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Moveout-based geometrical-spreading correction for converted waves

Geometrical-spreading correction is an important component of amplitude-
variation-with-offset (AVO) analysis, which provides high-resolution informa-
tion for anisotropic parameter estimation and fracture characterization. Here,
we extend the algorithm of moveout-based anisotropic spreading correction
(MASC) to mode-converted PSV-waves in VTI (transversely isotropic with a
vertical symmetry axis) media and symmetry planes of orthorhombic media.
While the geometrical-spreading equation in terms of reflection traveltime has
the same form for all wave modes in laterally homogeneous media, reflection
moveout of PS-waves is more complicated than that of P-waves (e.g., it can be-
come asymmetric in common-midpoint geometry). Still, for models with a hor-
izontal symmetry plane, long-spread reflection traveltimes of PS-waves can be
well-approximated by the Tsvankin-Thomsen and Alkhalifah-Tsvankin move-
out equations, which are widely used for P-waves. Although the accuracy of
the Alkhalifah-Tsvankin equation is somewhat lower, it includes less moveout
parameters and helps to maintain the uniformity of the MASC algorithm for P-
and PS-waves. The parameters of both moveout equations are obtained by least-
squares traveltime fitting or semblance analysis and are different from those for
P-waves.
Testing on full-wavefield synthetic data generated by the reflectivity method for
layered VTI media confirms that MASC accurately reconstructs the plane-wave
conversion coefficient from conventional-spread PS data. Errors in the estimated
conversion coefficient, which become noticeable at moderate and large offsets,
are mostly caused by offset-dependent transmission loss of PS-waves.