Backus averaging generalized for poroelasticity

Typical sedimentary rocks are not purely elastic materials but fluid saturated, porous composites. It seems natural to investigate the influence of porosity fluctuations and other fluid properties in the context of Backus averaging for thinly layered reservoir rock. By averaging over many thin layers consisting of materials with different bulk- and shear moduli the vertically heterogeneous, isotropic medium will be replaced by a homogeneous, anisotropic (TI) effective medium. The layer thicknesses must be small compared to the wavelength of seismic waves propagating in the medium. We determine the five resulting poroelastic constants Bi, Bi, B; of the TI effective medium in terms of the original Backus constants MB, BB, FB, CB and LB and of further terms describing the influence of fluid properties. Hereby we also determine the poroelastic Biot constants Bs, B; and Bs to describe the TI poroelastic medium completely. Further we generalize this approach to layers which are poroelastic and itself TI. These results can serve as a basis to study the influence of porosity fluctuations and fluid properties on the propagation of obliquely incident P-,SV- and SH- seismic plane waves in a poroelastic, fluid-saturated, and finely layered medium. Since the permeability of a porous medium will vary from layer to layer as the poroelastic constants do, we calculate the effective anisotropic permeability as a function of the fluctuations of porosity.