matical treatment of analytical methods of processing data by filtering to remove or emphasize particular wavelength components of potential fields and describes the funda- mentals of the processing methodologies for the isolation and enhancement of particular anomalies. In this section, these methods and others are explained in terms of their potential usefulness to gravity anomaly analysis.
6.5.1 Residual and regional gravity anomalies Corrected observed gravity data are presented in either map or profile form for analysis and interpretation depend- ing on the objectives and coverage of the survey and the attributes of the observed anomalies. The scales and con- tour intervals of these presentations are a function of the magnitude and areal size of the significant anomalies of interest in the study, the accuracy of the data, and the range of the anomaly values. These data are the summation of all anomaly sources regardless of their depth or distance from the observation point and any errors in the processing of the data. The errors are assumed to be negligible in com- parison to the magnitude of the anomalies of interest. As a result of the inverse distance function of gravity anomalies, which describes the exponential attenuation of anomalies with increasing distance, the gravity anomaly is domi- nated by the effect of nearby sources and large-volume geological features at depth. The gravitational effects of other horizontal variations contribute less significantly to the overall observations.
The cumulative effect of gravity anomalies is illus- trated in Figure 6.18. The schematic gravity effect of four geological sources of excess mass (density) are portrayed over the simplified geological cross-section showing the anomaly sources. Sources 1 and 2 are equivalent sources located near to the surface which are the anomalies of interest in the survey. These sources produce anomalies that are relatively high amplitude and sharp with resulting high anomaly gradients. Source 3 is equivalent to sources 1 and 2, but is barely discernible in the profile because it is buried at a greater depth, and thus is lower in ampli- tude, and the anomaly is broader with low gradients. This anomaly source is not a viable target for a gravity survey.
Source 4 is deep, as is source 3, but its volume is large, and
158 Gravity data processing
Depth Δg
3 1
1 2
3
4 4
2
FIGURE 6.18 Schematic gravity anomaly profile over four positive density differential sources and their cumulative effect. This profile illustrates the concept of regional and residual anomalies, and the need for isolation and enhancement of residual gravity anomalies in order to identify and analyze them. The profiles are identified with the number of the anomalous source.
thus produces a large-amplitude anomaly. As a result, it is readily observed despite the low gradient of the anomaly.
This figure is independent of scale in terms of both areal size and amplitude of anomalies. That is, the superposition of anomalies and their cumulative effect is valid regardless of the size and depth of the anomaly sources.
In most gravity surveys, especially those for explo- ration purposes, the anomalies of interest are derived from relatively shallow sources, such as sources 1 and 2 in Fig- ure 6.18. These are called the residual anomalies. The definition of residual anomaly is not very precise (e.g.
Nettleton, 1954;Skeels, 1967), but generally it is defined as the anomaly derived from a source of interest.
In exploration surveys, the residual anomaly is the one arising from, for example, a cave, ore body, or buried anti- cline that is the target of the survey. The anomaly derived from source 4 is called the regional anomaly, which is defined as the anomaly or anomaly gradient that is are- ally larger than the anomaly of interest, that is the residual anomaly. The amplitude is not necessarily a defining qual- ity of the regional anomaly, although the obvious regional gravity anomaly is usually of greater amplitude than the residual anomaly. In Figure 6.18 the anomaly of source 3 is a regional anomaly or part of the sum of the regional anomalies, but is insignificant because of its low ampli- tude.
To illustrate the scale independence of the figure and the residual–regional concept, let source 4 be the target
of interest in the survey, for example a dense mass in the bedrock. In this case the anomaly from source 4 would be the residual anomaly, and deeper sources of large volume would cause the regional anomaly of the survey. Thus, the specification of a residual anomaly depends on the survey objectives. A specific anomaly may be the residual in one survey and the regional in still another.
In the case where the target of the survey is source 4, the anomalies of sources 1 and 2 constitute areally smaller variations which are considered noise in the survey. Noise can be described as variations in gravity smaller in size than the residual anomaly. Noise may originate from shal- low geological features which are restricted in horizontal dimensions, or from errors in the surveying and processing of the data. However, shallow features and errors also may produce anomalies of equivalent or greater size than the residual anomaly.
