Regularized Sparse-grid Geometrical Sampling for Uncertainty Assessment in Nonlinear Inverse Problems - CSEM and Seismic

Abstract

A new method for a reliable uncertainty assessment of nonlinear geophysical inverse problems was introduced by Tompkins et al. in 2011. As opposed to Bayesian approaches, this method exploits the posterior model space based on: a parameter reduction technique; constraint parameter mapping; a hypercube approximation; a sparse geometric sampling scheme; and a forward model operator. Here, we show an improvement of the method’s performance by rotating the space of feasible models, computed by the constraint mapping step, along the direction of maximum variance by applying a PCA. This introduction allows a more complete sampling of the posterior model space. The new methodology was successfully implemented and tested for the 1D CSEM inversion example (introduced in Tompkins et al (2011)), increasing the efficiency in searching the posterior space by almost 50%, and for a new 1D synthetic seismic AVO example.