Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media

Propagating decoupled elastic wavefields

Above pseudo-spectral operators propagate the elastic wavefields as a superposition of qP- and qS-wave modes. To obtain physically interpretable results for seismic imaging and waveform inversion, wave mode decoupling is required during wavefield extrapolation. The key concept of mode decoupling is based on polarization. In a general anisotropic medium, the qP and qS modes do not polarize parallel and perpendicular to the wave vectors. Moreover, unlike the well-behaved qP mode, the two qS modes do not consistently polarize as a function of the propagation direction (or wavenumber) and thus cannot be designated as SV and SH waves, except in isotropic and TI media (Crampin, 1991; Winterstein, 1990). Even for a TI medium, it is a challenge to find the right solution of the shear singularity problem and obtain two completely separated S-modes with correct amplitudes (Cheng and Fomel, 2014; Yan and Sava, 2011). Therefore, we restrict to extrapolate the decoupled qP- and qS- wave modes in this paper.

Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media