The gravity anomaly (A) resulting from the reduction of observed gravity data thus consists of three compo- nents; the residual anomaly (Ar) which is the target of the survey, the regional anomaly (AR) which is spatially larger than the residual anomaly, and the noise (N) which is spa- tially smaller than the residual. That is,
A=Ar+AR+N . (6.57)
Generally, the noise,N, is considered to be negligible and disregarded, in which case the anomaly of interest, the residual gravity anomaly, is simply
Ar=A−AR. (6.58)
In actual practice, the subtraction is directly performed graphically or arithmetically, or indirectly performed by emphasizing the residual anomaly at the expense of the regional anomaly.
Elimination of the regional gravity anomaly from the observed anomaly is a critical step in the identification and analysis of gravity anomalies. Improper definition ofAR
can cause errors in the attributes of the residual anomaly, its amplitude, gradients, trend, etc. Interpretation, both qual- itative and quantitative, is particularly sensitive to errors in amplitudes and gradients. However, the definition pro- cess can be problematic and especially difficult where the character of the regional anomaly approximates that of the residual anomaly. This is illustrated diagrammatically in Figure 6.19 in which the fields of the amplitude and maximum gradient of the regional and residual gravity anomalies, as well as the noise, are mapped as a function of the areal dimension of the anomaly.
In the cases illustrated in Figure 6.19(a) and (c), the characteristics of the residual anomalyArare well sepa- rated from the noise and regional gravity anomaly. In these
6.5 Anomaly isolation and enhancement 159
(a)
Anomaly amplitude
Areal dimension of anomaly
(b)
Anomaly amplitude
Areal dimension of anomaly (c)
Anomaly amplitude
Areal dimension of anomaly
(d)
Anomaly amplitude
Areal dimension of anomaly N
N
N N Ar
Ar Ar
AR
AR
AR Ar AR
FIGURE 6.19 Diagrammatic illustration of the fields of residual gravity anomaliesAr, regional gravity anomaliesAR, and gravity anomaly noiseNplotted as functions of their amplitudes and spatial dimensions. In the cases mapped in panels (a) and (c), the residual anomaly is likely to be easily distinguished from the noise and regional. But in the cases of panels (b) and (d), it is more difficult to identify the residual anomaly because the anomaly amplitudes and spatial dimensions overlap each other.
cases, the separation of the residual anomaly is likely to be accomplished rather accurately, but in the cases illustrated in Figure 6.19(b) and (d), the fields overlap, making the process more difficult.
In any event, there is no unique solution to identify- ing the residual anomaly from the observed anomaly. The process is indeterminate because two parameters must be solved from a single equation, Equation 6.58. Although there are an indefinite number of solutions to this equation, in practice the bounding characteristics of regional anoma- lies and geologic considerations combined with experience and judgment of the analyst limit the number of effective solutions.
The problem of separating the regional gravity anomaly from the residual anomaly is not only a matter of iso- lating the regional anomaly, but also of obtaining suf- ficient survey coverage to identify it. By definition the regional anomaly is broader, more extensive than the resid- ual anomaly. As a result, gravity surveys must be extended beyond the immediate area of interest to delineate the regional gravity anomaly. This is clearly illustrated in Figure 6.18. The residual gravity anomaly could not be
determined without observations extending beyond the location of these anomalies. Extending the surveys beyond the area of immediate interest increases the cost of sur- veys and is often made difficult because of surface physi- cal features and access problems. In some circumstances, observations from regional gravity data sets may be used to supplement survey data, and thus minimize the areal extent of the survey. A useful rule of thumb is to have spa- tial control in excess of twice the anticipated size of the objective anomalies. For example, if residual anomalies of exploration interest have a 1 kilometer wavelength, it would be appropriate to obtain survey data that extends to 2 kilometers or more.
Numerous schemes have been developed for elimi- nating regional anomalies (e.g.Zurflueh, 1967; Ku et al., 1971;Meyer, 1974;NaiduandMathew, 1998).
An aura of mystery has developed around these methods because of the indeterminate nature of the problem and lack of understanding of the advantages and limitations of the methods. In addition, industry rumors pertaining to secret or patented techniques are not uncommon. As a result, the residual anomalies derived from the residual–
regional separation process are sometimes viewed with skepticism by the end user of the gravity analysis.
