In this research, we studied the problems when recovering elastic parameters (P-wave velocity, S-wave velocity and density) including cycle-skipping problem, density effect, and inter-parameter crosstalk issue. We ﬁnd that elastic wave equation trave time method with a cross-correlation misﬁt function can be employed to build long wavenumber components for P-wave velocity and S-wave velocity, which helps to overcome the cycle-skipping problem in elastic FWI. Then elastic wave equation waveform inversion can be used to provide high resolution estimates of the model parameters. Density is quite difﬁcult to be recovered, which may be caused by its insensitivity to travel time or the inter-parameter tradeoff. We also propose to quantify the parameter trade-off by probing the multi-parameter Hessian. The multi-parameter point spread functions, which is proportional to one column of the multi-parameter Hessian, measure the parameter trade-off between different physical parameters more completely compared to traditional studies based on scattering patterns. The studies are veriﬁed using numerical examples with reﬂection survey and transmission survey.
View full article as PDF (9.28 Mb)