Elastic full waveform inversion based on equivalent staggered grid FDM and inter-parameter trade-off mitigation

Elastic full waveform inversion (EFWI) has increasingly been applied in seismic exploration as computer performance improves. EFWI significantly improves calculation efficiency, but requires very large computer storage space and suffers inter-parameter trade-off and local minima problems. Preconditioning the gradients based on elastic wave mode decomposition can effectively mitigate inter-parameter trade-offs, but the decomposition-based scheme may further increase the memory usage, which limits EFWI application. The equivalent staggered grid (ESG) scheme in acoustic medium requires less memory usage and generates results numerically equivalent to those using the standard staggered grid (SSG) scheme. In this paper, we extend the ESG scheme to second-order elastic wave equations in terms of velocity, producing results numerically equivalent to the SSG ones based on first-order velocity-stress wave equations while reducing memory usage by 45% compared with the SSG scheme. We then apply the ESG scheme to EFWI and derive the formula of the preconditioned gradient of the S-wave velocity. Finally, three numerical examples demonstrate that applying the ESG scheme to decomposition-based EFWI can significantly reduce computer memory usage and mitigate the trade-offs between the P- and S-wave velocities.