To illustrate the various interpolation techniques I will use a 2-D surface
that is a plane wave of frequency, , and slowness, *p*,

Figure 1

If this data is
sampled using typical seismic data sampling rates, 4*ms* in time and 25*m* in
space, the data shown in figure is obtained.
This is the input data to the various interpolation schemes,

Figure 2

In the following examples I consider the case of an integral path on
a 2-D surface that is defined by time as a function of space, *t*(*x*).
The aim of this paper is to
obtain the integral along a particular path as the sum over all the
traces of the trace scaled by a weighting function which is localized
around the intersection of the integration trajectory and each trace,
*t*(*x*_{ix}), with nearest sample point *it*(*ix*). The curve integral
can then be expressed as a sum over the sampled data points.

11/17/1997