Over 15 years ago, Backus (1965) demonstrated approximate equations for the velocity variations of body waves in weakly anisotropic solids. The P wave equation is widely quoted (Aki and Richards (1980) and many others) as modeling P wave variations over all planes in all anisotropic solids. As there appears to be revival of interest in anisotropy, it is worthwhile to note a minor limitation to the application of the P wave equation and to draw attention to some similar linear equations for shear waves, which combined with the P wave equation are very successful in modeling the velocity variations of anisotropic solids.
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Stuart Crampin (1982) studied this question.
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