摘要：An important upscaling effect in heterogeneous poroelastic Biot media is the
dissipation mechanism due to wave-induced fluid flow caused by mesoscopic
scale heterogeneities, which are larger than the pore size but much smaller
than the average wavelengths of the fast waves in the seismic range
of frequencies. To perform numerical simulations using Biot’s equations of
motion, it would be necessary to employ extremely fine meshes to properly
represent these mesoscopic heterogeneities. An alternative approach to model
this type of Biot medium is to determine effective complex moduli defining
locally a viscoelastic medium having in the average the same properties than
the original medium. This work presents a finite element procedure combined
with a Montecarlo approach to estimate the effective phase velocity and
mesoscopic attenuation in highly heterogeneous porous rocks. The method involves
the use of stochastic fractals to generate different stochastic parameter
patterns within the porous sample. For each realization of the stochastic
parameters, a local boundary value problem is solved on a
representative volume of bulk material. Numerical experiments showing the
implementation of the procedure are presented.
