Semi-global inversion of vp to vs ratio for elastic wavefield inversion

Abstract

We introduce an approach to estimate the ratio between P- and S-wave velocities, vp/vs, in the scope of elastic full waveform inversion (FWI). Elastic FWI is generally implemented with local optimization methods relying on initial estimates of the long wavelengths of P- and S-wave models. However, successful inversions can be hindered if an accurate enough relation between vp and vs velocities is not used as a constraint. This relation can be estimated from empirical relations. Herein, we introduce an alternative approach based upon a semi-global inversion scheme. We observe that for a large number of cases, and particularly in the context of FWI, vp/vs can be represented on a sparse basis. This sparse basis has a much smaller dimension than that of the typical model space in elastic FWI. This creates the possibility of using global optimization methods. The optimal estimate of vp/vs is obtained with quantum particle swarm optimization (QPSO). This method probes a population of possible models. The assessment of each model of vp/vs in the population is obtained with nested local iterations updating for vp only. Conventional elastic FWI is then carried out for jointly estimating high-resolution models of vp and vs. We demonstrate with synthetic examples that the estimates of vp are relatively robust to errors in the estimated vp/vs, and that effectively a sparse representation of the model of vp/vs is feasible for the reconstruction of a model of vs. We also demonstrate that the proposed approach performs better than constraining elastic FWI with an empirical relation between vp and vs, leading to improved estimates of models of vp and vs from seismic data.