To minimize this problem, it is important that each residual anomaly map or profile be clearly annotated with the attributes of the method used to determine the residual anomaly. In addition, the analyst should be careful to con- sider not only the residual anomaly, but also the regional anomaly and its viability in view of the geology of the site. One of the significant advantages of the current ease in performing calculations and presenting the results on maps and profiles is that a number of methods of residual separation can be tested and compared to obtain optimum results and a range of possible solutions.
6.5.2 Fundamental principles
There are two broad approaches to the residual–regional anomaly separation problem that can be classified as either isolation or enhancement techniques (Hinze, 1990). Iso- lation techniques attempt to eliminate from the observed anomaly field all anomalies that do not have a certain set of specified characteristics as defined by the objective of the survey. Thus, the anomaly that is isolated, the residual anomaly, is the gravity expression of the significant source.
The fundamental premise of the isolation approach is that the geologically significant anomaly is minimally modi- fied by the regional gravity field and by the process. As a result, the residual anomaly is amenable to quantitative analysis, inversion and modeling.
160 Gravity data processing
Log (A)
Anomaly (mGal)Normalized amplitude (A)
Frequency (cycles/km) Frequency (cycles/km) Observation surface
0
0 10 20 30 40 50 60 70 0 10 20 30 40 50 60
10 20 30 40 50 60 70
km 80
–8 –4 0 4 8
90 100 120 140 150
FIGURE 6.20 Gravity anomaly in milligals and frequency spectra of a prism source with dimensions in kilometers. The source of the gravity anomaly is a10×10 kmvertical prism that is located at a depth of1 kmbeneath the observation surface and extends vertically for50 km.
Enhancement techniques, in contrast, are a broad group of methods which accentuate a particular characteristic or group of attributes that is definitive of anomalies that have significance to the objective of the analysis. In the process of enhancing these characteristics, the anoma- lies are accentuated to increase their perceptibility. As a result, the anomalies are distorted and may no longer be generally useful for quantitative analysis or inversion.
Enhanced anomaly maps and profiles are widely used in qualitative visual inspection analysis and interpretation, although they do have some specialized uses in quantitative analysis.
The residual–regional separation process is compara- ble to the use of filters to pass/reject only the desired anomaly frequencies (or wavenumbers or their inverse, wavelengths) as described in Appendix A.5. The ideal residual–regional separation method will pass only those anomalies that are significant to the investigation without distortion and reject all other components of the observed anomaly, both larger and smaller. Properly designed meth- ods have very useful filtering characteristics, but the cut- offs of these filters usually are not sharp, and they can lead to both amplitude and phase distortion.
This problem is complicated by the wide spectrum of wavenumbers that may be present in a gravity anomaly, as illustrated for the anomaly derived from a prism source in Figure 6.20. In filtering, that is in residual–regional separation, it is impossible to retain the entire spectrum of the residual anomaly without also passing components of the regional anomaly through the filter. As a result, the emphasis in the process is to minimize the distortion of the anomaly associated with a target source.
Filtering of gravity anomalies can be on the basis of the amplitude, spatial dimensions, sharpness (gradients), and directional characteristics of the anomaly. All of these attributes are useful for interpretation, but as the character- istics of residual anomalies become similar to the regional anomaly or noise, they become increasingly difficult to separate. Such is the case in situations illustrated by the plotted anomaly attributes in Figure 6.19(b) and (d). In these and similar cases, mathematical filters can be help- ful for mapping residual anomalies based on one or more of the anomaly characteristics.
6.5.3 Isolation and enhancement methods As described in Appendix A.5, numerous methods of vary- ing complexity have been used to isolate and enhance gravity methods for interpretation. They are referenced in a variety of geophysical journals and books (e.g.Gupta and Ramani, 1980; Roach et al., 1993; Blakely, 1995;NaiduandMathew, 1998;HearstandMor- ris, 2001;Nabighian et al., 2005a). Most are briefly described here in the context of their use in dealing with gravity anomalies. Some of the methods, particularly those that are of a more subjective nature, have been largely superseded by more objective analytical techniques that depend heavily upon the ready availability of massive com- puting power, like the spectral techniques. However, more subjective methods are also included because occasionally they have a role in gravity processing. Numerous subjec- tive methods are documented and many gravity surveys have been interpreted based on these methods. Thus, it is advantageous to understand them in comparison with other
6.5 Anomaly isolation and enhancement 161 more current methods of anomaly isolation and enhance-
ment.
