## P and S velocity approximations in a poroviscoelastic medium

### P. F. Daley

Biot's equations of particle motion for wave propagation in a fluid saturated poroviscoelastic medium are manipulated to obtain zero and first order approximations to the fast compressional (P) wave and shear (S) wave velocities. The expressions obtained are used in the numerical investigation of the effects on these velocities resulting from the variation of quantities defining the solid and the fluid, specifically porosity and permeability, as well as others, inherent in the theory. In addition, the first order velocity approximations are complex functions, in terms of the quality factors, QP and QS, which define the attenuation properties in a poroviscoelastic medium. There are numerous formulations of the equations of motion for this problem, together with differences in notation. A fairly standard definition has been chosen for use here, where the vector quantities indicate the particle displacement vector in the solid and the particle displacement vector of the fluid relative to that in the solid. Zero and first order expressions for the complex fast compressional wave velocity and the shear wave velocity are obtained and used within the context of viscoelasticity to obtain some initial insight into the more general poroviscoelastic problem.