. 531

GEOLOGICAL SURVEY CIRCULAR 531

The Promise of Precise 

Borehole Gravimetry in 

Petroleum Exploration 

and Exploitation
The Promise of Precise 

Borehole Gravimetry in 

Petroleum Exploration 

and Exploitation

By Thane H. McCulloh

GEOLOGICAL SURVEY CIRCULAR 531

A paper presented at the Third Symposium 

on the Development of Petroleum Resources 

of Asja and the Far East, ECAFE, Tokyo, 

Japan, November 1965

Washington 7966
United States Department of the Interior

STEWART L UDALL, Secretary

Geological Survey

William T. Pecora, Director

Free on application to the U.S. Geological Survey, Washington, D.C. 20242
CONTENTS

Abstract __________________________ _

Introduction. ________________________

Underlying physical relationships _____

Potential uses of borehole gravimetric 

data in petroleum exploration and 

exploitation _______________________

Determination of rock density in situ__ 

Uses of borehole gravimetric data 

in petroleum exploration _________

Page 

1

1

2

Borehole gravimeter precision 

requirements. _________________

Other instrumental and operational 

considerations. ________________

Ref erenc es _ ______________ _____

Page 

_ 9

10

11

ILLUSTRATIONS

Page 

Figure 1. Underground (borehole) vertical gradients of gravity versus bulk rock density

in situ___.__________________________________________________________ 3

2. Gravimetric effects at the axis (borehole) of cylindrical plates of unit density

and thickness AZ, as functions of different cylinder radii _____________ __ 4

3. Density in situ of fluid-saturated reservoir sandstones as functions of total 

porosity, different fluid compositions, and different temperatures and 

pressures _____________________________________________________________ 7

4. Borehole gravimeter precision versus precision of bulk density determinations

for different values of AZ (vertical interval measured) __________________ _ 10

UI
The Promise of Precise Borehole Gravimetry in 

Petroleum Exploration and Exploitation

By Thane H. McCulloh

ABSTRACT

The underground vertical gravity gradient is related to 

rock density in situ, gravimetric effects of nonlevel surfaces 

of equal rock density beneath and around the borehole (including topographic effects), and the free-air vertical gravity 

gradient.

Accurate determinations of average rock density in situ 

underground could be calculated from properly interpreted 

precise borehole gravimeter measurements. Such determinations would be relatively free from the effects of rock damage due to drilling or invasion by mud filtrate. The measurements could be made in cased wells, and they would be 

based on much larger volumes of rock than are sampled by 

any other method. Such measurements would be independent 

of core-analysis data and would therefore provide a standard 

against which to judge the core-analysis data as well as to 

evaluate conclusions drawn from gamma-gamma or other logs.

Conversely, independent knowledge of rock density at a 

borehole would permit separation of the gravitational effects 

of rocks beneath and around the surveyed borehole from 

other effects naturally integrated in the borehole gravimeter 

measurements and thereby offer unique opportunities for 

geological exploration.

Ideally, precision of a borehole gravimeter should be 

±0.001 milligal to permit effective use in the full variety of 

applications outlined in petroleum exploitation and exploration. However, an instrument having the probable presently 

attainable greatest precision of ±0.01 milligal would serve 

for many desirable purposes, and one having a precision of 

±0.02 milligal would be marginally useful. Other instrumental and operational characteristics of an experimental 

prototype borehole gravimeter are described.

INTRODUCTION

The first underground measurements of 

gravity were made in England by Airy (1856) 

to determine the mean density of the Earth. 

He used pendulums to measure the vertical 

gradient of gravity between the top and bottom of a vertical shaft sunk through sedimentary rocks, the average density of which 

was estimated from laboratory measurements of bulk density of hand samples.

Many subsequent papers have been published that consider the principles, practice, 

instrumentation, or results of underground 

measurements of gravity in shafts, mines, 

tunnels, and boreholes. Lorenz (1938), Smith 

(1950), and Domzalski (1955b) are noteworthy 

for their contributions to the development of 

theory or principles; Jung (1939), Hammer 

(1950), Domzalski (1954),and McCulloh(1965) 

illustrate methods; Smith (1950), Gilbert 

(1952), Dolbear (1959), Lukavchenko (1962), 

and Good ell and Fay (1964) record instrumental considerations; and Jung (1939), Hammer (1950), Domzalski (1955b), Whetton, 

Myers, and Smith (1957), McLean (1961), 

Lukavchenko (1962), and McCulloh (1965) 

present particularly important observational 

data. Other pertinent papers are those of 

Rogers (1952), Miller and Innes (1953), Domzalski (1955a), Egyed (1960), Plouff (1961), 

Gran (1962),Hammer (1963a,b), Secor, Meyer, 

and Hinze (1963), and Thyssen-Bornemisza 

(1963, 1964).

Despite the considerable interest in the 

potential value of underground and borehole 

gravimetry manifested by this rather extensive literature and because of the technical 

difficulties and expense of designing and fabricating a gravimeter capable of operating 

with high precision in a borehole, publicized 

attempts have thus far met with only limited 

success (Gilbert, 1952; Lukavchenko, 1962; 

Van Melle and others, 1963, p. 475; and 

Goodell and Fay, 1964). In considering these 

difficulties and the remaining obviously formidable design problems, it is desirable to 

take stock of the practice and promise of precise borehole gravimetry in petroleum exploration and exploitation, with the objective 

of determining those instrumental objectives 

that now appear desirable in view of the 

geologic problems and those which are worth

1
THE PROMISE OF PRECISE BOREHOLE GRAVIMETRY IN PETROLEUM EXPLORATION AND EXPLOITATION

pursuing, considering their technical difficulty and high cost.

