Abstract
A gridding method commonly called minimum curvature is widely used
in the earth sciences. The method interpolates the data to be gridded
with a surface having continuous second derivatives and minimal total
squared curvature. The minimum-curvature surface has an analogy in
elastic plate flexure and approximates the shape adopted by a thin
plate flexed to pass through the data points. Minimum-curvature surfaces
may have large oscillations and extraneous inflection points which
make them unsuitable for gridding in many of the applications where
they are commonly used. These extraneous inflection points can be
eliminated by adding tension to the elastic-plate flexure equation.
It is straightforward to generalize minimum-curvature gridding algorithms
to include a tension parameter; the same system of equations must
be solved in either case and only the relative weights of the coefficients
change. Therefore, solutions under tension require no more computational
effort than minimum-curvature solutions, and any algorithm which
can solve the minimum-curvature equations can solve the more general
system. We give common geologic examples where minimum-curvature
gridding produces erroneous results but gridding with tension yields
a good solution. We also outline how to improve the convergence of
an iterative method of solution for the gridding equations.
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