A least‐squares minimization approach to shape determination from gravity data

Abstract

The gravity anomaly expression produced by most geologic structures can be represented by a continuous function of both shape (shape‐factor) and depth‐related variables with an amplitude coefficient related to mass (Abdelrahman and El‐Araby, 1993). Few methods have been developed to determine the shape of the buried geologic structure from residual gravity anomaly profiles. These methods include a Walsh transform approach (Shaw and Agarwal, 1990) and the employment of a correlation factor between successive least‐squares residuals (Abdelrahman and El‐Araby 1993). In the present note, a least‐squares minimization approach to shape‐factor determination from a residual gravity anomaly profile is presented. The problem of the shape‐factor determination is transformed into the problem of finding a solution of a nonlinear equation of the form f(q) = 0.