Measurement and use of the vertical gravity gradient in correcting repeat microgravity measurements for the effects of ground subsidence in geothermal systems

Measurement and use of the vertical gravitygradient in correcting repeat microgravitymeasurements for the effects of groundsubsidence in geothermal systems

Trevor Hunta,*, Mituhiko Sugiharab, Tatsuya Satoc,Tomoyuki Takemurad

aInstitute of Geological & Nuclear Sciences, Private Bag 2000, Taupo, New ZealandbInstitute for Geo-Resources and Environment, AIST, Central 7, 1-1-1 Higashi, Tskuba 305-8567, JapancGeothermal Energy Research and Development Co., 11-7 Kabuto-cho, Nihonbashi, Tokyo 103-0026, Japan

dOkuaizu Geothermal Company, Tokyo, Japan

Received 19 November 2001; accepted 29 January 2002

Abstract

Changes in mass resulting from production and reinjection in geothermal fields can be

monitored using repeat microgravity measurements. The measured changes in gravity, how-ever, need to be corrected for the effects of any exploitation-induced ground subsidence. Thecorrection required at each measurement point is the product of the amount of ground sub-

sidence and the vertical gravity gradient at that point. Measurements of the gravity gradient,made using a portable tower, show that it varies from place to place depending mainly on thelocal topography. Measured gradients, in areas of high subsidence rate, range between �276and �339 mgal/m at 30 sites in the Wairakei–Tauhara field and between�296 and�321 mgal/mat nine sites in the Ohaaki field (New Zealand). These values are similar to those used pre-viously. At 37 sites measured in the Yanaizu–Nishiyama field (Japan) the gradient variedbetween �244 and �352 mgal/m. Measurements at six sites showed no significant change ingravity gradient with height above the ground surface; a single value for the gradient cantherefore be used at each site to correct for the gravitational effect of any ground movement.Calculations show the effects on the vertical gravity gradient of groundwater level variations,

mass changes associated with the ground subsidence, and reservoir mass changes are negli-gible at Wairakei. # 2002 CNR. Published by Elsevier Science Ltd. All rights reserved.

Keywords: Microgravity; Monitoring; Subsidence; Gravity gradient; Yanaizu; Wairakei; Ohaaki; Japan,

New Zealand

Geothermics 31 (2002) 525–543

www.elsevier.com/locate/geothermics

0375-6505/02/$20.00 # 2002 CNR. Published by Elsevier Science Ltd. All rights reserved.

PI I : S0375-6505(02 )00010 -X

* Corresponding author. Tel.: +64-7-374-8211; fax.: +64-7-374-8199.

E-mail address: [email protected] (T. Hunt).

1. Introduction

Microgravity (precision gravity) monitoring of the effects of exploitation of geo-thermal systems involves measuring the very small changes in the Earth’s gravityfield at different points on the surface (Allis and Hunt, 1986). These changes areassociated with the changes in mass resulting from production and reinjection, andmay be several hundred microgal (1 microgal (mgal)=10�8 m/s2) but are usuallymuch less; we now seek to make measurements with a precision of 1–5 mgal, similarto the precision currently obtainable using portable gravity meters. However, thevalue of gravity at a point (adjusted for Earth-tide effect and instrumental factors)may vary with time for a number of reasons other than mass changes in the reser-voir, so that the measurements may need to be corrected for (in approximate orderof importance): vertical ground movements, changes in groundwater level, changesin saturation in the Vadose Zone, changes in gravity at the base or reference station,and changes in local topography.The effects of vertical ground movement may be large. At the Wairakei–Tauhara

geothermal field (New Zealand) there has been up to 15 m of ground subsidence inpart of the field: at a point in the centre of this subsidence the gravity change due tothis movement is more than +4000 mgal (4 milligal). This is, however, an extremecase as the ground subsidence in most geothermal fields is much smaller (<1 m), butstill sufficient to require a correction. This paper examines the corrections needed forsuch movements. The analysis is also applicable to microgravity monitoring ofhydrocarbon and groundwater extraction.

