Gravity exploration
DATY 21 DATY 2 − DATY 1 Saad and Bishop, 1989
4.6 Density measurements
Sandstone
Dry bulk density (g/cm3)
Fraction of all samples
Granite Basalt
0.7 1.4 2.1 2.8 3.5
FIGURE 4.8 Comparison of frequency distributions of dry bulk densities of granite, basalt, and sandstone samples. Adapted from J o h n s o nandO l h o e f t(1984).
4.5.4 Summary
Several of the factors controlling the density of rocks are illustrated by the histogram of bulk density measurements of granite, basalt, and sandstone compiled byJohnson andOlhoeft(1984) that is reproduced in Figure 4.8. The distribution of the densities of granite is largely restricted to a tight normal distribution around an average value of roughly 2,650 kg/m3. Variations around this central value probably reflect slight differences in the relative proportion of quartz and feldspars and, primarily, the minor propor- tion of mafic minerals. A few lower densities extending from the central peak are probably associated with alter- ation of the feldspars and mafic minerals to less dense min- erals, and perhaps with intergrain voids. In contrast, the histogram for basalt peaks at roughly 2,900 kg/m3with a broader range of values reflecting variations in the mineral content, largely the types of feldspars and mafic miner- als, and even the presence of limited quantities of metallic oxides or sulfides, and, particularly at lower densities, the existence of voids, probably largely gas cavities.
The third histogram in this figure is for sandstone which shows a broad, irregular distribution between 1,800 and 2,600 kg/m3. The broad distribution primarily reflects the variation in the interstitial pore volume, although minor effects may be due to mineral content. Clearly, the tighter the distribution of the measurements, which is indicative of greater homogeneity, the more likely the density of the rock can be estimated correctly from tables or from fewer measurements. Based on the above analysis, the natural density (saturated bulk density) of granite likely will not change significantly from the bulk densities shown in Figure 4.8, but because of water filling of the voids, all the values of the sandstone will increase, as will the lower
values of the basalt extending from the major grouping of measurements.
4.6 Density measurements
In many gravity investigations, rock and sediment densi- ties for planning, reduction, and interpretation of surveys are estimated from tables of densities or extrapolated from tables using knowledge of the geology of the area and the effects of various geological processes on densities.
This is a necessity in many surveys because of lack of access to samples or instrumentation for measurements or because of limitations in time and resources. However, where information on densities is sparse within a survey region, it is desirable to determine the local formation and rock densities. Furthermore, surveys commonly require an accuracy in densities that cannot be achieved from avail- able tabulations. This is particularly true of surveys that involve near-surface materials including unconsolidated sediments, poorly compacted and highly fractured rocks, and weathered materials that are inadequately represented in most compilations. Thus, measuring rock densities in a survey area is highly desirable if not absolutely necessary.
In principle, determining rock density is simple, but in practice these measurements can be complex and subject to sometimes significant errors. Problems arise particu- larly from the heterogeneous nature of rocks and difficul- ties in making accurate measurements on friable samples and those with irregularly distributed, high void space.
Densities are measured in three general ways: (1) labora- tory measurements on samples; (2) gravity measurements;
and (3) measurement of correlative properties. Another method is to calculate densities knowing the mineralog- ical or chemical composition of generic rock types (e.g.
SobolevandBabeyko, 1994 ), but this is rarely used in geophysical exploration because the composition of rocks is seldom known accurately enough. Each of these meth- ods has its relative advantages and disadvantages that must be considered in selecting the appropriate method for a particular survey problem.
Laboratory measurements are the simplest and least expensive when representative samples of the rocks of the area can be collected from the site and taken to the labo- ratory for investigation. Gravity measurements are partic- ularly useful because they providein situvalues of rela- tively large volumes of rocks, but they require specialized instrumentation and surveys either in drill holes or on the Earth’s surface. Correlative measurements, especially seismic velocity and gamma-ray attenuation, can pro- vide more volume-restrictedin situdensity determinations of the subsurface provided that these measurements are
78 Density of Earth materials
available by virtue of other studies or can readily be made in drill holes.
4.6.1 Laboratory measurements
With reasonable care, laboratory measurements of most consolidated rocks of low void space closely approximate in siturock densities (McCulloh, 1965). However, dif- ficulties are encountered in selecting representative sam- ples, obtaining unweathered samples from outcrops, mak- ing measurements on friable, unconsolidated samples, and measuring the density of rocks with high porosity. As a result,in situmeasurements of density should be pre- ferred where these difficulties are anticipated. As this is not always possible, care should be exercised to avoid problems associated with these difficulties. Representative samples need to be acquired in proportion to the volume representation of the variable attributes of the rock units.
