A Multi-Objective Optimization Framework for Joint Inversion

Abstract

Different geophysical data sets such as receiver functions, surface wave dispersion measurements, and first arrival travel times, provide complementary information about the Earth structure. To utilize all this information, it is desirable to perform a joint inversion, i.e., to use all these datasets when determining the Earth structure. In the ideal case, when we know the variance of each measurement, we can use the usual Least Squares approach to solve the joint inversion problem. In practice, we only have an approximate knowledge of these variances. As a result, if a geophysical feature appears in a solution corresponding to these approximate values of variances, there is no guarantee that this feature will still be visible if we use the actual (somewhat different) variances. To make the joint inversion process more robust, it is therefore desirable to repeatedly solve the joint inversion problem with different possible combinations of variances. From the mathematical viewpoint, such solutions form a Pareto front of the corresponding multi-objective optimization problem.