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Role of the inhomogeneity angle in anisotropic attenuation analysis

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Abstract

The inhomogeneity angle (the angle between the real and imaginary parts of the wave vector) is seldom taken into account in estimating attenuation coefficients from seismic data. Wave propagation through the subsurface, however, can result in relatively large inhomogeneity angles ξ, especially for models with significant attenuation contrasts across layer boundaries. Here, we study the influence of the angle ξ on phase and group attenuation in arbitrarily anisotropic media using the first‐order perturbation theory verified by exact numerical modeling. Application of the spectral‐ratio method to transmitted or reflected waves yields the normalized group attenuation coefficient Ag, which is responsible for the amplitude decay along seismic rays. Our analytic solutions show that unless the inhomogeneity angle is uncommonly large, the coefficient Ag is close to the normalized phase attenuation coefficient A computed for ξ=0° (Aξ=0°). The coefficient Aξ=0° can be inverted directly for the attenuation‐anisotropy parameters, so no knowledge of the inhomogeneity angle is required for attenuation analysis of seismic data. This conclusion remains valid even for high attenuation with the quality factor Q less than 10 and strong velocity and attenuation anisotropy.