Anisotropy in sedimentary rocks modeled as random media

Abstract

The anisotropic behavior to be expected from various types of sediments is investigated by considering them as laminated media, with randomly varying velocity depth distributions. Two different stochastic processes are used to model transitional and cyclic layering. The kinematics of waves propagating through the laminated media is studied by evaluating overall elastic parameters of the transversely isotropic medium in the long wavelength limit using averaging techniques. Models with strong velocity fluctuations and high correlation between P‐ and S‐wave velocities exhibit significant anisotropy, comparable in magnitude to field and laboratory measurements. Elastic wavefields for the stochastic models were computed and the results were compared with analytical and numerical results for homogeneous anisotropic media computed with the derived overall parameters. The wavefield modeling shows that anisotropy and scattering are not simply effects influencing waves on the opposite ends of the wavelength scale but that there is an intermediate range where both effects profoundly influence wave propagation.