Pareto-optimal solutions of the inverse problem of gravimetry with indeterminate a priori information

Abstract

The paper discusses theoretical aspects of solving the nonlinear inverse problem of gravimetry with uncertainty of a priori information. The a priori information is described by fuzzy sets. Special-purpose geophysical problem with uncertain a priori information is transformed into a multi-objective optimization problem. One of the criteria is the membership function of a fuzzy set of possible solutions. Solution of the problem is a set of Pareto-optimal solutions, which is constructed in the parametric space applying a three-step search algorithm. The advantage of the proposed method is that it provides a possibility of including the wide range of non-probabilistic a priori information in the inversion procedure and can be applied to the solution of highly nonlinear problems. This reduces the number of direct computing problems by selective modeling of sample points in the parametric space.A test example has been given of the algorithm applied to the inverse problem of gravimetry for a single contact surface.