Rillito Creek. The gravity data at these stations do
not appear to show increases due to unsaturated-zone effects resulting
from stream flow in Rillito Creek. The remaining stations lie at distances
from zero to 750 feet from the creek. The gravity data for these close-by
stations all appear to show unsaturated-zone effects which may be cor-
related with runoff events.
It is concluded that an unsaturated-zone effect resulting from
surface-water flow in Rillito Creek occurred after the flow events of
November 1968, January 1969, August 1969, and March 1970. The in-
crease in gravitational field intensity due to excess vadose water re-
sulting from these flow events probably ranged from approximately 10 to
50 microgals at stations near Rillito Creek and from zero to 20 microgals
at the remaining field stations. The lateral limit of unsaturated-zone
effects which are due to infiltration from stream flow occurring during
the study period appears to be between 750 and 900 feet. The incomplete
record of field strength increases after periods of flow is due to the
small gravity effect with respect to the survey error and possibly is due
to permeability differences resulting from a nonhomogeneous aquifer.
Apparent field strength increases at times other than those coinciding
with a flow event or within a 3-week period following a flow event are
due to survey error.
Corrections Applied to Coefficient of Storage
Values Computed in the Ewing Farm Area
The magnitude of errors due to water-table tile and to the lim-
ited extent of the water-table decline may be expressed by the single
102
correction coefficient K = 1.02. This factor increases the measured
gravitational field intensity to a value which would be given by Bouguer
slab conditions. This factor is used and increases the coefficient of
storage computed at stations EW-2, EW-7, NW-3, and ENE-1 by one
digit. The corrected storage coefficients are shown on Table 4.
The result of unsaturated-zone effects due to infiltration from
irrigation and precipitation is to cause occasional gravity data points
to deviate in the positive direction by a computed maximum of three
microgals . Although a positive displacement of the line fitted through
the data points may be due to these effects, no change in slope is indi-
cated. For this reason no corrections aie made for unsaturated-zone
effects arising from irrigation and precipitation.
Errors resulting from unsaturated-zone effects due to infiltra-
tion from stream flow in Rillito Creek are not described with sufficient
accuracy to permit computation of corrections. The corrections applied
to the data are limited to discarding values which deviate greater than
+ 30 microgals from the line fitted through the data pairs. This proce-
dure results in the removal of the large unsaturated-zone effects, but
does not alter the effect of smaller errors. A further portion of errors
resulting from runoff are mitigated due to the periods in which the effect
is present, occurring both early and late in the study period. Therefore,
these errors may cause a positive displacement of the line showing the
slope of the data trend but may not cause a significant change in the
slope of this line. Conclus fons as to the proper coefficient of storage
for the Ewing farm must, however, take into account the errors intro-
duced by these unsaturated-zone effects.
103
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104
Statistical Measures of Ewing Farm Coefficient of Storage Values
Various statistical data were computed for the data plots shown
on Figures 15-31. Values of percent fit describe the scatter of the data
points about a line with 100 percent indicating perfect correlation and
zero percent indicating no correlation. The percent fit (P) may be related
ngto the standard error of the nt1966, p. 225):
slope by the following equation (Fryer,
Standard Error of Slope =100 ( SD y )n _2
SDx
where n is the number of data points, SD y is the standard deviation of
the relative gravity values, and SDx is the standard deviation of the
water-level data. The statistical data for each gravity station are shown
on Table 4. Figure 14 shows the distribution of S values and the uncer-
tainty associated with each value by the standard error.
The percent fit of the gravity and water-level data pairs ranges
from 91 at EW-2 to 22 at EW-13. Inspection of the data for each gravity
field station indicates that the percent fit is higher for those stations
which show both little correlation of increases in gravitational field in-
tensity with runoff in Rillito Creek and which have non-discarded gravity
data which extends throughout the study period.
