Attenuation and dispersion of P-waves in fluid-saturated porous rocks with a distribution of coplanar cracks — Scattering approach

Abstract

Wave-induced fluid flow (WIFF) between cracks and micro-pores is one of the major mechanisms in causing attenuation and dispersion within seismic frequency ranges. Previous non-interaction-approximation (NIA) models often assume the distribution of cracks is dilute, neglecting the influences of interacting cracks on dispersion and attenuation. To overcome this restriction, we investigate the interaction between coplanar cracks and their influences on seismic dispersion and attenuation. First, a scattering problem for a longitudinal (P) wave normally impinging on a plane with equally distributed coplanar cracks in a porous medium is solved using integral transform approach. Then, based on the solution, an effective wavenumber is derived for P-wave propagation in a porous material with coplanar cracks. It is found that the magnitude of dispersion and attenuation can significantly increase when the spacing between adjacent cracks decreases even if the crack density is unchanged. Moreover, frequency-dependent asymptotic behavior of inverse quality factor is also different from that of the NIA models at frequencies lower than the WIFF relaxation frequency. Specifically, the inverse quality factor scales with the square root of frequency at low frequencies. When the spacing between adjacent cracks is large, an additional frequency-dependent scale occurs at relatively higher frequencies (but still lower than the WIFF relaxation frequency) with inverse quality factor scales with the first power of frequency. When the spacing becomes much larger so that the interaction between the adjacent cracks is negligible, the present model exactly reduces to a NIA model for a distribution of aligned slit cracks and the first power scale can prevail attenuation within low frequencies.