Generally, a minimum of 30 samples is desirable where significant heterogeneity is anticipated in the units. Ide- ally, unweathered samples should be collected at appro- priate sites and stripped of any surficial effects. Unconsoli- dated formations require specialized procedures involving weighing in air a pre-set sample volume. In rocks which have significant porosity, generally over a few percent, it is advisable to determine the porosity of the rock inde- pendently and take the measured value of porosity into account in determining thein situdensity.
The measurement of density in the laboratory (Emerson, 1990) involves determination of the mass (weight) and volume of the sample. In low-porosity rocks or if the matrix or grain volume or density is desired, the volume can be determined by the loss of weight of the sample in water using Archimedes’ principle, which states that a mass in water is buoyed up by a force (weight) equal to the volume of the displaced fluid. The bulk density is calculated from
σB= Wa×σf
(Wa−Wf), (4.11)
whereWaandWfare the weights of the sample in air and fluid, respectively, andσfis the density of the fluid. It is advisable to use pure water in making these measurements, and the density of the water should be normalized to a constant temperature.
The total or bulk volume can be determined in porous rocks by sealing the sample from infiltrating water with a thin layer of paraffin or similar material before inserting the sample in water for measurement. In this way the natural density can be calculated. Care must be exercised to avoid air bubbles on samples by using warm water, agitating the
samples, or putting an additive in the water to decrease its viscosity. Water can be replaced with other fluids if the rocks contain water-soluble minerals, but account must be taken of the density of the fluid. Typically, samples of 200 to 1,000 g are used, but larger samples are subject to less error and may be more representative of the rock forma- tion. Samples that have been allowed to dry out before measurement need to have water drawn into their voids by vacuum or by soaking the samples for at least 24 hours to achieve water saturation for determining either grain or natural density using appropriate procedures. Simple soaking, however, will be ineffective when dealing with micropores which have low permeabilities.
A wide variety of methods have been developed for measuring density and pore volume using two of either void volume, bulk volume, or grain density, depending on the nature and size of the samples and the accuracy desired. They are discussed and evaluated byJohnson andOlhoeft(1984).
Commonly, density measurements have to be made on previously obtained rock samples and cores that have been allowed to dry out. The saturated bulk density or natural density, σn, can be obtained by resaturating the sample and performing volume and mass measurements or by determining the dry bulk density,σB, and calculating the natural density from this measurement. The latter requires estimation of the grain density,σg, and the density of the fluid occupying the void volume,σf. The natural density is calculated from
σn=σB
1− σf
σg
+σf. (4.12)
If the dried-out samples have undergone shrinkage, the calculated densities will be decreased by a few percent.
It may be useful to make measurements on cuttings from drill holes or other small, irregularly shaped speci- mens. The density of these rock fragments can be deter- mined by using a small glass flask of precisely determined volume, or pycnometer, which has a glass stopper extend- ing into a fine capillary tube that provides an overflow for excess water so that the flask is filled with a constant vol- ume of water. The density of the specimen is the quotient of the product the mass of the specimen in air and the den- sity of the water in the pycnometer divided by the sum of the mass of the specimen and the pycnometer filled with water minus the mass of the pycnometer. Gas pycnome- try, in which the volume of specimens is determined by the gas displacement method, is widely used to determine the density of small, irregular specimens. The sample is sealed in a chamber of known volume, then an inert gas such as helium is admitted into the chamber, and the gas
4.6 Density measurements 79 expanded into a connecting chamber of precise volume.
The measured pressure change upon expansion into the secondary chamber is proportional to the volume of the specimen. This volume together with the mass of the spec- imen can be used to calculate the bulk density. Detailed protocols for conducting density measurements of small sample fragments and soils are given in publications of the American Society for Testing Materials.
4.6.2 Gravity measurements
Gravity measurements are directly related to the mass of the adjacent materials, and thus can be used with spe- cialized techniques to determine the in situ density of subsurface materials. These gravity observations can be made over the surface to determine the density of the material included over the elevation range of the measure- ments, or in mines and drill holes to measure the density of the rock formations between vertically separated obser- vations. These methods have the advantage of determining density under natural conditions and over a large volume.
They are used not only for determining density for use in planning, analyzing, and interpreting gravity data, but increasingly in remotely sensing density, and thus investi- gating numerous significant characteristics of the nearby Earth.
