Acoustic axes can exist even under an infinitesimally weak anisotropy, and occur when slowness surfaces of the S1 and S2 waves touch or intersect. The maximum number of isolated acoustic axes in weak triclinic anisotropy is 16 as in strong triclinic anisotropy. The directions of acoustic axes are calculated by solving two coupled polynomial equations in two variables. The order of the equations is 6 under strong anisotropy and reduces to 5 under weak anisotropy. The weak anisotropy approximation is particularly useful, when calculating the acoustic axes under extremely weak anisotropy with anisotropy strength less than 0.1 per cent because the equations valid for strong anisotropy might become numerically unstable and their modification, which stabilizes them, is complicated. The weak anisotropy approximation can also find applications in inversions for anisotropy from the directions of acoustic axes.
Elastic-wave theory, perturbation methods, polarization, seismic anisotropy, seismic-wave progagation, shear-wave splitting.
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