An accurate estimation of the gradient of the slowness field is necessary if we are to trace rays in a velocity model with high velocity contrast. Therefore, I have chosen to use cubic B-splines Inoue (1986) to parametrize the slowness model, which enables me to calculate the slowness gradient at an arbitrary point in the model. Another reason for using splines is that a wide variety of slowness models can be represented by a few spline coefficients. This means that the number of parameters in an optimization scheme that inverts for slowness can be reduced considerably.

The spline representation of a two-dimensional slowness model is

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2/5/2001