Reflection and transmission coefficients in terms of pressure for Biot’s compressional waves and the importance of the shear modulus for Biot’s slow wave

The method to determine reflection and transmission coefficients in terms of pressure at the fluid–sediment interface is presented. In general, reflection and transmission coefficients derived from the Biot theory have been computed using displacement potentials. Within the framework of the Biot theory it is assumed that the fluid‐saturated unconsolidated sediment has low values of frame bulk and shear moduli relative to the other moduli of the medium and the shear wave is negligible. This enables to treat the Biot theory easier. By introducing effective densities, reflection and transmission coefficients can be treated as if the medium is a fluid. This approach using the models decoupling method is fairly different from the effective density fluid model [K. Williams, J. Acoust. Soc. Am. 110, 2276–2281 (2001)]. It is shown that pressure coefficients give the same results as computed using displacement potentials. This method gives the advantage of directly computing the pressure for problems of reflection, transmission, and scattering. However, boundary conditions should be carefully treated. The pressure coefficient for Biot’s slow wave cannot be accurately calculated when the equilibrium of solid pressure at the interface is constrained instead of the normal traction. This disagreement demonstrates that the shear modulus plays an important role in the generation of the slow wave.