The correlation factors between successive least‐squares residual (or regional) gravity anomalies from a buried sphere, a two‐dimensional (2‐D) horizontal cylinder, and a vertical cylinder and the first horizontal derivative of the gravity from a 2‐D thin faulted layer are computed. Correlation values are used to determine the depth to the center of the buried structure, and the radius of the sphere or the cylinder and the thickness of the fault are estimated. The method can be applied not only to residuals but also to the Bouguer‐anomaly profile consisting of the combined effect of a residual component due to a purely local structure and a regional component represented by a polynomial of any order. The method is easy to apply and may be automated if desired. It can also be applied to the derivative anomalies of the gravity field. The validity of the method is tested on two field examples from the United States and Denmark.
We have extended our earlier derivative analysis method to higher derivatives to estimate the depth and shape (shape factor) of a buried structure from selfpotential (SP) data. We show that numerical second, third, and fourth horizontal-derivative anomalies obtained from SP data using filters of successive window lengths can be used to simultaneously determine the depth and the shape of a buried structure. The depths and shapes obtained from the higher derivatives anomaly values can be used to determine simultaneously the actual depth and shape of the buried structure and the optimum order of the regional SP anomaly along the profile. The method is semi-automatic and it can be applied to residuals as well as to observed SP data.We have also developed a method (based on a leastsquares minimization approach) to determine, successively, the depth and the shape of a buried structure from the residual SP anomaly profile. By defining the zero anomaly distance and the anomaly value at the origin, the problem of depth determination has been transformed into the problem of finding a solution of a nonlinear equation of form f (z) = 0. Knowing the depth and applying the least-squares method, the shape factor is determined using a simple linear equation.Finally, we apply these methods to theoretical data with and without random noise and on a known field example from Germany. In all cases, the depth and shape solutions obtained are in good agreement with the actual ones.
Three different least‐squares approaches are developed to determine, successively, the depth, shape (shape factor), and amplitude coefficient related to the radius and density contrast of a buried structure from the residual gravity anomaly. By defining the anomaly value g(max) at the origin on the profile, the problem of depth determination is transformed into the problem of solving a nonlinear equation, [Formula: see text]. Formulas are derived for spheres and cylinders. Knowing the depth and applying the least‐squares method, the shape factor and the amplitude coefficient are determined using two simple linear equations. In this way, the depth, shape, and amplitude coefficient are determined individually from all observed gravity data. A procedure is developed for automated interpretation of gravity anomalies attributable to simple geometrical causative sources. The method is applied to synthetic data with and without random errors. In all the cases examined, the maximum error in depth, shape, and amplitude coefficient is 3%, 1.5%, and 7%, respectively. Finally, the method is tested on a field example from the United States, and the depth and shape obtained by the present method are compared with those obtained from drilling and seismic information and with those published in the literature.
The interpretation of gravity data often involves initial steps to eliminate or attenuate unwanted field components in order to isolate the desired anomaly (e.g., residual‐regional separations). These initial filtering operations include, for example, the radial weights methods (Griffin, 1949; Elkins, 1951; Abdelrahman et al., 1990), the fast Fourier transform methods (Bhattacharyya, 1965; Clarke, 1969; Meskó, 1969, 1984, Botezatu, 1970), the rational approximation techniques (Agarwal and Lal, 1971) and recursion filters (Bhattacharyya, 1976), and the bicubic spline approximation techniques (Bhattacharyya, 1969; Inoue, 1986). The derived local gravity anomalies are then geologically interpreted to derive depth estimates, often without properly accounting for the uncertainties introduced by the filtering process. When filters are applied to observed data, the filters often cause serious distortions in the shape of the gravity anomalies (Hammer, 1977). Thus the filtered gravity anomalies generally yield unreliable geologic interpretations (Rao and Radhakrishnamurthy, 1965; Hammer, 1977; Abdelrahman et al., 1985, 1989.
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