Hierarchical wave-mode separation in the poroelastic medium using eigenform analysis

In the elastic medium, the scalar and vector P- and S-waves decomposition has been extensively studied and some strategies can be extended to the poroelastic medium to extract P- and S-wavefields. However, there are three propagation modes in the poroelastic medium in Biot’s theory, namely, a fast P wave, a slow P wave, and an S wave. Because the propagation characteristic of a slow P wave is different from that of a fast P wave and S wave, the wavefield separation methods in the elastic medium cannot be directly applied to the poroelastic medium to produce a complete wave-mode separation. Based on the eigenform analysis, we have developed a hierarchical wavefield decomposition method to completely separate S waves and fast and slow P waves in the poroelastic medium. Using the Helmholtz decomposition, we first compute scalar and vector potential wavefields to separate P and S waves. Then, a cross-product operator is proposed to decompose fast and slow P waves based on their different polarization directions. To produce correct amplitudes and phases, we apply another cross-product operator and an amplitude correction term to the separated wavefields. Three numerical examples demonstrate that our method can produce accurate fast P-wave, slow P-wave, and S-wave separation results, and the decomposed fast and slow P waves have the same phases and amplitudes as the P-wave potential wavefields.