Reflection and transmission of elastic waves by a fluid-filled crack located in a poroelastic formation

Abstract

Elastic wave propagation in the system: porous saturated half-space – plane-parallel layer (crack) filled with a viscous fluid – porous saturated half-space is considered in this paper. Reflection and transmission coefficients of compressional and shear waves propagating in such system are calculated. Within the frame of validity of the single-scattering approximation, an expression for the complex wave number of the compressional wave propagating in a rock containing a system of thin parallel layers (cracks) is obtained. The performed calculations have shown that this wave presents strong velocity dispersion, especially at low frequencies corresponding to seismic measurements. The reflection coefficient of the elastic compressional wave incident at the boundary between the elastic half-space and porous fractured medium is calculated. It was shown that the reflection coefficient of this wave strongly depends on the frequency, especially in the low frequency range. This frequency dependence is determined by the intensive hydrodynamic flows (mesoscopic flow) generated at the boundary between the cracks and the porous matrix. The importance of the effects associated with these mesoscopic flows is illustrated by calculations of synthetic seismograms.