The author appreciates the many stimulating discussions of some aspects of this 

report held with Dr. L. J. B. LaCoste, Mr. J. 

E. Schoellhamer, Dr. R. E. von Huene, Mr.L. 

A. Beyer, and Mr. R. R. Clawson. Appreciation is also expressed to the Research 

Corp. for financial assistance granted through 

the University of California, Riverside, which 

helped stimulate work that led indirectly to 

this report.

UNDERLYING PHYSICAL RELATIONSHIPS

Above the ground surface, the difference 

in the acceleration due to gravity bet ween two 

points vertically above one another may be 

expressed as

C (1)

where Aga = the gravity difference between

two points on a vertical line

in air; 

AZ = the elevation difference between

the two points; 

F = the free -air vertical gradient of

gravity; 

AQ = the difference between the two

points in the correction for

surf ace terrain irregularities;

and 

ACg= the difference between the two

points in the correction for

underground geology below the

local datum level.

The free -air gradient varies as a function 

of both latitude and altitude, according to the 

relation (Heiskanen and Vening Meinesz, 

1958, p. 54)

Ag = (0.30877 -0.00044 sin2 e)Zm -0.073Zfem2 (2)

where Ag = the gravity difference in milligals between a point at sea

level and another point in air

vertically above the first;

Zjn = the vertical distance between the

two points in meters; 

Zkm~ the vertical distance between the 

two points in kilometers; and 

6 = the latitude.

However, the total latitudinal variation at 

sea level is small only 0.00044 mgal per m 

(milligal per meter) between equator and

poles and the variation from the sea-level 

value because of elevation is also small 

0.00015 mgal per m less than the sea-level 

value at 1,000 meters for all latitudes. Thus, 

it is clear that measured large departures 

from the so -called normal free -air vertical 

gradient value of 0.3086 mgal per m must 

arise from surface terrain or subsurface 

geologic effects. Where the terrain is flat or 

where the gravitational effects of surface 

topographic irregularities may be calculated, 

only subsurface geologic irregularities remain to account for measured deviations 

from the normal value of F. This fact motivated Evjen (1936), among others, to examine 

the possible geologic utility of measurements 

or computations of the surface vertical 

gradient of gravity, and caused Hammer 

(1938), Thyssen-Bornemisza and Stackler 

(1956), and Kumagai, Abe, and Yoshimura 

(1960) to measure and analyze in various 

terms local departures from the normal 

value. Kumagai and others (1960) observed 

local departures of more than 10 percent 

from the normal value even after correction 

for terrain effects (fig. 1).

Beneath the ground surface, the vertical 

gradient of gravity is similarly a function of 

the free-air gradient at the particular latitude and elevation, and is similarly modified 

by surface topographic irregularities and 

subsurface geologic irregularities; in addition, it is influenced very strongly by the 

density of the plate of rocks between two 

vertically separated points of measurement, 

and may be significantly influence locally by 

the size and shape of the hole in which measurements are made. The relationships among these variables are expressed as

(F-4Tfe«r) AZ + AQ + ACg (3)

where Agu = the gravity difference between 

two points on a vertical line 

underground;

fe = the gravitational constant;

<r = the density of the horizontal 

plate of rock that separates 

the two points of measurement; 

ACg = the differential effect of departures from horizontality of 

the surfaces of equal rock 

density above and below the 

measurement interval,but below the local gravity survey 

elevation datum;
UNDERLYING PHYSICAL RELATIONSHIPS

= the differential gravitational effect of the borehole, its mud 

cake, its cement, its casing, 

and the borehole fluid density;

= the differential effect of terrain 

irregularities and unlevel surfaces of equal rock density 

above the local gravity survey 

elevation datum; 

the elevation difference between

the two points; and 

F = the free -air vertical gradient of 

gravity.

AZ =

Clearly, if Agy could be measured, if F is 

known or can be reliably assumed, if AZ can 

be accurately measured, and if the terms for 

the differential effects of surface terrain, 

subsurface geology, and borehole influence 

are negligible or can be evaluated, equation 

3 can be solved for tr, the bulk rock density 

in situ (Jung, 1939; Hammer, 1950; Smith, 

1950). Conversely, if <r could be accurately 

determined independently of gravity measurements (by core-sample analysis or by 

gamma-gamma logging, for example) and if 

accurate numerical values could be substituted

R

1

i 0.0800

100 120 140 160 180 200 220

BULK ROCK DENSm IN S3TU, IN GRAMS PER CUBIC CENTIMETER

Figure 1. Underground (borehole) vertical gradients of gravity versus bulk rock density in situ.

280
THE PROMISE OF PRECISE BOREHOLE GRAVIMETRY IN PETROLEUM EXPLORATION AND EXPLOITATION

for all but the ACg term of equation 3, the 

underground equivalent of the surface Bouguer gravity anomaly value could be obtained 

(Smith, 1950). From the standpoint of the 

underlying principles, therefore, borehole 

gravimetry has a direct bearing on questions 

of interest in both petroleum exploration and 

exploitation (as well as in other subsurface 

geologic investigations). Some practical consequences and requirements that emerge 

from consideration of these two major potential uses of borehole gravimetric data are 

reviewed or examined in detail below.

POTENTIAL USES OF BOREHOLE GRAVIMETRIC

DATA IN PETROLEUM EXPLORATION

AND EXPLOITATION

Most of the specific potential uses of 

borehole gravimetric data in petroleum exploration were recognized and thoroughly 

examined by Smith (1950). He classified the 

areas of application into three related but 

separate groups the understanding of borehole geology, interpretation of surface gravity 

surveys, and interpretation of seismic data. 

