We have investigated viscoelastic substitute models for seismic attenuation caused by fluid pressure diffusion in fluid-saturated porous media. Fluid pressure diffusion may locally occur associated with fracture leak off and/or squirt flow. We use a homogenization scheme with numerical model reduction (NMR), recently established in the literature, and we derive the corresponding viscoelastic material properties that are apparent at a larger scale (i.e., the observer scale). Moreover, we find that the rheology of the resulting viscoelastic model is of the Maxwell-Zener type. Based on a series of numerical experiments, we find that this method is able to accurately and efficiently predict the overall attenuation and stiffness moduli dispersion for a range of scenarios without resolving the substructure problem explicitly. Computational homogenization, together with NMR, can be useful to simulate seismic wave propagation using a viscoelastic substitute model that accurately reproduces the energy dissipation and dispersion of a heterogeneous medium in which squirt flow and/or fracture leak-off occurs.

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