An elastic full-waveform inversion based on wave-mode separation

Multi-parameter elastic full-waveform inversion (EFWI) attempts to find high resolution model parameters that are able to match observed data exactly by minimising residuals between the observed and predicted data. However, the coupling of V-p and V-s, and the cross-talk artefacts between P- and S-wave modes increase non-uniqueness and ill-conditionedness. We propose a new EFWI method based on P- and S-wave mode separation to mitigate these problems. In this method, we derive the gradient formulas with respect to various wave modes using a P- and S-wave mode separated first-order velocity-stress wave equation, and use a step search method in subspace to calculate the corresponding step lengths. The algorithm, called wave-mode separation EFWI (SEFWI), appears to be helpful to weaken non-uniqueness and ill-conditionedness of conventional EFWI by decoupling multiple parameters. Numerical examples conducted with a synthetic dataset modelled on a simple model with anomalies reveal that SEFWI can reduce the cross-talk artefacts between P- and S-wave modes. Synthetic tests on the Marmousi2 model demonstrate that SEFWI yields better inversion results than conventional EFWI. Although the computational cost of SEFWI per iteration is 1.81 times as much as that of EFWI, the total computational cost is almost at the same level, because of its faster convergence rate.