Slow waves in fractures filled with viscous fluid

摘要

Stoneley guided waves in a fluid-filled fracture generally have larger amplitudes than other waves; therefore, their properties need to be incorporated into more realistic models. A fracture is modeled as an infinite layer of viscous fluid bounded by two elastic half-spaces with identical parameters. For small fracture thickness, a simple dispersion equation for wave-propagation velocity is obtained. This velocity is much smaller than the velocity of a fluid wave in a Biot-type solution, in which fracture walls are assumed to be rigid. At seismic prospecting frequencies and realistic fracture thicknesses, the Stoneley guided wave has wavelengths on the order of several meters and a quality factor Q exceeding 10, which indicates the possibility of resonance excitation in fluid-bearing rocks. The velocity and attenuation of Stoneley guided waves are distinctly different at low frequencies for water and for oil. The predominant role of fractures in fluid flow at field scales is supported by permeability data, showing an increase of several orders of magnitude when compared with values obtained at laboratory scales. The data suggest that Stoneley guided waves should be taken into account in theories describing seismic wave propagation in fluid-saturated rocks.