A two-stage elastic FWI strategy for 2D VTI elastic media to improve c13 structure

To enhance the feasibility of the multi-parameter full waveform inversion (FWI) for field data, including various types of seismic waves, we introduce a new 2-stage elastic VTI FWI strategy. Because the influence of S-waves on FWI is dominant due to its strong amplitudes in partial derivative wavefields, some parameters may not be recovered well. In the elastic VTI FWI, c13 is a parameter that reverses direction in early stage of inversion due to reversed motions of S-S waves with strong amplitudes. To solve this problem, instead of the virtual source for c13, we use the virtual source for λ in isotropic parameterisation, which includes the Lamé constants and density. This approach is based on the fact that radiation patterns of P-P scattered waves for λ and c13 are similar to each other and that the virtual source for λ generates P-P dominant scattered waves. This approach allows us to enable the inversion process for c13 to behave as if we only use P-P scattered waves to invert c13. Next, we perform the multi-parametric elastic FWI again with original virtual source to compensate for the errors caused in the 1st stage and to conduct the FWI for c13 with full wavefields.