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.
其他摘要：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.