A fourth group of applications, aids to evaluation of petroleum reservoir characteristics and performance, can be foreseen also. 

Furthermore, some of the applications outlined by Smith deserve reexamination or 

emphasis in light of other developments 

since 1950.

DETERMINATION OF ROCK DENSITY IN SITU

The greatest benefits of a precise borehole gravimeter to the technology of petroleum exploration and exploitation would 

probably stem from its use as a tool for 

measuring rock density in situ(Lorenz, 1938; 

Jung, 1939), because precise borehole measurements of gravity would provide accurate 

measurements of bulk rock density in situ, 

independent of core samples or of any indirect method of measurement. Equation 3 

shows that the underground gradient of gravity is directly dependent on the rock density 

of the horizontal plate of rock between two 

vertically separated stations. The bulk rock 

density may be expressed as

is (4)

CT_ = the density of the mineral grains;

and 

^ = the porosity expressed as a

fraction.

Not only is the dependence of AgM on CTJ S 

direct, but measurement of CTJ$ .by borehole 

gravimetric methods would be in situ; thus, 

volume changes that might result from elastic expansion of the rock upon depressurization, exposure of the rock to the atmosphere, 

mechanical damage to cores during drilling, 

or changes in pore-fluid composition are 

absent or minimal. Questions of the type 

that perplex the interpreter of gamma-gamma logs or that should be of concern to the 

user of core analysis data could be circumvented by borehole-gravimeter density measurements. Furthermore, the volume of rock 

effectively sampled by the borehole-gravi - 

metric technique would be vastly larger and 

more representative than that sampled by 

any other known method of measurement. 

Figure 2 is a plot of the gravimetric effects 

of a series of cylindrical plates of thickness 

AC and unit density that are coaxial with a 

vertical borehole. The effects shown are expressed as percentages of the effect of an 

infinitely extended horizontal plate of the 

same thickness and density, and are plotted 

as a function of differing cylinder radii (expressed as multiples of their thickness). 

About 65 percent of the effect of an infinitely 

extended plate of thickness AZ arises from 

the volume of rock within a radius of the 

measured interval in the borehole of 1AZ,

where a^s = the bulk rock density in situ;

<*f = the density in situ of the porefilling fluid(s);

50 60 70 80 90 100

PERCENTAGE OP THE TOTAL GRAVIMETRIC 

EFFECT OF AN INFINITELY EXTENDED 

PLATE OF THICKNESS AZ

Figure 2. Gravimetric effects at the axis(borehole) of cylindrical plates of unit density and thickness dZ as functions of different cylinder radii.
POTENTIAL USES OF BOREHOLE GRAVIMETRIC DATA IN PETROLEUM EXPLORATION AND EXPLOITATION

and 77 percent arises from within a radius of 

2 AZ. Beyond a radius of 4 AZ, the rate of 

increase of the gravimetric effect begins to 

fall off sharply, and 90 percent of the total 

effect occurs from within a radius of only 

5 AZ. In theory, by adjusting the vertical 

measurement interval, average -interval density values could be obtained that would represent appropriately large volumes of rock; 

this would avoid nearly all problems that are 

due to formation invasion by drilling fluid 

filtrate, to formation damage by the drilling 

process, and to difficulties in obtaining a 

statistically valid sample from a formation 

interval by conventional cores. The gravimeter precision needed to accomplish this 

objective over depth intervals that would be 

generally meaningful is thoroughly considered in later pages.

If we grant that the borehole gravimetric 

technique in theory offers a promising method of directly measuring the average density 

of relatively large samples of undisturbed 

rock in situ underground and set aside for 

the moment the extremely important question 

of the gravimeter precision needed for such 

a task, in what ways would such density 

measurements be useful if they could be 

made?

Possibly the most significant single use 

of precise borehole gravimetric data would 

be to establish detailed density profiles to 

serve as absolute standards for evaluating 

core-analysis data and procedures. All presently available methods of estimating underground rock density or porosity in detail 

depend either directly or indirectly on laboratory analysis of core samples (Pickell 

and Heacock, 1960; L. E. Schneider, oral 

commun., June 23, 1965). The field gravimetric studies of Hammer (1950) revised 

by McCulloh (1965) and of Whetten, Myers, 

and Smith (1957) and the laboratory investigations of Fatt (1958) suggest that sedimentary rocks expand as they are cored and 

withdrawn, that rock damage during drilling 

may cause volume expansion, or both. Conversely, DomzalskL (1955b), finding laboratory density measurements of hand samples 

of faulted and brecciated rock and of partly 

mineralized ore specimens to be greater 

than the average density calculated from 

underground gravity measurements in Cumberland and Surrey, England, concludes that 

hand samples fail to reflect properly the 

amount of fracture porosity and the amount

of gangue in such rocks. Furthermore, the 

author (McCulloh, 1965) has shown that the 

effect of weathering of old cores is small but 

appreciable, even when they have been carefully stored, and that this effect also is one 

of volume expansion. The extent and variation of such differences between the volumes 

of core samples and the equivalent rock volumes in situ underground would be illuminated by comparison of gravimetrically derived density profiles and core-analysis data.

