Role of the inhomogeneity angle in anisotropic attenuation analysis

摘要

The inhomogeneity angle (the angle between the real andimaginary parts of the wave vector) is seldom taken into accountin estimating attenuation coefficients from seismic data. Wavepropagation through the subsurface, however, can result in rela-tively large inhomogeneity angles 6, especially for models withsignificant attenuation contrasts across layer boundaries. Herewe study the influence of the angle on phase and group attenua-tion in arbitrarily anisotropic media using the first-order pertur-bation theory verified by exact numerical modeling. Applicationof the spectral-ratio method to transmitted or reflected wavesyields the normalized group attenuation coefficient Ag, which isresponsible for amplitude decay along seismic rays. Our analyticsolutions show that for a wide range of inhomogeneity angles,the coefficient A_gis close to the normalizedphaseattenuationcoefficient A computed for ξ= 0° (Aξ=0°). The coefficient=0° can be inverted directly for the attenuation-anisotropyparameters, so no knowledge of the inhomogeneity angle is re-quired for attenuation analysis of seismic data. This conclusionremains valid even for uncommonly high attenuation with thequality factor Q less than 10 and strong velocity and attenuationanisotropy. However, the relationship between group and phaseattenuation coefficients becomes more complicated for relativelylarge inhomogeneity angles approaching so-called "forbiddendirections." We also demonstrate that the velocity function re-mains practically independent of attenuation for a wide rangeof small and moderate anglesIn principle, estimation of theattenuation-anisotropy parameters from the coefficientAξ=0°requires computation of the phase angle, which dependson the anisotropic velocity field. For moderately anisotropicmodels, however, the difference between the phase and groupdirections should not significantly distort the results of attenua-