Waves in strata

Nonhyperbolic curves

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

$$t^2 = \tau^2 + { x^2 \over v^2 } \ + x^4 \times {\rm parameter}$$ (34)

$$(t-t_0)^2 = (\tau-t_0)^2 + { x^2 \over v^2 }$$ (35)

Equation (3.34) has an extra adjustable parameter of no simple interpretation other than the beginning of a power series in $x^2$. I prefer Equation (3.35) where the extra adjustable parameter is a time shift $t_0$ 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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