Body waves propagation in a fluid-saturated transversely isotropic poroelastic solid with a potential method

This study is focused on the propagation of plane harmonic body waves in a transversely isotropic linear poroelastic fluid-saturated medium, where the material symmetry axes for both solid and fluid are coincide. Simplified formulation is considered as the framework. A set of two scalar potential functions is employed to decouple the coupled fluid continuity equation and equations of motion. The velocities and corresponding attenuation coefficients of both longitudinal and transverse waves are extracted from the presented acoustic equations for the body waves. To show the validity of the analytical solution given in this paper, degeneration to the case of a single phase transversely isotropic and consequently isotropic solid is presented to provide interesting comparisons with the solutions reported in the literatures. The incompressible solid and fluid are degenerated from the general slowness obtained in this study for some special cases. In addition, the effects of mechanical and hydraulic parameters of materials on the velocity of propagation and attenuation coefficient of the waves are investigated in more detail. To this end, various synthetic poroelastic transversely isotropic materials are defined and the dependency of wave motion to these parameters is illustrated by plotting the graphs.