From such comparisons, analyses could 

also be made of errors that result from defects in laboratory procedures for measuring 

volume of core samples for determination of 

density or porosity. Under optimum conditions, the weight and bulk volume of a core 

sample can be measured routinely in the 

laboratory with accuracies such that the density of the sample can be known within 

+0.005 g per cm3 . Tests and comparisons by 

the author have shown that some commercial 

laboratory procedures in routine use yield 

bulk-volume measurements that may be as 

much as 15 percent too high for rough-surfaced specimens of high total porosity. The 

need for an absolute standard for comparison, evaluation, and standardization is clear; 

and a precise borehole gravimeter, if properly used, could provide such a standard.

Inasmuch as conclusions reached about 

rock density or porosity from gamma-gamma 

radiation logs and acoustic velocity logs depend indirectly on core-analysis data, direct 

comparisons between such logs and gravimetrically derived density profiles would 

result in better under standing and more complete and intelligent use of such indirect 

methods of borehole measurement of rock 

density. Additionally, because a gravimetric 

profile of rock density would belittle changed 

by the effects of formation damage due to 

drilling and invasion by mud filtrate, from 

the differential effects of mud cake or variable thickness of mud cake, or from the effects of variable hole diameter, it would 

serve admirably as a basis for analyzing the 

relatively important effects that such variables have on a density profile obtained by 

gamma-gamma logging. The improvements 

to be expected from such comparisons in the 

interpretations of indirect techniques of density and porosity measurement presumably 

would eventually establish core-analysis and 

gamma-gamma log interpretations as completely reliable and trustworthy methods in
THE PROMISE OF PRECISE BOREHOLE GRAVIMETRY IN PETROLEUM EXPLORATION AND EXPLOITATION

their own right. This would, in turn, permit 

certain unique uses, to be described on later 

pages, of the ACg term of equation 3, with 

far-reaching consequences for petroleum 

exploration.

Sedimentary-rock density, and therefore 

porosity, has long been known from core 

analysis to vary systematically with depth 

because of gravitational consolidation during 

burial and loading (Athy, 1930; Hedberg, 

1936). With the acquisition of more detailed 

density and porosity data has come a growing 

awareness that lithology, age, temperature, 

sedimentary environment, structural history, 

and pore-fluid pressure history play important roles in determining or modifying 

these properties of sedimentary rocks (Nafe 

and Drake, 1957; Dallmus, 1958; Lerbekmo, 

1961; Meade, 1963; McCulloh, 1963; Maxwell, 

1964). Establishment of a reliable and accurate method of measuring density in situ 

in boreholes would permit more rapid and 

dependable investigation of these relations 

and their significance in petroleum exploration and exploitation. Such investigations 

might clarify such fundamentally important 

problems as (1) maximum depth of commercially attractive reservoir rocks, (2) the 

relation between degree of consolidation and 

extent of petroleum migration and accumulation in young sedimentary materials, (3) 

variation with age and other factors of the 

sedimentary rock depth-density function, and 

(4) the distribution of fracture porosity or 

vugular porosity in otherwise massive rocks.

Because fluid density (at of equation 4) 

constitutes an important fraction of the bulk 

rock density in rocks of more than a few 

percent porosity and because grain density 

varies so little among many sedimentary 

rocks (Davis, 1954), precise measurements 

of rock density in situ underground would 

provide a means of gaining information about 

the pore-fluid density in situ. Under various 

conditions, such information could be used to 

great advantage in evaluating a newly discovered potential reservoir or in monitoring 

the performance of a producing reservoir. 

As an illustration, assume that a porous zone 

suspected of being a potential reservoir has 

been drilled and cored, but mud cake and invasion of the zone by mud filtrate have made 

uncertain the degree of petroleum saturation 

in the cores and in the formation. Core and 

electric-log analysis will indicate the approximate average total porosity for the

zone. Examination of ditch cuttings will suggest an average lithology and grain density. 

Sufficiently precise measurement of the vertical gradient of gravity in or through the 

interval corrected for the effects of surface terrain, approximately for subsurface 

geology, and (if necessary) for borehole irregularities would permit computation of 

the bulk rock density in situ. Substitution of 

ais >aa> an<^ ^ *n equation 4 would then permit (computation of or. Knowing that interstitial water has a density at nearly all temperatures and pressures of 1.00 g per cm3 

and that most natural petroleum fluids have 

distinctively lower densities at nearly all 

temperatures and pressures, as shown in 

figure 3, a realistic decision could be made 

to test the zone (or persist in testing it) or to 

ignore it. Furthermore, if the zone temperature and approximate fluid pressure 

were known and if experience in the region 

led one to suspect a certain interstitial water 

content and a particular oil gravity in the 

possible oil zone, the analysis of fluid character could be made rather closely from the 

data specified above.

As a second illustration, take the hypothetical case of a known productive well in 

which it is desired to periodically monitor 

the performance of a producing reservoir 

unit. We presume that a considerable body 

of factual data regarding the physical properties of the reservoir unit has been gathered and is available. These data include estimates of the average total porosity, grain 

density, temperature, fluid pressure, tank 

oil gravity, and interstitial water content and 

salinity. The produced gas gravity and an 

estimate of the reservoir gas-oil ratio would 

also be available. From these quantities, the 

density of the fluids in the pore space could 

be calculated fairly accurately using, for 

example, the correlation equations of Standing (1947). Measurement of the underground 

vertical gradient of gravity through the producing interval (or a carefully selected part 

of it) could be made prior to production from 

the reservoir or early in its productive life 

by using a precise boreholegravimeter. Repeated measurements over the same interval, at time intervals dictated by the rate of 

production in relation to the reservoir volume, would show vertical gravity gradient 

changes, that would reflect only the changes 

in fluid density (and to a slight extent in pore 

volume, if diminution of reservoir volume 

occurs as the reservoir pressure falls). In
POTENTIAL USES OF BOREHOLE GRAVIMETRIC DATA IN PETROLEUM EXPLORATION AND EXPLOITATION