Analysis
The data for various stations are divided into three classes on
the basis of presence or absence of significant unsaturated-zone effects
and on length of record. The criteria of class I stations are (1) the devi-
ation of gravity data derived from measurements taken during or shortly
105
I - 3N3
1 - 3N0
93 N
g - 3N
1-0
17 -3N
91 -M3
G - N
2 - No
o
1-0
Z - N .c.7)1-----(D
-o
1N
£1 - M3
0 .17 -MN
2 -MN
Z -MN1-0
- 1 - M3
- Z -M31---0
I -M3 0
G-16
u-) O Lc)I) (NI
Lr) Lc)
o 6 6
oboAols ;o t.roloupoo
106
after periods of flow is not greater than deviations at other times and
(2) the length of record of non-discarded gravity data is equal to or
greater than from December 1968 to May 1970. The criteria for class II
stations are (1) the deviation of gravity data derived from measurements
taken during or shortly after periods of flow exceeds deviations at other
times and (2) the length of record of non-discarded gravity data is equal
to or greater than from February 1969 to May 1970. For class III stations,
the criteria are (1) the gravity data deviate widely and (2) the length of
record is less than from February 1969 to May 1970.
Using the above criteria, the stations of class I are EW-1,
EW-2, EW-7, and N-5. With the exception of N-5, the stations are
those located at 900 feet or more from Rillito Creek. The percent fit of
the class I stations ranges from 76 to 91. The average coefficient of
storage for these stations is 0.29.
The class II stations are NW-2, NW-3, NW-4, N-2, N-3,
NE-4, NE-5, NE-6, and NE-7. These stations are located from zero to
750 feet from the channel of Rillito Creek. The percent fit of the data
for these stations ranges from 45 to 79. The average coefficient of stor-
age for class II stations is 0.20.
The class III stations are EW-13, N-1, EW-16, and ENE-1,
which are located 750 feet or closer to Rillito Creek. The percent fit of
the data from these stations ranges from 22 to 44. The average coeffi-
cient of storage for the class III stations is 0.17. The average and the
range of the storage coefficient for each class of stations are summa-
rized below.
107
Class Average S Range of S
0.29 0.21 - 0.41
II 0.20 0.15 - 0.32
III 0.17 0.11 - 0.28
The reliability of the class I values should be greatest and of
class III should be the least due to increasing potential error with class
number. For this study it appears that greater errors resulted in lower
storage coefficients. This relationship is due in large part to the re-
charge errors occurring in the summer of 1969. Unsaturated-zone effects
due to runoff during that summer occur predominantly in the lower half of
the data plots. The position of these positive deviations results in the
lower portion of the fitted line being displaced further in the positive
direction than the upper portion of the line. The greater displacement at
the lower end results in a smaller slope and hence in a smaller coeffi-
cient of storage.
Examination of the data plots for the class II and III stations
reinforces the correlation of low S value with deviation of data points
derived from measurements in the summer of 1969. The average storage
coefficient computed for the class II and III stations which do not show
large deviations through that period (NW-3, N-3, NE-4, NE-5, NE-7,
and ENE-1) is 0.22. The average S of the class II and III stations which
show large deviations (NW-2, NW-4, N-2, NE-6, EW-13, N-1, and
EW-16) is 0.17. Therefore, removal of the series of data pairs which
show the strong positive deviations through that period increases the
coefficient of storage for class II and III stations.
108
The average of the coefficients of storage which were computed
for class I stations, those stations deemed most reliable due to apparent
absence of recharge effects, is 0.29. This S value is near the maximum
water table S cited by Ferris et al. (1962, p. 78) which was 0.30. The
largest storage coefficient is 0.41 computed for EW:7, a class I gravity
field station. This station is located immediately adjacent to pumping
well E-2R, and the large value may be in some way due to pumpage; how-
ever, prior analysis has indicated that no large effect is anticipated near
pumping wells if measurements are only made during times when the well
is not producing. Therefore, the coefficient determined for this station,
although it is suspect, is probably correct within 20 percent or two
standard errors.
The range of values computed for the class I and II stations is
large. In each case the low value of S is half of the high. This range of
values is in part attributable to the scatter of the gravity data which is
unavoidable due to the survey error; however, the scatter of the gravity
data is described by the standard error of each value. This error, when
added to the low values and subtracted from the high values, does not
alter the coefficients of storage sufficiently to enable them to describe
a common value. Therefore, the correct value of the storage coefficient
may vary through the aquifer from a high of approximately 0.37 to a low
of approximately 0.20 due to local changes in aquifer fabric.
