Wave-induced fluid flow is an important dissipation mechanism of seismic waves in heterogeneous porous solids and several models are reported to quantify the wave attenuation. However, its characteristic frequency dependence in randomly heterogeneous structures remains unclear. For a generic double-porosity structure the specific attenuation of compressional waves is computed from first principles. It is shown how contrasts in material properties and heterogeneity scales translate into characteristic frequency dependencies of attenuation. The results explain the observed discrepancy of the asymptotic behavior of seismic attenuation in layered porous media with periodic and random disorder.