2. Ground movement

Vertical ground movements have generally been monitored by making repeatsurveys using traditional optical levelling techniques (2nd–3rd Order Standard) atpermanent survey marks (benchmarks). Both upward (inflation) and downward(subsidence) movements have occurred in many geothermal fields as a result of masswithdrawal and reinjection (Table 1). Subsidence is generally associated with pro-duction, and inflation with reinjection, but subsidence is generally much greater inmagnitude and extent than inflation. The location and magnitude of subsidence aredifferent in different fields, and may occur outside the production area. Inflation,however, generally appears to be located in the immediate vicinity of reinjectionwells. The location and rate of ground movement cannot be predicted beforemovement begins, and the amount of ground movement appears to be largely inde-pendent of the size of the field or the amount of fluid withdrawn and reinjected.Exploitation-induced ground movements are generally orders of magnitude greaterthan steady tectonic ground movements in the area. Horizontal ground movementsassociated with the vertical movements also occur, but their magnitude is much lessand their gravity effect can be neglected.In New Zealand geothermal fields the movements are mainly subsidence, and the

greatest movements are confined to 1–2 km2 areas known as subsidence bowls. In

526 T. Hunt et al. / Geothermics 31 (2002) 525–543

the centre of the main bowl at Wairakei–Tauhara the total subsidence now exceeds15 m. Here, the maximum rate of subsidence was 470 mm/year in the mid-1970s, buthas since declined to about 215 mm/year (Allis, 2000). At Ohaaki the maximum rateof subsidence exceeded 400 mm/year during the mid-1990s but has since declined,and the total subsidence in the centre of the kidney-shaped bowl is now about 2 m. Thecause of the subsidence in these fields has been associated with compression of a rela-tively impermeable rock formation (lacustrine sediments, 0.05–0.3 mD) that has largevertical compressibility (0.15–0.45MPa�1). This formation exists above the reservoir inparts of the fields. Mass withdrawal has caused a decline in deep reservoir pressures ofup to 2.5 MPa, causing pore fluid within the formation to drain downwards into thereservoir (Allis et al., 1997; Allis and Zhan, 2000). Removal of the pore fluid has causedcompaction of the formation. The overlying rocks (poorly-compacted volcanic tephra)have little strength and have collapsed, resulting in subsidence of the ground surface.However, it is difficult to invoke such a mechanism for ground movements in

geothermal fields situated in old basement rocks, such as at The Geysers field(USA). Here, it was initially thought (Lofgren, 1981) that the subsidence was relatedto a decline in reservoir steam pressures; however, Denlinger et al. (1981) noted thatthe small reduction in steam pressure (�P�1 MPa), combined with the large bulkmodulus determined from seismic data (Kd�3�10

10 Pa), was not consistent with theobserved subsidence. They thought the strain was due to a combination of thermo-elastic and poroelastic deformations, and that the major component was thermo-elastic. The thermoelastic strains occur because most of the reservoir water is storedas a liquid phase within the rock, and when the liquid water flashes into steam thephase change absorbs large amounts of heat and so lowers the reservoir tem-perature. The cooling reservoir contracts and this is observed at the surface assubsidence. Recent modelling studies (Mossop and Segall, 1997), however, show

Table 1

Ground subsidence in some producing geothermal fields. Survey dates are the period for which subsidence

has been reported; it is not necessarily the whole production period. Note that the maximum amount of

subsidence and subsidence rates change with time

Field Country Survey

period

Maximum

subsidence

(m)

Maximum

rate

(mm/year)

Mass change during

survey period (approx.)

Reference

Production

(Mt/year)

Reinjection

(Mt/year)

Wairakei NZ 1955–1998 15 470 10–74 0 Allis (2000)

Ohaaki NZ 1988–1998 1.7 500 14–17 10–13 Allis et al. (1997)

Kawerau NZ 1970–1996 0.48a 30 10 1.7–2.6 Allis (1997)

The Geysers USA 1977–1996 0.90 47 70 21 Mossop and Segall (1997)

Bulalo Philippines 1980–1999 0.57 32 Protacio et al. (2000)

Travale Italy 1973–1991 0.4 25 2.3–3.9 Negligible di Filippo et al. (1995)

Takigami Japan 1992–1998 <0.02 11 9 Fujimitsu et al. (2000)

Hatchobaru Japan 1990–1996 0.015 16 12 Tagomori et al. (1997)

Cerro Prieto Mexico 1994–1997 0.5 120 100 1 Glowacka et al. (2000)

Svartsengi Iceland 1976–1999 0.24 14 0–9 Eysteinsson (2000)

a Corrected for movement associated with the 1987 March 3 Edgecumbe earthquake.

