184 Gravity anomaly interpretation
2 1
(a)
1
1 2 2
2 1 1 2
(b)
10 20 30 40 4.5 4.0 3.5 3.0 2.5 2.0 1.5 1.0 0.5
10 20 30 40 50 60 70 80 90 100
10 20 30 40 50 60 70 80 90 100
Anomaly (mGal)
20 18 16 14 12 10 8 6 4 2
Anomaly (mGal)Depth (km)
10 20 30 40
Depth (km)
Δσ = 100 kg/m3
Δσ = 100 kg/m3 Distance (km)
Distance (km)
FIGURE 7.6 Gravity anomalies of two different anomalous source shapes at two different depths.
The isolation of a source from other anomalous sources is also a key factor in determining whether the gravity method is a suitable approach to solving a particular prob- lem. This results from the potential overlap of anomalies and the resulting distortion of the individual anomalies.
The extreme of this distortion is the superposition of effects to the point where the existence of multiple source bodies is not discernible.
The resolution, which is the minimum horizontal dis- tance between equivalent sources that still permits recog- nition of the individual sources, is a function of the sharp- ness of the anomaly, controlled by the shape and depth of the source. A general rule is that identical individual sources located at the same depth must have a horizontal separation of at least twice the depth to the sources. How- ever, in optimal cases, resolution for concentrated sources can be achieved at separation approximately equal to the depth.
This key variable is a major concern in many engineer- ing and environmental as well as mineral exploration stud- ies where the resolution of multiple sources is of particular concern. An example of the effect of overlapping anoma- lies due to equivalent sources is illustrated in Figures 7.7(a) and (b). The concerns with isolation are not just limited to the superposition of the effects of sources at the same depth, but also include multiple sources at different depths.
This is especially problematic where the sources are not separated by a vertical distance that exceeds several times the depth to the shallowest source. As illustrated in Fig- ure 7.7(c), the individual sources lying above one another cannot be distinguished until their vertical separation is several times the depth to the upper source.
The vertical resolution problem becomes more critical as the geometric shape of the source causes their anoma- lies to broaden out. Figure 1.2, for example, illustrated the problems in identifying anomalous sources by the grav- ity method caused by vertical superposition of anomalies due to a faulted, high-density layer within a lower-density medium. In Figure 1.2(a), the individual anomalies of the two high-density units are shown together with their summed anomaly where the fault is vertical. The upper high-densityA-layer causes a positive anomaly to the left and the lowerB-layer causes a positive anomaly to the right. These effects destructively interfere, but because the sources are at different depths, the summation (A+B)- anomaly shows a positive to the left and a negative to the right, and the typical fault anomaly is no longer present.
Further complications in the summed effects occur where the fault is dipping as shown in Figures 1.2(b) and 1.2(c), with the inflection point of the summation anomaly no longer at the midpoint of the fault.
The effect of various geologic variables on gravity anomalies is illustrated in Figures 7.8 to 7.11. Grav- ity anomaly profiles in Figures 7.8 and 7.9 illustrate a long subsurface void with an approximately 12 m by 12 m cross-section and a density contrast of 2,700 kg/m3. The gravity anomalies decrease rapidly with increasing depth to the top of the void from roughly 1.5 to 30 m (Figure 7.8). However, the amplitudes of the gravity anomalies do not change significantly as the strike length of the void whose upper surface is at 3 m changes from 6 m to infinity on either side of the cross-section shown in the figure.
The anomalies of Figure 7.8 support the use of 2D methods of gravity interpretation. The gravity anomalies from equivalent mass differences used in Figures 7.8 and 7.9 are shown in Figures 7.10 and 7.11, except the void shape has been changed by halving its vertical extent and doubling its width. The amplitudes of the resulting
7.3 Interpretation parameters 185
1 2 3 4
1+31+2 1+4
(a) (c)
(b)
10
20
30 10 9 8 7 6 5 4 3 2 1
10 20 30 40 50 60 70 80 90 100
Anomaly (mGal)
7 6 5 4 3 2 1
Anomaly (mGal)Depth (km) 10
15 20 25 30 2.0 1.8 1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 5 Anomaly (mGal)Depth (km)
10 20
30
Depth (km)
Δσ = 100 kg/m3
Δσ = 100 kg/m3 Distance (km)
10 20 30 40 50 60 70 80 90 100
Distance (km)
35 45 55 65 75
Distance (km)
Δσ = 100 kg/m3
FIGURE 7.7 Effect of overlapping gravity anomalies on the resolution of individual 2D sources. (a) Individual horizontally separated sources are too close together to be recognized. (b) Individual sources of (a) are separated sufficiently to recognize the existence of two anomalies.
(c) Summation effects of anomalies caused by prismatic sources centered on the same vertical line. Note the difficulty in isolating the individual sources owing to lack of vertical resolution.
anomalies have not been modified greatly, but the widths of the anomalies have increased in response to the greater widths of the sources.
7.3.2 Key geophysical variables
Key geophysical variables address the inverse problem of estimating the geological parameters. Here, the problem is the interpretation of the nature of the subsurface from the gravity anomalies. Key geophysical variables used in interpretation are the amplitude, sharpness, shape, and per- ceptibility of the gravity anomaly, as well as its correlation with other geophysical and geological features.
Amplitude is the most important of the geophysical variables. It is the most obvious thing observed on a grav- ity anomaly map or profile, and portions of the survey area
are defined in terms of their relative amplitude. The mass differential, a product of the volume and density contrast of the source, directly controls the amplitude of the anomaly as explained in Section 3.4.2. In fact the mass differen- tial can be determined uniquely by Gauss’ law (Equation 4.46), which relates this quantity to the numerical integra- tion of the energy of the anomaly.
As pointed out above, the anomaly amplitude depends on the depth to the source, but the sensitivity to depth changes with the shape of the causative mass. The ampli- tude of an anomaly from a concentrated mass such as an ore body or a solution cavity in a limestone formation will be most sensitive to depth, where the inverse distance func- tion, 1/rn, varies withn=2. The anomaly from a long, concentrated source such as a buried bedrock ridge or a tubular solution cavity in limestone, on the other hand, will