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Oscillatory fluid movements in heterogeneous porous rocks induced by seismic waves cause dissipation of wave field energy. The resulting seismic signature depends not only on the rock compressibility distribution, but also on a statistically averaged permeability. This so-called equivalent seismic permeability does not, however, coincide with the respective equivalent flow permeability. While this issue has been analyzed for one-dimensional (1D) media, the corresponding two-dimensional (2D) and three-dimensional (3D) cases remain unexplored. In this work, this topic is analyzed for 2D random medium realizations having strong permeability fluctuations. With this objective, oscillatory compressibility simulations based on the quasi-static poroelasticity equations are performed. Numerical analysis shows that strong permeability fluctuations diminish the magnitude of attenuation and velocity dispersion due to fluid flow, while the frequency range where these effects are significant gets broader. By comparing the acoustic responses obtained using different permeability averages, it is also shown that at very low frequencies the equivalent seismic permeability is similar to the equivalent flow permeability, while for very high frequencies this parameter approaches the arithmetic average of the permeability field. These seemingly generic findings have potentially important implications with regard to the estimation of equivalent flow permeability from seismic data. [ABSTRACT FROM AUTHOR]