A Fast Least-squares Method for Inverse Modeling of Gravity Anomaly Profiles due Simple Geometric-shaped Structures

Abstract

An inversion technique using a fast least-squares method is developed to estimate, successively, the shape factor (q-parameter), the depth (z-parameter) and the amplitude coefficient (A-parameter) of a buried structure using normalized residual anomalies obtained from gravity data. By defining the anomaly value at the origin and the anomaly value at different points on the profile (N-value), the problem of shape factor estimation is transformed into a problem of finding a solution of a non-linear equation of the form f(q)=0. Knowing the shape factor and applying the least-squares method, the depth is estimated by solving a nonlinear equation of the form ψ(z) = 0. Finally, knowing the shape factor and the depth, the amplitude coefficient is determined in a least-squares way using a simple linear equation. This technique is applicable for a class of geometrically simple anomalous bodies, including the semi-infinite vertical cylinder, the infinitely long horizontal cylinder, and the sphere. The technique is tested and verified on a theoretical model with and without random errors. It is also successfully applied to real data from mineral exploration in India, and the interpreted shape and depth parameters are in good agreement with the known actual values.