Reflection moveout approximation for a P-SV wave in a moderately anisotropic homogeneous vertical transverse isotropic layer

Veronique Farra & Ivan Psencik


Description of the subsurface is incomplete without the use of shear waves. Use of converted waves is one way how to involve shear waves. We present and test an approximate formula for the reflection moveout of a wave converted at a horizontal reflector underlying a homogeneous VTI (transversely isotropic with the vertical axis of symmetry) layer. For its derivation, we use the weak-anisotropy approximation, i.e., we expand the square of the reflection traveltime in terms of weak-anisotropy (WA) parameters. Travel times are calculated along reference rays of converted reflected waves in a reference isotropic medium. This requires the determination of the point of reflection (conversion point) of the reference ray, at which the conversion occurs. This can be done either by a numerical solution of a quartic equation or using a simple approximate solution. Presented tests indicate that the accuracy of the proposed moveout formula is comparable with the accuracy of formulae derived in a weak-anisotropy approximation for pure-mode reflected waves. Specifically, the tests show that the maximum relative traveltime errors are well below 1% for models with P- and SV-wave anisotropy about 10% and below 2% for models with P- and SV-wave anisotropy of 25% and 12%, respectively. For isotropic media, the use of the conversion point obtained by numerical solution of the quartic equation yields exact results. The approximate moveout formula is used for the derivation of approximate expressions for the two-way zero-offset traveltime, the normal moveout velocity and the quartic term of the Taylor series expansion of the squared traveltime.

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Geophysics, 84 (2019), C75-C83.