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10.1190/1.1442837 Society of Exploration Geophysicists Society of Exploration Geophysicists 186 4723818 5981 2020101514384900322 10.1190 2020-10-15T21:39:07Z 2002-10-11T19:40:18Z 1071 GEOPHYSICS GEOPHYSICS 0016-8033 1942-2156 03 1990 55 3 Gridding with continuous curvature splines in tension W. H. F. Smith Lamont‐Doherty Geological Observatory of Columbia University, Route 9W, Palisades, NY 10964 P. Wessel Lamont‐Doherty Geological Observatory of Columbia University 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. 03 1990 293 305 10.1190/1.1442837 10.1190/1.1442837 https://library.seg.org/doi/10.1190/1.1442837 https://library.seg.org/doi/pdf/10.1190/1.1442837 http://geophysics.geoscienceworld.org/cgi/doi/10.1190/1.1442837