There is increasing evidence to suggest that the presence of mesoscopic
heterogeneities constitutes the predominant attenuation mechanism
at seismic frequencies. As a consequence, centimeter-scale perturbations
of the subsurface physical properties should be taken into account
for seismic modeling whenever detailed and accurate responses of
the target structures are desired. This is, however, computationally
prohibitive since extremely small grid spacings would be necessary.
A convenient way to circumvent this problem is to use an upscaling
procedure to replace the heterogeneous porous media by equivalent
visco-elastic solids. In this work, we solve Biot's equations of
motion to perform numerical simulations of seismic wave propagation
through porous media containing mesoscopic heterogeneities. We then
use an upscaling procedure to replace the heterogeneous poro-elastic
regions by homogeneous equivalent visco-elastic solids and repeat
the simulations using visco-elastic equations of motion. We find
that, despite the equivalent attenuation behavior of the heterogeneous
poro-elastic medium and the equivalent visco-elastic solid, the seismograms
may differ due to diverging boundary conditions at fluid-solid interfaces,
where there exist additional options for the poro-elastic case. In
particular, we observe that the seismograms agree for closed-pore
boundary conditions, but differ significantly for open-pore boundary
conditions. This is an interesting result, which has potentially
important implications for wave-equation-based algorithms in exploration
geophysics involving fluid-solid interfaces, such as, for example,
wave field decomposition.