T. Hunt et al. / Geothermics 31 (2002) 525–543 527

that the major part of the subsidence at The Geysers cannot be explained bythermoelastic contraction, but can be explained by poroelastic contraction asso-ciated with the reduction in steam pressures. A similar explanation may be valid forother fields located in volcanic rocks where subsidence has been less than one metre.

3. Gravity effect of subsidence

To compare gravity measurements at a site, at different times (t1, t2), it is neces-sary to examine the gravity values at the same position P in a time-invariant refer-ence system F. Assuming (initially) that no mass changes are involved, the effect ofvertical ground movement at a point, between gravity surveys, is to move the gravitymeter vertically through the Earth’s gravity field from P1!P2. Subsidence willresult in the instrument being brought closer to the centre of mass of the Earth thusincreasing the value of gravity, and conversely inflation will decrease gravity. Inpractice it is generally difficult or impossible to re-occupy the same position P1 aftersubsidence or inflation have occurred, and the gravity measurements at t2 can onlybe made at a point P2 vertically above or below P1. The measurements at P2 (t2)need to be corrected for the gravitational effects of the vertical movement in order todetermine the value of gravity at P1 (t2).The amplitude of any gravity change (�g�h) associated with a displacement �h of

the gravity meter from P1!P2 is:

�g�h ¼ @g=@zð Þ�h ð1Þ

where @g/@z is the vertical gravity gradient (VGG), and � h is small enough thatchanges in the gradient over the range of � h can be neglected. If the measurementsite at t2 is at � h (in F) vertically below what it was at t1, then the value of gravityat the original site P=P1 (now above ground surface) can be calculated:

g t 2P ¼ g t 2P1 ¼ g t 2P 2 � @g=@zð Þ�h ð2Þ

To correct for the effects of ground movements it is therefore necessary to deter-mine the gravity gradient, in addition to measuring the amount of vertical groundmovement (� h). A traditional unit of gravity gradient is the Eotvos unit (1 E=10�9

s�2=0.1 mgal/m) but, for simplicity, gradients will be expressed here in terms ofmicrogal/m.A first approximation for the vertical gradient can be determined from the gravity field

of aReference Ellipsoid derived fromworld-wide gravitymeasurements (Garland, 1965).

@g=@z ¼ �308:55� 0:227cos2�þ 0:145 h mgal=mð Þ ð3Þ

where � is the geocentric latitude (deg) and h is the elevation of the point (km, asl).This yields the value of �308.55 mgal/m (at sea level, lat. 45), which is commonlyused for the free-air correction in Bouguer Anomaly surveys and often called the


‘‘normal’’ gradient. However, measurements show that the vertical gradient variesfrom place to place by up to 20%, depending not only on the latitude and elevationof the point, but also (and more importantly) on the geology and topography nearthe point (Kumagai et al., 1960; Fajklewicz, 1976; Ager and Liard, 1982). Previouslyreported values of the gradient range from about �252 to �369 mgal/m (Table 2).Ager and Liard (1982) show a value of about �215 mgal/m in a diagram showinggradient measurements along a profile from Vancouver to Kamloops (BritishColumbia, Canada); however, this single value is much lower than others along theprofile and must be treated with caution.In mountainous areas the topography can have a significant effect on the gradient.

Modelling suggests that topography may increase or decrease the gradient by up toabout 40 mgal/m (Fig. 1). Similar modelling also shows that near-surface densityvariations may affect the gradient by about 10 mgal/m (Fig. 1). The gradient istherefore composed of the ‘‘normal’’ gradient plus the gradients associated with thetopography and the near surface geology.In Eq. (2) it is assumed that the gradient has not been changed by the displace-

ment. This was tested by modelling the gravity values along a profile that crosses asteep, 50 m high scarp (Fig. 2). The gravity values were computed, and then com-pared with the values at the original measurement points computed after sub-sidences of 5 and 10 m associated with compaction (and thus density increase) in a50 m thick zone at a depth of 150 m (which approximates to the situation at Wair-akei field). The results (Fig. 2) indicate that at the upper edge of the scarp the gra-dient is greater, and at the base of the scarp it is less than the ‘‘normal’’ gradient; thiscan be visualised by considering the distribution of equipotential gravity surfaces inthe vicinity of the scarp. The modelling shows that the gradient varies with theamount of subsidence; the topographic effect at the top of the scarp the gradient isincreased by 28.7 mgal/m for 5 m, and 24.7 mgal/m for 10 m of subsidence. However,in steep topography the amount of subsidence is likely to be small relative to thetopography and so the effect of this variation will be small.

