Full waveform inversion strategy for density in the frequency domain

To interpret subsurface structures properly, elastic wave propagation must be considered. Because elastic media are described by more parameters than acoustic media, elastic waveform inversion is more likely to be affected by local minima than acoustic waveform inversion. In a conventional elastic waveform inversion, P- and S-wave velocities are properly recovered, whereas density is difficult to reconstruct. For this reason, most elastic full-waveform inversion studies assume that density is fixed. Although several algorithms have been developed that attempt to describe density properly, their results are still not satisfactory. In this study, we propose a two-stage elastic waveform inversion strategy to recover density properly. The Lame constants are first recovered while holding density fixed. While the Lame constants and density are not correct under this assumption, the velocities obtained using these incorrect Lame constants and constant density may be reliable. In the second stage, we simultaneously update density and Lame constants using the wave equations expressed through velocities and density. While density is updated following the conventional method, the Lame constants are updated using the gradient obtained by applying the chain rule. Among several parameter-selection strategies tested, only this strategy gives reliable solutions for both velocities and density. Our elastic full waveform inversion algorithm is based on the finite-element method and the backpropagation technique in the frequency domain. We demonstrate our inversion strategy for the modified Marmousi-2model and the SEG/EAGE salt model. Numerical examples show that this new inversion strategy enhances density inversion results.