Approximation for reflection and transmission at a thin isotropic poroelastic bed between two isotropic elastic half-spaces

Seismic responses from a horizontal poroelastic layer provide chances to detect fluids and characterize reservoirs. The poroelastic layer can be considered a thin poroelastic bed if the layer's thickness is less than about one-eighth of the P-wave wavelength. Most previous theoretical studies on the reflection and transmission of waves in a model containing a thin poroelastic bed employ fluid or poroelastic medium as the overlying media. Existing approximate formulas of PP-wave reflection coefficients are given for P-wave normal-incidence. Thus, this paper derived the wave reflection and transmission approximate formulas of a thin poroelastic bed between two elastic half-spaces with P-wave oblique incident. First, we illustrated the exact reflection and transmission matrix equations for P-wave incidents based on poroelasticity theory and the boundary conditions. Assuming the poroelastic bed's thickness is far less than wavelengths of S- and P-waves, approximate reflection and transmission formulas are expanded in Taylor series centred at value of the parameter defined as the product of angular frequency, thickness and slowness. Numerical results show that the thinner the poroelastic layer, the closer the approximate reflection and transmission coefficients are to the exact ones. The approximate formulas are valid for small and medium angles. Approximated PP-wave reflection and transmission coefficients are closer to the exact values than those of the converted waves, which is caused by the fact that P-wave has a lower slowness than S-wave.