Table 2

Some previously reported ranges of values for vertical gravity gradient (VGG). None of these data are

from geothermal fields

Location Number

of sites

VGG min

(mgal/m)VGG max

(mgal/m)Reference

Poland 29 �307.2 (0.1) �313.0 (0) Fajklewicz (1976)

Germany 14 �303.0 �319.6 Janle et al. (1971)

Japan 55 �269 (2) �369 (2) Kumagai et al. (1960)

Canada 11 �280.7 (0.4) �321.8(0.6) Thyssen-Bornemisza and Stackler (1956)

Canada 38 Approx �215a Approx �330 Ager and Liard (1982)

France 6 �251.8 (1.2) �311.8 (0.6) Roder and Wenzel (1986)

Italy 6 �307 (4) �363 (4) Berrino et al. (1998)

Italy 9 �266 (3) �354 (3) Berrino (1995)

a Value at one point on graph showing VGG values on a profile along the highway through the

mountains between Vancouver and Kamloops in British Columbia, Canada.


Although it is possible to compute the gravity gradient associated with topo-graphy from detailed topographical maps or digital terrain data, this would notaccount for any local near-surface density variations. The best value for the verticalgravity gradient to use in calculating the effect of subsidence is therefore a measuredvalue at each gravity station.

Fig. 1. Variations in gravity and vertical gravity gradient along profiles over: (a) scarp, 50 m high; (b) an

anomalous near-surface mass distribution. Values shown are for 1 m (solid dots) and 6 m (crosses) above

ground. Triangles indicate computation points. Note that the diagram showing gravity effect of the scarp

has been split vertically into two parts to enable detail to be shown. Calculations (2-d) were made using

Webring (1985).


4. Measurement of vertical gradient

4.1. Methods of measurement

One method of determining the vertical gradient at a point is to make precisegravity measurements at and around the point, and from these data compute thegradient using the Hilbert transform (Morelli and Carrozzo, 1963). However, this is

Fig. 2. Calculated gravity and vertical gravity gradients associated with 5 and 10 m of ground subsidence

along a profile over a 50 m high scarp. Density of topography is 2000 kg/m3. Triangles indicate the points

at which the gravity effects have been calculated. Initial gravity values before subsidence are shown by

crosses, and after 10 m of subsidence by open squares. The effects on the value of gravity and vertical

gravity gradient as a result of subsidence are shown by solid dots (10 m subsidence) or open circles (5 m

subsidence). Calculations (2-d) were made using Webring (1985).


difficult and time consuming because, to provide sufficient precision, the value ofgravity and the elevation of the gravity meter must be very precisely measured at alarge number of points (Kumagai et al., 1960). The gradient may also be measuredusing a gradiometer (Torge, 1989), but these are now generally confined to labora-tories or to moving platforms (aircraft, satellites).A simpler method is to determine the vertical gradient directly by making gravity

measurements at several different heights on the various floors of a multi-storeybuilding, or using a portable tower. In the case of making measurements in abuilding, a correction may be needed for the mass of the floor(s); this can easily becalculated using the Bouguer infinite plate equation and knowledge of the thicknessand density of the floor(s). In the past, the best results have been obtained using aportable tower (Kumagai et al., 1960; Janle et al., 1971); the mass of the tower andobserver is too small to significantly affect the gradient. Such studies were made tolocate shallow geological features and caves (e.g. Thyssen-Bornemisza and Stackler,1956; Fajklewicz, 1976; Butler, 1984).The vertical gravity gradient @g/@z is approximated by �g/� h:

@g

@z¼ lim

h!o

�g

�hð4Þ

If measurements are made using a tower with a height difference (� h) of 1 m,and there are errors of 5 mgal in �g and 2 mm in � h, then the error in thegradient is about 5.6 mgal/m. However, as � h gets smaller, the error in the gra-dient increases rapidly. For the same errors in �g and � h, over a height differ-ence of 0.3 m, the error in the gradient will be about 17 mgal/m. This shows thatthe measurement of gravity needs to have a precision of about 1 mgal to enablemeasurements of the gradient to be made over vertical intervals of less than 0.5m. For the best results, the tower needs to be very stable and unaffected by windor vibration; such conditions are difficult but not impossible to obtain in thefield.Measurements were made using portable towers at two geothermal fields (Wair-

akei–Tauhara, Ohaaki) in New Zealand where there has been significant subsidence,and at one field (Yanaizu–Nishiyama) in Japan where there has been little sub-sidence. The measurements were made with Scintrex CG-3M gravity meters. Detailsof the measurement techniques and preliminary results are given in Hunt et al.(1999) and Hunt and Sugihara (2000). In the New Zealand fields the measurementswere largely confined to areas of significant ground subsidence.

4.2. Measurements at Wairakei–Tauhara field (New Zealand)

Wairakei and Tauhara are two contiguous parts of a geothermal field in NewZealand that covers a total area of about 50 km2. Production from the Wairakeipart of the field since the late 1950s has resulted in large subsidence in the mainsubsidence bowl, which has an area about 1 km2 and is centred at benchmark P128


located about 500 m north-east and outside the production area (Figs. 3 and 4).There has been no production directly from the Tauhara part of the field, except forminor discharges during well-testing. However, a hydrological connection betweenthe two parts has resulted in a pressure drawdown of about 1.8 MPa at Tauhara andthe formation of three small subsidence bowls in the northern part of Tauhara, nearthe connection to Wairakei (Fig. 5). The maximum measured subsidence rates inthese bowls are about 40 mm/year.Thirty measurements of the gravity gradient have been made in the field (Figs. 4

and 5); most were at sites used in repeat microgravity gravity surveys (Hunt, 1995).At Wairakei the errors in the gradient often exceeded 10 mgal/m because of

Fig. 3. Rates of ground subsidence (mm/year) in the Wairakei–Tauhara field. Note the presence of sub-

sidence bowls in separate parts of the field. The rates are averages for the 1980s and early 1990s, and are

taken from Allis (2000).


microseisms generated by the near-continuous passage of heavy vehicles travellingon nearby highways (SH1, SH5: Fig. 4).The mean value for the gradient is �302 (13) mgal/m. Examination of the data

shows that the gradient at the centre of the main subsidence bowl (subsidence rate>100 mm/year) is not significantly different: mean value �306 (15) mgal/m. Totest whether large lateral variations in the gradient exist at the centre of the sub-sidence bowl, a measurement was made 2 m distant from that at P128, but no sig-nificant difference was found. The largest gradient measured (�33914 mgal/m) wasat BM 9746 situated on the side of the road leading to Geyser Valley at Wairakei;this point had the greatest topographic relief. The lowest gradient measured(�2765 mgal/m) was at H9735 at Tauhara, a site close to the foot of a steep bank.Values of the gradient at sites with the greatest subsidences (P127, P128 and P130)

are all close to the value used in previously reported measurements (Hunt, 1995), sono significant errors will have arisen.

4.3. Measurements at Ohaaki field (New Zealand)

Ohaaki field is situated about 20 km north-east of Wairakei–Tauhara. Explora-tory drilling began in 1965 and during 1967–1971 there was a period of well testingduring which time reservoir pressures declined and ground subsidence of up to 0.2 mwas measured. Between 1972 and commissioning of the Ohaaki power station in

Fig. 4. Measured values of vertical gravity gradient (bold numbers, microgal/m) and contours of ground

subsidence rate (mm/year) in the main subsidence bowl at the Wairakei–Tauhara field. EB marks the

position of the Eastern Borefield, where the largest gravity changes have been measured.


1988 there was little mass withdrawal, and during this period reservoir pressurespartly recovered and subsidence stopped. However, after production began in 1988reservoir pressures again declined and ground subsidence resumed. This subsidenceoccurs mainly in a crescent-shaped bowl in the north-western part of the field(Fig. 6). At the centre of the bowl about 1.7 m of total subsidence and subsidencerates of nearly 500 mm/year had been measured by 1995 (Allis et al., 1997).Measurements of gravity gradient were made at nine sites and range from �296 to

�321 mgal/m (Fig. 6), with a mean value of �3128 mgal/m. The site with the lar-gest deviation from the mean value is at benchmark H1158, which has a value of�29610 mgal/m. This site is in a road cutting at the base of a bank about 5 m high,so a low gradient is to be expected.

