SH waves, rays, and full waveform inversion

Laurence R. Lines, P. F. Daley

With the continuous advances in high performance computing and multicomponent seismic recording, there continues to be increased interest in full waveform inversion (FWI) of seismic data. The SH-wave mode is appealing since unlike P-wave and SVwave modes, this seismic mode does not undergo mode conversions at a boundary. SHwaves have a viscoelastic reflection response that can be modeled by finite-difference modeling, ray tracing or analytic methods. Since these modeling methods could be used in the full waveform inversion of real shear-wave data, it is important to know the differences and similarities of these methods. For precritical arrivals, the finitedifference (FD) viscoelastic wave modeling agrees with the viscoelastic reflection coefficients from analytic expressions even though the 2-D FD method assumes a cylindrical wave source and the reflection coefficient expression is derived for plane wave reflections. It is shown that the plane waves can be constructed from a sum of cylindrical waves with varying time delays. Near the critical angle, the plane wave method breaks down, and the 2-D FD expression would seem to be favored. However, amplitudes for the 2-D FD method with cylindrical spreading does depart from the 2.5D hybrid method of Daley et al. (2009) which accounts for a point source undergoing 3-D spreading. For real data of recorded SH-waves, full waveform inversion should take into account these amplitude differences due to 3-D spreading when using FD models. Given these considerations and the need for methods that are computationally faster than 3-D finite-difference methods, it is recommended that the 2.5D hybrid scalar wave equation model be used for full waveform inversion of P-wave reflection data from flat interfaces.