An algorithm of geophysical data inversion based on non-probabilistic presentation ofa prioriinformation and definition of Pareto-optimality

This paper presents an inversion algorithm that can be used to solve a wide range of geophysical nonlinear inverse problems. The algorithm in based upon the principle of a direct search for the optimal solution in the parameter space. The main difference of the algorithm from existing techniques such as genetic algorithms and simulated annealing is that the optimum search is performed under control of a priori information formulated as a fuzzy set in the parameter space. In such a formulation the inverse problem becomes a multiobjective optimization problem with two objective functions, one of them is a membership function of the fuzzy set of feasible solutions, the other is the conditional probability density function of the observed data. The solution to such a problem is a set of Pareto optimal solutions that is constructed in the parameter space by a three-stage search procedure. The advantage of the proposed technique is that it provides the possibility of involving a wide range of non-probabilistic a priori information into the inversion procedure and can be applied to the solution of strongly nonlinear problems. It allows one to decrease the number of forward-problem calculations due to selective sampling of trial points from the parameter space. The properties of the algorithm are illustrated with an application to a local earthquake hypocentre location problem with synthetic and real data.