We study the discrepancy between the effective flow permeability and
the effective seismic permeability, that is, the effective permeability
controlling seismic attenuation due to wave-induced fluid flow, in
2D rock samples having mesoscopic heterogeneities and in the presence
of strong permeability fluctuations. In order to do so, we employ
a numerical oscillatory compressibility test to determine attenuation
and velocity dispersion due to wave-induced fluid flow in these kinds
of media and compare the responses with those obtained by replacing
the heterogeneous permeability field by constant values, including
the average permeability as well as the effective flow permeability
of the sample. The latter is estimated in a separate upscaling procedure
by solving the steady-state flow equation in the rock sample under
study. Numerical experiments let us verify that attenuation levels
are less significant and the attenuation peak gets broader in the
presence of such strong permeability fluctuations. Moreover, we observe
that for very low frequencies the effective seismic permeability
is similar to the effective flow permeability, while for very high
frequencies it approaches the arithmetic average of the permeability
field.