Shear reflectivity compensation in full-waveform inversion using least-squares reverse-time migration

Abstract

SUMMARY The computational cost of elastic-waveform inversion is too high for inverting PP reflections, while using acoustic full-waveform inversion (FWI) is inaccurate because it does not depend on the shear modulus/velocity/impedance that affects elastic PP wavefield amplitudes. To solve this problem, we develop a waveform inversion method that uses acoustic least-squares reverse-time migration (LSRTM) to compensate the shear reflectivity for acoustic FWI. Our method is based on the quasi-elastic-wave equation developed by Chapman et al. (2014). The quasi-elastic-wave equation uses a linearized acoustic-wave equation with shear modulus μ as a virtual source to correct the acoustic PP wavefield amplitudes toward elastic ones. Our waveform inversion method inverts for elastic parameters by minimizing the L2 norm of the difference between recorded and predicted PP reflections modelled using the quasi-elastic-wave equation. Numerical tests on synthetic and field data show that our method can properly handle the amplitudes of elastic PP reflections and provides an accurate estimate of the P- and S-wave velocities/impedances and, in some cases, the density. The method does not need the computationally expensive numerical solution to the elastic-wave equation. It also gives a better estimate of elastic parameters than a pure LSRTM method for elastic PP reflections.