Joint wave-equation traveltime inversion of diving/direct and reflected waves for P- and S-wave velocity macromodel building

Abstract

Full-waveform inversion (FWI) suffers from the local minima problem and requires a sufficiently accurate starting model to converge to the correct solution. Wave-equation traveltime inversion (WETI) is an effective tool to retrieve the long-wavelength components of the velocity model. We have developed a joint diving/direct and reflected wave WETI (JDRWETI) method to build P- and S-wave velocity macromodels. We estimate the traveltime shifts of seismic events (diving/direct waves and PP- and PS-reflections) through the dynamic warping scheme and construct a misfit function using the time shifts of diving/direct and reflected waves. We derive the adjoint wave equations and the gradients with respect to the background models based on the joint misfit function. We apply the kernel decomposition scheme to extract the kernel of the diving/direct wave and the tomography kernels of PP- and PS-reflections. For an explosive source, the kernels of the diving/direct wave and PP-reflections and the kernel of the PS-reflections are used to compute the P- and S-wave gradients of the background models, respectively. We implement JDRWETI by a two-stage inversion workflow: First, we invert the P- and S-wave velocity models using the P-wave gradients, and then we improve the S-wave velocity model using the S-wave gradients. Numerical tests on synthetic and field data sets reveal that the JDRWETI method successfully recovers the long-wavelength components of P- and S-wave velocity models, which can be used for an initial model for the subsequent elastic FWI. Moreover, the JDRWETI method prevails over the existing reflection WETI method and the cascaded diving/direct and reflected wave WETI method, especially when large velocity errors are present in the shallow part of the starting models. The JDRWETI method with the two-stage inversion workflow can give rise to reasonable inversion results even for the model with different P- and S-wave velocity structures.