Wavefield Simulation In Isotropic And Anisotropic Media By A High-order Staggered-grid Finite Difference Method

In seismic exploration, it is common practice to separate the P-wavefeld from theS-wavefeld by the elastic wavefeld decomposition technique, for imaging purposes.However, it is sometimes difficult to achieve this goal, especially when the velocity feld iscomplex. A useful approach in multi-component analysis and modeling is to directly solve theelastic wave equations for the pure P or S wavefelds, referred as the separate elastic waveequations. In this study, we first compare two kinds of such wave equations: the frst-order(velocity–stress) and the second-order (displacement–stress) separate elastic wave equations,with the frst-order (velocity–stress) and the second-order (displacement–stress) full (ormixed) elastic wave equations using a high-order staggered grid fnite-difference method.Comparisons are given of wavefeld snapshots, common-source gather seismic sections, andindividual synthetic seismogram. The simulation tests show that equivalent results can beobtained, regardless of whether the frst-order or second-order separate elastic wave equationsare used for obtaining the pure P-or S-wavefeld. The stacked pure P-and S-wavefelds areequal to the mixed wave felds calculated using the corresponding frst-order or second-orderfull elastic wave equations. These mixed equations are computationally slightly lessexpensive than solving the separate equations. The attra ction of the separate equations is thatthey achieve separated P-and S-wavefelds which can be used to test the efficacy of wavedecomposition procedures in multi-component processing. The second-order separate elasticwave equations are a good choice because they offer information on the pure P-wave orS-wave displacements.Secondly we also use the high-order staggered-grid finite-difference method to simulatethe mixed wavefield in anisotropic media, which contains the mixed wavefield with quasi-Pand quasi-S waves. In order to separate the pure qP from qSV wavefield in anisotropic media,it is useless to use the divergence and curl operation as we did in isotropic media. It isconstructive to use a pseudo-derivative operator to separate the pure qP and qSV wavefieldsbased on the solution of the Christoffel equation. Although the pseudo-derivative operator canget pure qP and qSV wavefield, it requires a large memory in the calculation and is more complex in actual model simulation.