Effective attenuation anisotropy of layered media

Abstract

Assuming that the stiffness contrasts, as well as the intrinsic velocity and attenuation anisotropy, are weak, we develop explicit first-order (linear) and secondorder (quadratic) approximations for the attenuationanisotropy parameters Q , δQ , and γQ of effective VTI (transversely isotropic with a vertical symmetry axis) media. Whereas the first-order approximation for each parameter is given simply by the volume-weighted average of its interval values, the second-order terms reflect the coupling between various factors related to both heterogeneity and intrinsic anisotropy. Interestingly, the effective attenuation for Pand SV-waves is anisotropic even for a medium composed of isotropic layers with no attenuation contrast, provided there is a velocity variation among the constituents. Contrasts in the intrinsic attenuation, however, do not create attenuation anisotropy, unless they are accompanied by velocity contrasts. Extensive numerical testing shows that the second-order approximation for Q , δQ , and γQ is close to the exact solution for most plausible subsurface models.