Surface measurements
The density of surface materials which often are of interest to near-surface studies can be measured by making a series of gravity observations over a topographic feature using the so-called Nettleton density profile method (Nettle- ton, 1939). The density of the material included within the topography can be determined by finding the density that will produce the minimum correlation between the Bouguer gravity anomaly and the topography. In deter- mining the Bouguer gravity anomaly at an observation site the gravitational attraction of the mass of the Earth between the datum of the survey and the site is calcu- lated. If the correct density has been used to determine the gravitational attraction, the observed effect and thus the relationship between the anomaly and the topography will be cancelled in the anomaly calculation. As a result the density of the surface material can be estimated from the density used in the mass calculation which leads to the min- imum correlation between the Bouguer gravity anomaly and the topographic relief. The method is normally imple- mented by taking a series of closely spaced observations over an erosional feature that is not correlated with sub- surface anomaly sources and primarily consists of a single geologic formation (Parasnis, 1952). Gravity anomalies
Distance 2,600 2,400 2,200 1,800
1,600 kg/m
3
Bouguer gravity anomalyElevation
FIGURE 4.9 Illustration of the use of a profile of gravity observations over a topographic feature to determine the included density by minimizing the correlation between the elevation of the stations and the gravity anomaly calculated assuming a range of densities. The density of the material making up the hill in this illustration is2,200 kg/m3.
are calculated taking into account spatial and elevation effects using a variety of densities to determine the effect of the mass between the lowest observation level and the elevation of the stations. The density which shows mini- mum correlation between the calculated gravity anomaly and the topography is the density of the surface material making up the topography.
This method is illustrated in Figure 4.9, where 2,200 kg/m3is shown to be the density of the surface mate- rial by the lack of correlation between the anomaly, cal- culated using this density in the mass correction, and the topography. Anomalies calculated with densities higher than 2,200 kg/m3have an inverse relationship to the topog- raphy because they remove too much mass from the observed gravity, and lower densities produce the con- verse. The relationships between too great or too low a density are reversed for a topographic depression. Several stations are placed outside of the topographic feature in order to establish the gradient of the gravity anomaly upon which the local topographic anomaly is superimposed.
The required elevation range of the feature, E in meters, can be determined by considering the accuracy of the gravity anomaly,gin milligal, and the desired accu- racy of the density,σ in kg/m3, using the relationship E=(24×103)g
σ. (4.13)
Thus, if the density needs to be determined to an accuracy of 10 kg/m3 and the gravity anomaly has an accuracy of 0.02 mGal, the elevation range must be 48 m. By the very
80 Density of Earth materials
nature of the observations over topographic features, the gravitational effect of the terrain can produce significant errors in the results, so it is important to apply terrain corrections to the observed data.
Numerous variations on this graphical method of determining densities have been devised using analyti- cal methods based on least-squares techniques that mini- mize the correlation between gravity anomaly and topog- raphy. These methods as applied to either gravity pro- files or maps assume that the deviation of the gravity anomaly due to topographic effects can be treated as ran- dom errors (e.g.Legge, 1944;Parasnis, 1952;Grant andElsaharty, 1962). The method can be used to deter- mine variations of surface density over a survey region using a moving-window approach to minimize the cor- relation between topography and gravity on a region-by- region basis.Siegert(1942) has suggested an alterna- tive method to minimize the subjectivity of the density determination, referred to as the triplet method. It is based on estimating the elevation correction factor, and thus the density of the surface material, from three successive grav- ity observations along a survey line. The difference (hi) between the elevation of the intermediate station and the weighted mean of the elevations of the adjacent stations is compared with the difference (gi) between the observed gravity reading and the weighted mean of those of the adja- cent stations to determine the correction factor. Weighting is normally inversely proportional to the distance between the stations. The correction factor is given by
k= − 2
ihigi 2
ihi , (4.14)
where the summation is over the triplets in the gravity survey line. Siegert also suggested a methodology for esti- mating the error in the determination of the correction factor.
Another method to determine the density of the topog- raphy from gravity measurements takes advantage of the fact that, in general, topography is scale-independent or self-similar, and thus can be studied using fractal meth- ods (e.g.Turcotte, 1997). Although various techniques have been used for this (e.g.ThorarinssonandMag- nussson, 1990;Chapin, 1996;HisarliandOrbay, 2002), the basic approach is to determine the density that reduces the fractal nature of the Bouguer gravity anomaly, that is the surface density which has the minimum relation- ship to topography.Chapin(1996) achieves this by deter- mining the fractal dimension corresponding to the straight line slopes in log–log plots of the radially averaged power spectra of the Bouguer gravity anomaly calculated over a range of densities. Removal of the linear effect, caused
by the scale-dependence term of the Bouguer correction, from a plot of fractal dimensions versus density values is used to identify the minimal fractal dimension, corre- sponding to the density which has the least relationship to topography.
Underground measurements
Underground gravity measurements also are used to deter- mine the density between two co-located but vertically dis- placed observations. Originally, these measurements were made with surface gravimeters with observations on the surface and in mines and tunnels (e.g.Algermissen, 1961;Hammer, 1950;McCulloh, 1965). Studies of this nature continue (e.g.Capuanoet al., 1998), but with the advent of drillhole gravimeters of sufficient stability and precision, measurements are now routinely made in drill holes (e.g.McCulloh, 1966;LaFehr, 1983).