Geological methods
One of the more successful methods of isolating gravity anomalies is the elimination of the gravity effects of known or hypothesized geological sources in the calculation of the geological gravity anomalies as described previously.
The isostatic residual gravity anomaly is only one of these anomalies that are widely used in gravity interpretation.
It seeks to eliminate upper mantle sources of anomalies by removing those related to supporting regional topo- graphic changes. The isostatic residuals are essentially derived by subtracting a 3D mathematical model of the crust based on topography. On a much smaller scale, a similar approach can be used to remove the gravitational effects of, for example, plutons or salt domes that are known from supplemental geologic and geophysical stud- ies so as to isolate residual gravity anomalies associated with much smaller features or more subtle sources. In con- trast to automated, numerical methods of residual–regional separation which are relatively rapid, geological methods can be time-consuming. Nonetheless, it is advantageous to eliminate all known sources of gravity anomalies from an observed data set prior to interpretation. For exam- ple,Roach et al.(1993) have compared the geological (or forward modeling in their nomenclature) method in isolating residual anomalies of Tasmania, Australia with those of trend surface, upward continuation, and spectral filtering. After removal of known or hypothesized gravity effects due to the differences in the oceanic and continen- tal crust, the depth to the base of the crust, and oceanic water surrounding the island, they find that the geological method provides a superior residual gravity anomaly for quantitative analysis.
A specialized form of this method is the gravity stripping method (Hammer, 1963). In this method the gravitational effect of near-surface geologic features are determined by computing their gravity response from information obtained, for example, from shallow drill holes. The method is illustrated in Figure 6.21, where the gravity effect of a geological cross-section as deter- mined by drill holes and geologic inference is calculated to a depth datum which marks the lower limit of the infor- mation. The sum of the gravity response of the known geology, which in effect is a part of the regional anomaly is shown as the total correction in the figure. The gravity effects, as explained by Hammer, commonly are calculated assuming the geology specified in the drill holes can be approximated by horizontal slabs. This greatly simplifies the calculation procedure, but more complicated shapes
involving either two or three dimensional sources can be readily calculated as well. The observed gravity anomaly minus the total correction for the known geology is the geologically corrected anomaly which can be used directly as the residual gravity for interpretation or can be sub- ject to further residual–regional separation procedures if required.
This method assumes there are many constraints to the understanding of subsurface geology. If any of these assumptions are incorrect, they can severely distort the results in a way that is unpredictable and confusing. How- ever, if the subsurface is understood at least to some degree, then it can produce highly desirable results that are essen- tially the unknown aspects of the subsurface.
Graphical methods
As described in Appendix A, a variety of graphical meth- ods are available to separate the residual from regional gravity anomalies. The methods are appropriately consid- ered non-linear, in the sense that it is unlikely that results from multiple analysts will duplicate each other. However, they are simple and easily applied and are flexible, permit- ting the use of analyst’s experience and auxiliary data in their application. The success of the methods is dependent on the experience of the analyst, especially in the use of gravity for a specific geological objective, the simplicity of the regional anomaly, and the perceptibility of the residual anomaly. The methods were used extensively before com- puters were commonly available to perform analytical, linear residual–regional separations rapidly and inexpen- sively. Generally, the methods are currently only applied to surveys of limited extent with simple regionals and rel- atively obvious residual anomalies. In this situation the residual anomaly can be isolated relatively free of dis- tortion. When graphical methods are used, the geological reasonability of the regional should be ascertained as fully as possible as a means of validating the viability of the separation process.
Graphical methods can be used on gravity anomaly data in either profile or map format. In profile data the regional anomaly is visually established as a smooth curve through the gravity anomaly values that excludes the anomalous portion of the profile that includes the residual anomaly.
The process is illustrated in Figure 6.22(a), where the residual and regional can be easily distinguished from one another. Successful application of the method requires gravity data well beyond the limits of the target area. The regional anomaly is subtracted from the observed anomaly to determine the residual anomaly. In a situation where the regional is more complex and the residual less identifi- able, as in Figure 6.22(b), the separation of regional from