35

30

25

B 20

oI 15

10

Pure methane saturation

\ Petroleum of 60° API \ gravity saturation

\ Petroleum of 30° API 

\ gravity saturation \

Water saturation

ASSUMED CONDITIONS

At 35 percent porosity 93 °P and 980 psi

At 20 percent porosity 1B6 °F and 3T&X) psi

At 10 percent porosity 36O °F and 8900 psi

Grain density of 2.6? g per cm3

1.7 2.0 2.3 2.6

FLUID-SATURATED SANDSTONE DENSITY, IN (HAMS PER CUBIC CENTIMETER

Figure 3. Density in situ of fluid-saturated reservoir sandstones as functions of total porosity, different fluid compositions, and different

temperatures and pressures.

an initially undersaturated reservoir in 

which gas expansion and gravity drainage 

dominate, and water drive is absent or of 

slight importance, the fluid density throughout the reservoir would decrease during production and pressure decline until a free 

gas -cap of very low density began to develop 

and expand. In an undersaturated reservoir 

in which an active water drive provides most 

of the reservoir energy, the encroachment of 

relatively dense water could be observed as 

the oil-water interface changes position. In 

either reservoir type, irregularities in the 

fluid behavior could be observed indirectly, 

and thereby possibly could be controlled 

through adjustment of rates of production in 

wells causing the irregularities.

Reservoir monitoring of the sort described above would also probably find use in 

water-flooding operations and in other types 

of secondary recovery operations. However,

it is equally probable that considerable experimentation and empirical observation 

would be required to develop a satisfactory 

understanding of both the uses and the limitations of such applications.

A final statement is in order regarding 

the suitability of the methods described 

above in cased wells. Smith (1950, p. 630 

635 and fig. 16) has shown that factors such 

as casing, changes in casing size, and cement behind casing generally influence the 

underground vertical gradient of gravity so 

slightly as to be negligible. Only if the borehole gravimeter were read within four to 

five times the diameter of the well from the 

end of a casing or of a casing joint of different size would differential effects appear. 

Thus, the borehole gravimeter would be 

ideally suited to measure rock density in situ 

in cased wells without excessive interference 

from casing or cement, as long as tops and
8 THE PROMISE OF PRECISE BOREHOLE GRAVIMETRY IN PETROLEUM EXPLORATION AND EXPLOITATION

bottoms of casing joints of different size or 

of cement columns behind casing are known 

and avoided. This matter is referred to later 

in connection with consideration of borehole 

gravimeter precision requirements.

USES OF BOREHOLE GRAVIMETRIC DATA IN 

PETROLEUM EXPLORATION

Although a precise borehole gravimeter 

probably would at first have its greatest 

value as atool for accurately measuring rock 

density in situ, it would be immediately useful and important as a tool for improving in 

several ways the interpretations of surface 

gravity data. Its value for sub surf ace gravity 

mapping and prospecting in extensively developed productive basins might ultimately 

equal (or possible even exceed) its value to 

logging and petroleum exploitation technology.

Smith (1950, p. 614) effectively presented 

strong arguments for-utilizing precise borehole gravity data from shallow holes to compute reliable elevation correction factors for 

use in reduction of surface gravity data. 

This refinement of the method of Nettleton 

(1939) should also be accompanied by measurements, at each site, of the free-air gradient of gravity above the ground surface, for 

use in calculating rock density from equation 

3 and for use in reducing the surface gravity 

data, as suggested by Kumagai and others 

(1960).

Smith (1950, p. 616-617) and Hammer 

(1950) also make a strong case for using a 

borehole gravimeter to establish the depthdensity function on a more-or-less regional 

basis to serve as background against which 

to interpret local undrilled surface gravity 

anomalies. Neither core-analysis data nor 

gamma-gamma logs provide completely 

trustworthy bases for such conclusions, although core-analysis data have been used 

with surprisingly good results by the writer 

(McCulloh,1960 and 1965) and gamma-gamma 

logs have yielded similarly interesting results (Hammer, 1963).

Other uses of precise borehole gravity 

measurements in petroleum exploration depend on interpretation of the ACg term of 

equation 3. We have seen that substitution of 

F, a, AQ and AQ> in equation 3 would permit computation of ACfl. Because ACfl is

o o

the term that arises mainly from the geology 

beneath and above the measurement interval 

in the borehole and because the strata above 

the interval presumably could be fairly well 

evaluated in terms of rock density in general, 

reliable computation of the ACg term provides a measure of the effect of the unknown 

rocks beneath the borehole. Interpretations 

of such ACg terms measured in intervals 

along a borehole especially when coupled 

with interpretations of surface gravity data 

from geologic and density models based on 

syntheses of structural, stratigraphic, and 

seismic data would provide a powerful 

means of extending to depth interpretations 

that would otherwise be meaningless because of the attenuating effect of depth on 

gravity anomalies of small height-to-width 

ratio.

Problems that would plague early efforts 

to interpret borehole gravity measurements 

in terms of the geologic correction term can 

be expected to diminish with application of 

such a tool. It is apparent that departures 

from level of surfaces of equal rock density 

beneath a surveyed well create disturbances 

in the free-air gradient of gravity underground as well as at and above the ground 

surface. Presumably, the F term could be 

measured above the ground surface at the 

surveyed well site, and surface gravity maps 

around the well site could be used for estimating the underground variations in the F 

term along the vertical hole (Eyjen, 1936; 

Hammer, 1938; Henderson and Zietz, 1949). 