The correct numerical value of the average coefficient of stor-
age in the Ewing farm may be near the average of the class I stations
which is 0.29. If station EW-7 is omitted from this average, the value
drops to 0.25, near the average of those class II stations which do not
109
show large data deviations due to the flow events of summer 1969.
Therefore, the correct coefficient of storage for the Ewing farm area is
believed to lie in the range of 0.25 to 0.29.
The values computed for each field station tend to be minimum
values due to coincidence of location of the major recharge effects. If
all stations are affected by varying degrees of unsaturated-zone effects
which may be too small to be noted at class I stations, all the computed
coefficients may be in error, giving values which are consistently too
small. Therefore, the correct average may be larger than that given
above, and possibly greater than 0.30.
Conclusions
Although the scatter of gravity data is large, a correspondence
between trend of water-level decline and of gravitational field intensity
on the Ewing farm may be analyzed to determine the coefficient of stor-
age through the use of equation (1). The errors due to the limited area of
water-level decline and to water-table slope may be corrected using a
K factor of 1.02. Errors due to unsaturated-zone effects resulting from
irrigation and precipitation are negligible. The errors due to unsaturated-
zone effects resulting from runoff in Rillito Creek may not be corrected
through model analysis due to lack of data on the volume and lateral
migration and of variation of volume with time of this water. The data
at all field stations which are less than 750 feet from Rillito Creek ap-
pear to show positive changes in gravitational field intensity due to
infiltration from runoff. The storage coefficient values computed for the
various field statiOns range from 0.11 to 0.41 . Most of the values are
too low due to unsaturated-zone effects resulting from recharge. The
110
correct average value of the coefficient of storage for the Ewing farm is
believed to lie between 0.25 and 0.29.
EVALUATION OF THE GRAVITY METHOD
The precise numerical value of the coefficient of storage was
not determined for the Ewing farm through the use of the gravity method.
The ambiguity in the values computed is due in large part to the com-
puted survey error and to unresolved unsaturated-zone effects. The
probable range of 0.25 to 0.29 derived from the gravity method exceeds
most values determined by other methods.
The computed range agrees favorably with the "average moisture
content change" given by Wilson and DeCook (1968, p. 1232) of 0.25 for
sediments in the basin-fill aquifer at the Water Resources Research Cen-
ter; although later Wilson (1969, p. 34) reported a storage coefficient of
0.16. The second value given by Wilson is significantly lower, although
it appears to be more reasonable for the finer sediments found at the
Water Resources Research Center with respect to those encountered at
the Ewing farm.
Anderson's (1968) study indicated that the coefficient of storage
along the channel of Rillito Creek should be "much greater" than 0.15.
The range of 0.25 to 0.29 computed here is in agreement with that state-
ment.
Matlock (1970) used values ranging from 0.15 to 0.30 for his
simulation study for the Ewing farm. However, he determined an "opti-
mum" value of 0.20 from his analysis. His analysis for the same study
area as was used in the present work would indicate that the value com-
puted here may be too large. Matlock used 0.20 as an "effective
111
112
porosity," a measure of the void space through which ground water may
flow. Perhaps there may be a difference in number and size of voids
through which effective flow may occur and those which may give up
water due to prolonged drainage. If this is the case, there may be no
conflict between the different measured values.
The numerical value of the coefficient of storage computed for
this study is among the largest proposed for the Tucson basin aquifer
system. Although the precise numerical value is not determined, the
range given tends to confirm the large values computed by other inves-
tigators. It is believed that the range given encompasses the true nu-
merical value of the coefficient of storage for the flood-plain alluvium
and the upper portion of the basin-fill aquifer in the Ewing farm vicinity.
Conditions under Which the GravityMethod May Be Used
Geohydrologic Conditions
A significant limitation of the gravity method is the large scat-
ter of the gravity data with respect to the change of gravitational field
intensity due to a change in storage. This defect may be eliminated by
future improvement in the sensitivity of portable gravimeters. The ac-
curacy of the present study may be increased by making additional grav-
ity measurements with continued rise and decline of the water table;
however, assuming that the present accuracy is acceptable, guidelines
may be established to apply the method elsewhere.
