Nonhyperbolic curves

Occasionally data does not fit a hyperbolic curve very well. Two other simple fitting functions are

$$\begin{eqnarray} t^2 &=& \tau^2 \ +\ { x^2 \over v^2 } \ +\ x^4 \times {\rm parameter} \\ (t-t_0)^2 &=& (\tau-t_0)^2 \ +\ { x^2 \over v^2 } \end{eqnarray}$$ (34) (35)

Equation (34) has an extra adjustable parameter of no simple interpretation other than the beginning of a power series in x². I prefer Equation (35) where the extra adjustable parameter is a time shift t₀ which has a simple interpretation, namely, a time shift such as would result from a near-surface low velocity layer. In other words, a datum correction.

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