The standard method assumes that the rock layers between observations are horizontal and of constant den- sity,σL, and that no local anomalies are present that will disturb the normal vertical gradient of gravity, (g)/(h), which is measured over a vertical rangeh. The observed gravity difference,g, between the two stations must be corrected for temporal variations due to instrumental drift and natural changes in gravity in the observations, and the effect of surface terrain features. The difference between the two vertically separated observations is the vertical gradient of gravity due to the mass of the Earth minus twice the effect of the mass of the plate of material between the observations; once for the increased gravity at the upper observation due to the mass of the plate between the two observations, and again at the lower site for the upward attraction of the slab. The density, σL in kg/m3, of the material between the two vertically separated stations is σL=
3.6816−128.5761
g−T
h ×103, (4.15) where T is the change in the surface terrain effect between the two observations.
In many petroleum applications, the terrain effect is negligible, and thus disregarded because the depth of the measurements below the surface is large in comparison to the vertical interval over which the measurements are made. However, terrain effects can be important depending on the local terrain where the observations are relatively shallow (<1 km). It should be noted that terrain effects for surface stations are always added to the observed gravity, but may be either added or subtracted for underground measurements depending on the variation of the surface topography from the elevation of the surface vertically above the measurements.
4.6 Density measurements 81
50
50 50
30
25 148.5 247.5
100 495
10 75
75 90
90
Radius of investigation (dimensions in ft)
Well bore
FIGURE 4.10 Percentage gravity effect as a function of distance of an infinitely extending slab on the vertical gravity gradient measured along a drill hole through the slab. Adapted fromH e a r s t(1977b), from a figure originally byM c C u l l o h(1966).
In Equation 4.15, the assumption is made that the verti- cal gradient of gravity is 0.3086 mGal/m. The accuracy of this gradient can be improved by considering second-order effects of elevation and the latitude of the observations.
However, the major variations from the assumed normal gradient of gravity are local anomalous effects unrelated to the density of the rocks between the two vertically sep- arated stations. The presence of these anomalous effects can be determined by considering the local variations in the gravity anomalies surrounding the drill hole. The vertical gradient can be calculated from these local observations and projected to the elevation of the drillhole observa- tions. Alternatively, measurements can be directly made of the vertical gradient of gravity with measurements on the surface and in a tower placed over the drill hole.
Drillhole gravity measurements are made at specified depths in drill holes with specialized instruments that employ a modified zero-length spring sensor (Chapter 5).
The standard instrument used for this purpose can oper- ate in holes that deviate up to 14◦ from the vertical and have diameters exceeding 10 cm. They are operative in environments that do not exceed a temperature of 260◦C.
Measurement precisions of 3μGal are approached where multiple individual measurements are made. A slim hole gravimeter is also available that can be used at depths of less than 3 km in holes that deviate from the vertical up to 60◦and that have diameters over about 5.75 cm. Great care is also used to achieve precision in the depth measure- ments and to locate observations at formation boundaries identified by other logging techniques.
The density calculated in Equation 4.15 is given numer- ous names in the geophysical literature to identify it as a calculated density from drillhole gravity observations.
The most widely used term is apparent density (LaFehr, 1983) which recognizes that the calculation is based on the assumption that the slab of rock between the observa- tions is horizontal, infinite, and of constant thickness and density. This density is an approximation to the saturated bulk density of the rock material. The calculation of den- sity from gravity measurements is complicated in regions of dipping formations (e.g.Hearst, 1977a;Brownand Lautzenhiser, 1982). However, as an approximation, bed dips of less than 7◦ from the horizontal can be ana- lyzed with Equation 4.15.
A consideration in drillhole gravity studies is the sen- sitivity of the measurements to the effects of adjacent for- mations at distances which are considerably greater than in typical (≤15 cm) formation density logging instrumen- tation. This is one of the significant advantages of the method, but it does have very definite limits imposed by the magnitude of the mass differentials, the distance from the observations, and the accuracy of the gravity and depth measurements. An illustration first shown in the context of drillhole gravimetry byMcCulloh(1966) displays the percentage of the gravimetric effect of an infinitely extend- ing slab (Figure 4.10). This figure shows that approxi- mately 90% of the gravitational effect is derived from the mass of the rock within approximately 5 times the vertical distancehbetween the stations. Unfortunately, this fig- ure has been erroneously interpreted to suggest that with increasing distance between observations, the range of the density measurements can be increased. This is not the case, rather the illustration simply shows that for a slab of homogeneous density, the outer part of the slab has far less effect than the inner part. Several articles provide further details on the effective range of investigation of drillhole