Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media |
For heterogeneous anisotropic media, the wavefield propagator (equation 6) and the vector decomposition operators (equation 18) are both in the general form of FIOs. Naturally, we merge them to derive a new mixed-domain integral solution for extrapolating the decoupled elastic wavefields:
To drive the time extrapolation of the decomposed wavefields using equation 19, we must update the total elastic wavefields by superposing qP- and qS-waves at each time-step using
To tackle strong heterogeneity due to fast varying stiffness coefficients, we suggest to split the displacement equation into the displacement-stress equation and then solve it using the staggered-grid pseudo-spectral scheme (Bale, 2003; Ozdenvar and McMechan, 1996; Carcione, 1999). Note when using staggered grids, the operators to extrapolate the decoupled wave modes must be modified in order to account for the shifts in medium properties and fields variables. We will investigate this issue in the future work.
Simulating propagation of decoupled elastic waves using low-rank approximate mixed-domain integral operators for anisotropic media |