Multi-parameter full waveform inversion using Poisson’s ratio for elastic media

Abstract

In multi-parameter full waveform inversion (FWI), the success of recovering each parameter is dependent on characteristics of the partial derivative wavefields (or virtual sources), which differ according to parameterisation. Elastic FWIs based on the two conventional parameterisations (one uses Lamé constants and density; the other employs P- and S-wave velocities and density) have low resolution of gradients for P-wave velocities (or λ). Limitations occur because the virtual sources for P-wave velocity or λ (one of the Lamé constants) are related only to P–P diffracted waves, and generate isotropic explosions, which reduce the spatial resolution of the FWI for these parameters. To increase the spatial resolution, we propose a new parameterisation using P-wave velocity, Poisson’s ratio, and density for frequency-domain multi-parameter FWI for isotropic elastic media. By introducing Poisson’s ratio instead of S-wave velocity, the virtual source for the P-wave velocity generates P–S and S–S diffracted waves as well as P–P diffracted waves in the partial derivative wavefields for the P-wave velocity. Numerical examples of the cross–triangle–square (CTS) model indicate that the new parameterisation provides highly resolved descent directions for the P-wave velocity. Numerical examples of noise-free and noisy data synthesised for the elastic Marmousi-II model support the fact that the new parameterisation is more robust for noise than the two conventional parameterisations.