Velocity-saturation relation for rocks with fractal distribution of the pore fluids

Abstract

Seismic attributes like attenuation and velocity dispersion are sensitive to the pore fluid distribution in rocks. That is because seismic waves induce local pressure gradients between fluid patches of different elastic properties and consequently induce local fluid flows that are accompanied by internal friction. This effect is known as wave-induced-flow and it has the potential to characterize the heterogeneous pore fluid distributions. In particular, velocity-saturation relationships are of practical importance because of their experimental accessibility. It is the purpose of this study to infer the dependencies of wave attenuation and phase velocity dispersion as a function of the pore fluid saturation assuming that the fluid patches are of fractal nature. We develop a model of elastic wave attenuation and dispersion for 3D patchy saturated rocks where the patch distribution is fractal. In this paper we show that field observations, where the velocity-saturation relationship is close to the Wood bound despite the existence of fluid patch sizes that suggest proximity to the Hill bound, can be consistently modeled using the proposed theory. The theory is also conform with seismic observations assuming quasi frequency-independent attenuation.