The general approach to the interpretation of geophysi- cal measurements was discussed in Section 1.5.4. In this chapter, the generalized interpretation approach is focused specifically on the gravity method. Gravity anomaly inter- pretation covers many techniques depending on the qual- ity of the data and the objectives of the analysis. It ranges from qualitative reviews of the data in various presentation forms to highly quantitative modeling.
The stages in the interpretation of gravity anomaly data have been discussed by a number of authors with varying procedures being described (e.g.Simpson and Jachens, 1989;Chapin, 1998). Differences in the pro- cedures reflect personal experience, the available data, computational facilities and software, and the objectives of the interpretation. However, the common view is to tune the interpretation techniques to the quality and coverage of the available data, and to integrate the interpretation with all pertinent subsurface information. Most importantly it
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178 Gravity anomaly interpretation
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FIGURE 7.1 Examples illustrating the equivalence of the Bouguer gravity anomaly derived from a variety of sources include octagonal and diamond distributions of mass at depth (gray shaded) that spread out with decreasing depth (unshaded). The depth and horizantal distancex are in arbitrary units. Adapted fromJ o h n s o nandv a n K l i n k e n(1979).
needs to incorporate known geological information from the surface and subsurface. This must be done as early as possible and not left to the final stages of interpretation.
The use of auxiliary geophysical and geological data is important in defining subsurface structure and formation lithologies. This is especially critical in estimating the densities of the formations. The amplitude of all gravity anomalies and geologically derived gravity noise which may perturb interpretations is directly related to the con- trast in densities. Wherever possible, these densities should be determined directly from measurements made on sam- ples obtained in the region or fromin situobservations using methodologies described in Section 4.3.5. However, the lack of samples orin situmeasurements may require evaluation of local densities on the basis of general tables, modified by consideration of local factors and lithological attributes as discussed in Section 4.3.6.
7.2.1 Ambiguity in gravity interpretation
An important reason for using auxiliary geophysical and geological data is to decrease the ambiguity of grav- ity interpretation (Skeels, 1947). Figure 7.1 illustrates a number of different subsurface bodies that all pro- duce equivalent gravity anomalies (Johnson and van Klinken, 1979). Non-uniqueness is an overriding con- cern in all gravity interpretation, although ambiguity is present to varying degrees in all geophysical interpreta- tions. Of course, the availability of appropriate constraints can limit these ambiguities.
Ambiguity in gravity analysis arises because of limita- tions in data coverage and quality, and the inherent nature of gravity fields. Limitations of data sampling may cause aliasing where station density is insufficient to provide a
minimum of two station intervals or three observations within each desired anomaly wavelength. Errors of the observation, anomaly calculation, and residual anomaly isolation procedures will distort the anomaly. Although these sources of ambiguity can be controlled to a signif- icant degree, they cannot be completely eliminated, pri- marily as a result of difficulties in isolating the desired residual anomaly.
The inherent ambiguity in gravity interpretation, even when the data are reliable, is a more fundamental problem.
This cannot be eliminated without auxiliary information on the sources of the anomalies. The inherent ambiguity of potential fields, such as gravity anomalies, is discussed in Sections 3.4 and 3.6 in dealing with Laplace’s and Pois- son’s equations, as well as in Section 4.4.2 where it was shown that any inverse problem in practice leads to non- unique solutions due to errors in the observations and the assumed forward problem. Figure 7.2, fromHutchin- son et al.(1983), gives a further example of the inher- ent ambiguity. This figure shows the gravity effects of three conceptual crustal models constrained by deep seis- mic studies that compare favorably with the Appalachian Mountain paired gravity anomaly found in profiles from New Jersey to Georgia. Even though all three models match the seismic refraction and gravity data, they are entirely different because there are not enough constraints available to distinguish geologically between them.