The water levels in the Ewing farm vicinity declined approxi-
mately 25 feet; results of repeated gravity measurements at 17 field
stations indicate that the probable average coefficient of storage in that
113
area is in the range of 0.25 to 0.29. If the coefficient of storage had
been found to be half of the above value, drawdowns of 50 feet would
be required to yield equal resolution of S. Therefore, the product of
water-level change and storage coefficient must exceed 6 (25 x 0.25) to
duplicate approximately the results of this paper. Products in excess of
6 would yield superior definition of S; those less would yield more am-
biguous results. It may be possible to achieve superior definition of S
with products of less than 6 if the number and accuracy of gravity meas-
urements are increased. Use of this product as a guideline requires the
assumption that the area of water-level change is extensive and that
unsaturated-zone effects are similar to those in the Ewing farm vicinity.
The gravity method may also be used with less ambiguity in
areas where unsaturated-zone effects are smaller than those noted at
stations near Rillito Creek. The unsaturated-zone effect may be minimal
over portions of an aquifer which are recharged by underflow rather than
by water which is derived from surface sources near or in the area of in-
vestigation.
Geographic Conditions
The limitations discussed above indicate that similar aquifer
systems to that below the Ewing farm or aquifer systems having large
storage coefficient values are most amenable to investigation using the
gravity method. Large water-table changes over wide areas due to in-
tensive agricultural, industrial, or municipal development are also re-
quired to cause lowering of the water table, and occasional recharge
to raise the water table. Aquifers having these characteristics are
generally limited geographically to basin floor areas in the vicinity of
114
large drainages. Although these geographic areas are not abundant with
respect to continental areas, they are the areas in which geohydrologic
investigations are concentrated.
Comparison of the Gravity Method with OtherConventional Methods of Determining
the Coefficient of Storage
The gravity technique was developed as a collaborative method
of es.timating the coefficient of storage in water-table aquifers. Evalua-
tion of a field area to determine if the gravity method may be used as-
sumes that estimates of S have been made. Future use will be made of
the gravity technique only if it provides unique data, not more easily
available by other methods.
Advantages of the Gravity Method
1. The characteristics of large volumes of aquifer are sampled by
each measurement which is in contrast to evaluation of point
samples through the use of some other methods.
2. The aquifer materials being sampled are undisturbed. Many
other methods measure properties of samples which have been
removed from the aquifer or have been disturbed by drilling
and occasionally by water-well development.
3. The coefficient of storage is computed by measuring the param-
eters that define it which are change in head and volume or
weight of water yielded or received by the aquifer materials
undergoing the change in head. Many other techniques directly
measure change in head but compute changes in volume of water
through measurement and evaluations of other parameters.
115
4. The total cost of the method is low in that only a gravimeter
and an operator must be supplied. Assuming observation wells
are preexisting, the method requires no drilling and does not
disturb occupants of the study area.
Disadvantages of the Gravity Method
1. The gravity method is dependent on measuring changes in mass
in the saturated zone. If mass changes occur elsewhere, as
in the unsaturated zone, a degree of ambiguity is encountered.
In the event large mass changes occur in the unsaturated zone,
it may be difficult to resolve the ambiguity except with the aid
of neutron probe studies. Study of the unsaturated zone using
the neutron probe may yield data on the location and change of
volume of vadose water but may also reduce the applicability
of the gravity method because of overlap of information.
2. The gravity method yield coefficient of storage data only on
that portion of the aquifer through which the water table de-
clines or rises. The properties of the remainder of the aquifer
may be different, and the data derived may be invalid when
applied to the entire aquifer. If S is measured through a water-
level decline, data are derived for a portion of the aquifer
which may not become resaturated.
Conventional Methods of Determining theCoefficient of Storage
Many method have been used in the past by various investiga-
tors to compute the coefficient of storage for water-table aquifers A
summary of the commonly used methods is given below.
116
Laboratory Analysis of Aquifer Samples. Small samples of
aquifer media may be collected and tested to determine the volume of
water the samples yield on gravity drainage and compute the specific
yield. The samples are disturbed when they are removed from the aquifer
and tested making the test results invalid to the degree that errors are
introduced by repacking and rearranging the rock skeleton of the original
sample. The volume of materials used in laboratory tests is only an in-
finitesimal portion of an aquifer that is generally quite heterogeneous.
