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A low-dispersive padé approximation method for wave propagation in isotropic and anisotropic poroelastic medium

ABSTRACT Seismic exploration of complex geological structure model has been paid much attention as the increasing complexity of geological structure in seismic exploration, and especially, the research on saturated porous medium saturated with fluid has become a hot topic. In our study, we propose a new Padé approximation (PAM) method of solving the elastic wave equation in the porous medium of low-frequency case. This method uses an implicit scheme derived from the rational function of time difference operator for the time discretization, which has the characters of low-dispersion and high-efficiency for time advancing. An explicit iteration for this implicit algorithm is obtained for avoiding solving a large linear system with a block tridiagonal coefficient matrix at each time step. Then, we employ the stereo-modelling method with the eighth-order accuracy for space discretization, which uses linear combination of wave field displacements and their gradients to discretize spatial derivatives and obtains a high-order approximation. Compared with the traditional method, this discretization operator has shorter operator radius and better compactness, which is beneficial for increasing the precision and imaging quality of seismic inversion and seismic migration. Theoretical analysis and numerical experiments verify that the PAM method is an accurate forwarding modelling tool. Waveforms obtained by the PAM method can well match the analytical solutions. Moreover, the seismic wave fields including fast P wave, S wave, and slow P wave for the saturated fluid porous medium can be observed clearly on coarser grids. This is in contrast with the FD method, which suffers from serious numerical dispersion.