On a Successive Approximation Method for Interpreting Gravity Anomalies

Abstract

A new method for quantitative interpretation of gravity anomalies is presented. The disturbing body is represented by a finite number of vertical prisms arranged on a pre‐determined, regular grid. The horizontal dimensions of the individual prisms are small enough that they can be approximated by vertical‐line mass elements at the axis of the prisms. Formulas for gravity due to one prism are derived and, for the case of Gulf Coast salt densities, plotted on Figure 1. Gravity due to the whole body is an algebraic sum of the contributions of all prisms at the appropriate depths and distances. This method makes possible the direct interpretation by successive approximations by introducing proper geologic limitations. All the numerical work can be conveniently done on a high‐speed digital computer. The method is especially suitable for features with predominant vertical dimension such as salt domes and igneous plugs. It gives at least the same, and possibly higher, degree of accuracy as the graphical dot chart methods and, carried out on a digital computer, should be about two thousand times faster.

Historical development of the gravity method in exploration

“…Bott (1960) first attempted to invert for basin depth from gravity data by adjusting the depth of vertical prisms through trial and error. Danes (1960) used a similar approach to determine the top of salt. Oldenburg (1974) adopted Parker's (1972) forward procedure in the Fourier domain to formulate an inversion algorithm for basin depth by applying formal inverse theory.…”

Gravity inversion of 2D bedrock topography for heterogeneous sedimentary basins based on line integral and maximum difference reduction methods

“…Conventionally, when the density contrast of the sediments of a sedimentary basin is constant, the non‐linear gravity anomaly inversion for bedrock depth starts with the initial estimate of the deposit thickness at each measurement point as the thickness of a homogeneous Bouguer slab of infinite lateral extent that produces the gravity anomaly at the point. The source body is usually approximated by a set of juxtaposed rectangular prisms and its gravitational field is then calculated iteratively, until the calculated gravity anomaly curve fits well the observed field within some convergence criteria such as the residual gravity anomaly, which is defined as the observed minus the calculated gravity anomaly, reaching a predefined value or as a specific number of iterations that has been completed in either the space domain (Bott 1960; Danes 1960; Corbató 1965; Tanner 1967; Barbosa, Silva and Medeiros 1999b) or the Fourier domain (Parker 1973; Oldenburg 1974; Pilkington and Crossley 1986). This method of successive approximations has been widely used to map bedrock topography of homogeneous sedimentary basins (Bhaskara Rao 1986; Jachens and Moring 1990; Abbott and Louie 2000; Annecchione et al .…”

3D vector gravity potential and line integrals for the gravity anomaly of a rectangular prism with 3D variable density contrast

“…The gravity anomaly from the whole mass body is an algebraic sum of the contributions of all vertical prisms at appropriate depths and distances from the observation point. This procedure is widely used in gravity-anomaly forward modeling and inversion ͑Danes, 1960;Nagy, 1966;René, 1986;Rao et al, 1990;García-Abdeslem, 1992;Bear et al, 1995;Barbosa et al, 1999;Silva et al, 2000;Gallardo-Delgado et al, 2003;García-Abdeslem, 2005;Sundararajan, 2007͒ andterrain corrections ͑Danés, 1982;García-Abdeslem and Martín-Atienza, 2001͒. Thus, rectangular prisms are building blocks for calculating the gravity anomaly of irregular 3D mass bodies.…”