Therefore, a representative S may be determined only if many samples
are collected at frequent depths and at numerous locations within the
area of interest.
Aquifer Test Analyses. Aquifer parameters including the coef-
ficient of storage may be evaluated through use of pumping and observa-
tion wells together with the Theis equation or a variant of the Theis (1935)
equation. The Theis equation is
where
1.87 r2 Su=
Tt
s drawdown in feet at a distance r in feet due to discharge
of the test well
Q = the discharge of the test well in gallons per minute
T = the coefficient of transmissibility of the aquifer in gal-
lons per day per foot
S = the coefficient of storage.
Several simplifying assumptions are made in the derivation of the Theis
117
equation, and its successful application is dependent on the degree to
which these qualifications are satisfied by the field conditions. Among
these assumptions are the following:
1. The aquifer is homogeneous, isotropic, and of infinite areal
extent.
2. The discharging well penetrates and receives water from the
entire thickness of the aquifer.
3. The coefficients of transmissibility and storage are constant
at all places and at all times.
4. The flow lines are horizontal and radial.
5. The quantity of water represented by S is released instantan-
eously with decline in head.
These assumptions are not rigorously duplicated in water-table
aquifers. Under water-table conditions a time lag which varies with the
vertical permeability of the aquifer occurs between decline in head and
drainage of water from storage and a significant vertical flow component
exists especially near the pumping well. The transmissibility decreases
as the aquifer is progressively dewatered. The computed value of S may
be seriously modified because the assumptions required by theory are not
rigorously met in the field application.
The areal extent of sediments sampled by an aquifer test are
roughly comparable to those sampled by a single gravity station; how-
ever, the aquifer test samples the coefficient of storage throughout the
vertical extent of the aquifer. Therefore, the volume of aquifer sampled
is greater with the pumping test method. Many pumping tests must be
continued for periods greater than two weeks to receive reasonable
118
coefficient of storage results. Each test is expensive due to equipment
and personnel costs. The costs may become much higher if wells must
be drilled for the testing program. Therefore, the cost of investigating
a wide area with aquifer tests using pumping wells may greatly exceed
the cost of investigation using the gravity method.
Water Budget Analyses. The coefficient of storage may be
computed using one of several variations of the equation of continuity:
inflow = outflow + change in storage.
Many aquifer analyses using mathematical models yield a value of the
coefficient of storage using the equation of continuity. Basic data used
to determine total inflow and outflow include:
1. Estimates of groundwater underflow into and out of the area
being investigated.
2. Estimates of gains or losses to groundwater storage due to
influent and effluent stream flow.
3. Estimates of water removed from storage through wells.
Assuming inflow and outflow may be determined accurately and the vol-
ume of sediments which have undergone drainage or resaturation may be
determined by change in water-level data, the coefficient of storage may
be computed as a residual unknown.
The accuracy of budget analysis results are largely dependent
on the accuracy of the estimates of the magnitude of the various com-
ponents. This type of analysis is difficult to apply to small areas of a
larger aquifer system due to errors in estimation of inflow and outflow
amounts within the larger system. The budget analysis also has a defect
in common with the gravity method in that the coefficient of storage is
determined only for the portion of the aquifer through which the water
level rises or declines.
119
SUMMARY OF CONCLUSIONS
The principal conclusions derived from this study are as fol-
lows :
1. A Bouguer slab interpretational model may in theory be used to
determine the coefficient of storage of a water-table aquifer.
The thickness of the slab is described by successive positions
of the water table. The density contrast of the model is equal
to the coefficient of storage. The coefficient of storage is com-
puted using a modification of the Bouguer equation in the form
ng ng S = 78.3 • The slope may be determined by plottingnt nt
change in gravitational field intensity versus change in water
level.
2. Defects in the interpretational model are (1) groundwater table
rises or declines are not infinite in lateral extent, (2) the
groundwater table does not change elevation uniformly through-
out the area of rise or decline, and (3) the attitude of the water
table is not horizontal. The errors due to these defects may be
computed through use of a finite tilted slab model, and correc-
tion factors may be applied to compensate for their effect.