4.4. Measurements at the Yanaizu–Nishiyama field (Japan)

The Yanaizu–Nishiyama field is situated in the mountains in the central part ofHonshu, Japan. Production (65 MWe) began in late 1994, but no significant groundsubsidence has been reported. The vertical gravity gradient, measured at 37 sites,ranges from �244 to �352 mgal/m, with a nearly normal distribution about a valueof �300 mgal/m (Fig. 7).A very low value of the gradient (�2446 mgal/m) was measured at a site on the

road between Yuyagisawa and Kubota, which is outside the production and rein-jection areas of the field. The site was originally chosen for a gradient measurementonly because of its proximity to a groundwater monitor well and no major topo-graphy within 10 m. To investigate this anomalously low value, the gradient wasmeasured at eight additional locations along the road, within about 300 m of the

Fig. 5. Measured values of vertical gravity gradient (bold numbers, microgal/m) and contours of ground

subsidence rate (mm/year) in the area of subsidence bowls in the Tauhara part of the Wairakei–Tauhara

field.


site. A profile through the area (Fig. 8) shows that large lateral changes in the gra-dient occur in the vicinity; the greatest is a change from �244 to �300 mgal/m over ahorizontal distance of only about 75 m. The changes are very much larger than theerrors in measurement. No explanation can be found at present for such a lowvalue.Measurements were made at different heights above ground level (up to 1.6 m) at

six sites in the field that had a wide range of gravity gradients. The results (Fig. 9)showed that there is no systematic change in the value of gradient with height, atleast to a height of 1.6 m above ground level. This suggests that a single value for thegradient can be used at each site to correct for the gravitational effect of any verticalground movement within this range. Since the topographic relief and the range ofmeasured gradient values at Wairakei–Tauhara and Ohaaki are less than atYanaizu–Nishiyama, it is probable that use of a single measured value of gradient at

Fig. 6. Measured values of vertical gravity gradient (microgal/m) and contours of ground subsidence rate

(mm/year) in Ohaaki field. The subsidence rates are for the period 1993–1995, and are taken from Allis

and Zhan (2000). WB and EB are the Western and Eastern borefields, respectively.


each site is valid when calculating the correction for subsidence in these New Zea-land fields.The Yanaizu–Nishiyama field is located in rugged topography and elevations of

the sites measured range from 330 to 510 m above sea level. A plot of gravity gra-dient against elevation (Fig. 10) shows that sites at lower elevations tend to have asmaller value of gradient and those at higher elevations a larger value. This probablyreflects the effect of topography. However, the graph indicates that at any particularelevation there is likely to be a wide range of gradient values.

Fig. 7. Measured values of vertical gravity gradient (mgal/m) at the Yanaizu–Nishiyama field. Contoursare of elevation (asl), at 100 m intervals; solid lines are roads. There has been no significant ground sub-

sidence in the field. Broken lines mark the locations of the production zone (P.Z.) and the reinjection zone

(R.Z.).


Comparison of the distribution of measured values of vertical gravity gradient atWairakei–Tauhara with that from Yanaizu–Nishiyama shows that at both fields themodal value of the gradient is about �300 mgal/m (Fig. 11); however the range ofvalues at the latter field is much wider, probably because of the greater topographicrelief there.

Fig. 8. Measured values of vertical gravity gradient on a profile along the road near the site with low

gradient at the Yanaizu–Nishiyama field. Note the large changes in gradient over a short distance.

Fig. 9. Variation of vertical gravity gradient with height above ground level at the Yanaizu–Nishiyama

field. Values of gradient are differences from the mean at each site. Note the lack of any correlation

between gradient and height.


Fig. 10. Variation of vertical gravity gradient with elevation of the measurement site (asl) at the Yanaizu–

Nishiyama field.

Fig. 11. Frequency distribution of measured values of vertical gravity gradient (VGG) at the Wairakei–

Tauhara and Yanaizu–Nishiyama fields. Note the similarity of modal values, but wider distribution at

Yanaizu–Nishiyama.


