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 six under strong anisotropy and reduces to five under weak anisotropy. The weak anisotropy approximation is particularly useful, when inverting for anisotropy from the directions of acoustic axes. The minimum number of acoustic axes, which can be inverted for weak anisotropy, is seven, and at the most 13 combinations of elastic parameters can be retrieved. Numerical tests have shown that the inversion is sufficiently accurate only for very weak anisotropy with strength less than 5%, and provided that the acoustic axes used in the inversion are determined with an accuracy better than 0.3°.
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