Dictionary:Nonhyperbolic normal-moveout (velocity) analysis

{{#category_index:N|nonhyperbolic normal-moveout (velocity) analysis}} Analysis that allows for typical vertical changes in velocity and anisotropy when using long offsets, that is, where the offset exceeds the reflector depth. In this case the hyperbolic equation for a reflection can often be expressed as

$t_{x}^{2}=t_{0}^{2}\left[1+\left({\frac {x}{t_{0}V}}\right)^{2}-{\frac {2\eta \left({\frac {x}{t_{0}V}}\right)^{4}}{1+(1+2\eta )\left({\frac {x}{t_{0}V}}\right)^{2}}}\right]$,

where t₀ is the zero-offset traveltime, x is offset, V is P-wave velocity, and $\eta ={\frac {\varepsilon -\delta }{1+2\delta }}$ where $\varepsilon$ and $\delta$ are Thomsen anisotropic parameters (q.v.).

Use of the 4^th-order term given by a Taylor expansion corrects for the undesirable "hockey-stick" effect.