P-wave attenuation and dispersion in a porous medium permeated by aligned fractures—a new poroelastic approach

Abstract

An alternative method is advocated to obtain the analytical expressions of pore pressure, relative flux distribution and frame displacement in a periodic layered porous medium (White model) based on quasi-static poroelastic theory, from which the expression of the effective medium model for a P-wave propagating vertical to the layer can be obtained. Then a dispersion equation for a P-wave propagating in the porous medium permeated by aligned fractures is also presented by considering fractures as thin and highly compliant layers, with which the influence of mesoscopic fluid flow on phase velocity dispersion and attenuation is discussed under the condition of varying fracture weakness and the length scale ratio of the background layer to the fracture layer. For both cases, fluid flow induced by the Biot slow wave can result in apparent attenuation and dispersion in the usual seismic frequency band (5–500 Hz). The magnitude of velocity dispersion and attenuation of the P-wave will increase with increasing fracture weakness or with decreasing length scale ratio, and also relaxation peak and maximum attenuation move towards low frequencies. In particular, the evolution of pore pressure and relative fluxes as a function of frequency in the medium for those two cases is present, which gives us a more physical understanding of the behaviours of P-wave velocity dispersion and attenuation due to wave-induced mesoscopic flow.