# Análisis de velocidad no hiperbólica de sobretiempo normal por distancia

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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

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

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

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