Examine the map at right. Note the regional and residual (or local) variations in the gravity field through the area.

The graphical separation method involves drawing lines through the data that follow the regional trend.

The green lines at right extend through the residual feature and reveal what would be the gradual drop in the anomaly across the area if the local feature were not present.

The residual anomaly is identified by marking the intersections of the extended regional field with the actual anomaly and labeling them with the value of the actual anomaly relative to the extended regional field.

-0.5-0.5

-1

After labeling all intersections with the relative (or residual ) values, you can contour these values to obtain a map of the residual feature.

0

Max = 0

Min ~-1.8

negative

6000’

Vertical Cylinder or Sphere?

Problem-

Determine which anomaly is produced by a sphere and which is produced by a horizontal

cylinder.

Diagnosticpositions

MultipliersSphere

ZSphere MultipliersCylinder

ZCylinder

X3/4 = 0.95 2.17 2.06 1.72 1.63X2/3 = 1.15 1.79 2.06 1.41 1.62X1/2 = 1.6 1.305 2.09 1 1.6X1/3 = 2.1 0.96 2.02 0.7 1.47X1/4 = 2.5 0.81 2.03 0.57 1.43

Which estimate of Z seems to be more reliable? Compute the range.

You could also compare standard deviations.Which model - sphere or cylinder - yields the

smaller range or standard deviation?

We will spend more time on simple geometrical objects during the next lecture, but for now let’s spend a few moments and review the problems that were assigned last lecture.

Pb. 4 What is the radius of the smallest equidimensional void (such as a chamber in a cave - think of it more simply as an isolated spherical void) that can be detected by a gravity survey for which the Bouguer gravity values have an accuracy of 0.05 mG? Assume the voids are in limestone and are air-filled (i.e. density contrast = 2.7gm/cm3) and that void centers are never closer to the surface than 100.

(feet) 00852.0

(feet) 00852.0

feetfor 00852.0

metersfor 02793.0

)3/4(

3

2max

3/12max

2

3

2

3

2

3

max

R

Zg

ZgR

Z

R

Z

R

Z

RGg

Begin by recalling the list of formula we developed for the sphere.

(feet) 02793.0

metersfor 02793.0

3/12max

2

3

ZgR

Z

R

Pb. 5: The curve in the following diagram represents a traverse across the center of a roughly equidimensional ore body. The anomaly due to the ore body is obscured by a strong regional anomaly. Remove the regional anomaly and then evaluate the anomaly due to the ore body (i.e. estimate it’s deptj and approximate radius) given that the object has a relative density contrast of 0.75g/cm3

Horizontal Position (km)

0.0 0.5 1.0 1.5 2.0

Bou

guer

Ano

mal

y (m

Gal

)

-1.50

-1.25

-1.00

-0.75

-0.50

-0.25

0.00

Problem 5

residual

Regional

You could plot the data on a sheet of graph paper. Draw a line through the end points (regional trend) and measure the difference between the actual observation and the regional (the residual).

You could use EXCEL or PSIPlot to fit a line to the two end points and compute the difference between the fitted line (regional) and the observations.

In problem 6 your given three anomalies. These anomalies are assumed to be associated with three buried spheres. Determine their depths using the diagnostic positions and depth index multipliers we discussed in class today. Carefully consider where the anomaly drops to one-half of its maximum value. Assume a minimum value of 0.

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

-1500 -1000 -500 0 500 1000 1500

Distance from peak (m)

Bo

ug

uer

An

om

aly

(mG

als)

A.

C.

B.

Nov. 16th Terrain correction

Nov. 18th Gravity lab Problems 4, 5, & 6.Gravity paper summariesExtra credit sphere or cylinder exercise