Physical-property-, lithology- And surface-geometry-based joint inversion using Pareto Multi-Objective Global Optimization

Abstract

This paper is concerned with the applicability of Pareto Multi-Objective Global Optimization (PMOGO) algorithms for solving different types of geophysical inverse problems. The standard deterministic approach is to combine the multiple objective functions (i.e. data misfit, regularization and joint coupling terms) in a weighted-sum aggregate objective function and minimize using local (decent-based) smooth optimization methods. This approach has some disadvantages: (1) appropriate weights must be determined for the aggregate, (2) the objective functions must be differentiable and (3) local minima entrapment may occur. PMOGO algorithms can overcome these drawbacks but introduce increased computational effort. Previous work has demonstrated how PMOGO algorithms can overcome the first issue for single data set geophysical inversion, that is, the trade-off between data misfit and model regularization. However, joint inversion, which can involve many weights in the aggregate, has seen little study. The advantage of PMOGO algorithms for the other two issues has yet to be addressed in the context of geophysical inversion. In this paper, we implement a PMOGO genetic algorithm and apply it to physical-property-, lithology- and surface-geometry-based inverse problems to demonstrate the advantages of using a global optimization strategy. Lithological inversions work on a mesh but use integer model parameters representing rock unit identifiers instead of continuous physical properties. Surface geometry inversions change the geometry of wireframe surfaces that represent the contacts between discrete rock units. Despite the potentially high computational requirements of global optimization algorithms (compared to local), their application to realistically sized 2-D geophysical inverse problems is within reach of current capacity of standard computers. Furthermore, they open the door to geophysical inverse problems that could not otherwise be considered through traditional optimization strategies.