next up previous [pdf]

Next: Can I abandon the Up: CURVED WAVEFRONTS Previous: Layered media

Nonhyperbolic curves

Occasionally data does not fit a hyperbolic curve very well. Two other simple fitting functions are
$\displaystyle t^2$ $\textstyle =$ $\displaystyle \tau^2  + { x^2 \over v^2 } \
+ x^4 \times {\rm parameter}$ (34)
$\displaystyle (t-t_0)^2$ $\textstyle =$ $\displaystyle (\tau-t_0)^2  + { x^2 \over v^2 }$ (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.