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, v p/v s, 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 v p and v s 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, v p/v s 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 v p/v s is obtained with quantum particle swarm optimization (QPSO). This method probes a population of possible models. The assessment of each model of v p/v s in the population is obtained with nested local iterations updating for v p only. Conventional elastic FWI is then carried out for jointly estimating high-resolution models of v p and v s. We demonstrate with synthetic examples that the estimates of v p are relatively robust to errors in the estimated v p/v s, and that effectively a sparse representation of the model of v p/v s is feasible for the reconstruction of a model of v s. We also demonstrate that the proposed approach performs better than constraining elastic FWI with an empirical relation between v p and v s, leading to improved estimates of models of v p and v s from seismic data.