Generalized Backus theory for poroelastic solids

The elastic upscaling of thinly layered rocks is typically performed by using the well- known Backus average. In layered porous structures the effect of pore- fluid pressure relaxation causes characteristic attenuation and dispersion of seismic waves. The poroelastic Backus average allows to compute the elastic high- and low- frequency limits of the layered medium, where the fluid pressure is either unrelaxed in the former and fully relaxed in the latter case, respectively. The theory of layered porous media is extended by combining the frequency dependent description of inter- layer fbw and the poroelastic Backus limits. This is generally possible due to a symmetry property of the effective elastic relaxation tensor. The result is a generalized Backus theory that allows to predict the attenuation anisotropy in addition to the dispersion anisotropy of poroelastic layered media.