Without an understanding of the geology and 

density distribution for a considerable distance around and beneath the surveyed well, 

however, estimates of F values underground 

could be little better than educated guesses 

because of uncertainties in calculated ACg 

terms. Similarly, until the reliability of 

core-analysis data as a measure of rock 

density in situ has been established beyond 

doubt by use of a precise borehole gravimeter at sites where the F term of equation 

3 can be determined with high accuracy, 

doubt will exist about the reliability of any 

values of a substituted in equation 3 and, 

therefore, about the reliability of values of 

ACg computed from them. One of the most 

compelling reasons for thorough investigation of the relationship between estimates 

of rock density in situ by each of several 

methods and actual density of rocks underground arises from the foreseeable need for
BOREHOLE GRAVIMETER PRECISION REQUIREMENTS

absolutely accurate values of a to substitute 

in equation 3.

Field use of a precise borehole gravimeter will result in fairly rapid clarification 

of the problems outlined above; and with the 

accumulation of observational data and experience, their consequences will diminish. 

It is clear that early efforts to use and interpret borehole gravity measurements 

would be most fruitful in extensively explored areas where much is already known 

about the subsurface geology. Thus a precise borehole gravimeter would be much 

more important in early applications to exploitation or development geology, and its 

contribution to purely exploratory operations 

might be slight at first. One exception to 

this statement is in regional interpretation 

of surface gravity maps, which would benefit extensively and quickly from density data 

gathered from exploratory wells.

BOREHOLE GRAVIMETER PRECISION 

REQUIREMENTS

The potential theoretical applications of a 

borehole gravimeter are as varied as they 

are interesting. Therefore, the precision 

required in an instrument to be used in any 

except a purely experimental program deserves reexamination in terms of each 

possible use.

Inasmuch as a borehole gravimeter would 

be ^ised mostly to obtain measurements of 

the vertical gradient of gravity underground, 

the precision requirements are somewhat 

less rigid than for an instrument intended to 

yield absolute measurements, because a loss 

of precision in measurement of Ag could be 

compensated in part by enlarging AZ to diminish the error in the ratio Ag/AZ . Figure 

4 is a graph of differing gravimeter precision 

(or alternatively, precision of Ag) plotted 

against differing precision of bulk density 

determinations based on the underground 

vertical gravity gradient for different values 

of AZ. If it is desired to measure density in 

situ over a depth interval of 10 meters, a 

borehole gravimeter having a reading precision and accuracy of +0.1 mgal will yield a 

determination having a precision of +0.24 

g per cm3 , and an instrument that can be 

read to +0.01 mgal will yield a determination 

of +0.024 g per cm3 Probably a practical 

limit to the precision of most modern surface gravimeters used in prospecting is 

+0.005 mgal, and reproducibility of +0.01 to 

+0.02 mgal is probably more characteristic. 

Therefore, it is difficult to envision a borehole instrument having a precision better 

than ±0.01 mgal at present (1965).

On an earlier page, it was stated that the 

density of an individual core sample of compact sedimentary rock can be measured in 

the laboratory with a precision of about 

+0.005 g per cm3 . However, sampling inadequacies and core volume changes, together with measurement errors, created a 

discrepancy of minus 0.013 g per cm3 when 

a core sample density profile was compared 

with a profile based on gravity measurements 

in a 2,500-foot mine shaft through Paleozoic 

rocks (McCulloh, 1965). If the precision of 

core sample determinations thus ranges in 

practice from +0.007 to about +0.013 g per 

cm3 , depending on the amount of effort spent 

to overcome sampling inadequacies, a borehole gravimeter having a precision of +0.01 

mgal could give an average value of equivalent or better precision over a depth interval 

of about 50 meters. Moreover, the gravimetric average value would be based on an 

almost infinitely larger sample in situ and 

mainly undisturbed. Obviously, for establishment of calibration standards or for 

gathering density and porosity data for any 

one of the varied applications outlined above, 

an instrument of this sensitivity would be 

extremely useful.

A borehole gravimeter having a precision 

and accuracy of +0.01 mgal would probably 

be marginally useful as a device for monitoring the fluid-density changes in most producing reservoirs, but it would be of very 

great importance in the evaluation of fluid 

content of newly discovered reservoirs. The 

densities of reservoir rocks saturated with 

petroleum fluids differ from the densites of 

the same rocks saturated with water by 0.35 

to 0.01 g per cm3 . For reservoir units 10 to 

100 meters thick, such density differences 

would produce discernible effects in the 

underground vertical gravity gradient, but 

changes in densities that would occur during 

production of such a reservoir might or 

might not be detectable. The gravity gradient 

would obviously be affected by expected 

changes in fluid density in a larger vertical 

petroleum column.
10 THE PROMISE OF PRECISE BOREHOLE GRAVTMETRY IN PETROLEUM EXPLORATION AND EXPLOITATION

Smith (1950, p. 618) concluded that for 

many subsurface exploratory applications a 

borehole gravimeter precision of +0.2 mgal 

would suffice. This conclusion has been 

justifiably questioned (Dolbear, 1959), but a 

precision 10 times as great, +0.02 mgal, 

would certainly provide an instrumental 

capability of broad value to petroleum exploration. Even greater precision would not 

be wasted, whereas an instrument much less 

sensitive than +0.02 mgal would appear to 

have limited practical value. Inspection of 

figure 4 suggests that an almost ideal instrument ought to have a precision of +0.001 

mgal. Density differences greater than 

+0.003 g per cm3 could then be readily detected in thickness intervals of only 10 meters. Such an instrument (or its equivalent, 

a vertical gravity gradiometer having a 

sensitivity of +0.0002 mgal per m) would be 

fully sensitive enough to provide data of 

great usefulness in each of the applications 

discussed here and by Smith (1950). In particular, it would permit a very substantial 

increase over any other method in the accuracy with which rock density can be measured.