3. Changes in mass in the unsaturated zone obscure useful
changes in mass which originate from changes of storage in the
saturated zone. Unsaturated-zone effects due to infiltration
from precipitation and irrigation may be modeled through the
use of a Bouguer slab, or a finite slab, and appropriate
120
121
corrections may be made. If the unsaturated-zone effect result-
ing from stream flow may not be modeled, the influence of this
effect must be evaluated at each measuring point and conclu-
sions be based on those measuring points which show the least
correlation of changes in gravitational field intensity with
periods of runoff. Unsaturated-zone effects may be minimal
over those portions of an aquifer which are not recharged by
surface sources.
4. Change in gravitational field intensity in a field area may be
determined by repeating gravity surveys over that area using
the same set of field stations. In the Ewing farm study area,
this method of gravity surveying yielded data which show large
scatter with respect to the significant range of change in field
intensity. Analysis of computed errors indicates that + 26
microgals may be a maximum value due to imprecision in the
gravity survey and in the reduction technique. Modifications
to the gravimeter and to the tidal correction method may reduce
the computed error to + 10 microgals.
5. The aquifer system in the Ewing farm area through which the
water table fluctuates is comprised of alluvial flood-plain
deposits of Rillito Creek and the uppermost portions of the
basin-fill deposits. In October 1968, the wafer table was with-
in the basal portions of the flood-plain alluvium below the
Ewing farm and in the basin-fill deposits to the north and south
of the farm. By June 1970, the water table had declined approx-
imately 25 feet and was entirely within the basin-fill aquifer in
122
the Ewing farm area. Change in subsurface mass due to gravity
drainage of water from previously saturated sediments occurred
in both the flood-plain alluvium and the basin-fill deposits.
Water in the vadose zone due to runoff in Rillito Creek
begins to decrease in volume within 6 days subsequent to flow
and is nearly completely drained by 3 weeks after the flow.
The maximum lateral movement of infiltration from runoff in the
Rillito Creek channel was several hundred feet after flow events
which occurred during the study period. Studies by other inves-
tigators indicate that the coefficient of storage for the Ewing
farm aquifer system is 0.20 or larger.
6. Errors in the Bouguer slab model due to limited area of water-
level decline and the slope of the water table in the vicinity of
the Ewing farm may be corrected using a K factor of 1.02. Er-
rors due to unsaturated-zone effects resulting from precipitation
and irrigation are negligible. The errors due to unsaturated-zone
effects resulting from runoff in Rillito Creek may not be modeled
because of incomplete knowledge of mass distribution. Re-
charge effects due to stream flow during the study period
extended to approximately 750 feet from the low flow channel.
The coefficient of storage for the Ewing farm aquifer sediments
dewatered during the study period lies in the range of 0.25 to
0.29.
7. Use of the gravity method for determining storage coefficient
is limited to water-table aquifers in which the product of the
estimated coefficient of storage and the water-table rise or
123
decline in feet is equal to or greater than 6, and where water-
level changes occur over areas whose dimensions exceed
several thousand feet. The accuracy of the method is decreased
if large unsaturated-zone effects are present in the aquifer.
The data derived from the gravity study are valid only for the
portion of the aquifer which is dewatered or resaturated during
the period of observation. The gravity method compares favor-
ably with cost of other methods, although longer times of study
may be required. The results are not precise but may be used
to compute the probable range of the coefficient of storage of a
water-table aquifer.
APPENDDC
PLOTS OF RELATIVE GRAVITY VERSUS WATER-
LEVEL DECLINE AT GRAVITY STATIONS
124
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REFERENCES
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Anderson, T. W., 1968, Electrical-analog analysis of the hydrologicsystem in Tucson basin, Arizona, U.S.A.: Extract of The Useof Analog and Digital Computers in Hydrology Symposium ofTucson, December 1968, p. 15-24.
Bhuyan, G. Ch., 1965, An analysis of some regional gravity data inArizona: unpub. M.S. thesis, Univ. of Arizona, 132 p.
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Damrel, J. B., Jr., n.d., Tidal gravity effect tables: Houston, Texas,Texas Instruments Corporation, 72 p.
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Davis, R. W., 1967, A geophysical investigation of hydrologic boun-daries in the Tucson basin, Pima County, Arizona: unpub.Ph.D. dissertation, Univ. of Arizona, 64 p.
