Dictionary:C-wave moveout

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With C-wave gathers the moveout will not be symmetric (as with split-spread P-wave gathers) and the arrival time expression, for 1D subsurface, is[1]

${\displaystyle t_{C}^{2}=t_{CO}^{2}\left[1+C_{1}\left({\frac {x}{t_{CO}V_{CNMO}}}\right)+{\frac {x^{2}}{t_{CO}^{2}V_{CNMO}^{2}}}+C_{3}\left({\frac {x}{t_{CO}V_{CNMO}}}\right)^{3}-{\frac {C_{4}\left(\displaystyle {\frac {x}{t_{CO}V_{CNMO}}}\right)^{4}}{1+C_{5}\left(\displaystyle {\frac {x}{t_{CO}V_{CNMO}}}\right)^{2}}}\right].}$

equation (5.2.5), Thomsen (2002), with the final Taylor expansion term modified by a physically-based denominator designed to enforce proper asymptotic behavior at long offsets.

The non-hyperbolic moveout coefficent ${\displaystyle C_{1}}$ tends to be small and may be ignored for large offsets. Nonhyperbolic moveout parameter ${\displaystyle C_{3}}$ tends to be positive.

The extra coefficient is defined by

${\displaystyle C_{5}={\frac {C_{4}}{\left(1-\displaystyle {\frac {V_{CNMO}^{2}}{V_{P90}^{2}}}\right)}}\qquad {\mbox{where}}\qquad V_{P90}=V_{PNMO}(1+2\eta )}$

where the anisotropic parameter ${\displaystyle \eta }$ governs long-offset P-wave moveout.

References

1. Thomsen, L. (2002), Understanding seismic anisotropy in exploration and exploitation, 2002 Distinguished Instructor Short Course, Distinguished Instructor Series, No. 5, Society of Exploration Geophysicists