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In the case of bilinear interpolation, the approximate function is given by,

Figure illustrates the geometry associated with bilinear
interpolation within a cell.

**bilin
**

Figure 10 Bilinear
interpolation. The function is approximated by bilinear interpolation within a
cell defined by the four corner samples. The interpolation weights depend on
the coordinates at which the path enters an leaves the cell.

The path within the cell, *t*(*x*), is approximated by a linear segment,

The Mathematica code in the appendix will calculate the appropriate
weights for each sample point. For example, the weight to be applied
to the sample point (*x*_{ix},*t*_{it}) is:
Figure shows the approximation to the original
function surface that is implied by this method. For this set of
parameters it is a reasonable approximation of the original surface.
In general bilinear interpolation is a reasonable interpolation method
for sampling intervals up to about half of the Nyquist frequency. If the
data has high dips and high frequencies the approximation may not be
valid.

**bilin-func
**

Figure 11 Input data sampled every 4ms in time
and 25m in space and then interpolated using bilinear interpolation in
space and time.

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Stanford Exploration Project

11/17/1997