Eaton, G. P., and Watkins, J. S., 1970, The use of seismic refrac-tion and gravity methods in hydrogeological investigations, inMining and groundwater geophysics/1967: Geological Surveyof Canada, Economic Geology Rept. No. 26, p. 544-568.
European Association of Exploration Geophysicists, 1969, Tidal gravitycorrections of 1970: Geophysical Prospecting, v. 17, p. 1-53.
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Fryer, H. C., 1966, Concepts in Methods of Experimental Statistics:Rockleigh, N. J., Allyn and Bacon, Inc., 157 p.
Ganus, W. J., 1965, Lithologic and structural influences on the hydro-dynamics of the Tucson basin, Arizona: unpub. M.S. thesis,Univ. of Arizona, 53 p.
Garland, G. D., 1965, The earth's shape and gravity: New York,Pergamon Press, 68 p.
Grant, F. S., and West, G. F., 1965, Interpretation theory in appliedgeophysics: New York, McGraw-Hill Book Company, Inc.,584 p.
Heindl, L. A., and White, N. D., 1965, Hydrologic and drill-hole data,San Xavier Indian Reservation and vicinity, Pima County, Ari-zona: Arizona State Land Department, Water-Resources Rapt.No. 20, 48p.
Hubbert, M. K., 1948, A line-integral method of computing the gravi-metric effects of two-dimensional masses: Geophysics, v. 13,p. 215-225.
Kidwai, Z. U., 1957, The relationship of ground water to alluvium inthe Tucson area: unpub. M.S. thesis, Univ. of Arizona, 55 p.
Maddox, G. E., 1960, Subsurface geology along northwest RillitoCreek: unpub. M.S. thesis, Univ. of Arizona, 232 p.
Matlock, W. B., 1970, Mathematical analysis of ground water re-charge: Preprint of paper presented at the Am. Soc. Agr. Engr.,Pacific Regional Annual Meeting, Bakersfield, Calif., Feb.1970, 15 p.
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Naval Hydrographic Office, 1967, 1968, 1969, The American NauticalAlmanac for 1968, 1969, and 1970.
Pashely, F. E. , 1966, Structure and stratigraphy of the central,northern, and eastern parts of the Tucson basin, Arizona: un-pub. Ph.D. thesis, Univ. of Arizona, 273 p.
Schwalen, H. C., and Shaw, R. T., 1957, Ground-water supplies ofSanta Cruz Valley of southern Arizona between Rillito stationand the international boundary. Univ. of Ariz., Agr. Experi-ment Station Bull. 288, 119 p.
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Schwalen, H. C., and Shaw, R. T., 1961, Progress report on study ofwater in the Santa Cruz Valley, Arizona: Univ. of Ariz., Dept.Agr. Engr. Rept. No. 205, 20 p.
Streitz, R., 1962, Subsurface stratigraphy and hydrology of the RillitoCreek-Tanque Verde Wash area, Tucson, Arizona: unpub. M.S.thesis, Univ. of Arizona, 60 p.
Theis, C. V., 1935, The relation between the lowering of the piezo-metric surface and the rate and duration of discharge of a wellusing ground water storage: Trans. Am. Geophys. Union, p.519-524.
Tolman, C. F., 1937, Ground water: New York, McGraw-Hill BookCompany, Inc., 593 p.
University of Arizona, Dept. Ag. Engr., 1970, Groundwater Contours,Middle Santa Cruz Valley: Open-File Map.
Voelger, K., 1953, Cenozoic deposits in the southern foothills of theSanta Catalina Mountains near Tucson, Arizona: unpub. M.S.thesis, Univ. of Arizona, 101 p.
Wilson, L. G., 1969, Observations of water content changes in strati-fied sediments during pit recharge: Preprint of paper presentedat the Annual Meeting of Am. Geophys. Union, Washington,D.C., April 1969, 40 p.
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Wells Near the Ewing Farm
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Ewing Farm Wells
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2275
2270Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun
1968
1969 1970
FIGURE 9. HYDROGRAPHS OF WELLS ON THE EWING FARM AND VICINITY
Errol L. Montgomery, Geology Dissertation, 1971
