Abstract

Elastic upscaling of thinly layered rocks typically is performed using the established Backus averaging technique. Its poroelastic extension applies to thinly layered fluid-saturated porous rocks and enables the use of anisotropic effective medium models that are valid in the low- and high-frequency limits for relaxed and unrelaxed pore-fluid pressures, respectively. At intermediate frequencies, wave-induced interlayer flow causes attenuation and dispersion beyond that described by Biot's global flow and microscopic squirt flow. Several models quantify frequency-dependent, normal-incidence P-wave propagation in layered poroelastic media but yield no prediction for arbitrary angles of incidence, or for S-wave-induced interlayer flow. It is shown that generalized models for P-SV-wave attenuation and dispersion as a result of interlayer flow can be constructed by unifying the anisotropic Backus limits with existing P-wave frequency-dependent interlayer flow models. The construction principle is exact and is based on the symmetry properties of the effective elastic relaxation tensor governing the pore-fluid pressure diffusion. These new theories quantify anisotropic P- and SV-wave attenuation and velocity dispersion. The maximum SV-wave attenuation is of the same order of magnitude as the maximum P-wave attenuation and occurs prominently around an angle of incidence of 45°. For the particular case of a periodically layered medium, the theoretical predictions are confirmed through numerical simulations.

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