GRIDDING WITH CONTINUOUS CURVATURE SPLINES IN TENSION

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. Minimum-curvature surfaces may have large oscillations and extraneous inflection points which make them unsuitable for gridding. These extraneous inflection points can be eliminated by adding tension to the elastic-plate flexure equation. 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. Common geologic examples are given where minimum-curvature gridding produces erroneous results but gridding with tension yields a good solution. Improvements to the convergence of an iterative method of solution for the gridding equations are suggested. -from Author