OTHER INSTRUMENTAL AND OPERATIONAL 

CONSIDERATIONS

Dolbear (1959) has given a rather complete review of the dimensional and other 

design characteristics desirable in a practical borehole gravimeter, and nothing need 

be added to his statements regarding these 

considerations. However, emphasis should 

be placed on the word "practical," in order 

to call attention to the fact that an experimental prototype need not have all the char - 

acteristics of a final instrument suitable for 

routine industrial applications. An instrument could be operated in enough places and 

depths to provide an ample test of the usefulness of the method if it had a sensitivity 

of +0.01 mgal, a worldwide range, a temperature tolerance of 100°C, a diameter of 

about 14.0 centimeters (5.51 in.) to fit inside 

a pressure vessel having an outside diameter 

of about 16.5 centimeters, and the capability 

of withstanding fluid pressures of 8,000 

pounds per square inch and if it could be 

leveled inside a cased borehole inclined 7y° 

from vertical. Moreover, it would be a 

vehicle for establishing the exceedingly

±0,001

±0.01

±0.1

±1

Practical limit to precision 

of surface gravimeters?

±0,002

±0*02

±0.2 8

±2

o

 H

PRECISION OF BUIIC DENSITY DETERMINATION, IN GRAMS PER CUBIC CENTIMETER 

Figure 4. Borehole gravimeter precision versus precision of balk density determinations for different values of AZ (interval thickness).
REFERENCES 11

important basis for comparison of gravimetric density profiles with core-analysis 

and gamma-gamma logging data, particularly 

in soft, highly porous clastic rocks where 

presently available methods of density measurement are least reliable. Lastly, it would 

provide an experimental and empirical basis 

for future decisions about more compact instruments of higher temperature tolerance 

better suited to routine industrial uses. Such 

a prototype instrument appears to be both 

technically and economically within reach 

(Dr. Lucien J. B. LaCoste, oral commun., 

July 16, 1965).

REFERENCES

Airy, G. B., 1856, Account of pendulum experiments undertaken in the Harton Colliery for the purpose of determining the 

mean density of the earth: Royal Soc. 

Philos. Trans., v. 146, nos. 14 and 15, p. 

297-342 and p. 343-355.

Athy, L. F., 1930, Density, porosity, and compaction of sedimentary rocks: Am. Assoc. 

Petroleum Geologists Bull., v. 14, no. 1, 

p. 1-24.

Dallmus, K. F., 1958, Mechanics of basin 

evolution and its relation to the habitat of 

oil in the basin, in Weeks, L. G., ed. 4 Habitat of oil a symposium: Tulsa, Okla., 

Am. Assoc. Petroleum Geologists, p. 883 

931.

Davis, D. H., 1954, Estimating porosity of 

sedimentary rocks from bulk density: 

Jour. Geology, v. 62, no. 1, p. 102-107.

Dolbear, D. W. N., 1959, Design considerations of a borehole gravimeter: Geophys. 

Prospecting, v. 7, no. 2, p. 196-201.

Domzalski, W., 1954, Gravity measurements 

in a vertical shaft: Inst. Mining Metallurgy 

Trans., Bull. 571, v. 63, p. 429-445.

 1955a, Three dimensional gravity survey: Geophys. Prospecting, v. 3, no. 1, 

p. 15-55.

 1955b, Relative determination of the 

density of surface rocks and the mean 

density of the earth from, vertical gravity 

measurements: Geophys. Prospecting, v. 3, 

no. 3, p. 212 227.

Egyed, Lazlo, 1960, Zur Frage der Schweremessungen in Bohrlochern: Freiburger 

Fbrschungshefte C 81, Geophysik, p. 167 

170.

Evjen, H. M., 1936, The place of the vertical 

gradient in gravitational interpretations: 

Geophysics, v. 1, no. 1, p. 127 137.

Fatt, Irving, 1958, Compressibility of sandstones at low to moderate pressures: Am. 

Assoc. Petroleum Geologists Bull., v. 42, 

no. 8, p. 1924-1957.

Gilbert, R. L. G., 1952, Gravity observations 

in a borehole: Nature, v. 170, no. 4523, 

p. 424-425.

Goodell, R. R., and Fay, C. H., 1964, Borehole gravity meter and its application: 

Geophysics, v, 29, no. 5, p. 774-782.

Gran, B. V., 1962, K teorii vertikal'nykh 

krutil'nykh vesov [On the theory of vertical torsion balances]: Leningrad. Univ. 

Uchenyye Zapiski, Voprosy Geofiziki, no. 

303, p. 278-287.

Hammer, Sigmund, 1938, Investigation of the 

vertical gradient of gravity: Am. Geophys. 

Union Trans., 19th Ann. Mtg., pt. 1, p. 

72-82.

 1950, Density determinations by underground gravity measurements: Geophysics, v. 15, no. 4, p. 637-652.

 1963a, Deep gravity interpretation by 

stripping: Geophysics, v. 28, no. 3, p. 

369-378.

 1963b, Rock densities and the vertical

gradient of gravity in the earth's crust: 

Jour. Geophys. Research, v. 68, no. 2, 

p. 603-604.

