Three least-squares minimization approaches to depth, shape, and amplitudecoefficient determination from gravity data

Three different least-squares approaches are developed to determine, succes sively, 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, f (z) = 0. Formulas are derived for spher es and cylinders. Knowing the depth and applying the least-squares method, the shape factor and the amplitude coefficient are determined using two sim ple linear equations. In this way, the depth, shape, and amplitude coeffici ent are determined individually from all observed gravity data. A procedure is developed for automated interpretation of gravity anomalies attributabl e to simple geometrical causative sources. The method is applied to synthet ic data with and without random errors. In all the cases examined, the maxi mum error in depth, shape, and amplitude coefficient is 3%, 1.5%, and 7%, r espectively. Finally, the method is tested on a field example from the Unit ed States, and the depth and shape obtained by the present method are compa red with those obtained from drilling and seismic information and with thos e published in the literature.