Interpolation Methods that Assume Continuous Gradients

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Most interpolation procedures assume that a smooth or continuous gradient exists between control points. This gradient may be linear or non-linear.

In cross-section, if we have observed values at 1000 and 2000 and we need to make an estimate for intermediate locations, a simple proportion can be used. The gradient in this case can be thought of as a type of transfer function:

z=f(x)

Of course, if this assumption changes and a non-linear gradient is used, the estimated value of z will change as well.

There are two types of interpolation modules that assume continuous gradients--inverse distance weighted interpolation and kriging. These two methods are explained through the links that follow.

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