Acoustic full waveform inversion with elastic wave equation forward modeling

Full-waveform inversion (FWI) is a high-resolution velocity inversion method. Currently, acoustic full waveform inversion (AFWI) has achieved promising results in marine data inversion, but it still faces significant challenges in land data inversion. One of the reasons for the failure of AFWI in land data inversion is that the acoustic wave equation does not account for the elastic effects of seismic waves, such as surface waves and converted waves. This results in errors between the synthesized acoustic waveform and the observed elastic waveform, particularly in the amplitude and phase of the P-wave. To reduce the error caused by the elastic effect, we have improved the inversion process of AFWI. During the forward modeling stage, we replace the original acoustic wave equation with the elastic wave equation to simulate the wavefield. This allows us to obtain synthetic waveforms that incorporate elasticity, thereby reducing the corresponding error. When computing model gradients, we still base on the acoustic wave equation and only update the P-wave velocity model. This approach helps maintain a lower computational cost. We tested the method on the Marmousi model and field land data, and the results demonstrate that the method successfully reduces the error caused by the elastic effect, thereby improving the clarity of the inversion results.