5. Changes in vertical gradient with time

The question now arises as to whether the vertical gradient changes significantlywith time as a result of development or of other mass changes. We now examine thisusing data from Wairakei, where there have been significant mass changes (andgravity changes) as a result of production during a development period of nearly 50years (Hunt, 1995).

5.1. Effect of groundwater level changes

Measurements in monitor holes at Wairakei show that the shallow groundwaterlevel generally varies by about 1 m as a result of seasonal variations in rainfall inthe area. However, in part of the Eastern Borefield the groundwater level has fallenby up to 30 m (Hunt, 1995) as a result of a cold downflow caused by the pressuredecline in the underlying geothermal reservoir. No groundwater level monitor dataare available for the area near the centre of the main subsidence bowl, but it is esti-mated to have reached 40–50 m in Geyser Valley (Allis and Zhan, 2000). Assumingthe groundwater level was originally at 10 m depth, porosity is 0.4, and the residualsaturation is 0.3, calculations (using Webring, 1985) show that the gravity effect (atthe surface) of a 30 m fall in groundwater level is about �170 mgal. However, as theassociated change in the gradient is less than 0.5 mgal/m, the effects of changes ingroundwater level on the gradient can be neglected.

5.2. Effect of mass changes associated with the ground subsidence

Modelling (Allis, 2000) and deformation of well casing in the Eastern Borefield(Bixley and Hattersley, 1983) indicate that the ground subsidence at Wairakei isassociated with fluid withdrawal at a depth of about 100 m. Assuming that thissubsidence is associated with withdrawal of 20 C fluid from a 600�600 m area atthis depth, and from rocks with a porosity of 0.3 and residual saturation of 0.2,modelling suggests that the maximum gravity effect of 15 m subsidence would beabout �380 mgal, but that the change in the gradient will be less than 1.5 mgal/m.Furthermore, if the water drains vertically downwards there will be no mass change,only a vertical redistribution of mass, and the change in the gradient at the surfacewill therefore be smaller. The effects of changes in the gradient caused by fluidmovements associated with the ground subsidence can therefore be neglected.

5.3. Effect of reservoir mass changes

Between 1950 and 1991, there was a net mass loss of about 325 Mt (Hunt, 1995)from the reservoir at Wairakei. This loss occurred in the upper part of the reservoir(low-pressure steam zone=3�3 km), which has its top at a depth of about 275 m;the rocks in this region have a porosity of 0.2 and residual saturation of about 0.2.Assuming that the loss resulted from water at 240 C flashing to steam (densitychange=�800 kg/m3), calculations (using Webring, 1985) show that the associated


gravity change at the surface would be up to �1500 mgal. However, the greatestchange in the gradient would be less than �1.2 mgal/m. The effects of reservoir masschanges on the gradient can therefore be neglected.

6. Summary

� A value for the vertical gravity gradient at a gravity measurement point isnecessary in calculating the gravity effect of ground subsidence between surveys.

� Variations in the gravity gradient from place to place are associated mainlywith topographic relief.

� The appropriate value of the gravity gradient to use for calculating thegravity effect of ground subsidence between surveys is that measured close tothe ground surface.

� Values of the gravity gradient measured in the areas of high subsidence rateat the Wairakei–Tauhara and Ohaaki fields are similar to those used pre-viously, so no significant errors will have occurred in previously reporteddata.

� At sites measured in the Yanaizu–Nishiyama field, there is no significantchange in the gravity gradient with height above the ground surface. A singlevalue for the gradient can, therefore, be used at each site to correct for thegravitational effect of any ground movement.

� Variations of gravity gradient at Wairakei caused by groundwater level var-iations, mass changes associated with the ground subsidence, and reservoirmass changes are negligible.

Acknowledgements

The authors are grateful to Okuaizu Geothermal Co. Ltd and Contact Energy forpermission to access the measurement points. They also thank Okuaizu GeothermalCo. Ltd, Geothermal Energy Research and Development Company (GERD), NewEnergy and Industrial Technology Development Corporation (NEDO, Japan) andthe Foundation for Research, Science and Technology (New Zealand) for providingfunding for this work (C05X0004). G.F Risk and D.J. Woodward are thanked forhelpful comments on an earlier draft of the paper.

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Documents

Measurement and use of the vertical gravity gradient in correcting repeat microgravity measurements for the effects of ground subsidence in geothermal systems