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Homogeneous VTI layer

Our next analytical example is a horizontal reflector in a homogeneous VTI (vertically transverse isotropic) medium. As derived in Appendix E, the approximation coefficients, under the assumption of the acoustic approximation of Alkhalifah (1998), take the form

$\displaystyle A$ $\textstyle =$ $\displaystyle -4\,\eta\;,$ (34)
$\displaystyle B$ $\textstyle =$ $\displaystyle \frac{1 + 8\,\eta + 8\,\eta^2}{1 + 2\,\eta}\;,$ (35)
$\displaystyle C$ $\textstyle =$ $\displaystyle \frac{1}{(1 + 2\,\eta)^2}\;.$ (36)

Equation 2 with coefficients given by equations 34-36 is precisely equivalent to the traveltime approximation suggested previously by Fomel (2004). Fomel (2004) shows comparisons with alternative non-hyperbolic approximations, which demonstrate superior accuracy of equation 2 in case of strongly anisotropic media.