One of the most important mechanisms of P?wave attenuation at seismic
frequencies is known as ?mesoscopic loss?, and is caused by the presence
of heterogeneities larger than the pore size but smaller than the
predominant wavelengths (mesoscopic?scale heterogeneities). These
effects are caused by equilibration of wave?induced fluid pressure
gradients via a slow?wave diffusion process. To perform numerical
simulations in these type of media using Biot's equations of motion
at the macroscale, it is necessary to employ extremely fine meshes
to properly represent these mesoscopic heterogeneities and their
attenuation effects on the fast waves, which makes this procedure
computationally very expensive or even not feasible. An alternative
approach is to employ the numerical upscaling procedure recently
presented by the authors, to determine equivalent undrained complex
frequency dependent plane wave and shear moduli defining at the macroscale
a viscoelastic medium behaving in similar fashion as the original
Biot medium. These equivalent moduli are determined performing numerical
compressibility and shear tests on a representative sample of heterogeneous
bulk material, allowing to reduce in several orders of magnitude
the degrees of freedom needed to characterize the material. In this
paper we present a finite element procedure, formulated in the space?frequency
domain, to perform numerical simulations of wave propagation in highly
heterogeneous fluid?filled porous sandstone employing a viscoelastic
model with complex moduli determined using the mentioned upscaling
procedure. The methodology is first validated by comparison with
previous numerical experiments using Biot's equations of motion.
Finally, the procedure is applied to simulate and analyze the effect
of underground carbon dioxide (CO2) accumulations on the amplitude
and attenuation of seismic waves.