Hedberg, H. D., 1936, Gravitational compaction of clays and shales: Am. Jour. 

Sci., 5th ser., v. 31, no. 184, p. 241-287.

Heiskanen, W. A., and Vening Meinesz, F. 

A., 1958, The Earth and its gravity field: 

New York, McGraw-Hill Book Co., Inc., 

470 p.

Henderson, R. G., and Zietz, Isidore, 1949, 

The upward continuation of anomalies in 

total magnetic intensity fields: Geophysics, v. 14, no. 4, p. 517-535.

Jung, Heinrich, 1939, Dichtebestimmung ixa 

anstehenden Gestein durch Messung der 

Schwerebeschleunigung in verschiedenen 

Tiefen unter Tage: Zeitschr. Geophysik, 

v. 15, p. 56-65.

Kumagai, N., Abe, E., and Yoshimura, Y., 

1960, Measurement of vertical gradient of 

gravity and its significance: Boll. Geofisica, v. 2, no. 8, p. 607-630.

Lerbekmo, J. F., 1961, Porosity reduction in 

Cretaceous sandstones of Alberta: Alberta 

Soc. Petroleum Geologist Jour.,v. 9,no. 6, 

p. 192-199.

Lorenz, H., 1938, Beitrage zur Theorie des 

Erdaufbaus: Zeitschr. Geophysik, v. 14, 

p. 142-152.
12 THE PROMISE OF PRECISE BOREHOLE GRAVIMETRY IN PETROLEUM EXPLORATION AND EXPLOITATION

Lukavchenko, P. I., 1962, Nablyudeniya s 

gravimetrami v burovykh skvazhinakh i 

shakhtakh [Observations with gravimeters 

in wells and mine shafts]: Razvedochnaya 

i Promyslovaya Geofizika, no. 43, p. 52 64.

Maxwell, J. C., 1964, Influence of depth, temperature, and geologic age on porosity of 

quartzose sandstone: Am. Assoc. Petroleum Geologists Bull., v. 48, no. 5, p. 

697-709.

McCulloh, T. H., 1960, Gravity variations and 

the geology of the Los Angeles basin of 

California, in Synopsis of geologic results: 

U.S. Geol. Survey Prof. Paper 400-B, 

p. B320-B325.

 1963, Factors controlling subsurface 

density variations in post-Oligocene sedimentary rocks [abs.]: Geol. Soc. America 

Spec. Paper 76, p. 112.

 1965, A confirmation by gravity measurements of an underground density pro - 

file based on core densities: Geophysics, 

v. 30, no. 6, p. 1108-1132.

McLean, A. C., 1961, Density measurements 

of rocks in Southwest Scotland: Royal Soc. 

Edinburgh Proc., sec. B., v. 68, pt. 2, 

p. 103-111.

Meade, R. H., 1963, Factors influencing the 

pore volume of fine-grained sediments 

under low-to-moderate overburden loads: 

Sedimentology, v. 2, no. 3, p. 235-242.

Miller, A. H., and limes, M. J. S., 1953, Application of gravimeter observations to the 

determination of the mean density of the 

earth and of rock densities in mines: Dominion Observatory Ottawa Pubs., v. 16, 

no. 4, p. 3-17.

Nafe, J. E., and Drake, C. L., 1957, Variation 

with depth in shallow and deep water marine sediments of porosity, density and the 

velocities of compressional and shear 

waves: Geophysics, v. 22, no. 3, p. 523 

552.

Nettleton, L. L., 1939, Determination of 

density for reduction of gravimeter observations: Geophysics, v. 4, no. 3.

Pickell, J. J., and Heacock, J. G., 1960, 

Density logging: Geophysics, v. 25, no. 4, 

p. 891-904.

Plouff, Donald, 1961, Gravity profile along 

Roberts Tunnel, Colorado, in Short papers 

in the geologic and hydrologic sciences: 

U.S. Geol. Survey Prof. Paper 424-C, 

p. C263-C265.

Rogers, G. R., 1952, Subsurface gravity 

measurements: Geophysics, v. 17, no. 2, 

p. 365-377.

Secor, G. B., Meyer, H. J., and Hinze, W. J., 

1963, A density determination by underground gravitymeasurements in Michigan: 

Geophysics, v. 28, no. 4, p. 663-664.

Smith, N. J., 1950, The case for gravity data 

from boreholes: Geophysics, v. 15, no. 4, 

p. 605-636.

Standing, M. B., 1947, A general pressurevolume-temperature correlation for mixtures of California oils and greases: Oil 

and Gas Jour., v. 46, no. 2, p. 95-101.

Thyssen-Bornemisza, Stephen, and Stackler, 

W. F., 1956, Observing vertical gravity 

gradient: Geophysics,v. 21, no. 3, p. 771 

779.

Thyssen-Bornemisza, Stephen, 1963, The 

vertical gravity gradient in borehole exploration: Geophysics, v. 28, no. 6, p. 

1072-1073.

 1964, Determination of Bouguer density in shallow holes: Geophysics, v. 29, 

no. 3, p. 445-446.

Van Melle, F. A., Faass, D. L., Kaufman,S., 

Postxna, G. W.,-and Seriff, A. J.,1963, 

Geophysical research and progress in exploration: Geophysics, v. 28, no. 3, p. 

466-478.

Whetten, J. T., Myers, J. O., and Smith, R., 

1957, Correlations of rock density determinations for gravity survey interpretation: 

Geophys.Prospecting, v. 5,no. l,p. 20-43.

* U. S. GOVERNMENT PRINTING OFFICE : 1966 O - 212-594