Computational Homogenization of Seismic Attenuation in Fractured Rock

Paper in proceeding, 2017

© ASCE. Fluid-saturated fractured rock is well-known to exhibit a pronounced attenuation of elastic waves at low seismic frequencies due to the equilibration of wave-induced pressure gradients by pressure diffusion. At low seismic frequencies, the Poiseuille flow model results in a Darcy-type behavior for the pressure diffusion along the fractures. Moreover, it is reasonable to assume that pressure diffusion occurs on a length scale much smaller than the seismic wave length, and we, therefore, consider it as a local process. On the geological scale the material can then be interpreted as a viscoelastic medium. In the present contribution we aim to develop a computational homogenization scheme substituting the heterogeneous fractured medium by a homogeneous viscoelastic substitute model. We make use of the system's linearity and derive a reduced order formulation for the upscaling problem. Hence, we detect a reduced basis for the fluid pressure field and superimpose the stress response due to transient external loadings. Altogether, the viscoelastic substitute model can be identified at reasonable numerical costs and can be validated by numerical simulations at full mesoscopic resolution.