Gravity Methods
2.6 Interpretation methods
2.6.6 Sedimentary basin or granite pluton?
It is very important in the interpretation of gravity data for hydro- carbon exploration to be able to distinguish between a sedimentary basin (a good possible hydrocarbon prospect) and a granitic plu- ton (no prospect for hydrocarbons), as both can produce negative gravity anomalies of comparable magnitude.
For example, Arkell (1933) interpreted a minimum in an initial Bouguer gravity survey in the Moray Firth, northeast Scotland, as being due to a granite pluton. It was only after further geological
work (Collette, 1958) and gravity work (Sunderland, 1972) that it was realised that the minimum was due to a sedimentary basin.
Simultaneously, the Institute of Geological Sciences undertook seis- mic reflection surveys and initiated some shallow drilling. It was not until 1978 that the Beatrice Field was discovered (McQuillin et al., 1984). Had the 1933 interpretation been different, the history of the development of the North Sea as a major hydrocarbon province might have been very different.
In 1962, Bott proposed a set of criteria to distinguish between a sedimentary basin and a granite boss as interpretations of gravity minima. His argument was based on the second vertical deriva- tive of the gravity anomaly due to a semi-infinite two-dimensional horizontal slab with a sloping edge. He found that the ratio of the moduli of the maximum and minimum second vertical derivative (|gmax|/|gmin|) provides a means of distinguishing between the two geological structures, as outlined in Box 2.26 and illustrated in Figure 2.45. McCann and Till (1974) have described how the method can be computerised and the application of Fourier analy- sis to Bott’s method. Some authors calculate the second horizontal derivative (δ2g/δx2) (e.g. Kearey et al., 2002: Fig. 6.19), which re- sponds in exactly the same way as the vertical derivative except that the maxima and minima are reversed, as are the criteria in Box 2.26.
In order for the method to work, the gravity anomaly attributed to the appropriate geological feature (sedimentary basin or granitic pluton) needs to be clearly isolated from adjacent anomalies due to other features. The method is not applicable, however, in cases where extensive tectonic activity has deformed either a sedimentary basin by basin shortening or a granitic pluton by complex fault- ing, thereby changing the gradients of the flanks of both types of model.
The vertical variation of density of sediments with depth in a sedimentary basin can be represented in a number of ways. Mov- ing away from Bott’s uniform density model, consideration of the variation in density in terms of exponential and hyperbolic density contrast has been given by Rao et al. (1993, 1994), for example.
1.0 1.2 1.4 1.6 2.01.8 2.2
East
1.4 1.2 1.0
0.8 0.6 0.4
0.2 0.0
North
0.2
2.0 0.4 0.6 0.8 1.0
West 3.0
2.6
2.4
2.2
2.0 1.0
1.2 1.4 1.6 2.01.8 2.2
East
1.4 1.2 1.0
0.8 0.6 0.4
0.2 0.0
North
0.2
2.0 0.4 0.6 0.8 1.0
West 3.0
2.6
2.4
2.2 2.0
South South
0 100 200 m
(A)
(B)
Positive centres Negative centres
0 100 200 m
Figure 2.41 An example where the Bouguer anomaly map (A) (contour interval 2 mGal) exhibits more than the corresponding second vertical derivative map (B) for the Jjaure titaniferous iron-ore region in Sweden. Contours: 0 (dashed),±0.1,±0.2,±0.4 in units of 0.0025 mGal/m2). From Parasnis (1966), by permission.
Airborne Bouguer
Land Bouguer upward continued
Land Bouguer
Gravity 2 milliGals per unit
Cap
Salt
Cap
Salt
High Island Dome km Big Hill Dome
Due to salt
Due to cap rock
Flight elevation 305 m
20 10
0 30 40 km
0 2 4 6
Terrain elevation
Figure 2.42 Comparison of airborne and upward continued land Bouguer gravity data with those obtained by airborne gravity surveying.
From Hammer (1984), by permission.
200 300
E Rouguer gravity
45/NE/0.8
C
400 600
N
Figure 2.43 Structural analysis, based on lineations from a series of colour and greyscale shaped-relief images of geophysical data, can provide a basis for reassessment of regional structure, mineralisation potential and fracture patterns. This image is of observed regional Bouguer gravity data, over an area of 200 km x 140 km of the Southern Uplands, Scotland (C: Carlisle; E: Edinburgh). The data have been reduced to Ordnance Datum using a density of 2.7 Mg/m3, interpolated to a square grid of mesh size 0.5 km and displayed as a greyscale shaded-relief image. Sun illumination azimuth and inclination are NE and 45◦, respectively. A series of NE trending features parallel to the regional strike and the Southern Uplands fault have been suppressed by the NE illumination, whereas subtle NW trending features linked to development of the Permian basins are enhanced and seen to be more extensive. For comparison, see Figure 3.50. Image courtesy of Regional Geophysics Group, British Geological Survey.
Box 2.24 Conventional Euler deconvolution equation (Zhang et al., 2000)
The conventional Euler deconvolution equation is given by:
(x−x0)Tzx+(y−y0)Tzy+(z−z0)Tzz=N(Bz−Tz) for the gravity anomaly vertical component Tzof a body hav- ing a homogeneous gravity field. The parameters x0, y0and z0
represent the unknown coordinates of the source body centre or edge to be estimated, and x, y and z are the known coordinates of the observation point of the gravity and gradients. The values Tzx, Tzyand Tzzare the measured gravity gradients along the x, y and z directions; N is the structural index, and Bzis the regional value of the gravity to be estimated.
Rewriting the first equation, we have:
x0Tzx+y0Tzy+z0Tzz+NBz=xTzx+yTzy+zTzz+NTz
in which there are four unknown parameters (x0, y0, z0and Bz).
(A)
Grid Conventional Euler 3
2 10
5
5 0
–5 0 –5
5
5 0
–5 0 –5
5
5 0
–5 0 –5
5
5 0
–5 0 –5 5
5 0
–5 0 –5 5
5 0
–5 0 –5 5
5 0
–5 0 –5 5
5 0
–5 0 –5 5
5 0
0 –5
–5
5
5 0
0 –5
–5
5
5 0
0 –5
–5
5
5 0
0 –5
–5
1 2
3
2
10 1 2
3
2
10 1 2
3
2
10 1 2
(a): Point(b): Prism (0)(c): Prism (45)(d): Cylindrical
Grid Tensor Euler
line direction –> line direction –>
Line Tensor Euler Line
Conventional Euler
(B)
(C)
(D)
Figure 2.44 Euler deconvolution results from four models (a small circle denotes the position of each solution). From Zhang et al. (2000), by permission.
Box 2.25 Tensor Euler deconvolution equations (Zhang et al., 2000)
In addition to the first equation given in Box 2.24, tensor Euler deconvolution uses two additional equations:
(x−x0)Txx+(y−y0)Txy+(z−z0)Txz=N(Bx−Tx) (x−x0)Tyx+(y−y0)Tyy+(z−z0)Tyz=N(By−Ty) where the values Txand Tyare the horizontal components of the gravity vector along the x and y directions, respectively. The values Txx, Txy, Txz, Tyx, Tyyand Tyzare gravity tensor gradients.
Bxand Byare the regional values of the horizontal components to be estimated if values of Txand Tyare available. Otherwise (Bx−Tx) and (By−Ty) can be estimated in the process.
Box 2.26 Bott criteria (see also Figure 2.45)
(1) For a sedimentary basin:
|gmax|/|gmin|>1.0 Basin sides slope inwards.
(1) For a granite pluton:
|gmax|/|gmin|<1.0 Granite pluton sides slope outwards.