7.2.2 Two- versus three-dimensional interpretation
A decision that needs to be made early in the interpretation of gravity data is whether the interpretation will be made using 2D or 3D approaches. Although these are seldom
7.2 Introduction 179
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FIGURE 7.2 Ambiguity of the gravity anomaly interpretation illustrated by three different subsurface models that are consistent with seismic constraints and the observed gravity anomaly profiles. Densitiesσare given ing/cm3. Adapted fromH u t c h i n s o net al.(1983).
mutually exclusive, in most interpretations the emphasis is either on the interpretation of profiles or maps.
Profile interpretation normally is performed on the principal profile that is positioned through the central max- imum or minimum amplitude of the anomaly and perpen- dicular to the anomaly contours. This method is commonly used for two reasons. First, there may already be a seismic or geologic cross-section over the same location. Second, generally speaking, a single profile interpretation is rela- tively fast and efficient to perform. Profile interpretation is commonly described as two-dimensional (2D), based on the assumption that the geological cross-section extends to infinity without change into or out of the profile. When the strike length of the source is finite, two-and-a-half dimen- sional (2.5D) interpretations are invoked where the strike lengths from the profile to each end of the source are the same. When the ends of the source are at unequal distances
from the profile, or the source strikes at an angle differ- ent from perpendicular to the profile, the interpretations are sometimes called two-and-three-quarters dimensional (2.75D).
Map interpretation assumes a finite extent of sources within the boundaries of the map. Gravity data are acquired along multiple traverses directed perpendicular to the anticipated strike direction of the sources of interest, or more commonly on a more or less regular grid pattern with one of the grid directions perpendicular to the pre- vailing geological strike of the region. The data of the grid or series of traverses are combined into a contour map and subjected to an evaluation of the source of the anomalies.
Circular or elliptical anomalies indicate sources of limited strike length (7.3(a)) which need to be analyzed on a 3D or at a minimum of a 2.5D or 2.75D basis.
In contrast, elongate anomalies (Figure 7.3(b)) may be
180 Gravity anomaly interpretation
(a)
Subsurface fault
Subsurface fault (b)
(c)
FIGURE 7.3 Gravity anomaly contour maps. (a) Roughly equidimensional anomalies requiring analysis by 3D interpretational methods. (b) Linear gravity anomaly that can be analyzed by 2D methods. The right-lateral offset of the anomaly shows the position of a subsurface fault. (c) Complex anomaly pattern with different gradients indicating high-angle subsurface faults which offset the source of the anomaly. An alternative interpretation is that the variable gradients are due to a source which has dipping margins.
considered on a 2D or 2.5D basis.Nettleton(1940) showed that the error in gravity calculations assuming an infinite strike length for the source (i.e. 2D source) will be less than 10% where the strike length of the source is a minimum of four times the depth to the center of the source on either side of the profile. This is a commonly employed approximation to determine whether 2D analy- sis can be used. However, Nettleton’s evaluation is based on the gravity effect of a horizontal rod whose radius is small in comparison with the depth to its center. As the source width increases, the required strike length needed to maintain two-dimensionality increases, but very slowly.
The length must increase significantly to maintain two- dimensionality as the depth extent or depth to the top of the source increases. The maximum horizontal dimensions of the source can be approximated to first order from the horizontal distance between the inflection points of the anomaly gradients.
Figure 7.3 shows schematic examples of gravity anomaly contour maps illustrating the patterns of anoma-
lies that are considered in making decisions regarding 2D and 3D analysis. Figure 7.3(a) illustrates the near-equal dimensions of circular to elliptically shaped anomalies where the low gradients relative to the dimensions of the sources suggest deep depths to the sources. These anoma- lies are best analyzed by 3D methodologies.
The elongate anomalies of Figure 7.3(b) can be ana- lyzed by 2D techniques providing that the ends of the anomalies and the segment of the anomalies near the flex- ure in the pattern are avoided. The flexure in the anomaly can be interpreted as fault offset of the linear source.
Figure 7.3(c) shows the complication in the anomaly pattern where offsets along vertical faults have disturbed the source of the anomaly. Faults may either cause a flexure in the anomaly pattern as shown in Figure 7.3(b) or marked changes in gradients as in Figure 7.3(c). The anomaly asso- ciated with the fault which parallels the long dimension of the source can be readily incorporated into the profile interpretation. However, profiles drawn across the elongate anomaly in the vicinity of the cross fault will be disturbed, preventing a 2D interpretation approach. This illustration shows the importance of evaluating the contour map pat- tern of anomalies before deciding on the interpretation methodology and selecting the profiles for 2D analysis.
Where the nature of the anomaly pattern suggests 3D interpretation, sources of limited horizontal extent must be considered, using either simple idealized source geome- tries or general source geometries with complex, irreg- ularly shaped bodies. The latter may be more realistic, but commonly is unjustified considering the effort that is needed to analyze complex sources. Often 2.75D analysis can be used to approximate a 3D body as a starting point in the interpretation.
The 2D, or 2.5D, or 2.75D interpretation techniques are commonly preferred over 3D methods because they are faster, simpler to implement, and provide greater detail than all but the most exhaustive 3D analyses. As long as the observation traverses are effectively perpendicular within a few tens of degrees to the strike of the anomaly pattern, it is advantageous to use the actual anomaly values in constructing the profiles for analysis. Profiles extracted for analysis from contour maps so as to achieve an orthogonal relationship to the anomaly strike direction are always high-cut filtered as a result of the gridding and contouring process. The effect may be detrimental to the analysis depending on the nature of the data.
7.2.3 The interpretation process
The above discussion makes it clear that there is no standard template for gravity interpretation. There are
7.2 Introduction 181
Answer questions posed in study
Transform into geological model Establish physical
model Forward and/or inverse modeling
Develop constrained conceptual model
Apply simplified inversion techniques
Residual anomalies Perform
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Identify and locate residual
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Survey objectives Develop geologic
conceptual model Assemble data
Gravity survey data Existing gravity data
Geological information Regional/local Surface/subsurface
FIGURE 7.4 Flow chart showing the components involved in the interpretation of gravity data and their inter-relationships.
too many variables that enter into the process. Evalu- ation of these variables is a matter of knowledge and experience, which vary among interpreters. Nonethe- less, there are certain common steps (Figure 7.4) that should be considered in the interpretation process after the gravity data are assembled and conceptual forward models of the anomaly sources are developed or inver- sion is performed on the basis of the objectives of the survey and the auxiliary surface and subsurface information.
For example, after the survey data have been reduced to anomaly values and the ancillary data are assembled, enhancement techniques may be applied to the gravity anomaly data if the residual anomalies are not readily apparent in the anomaly data. Enhancement techniques
(Section 6.5.3) may distort the anomaly pattern by empha- sizing certain characteristics of the sought-after anomalies.
As a result, these techniques help to identify and locate residual anomalies.
In qualitative interpretation, the process terminates with the evaluation of the residual gravity anomaly and the derived or enhanced anomalies, either in map or pro- file form. However, it is very desirable for map views to supplement profile analyses.
In quantitative interpretation, on the other hand, iso- lation techniques are applied to gravity anomaly data to help extract anomalies of interest in the survey from other anomalies of either shorter or longer wavelength. This stage is necessary because anomalies located by enhance- ment techniques commonly may be distorted to a degree
182 Gravity anomaly interpretation
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FIGURE 7.5 (a) Gravity anomalies of two gray-shaded sources of the same volume and density contrast, and thus mass differential, and central source depth. The two anomalies, although of quite different amplitude and shape, have equivalent total integrated anomaly energy.
(b) Doubling the density contrast of one of the sources shown in (a) doubles the amplitude of the anomaly without changing its shape.
(c) Doubling the volume of one of the sources shown in (a) changes the amplitude and shape of the anomaly.