Automatic interpolation methods for mapping piezometric surfaces

Abstract The purpose of analysis of spatial data should determine the approach to be adopted. If estimation is concerned with detailed local interpretation rather than some form of global averaging, then kriging would seem to be an inappropriate method. This is especially so for the interpolation of precise observations which consequently are better estimated by deterministic methods. Five such efficient direct automatic interpolation methods are discussed and applied to the contour mapping of a piezometric surface.

[1]  D. Watson.  A refinement of inverse distance weighted interpolation , 1985 .

[2]  Hiroshi Akima,et al.  A method of bivariate interpolation and smooth surface fitting based on local procedures , 1974, Commun. ACM.

[3]  D. F. Watson,et al.  Some limitations in the geostatistical evaluation of ore deposits , 1985 .

[4]  Hiroshi Akima,et al.  A Method of Bivariate Interpolation and Smooth Surface Fitting for Irregularly Distributed Data Points , 1978, TOMS.

[5]  Andre G. Journel,et al.  Geostatistics: Models and tools for the earth sciences , 1986 .

[6]  D. F. Watson,et al.  Triangle based interpolation , 1984 .

[7]  D. F. Watson,et al.  Systematic triangulations , 1983, Comput. Vis. Graph. Image Process..

[8]  R. Sibson.  A vector identity for the Dirichlet tessellation , 1980, Mathematical Proceedings of the Cambridge Philosophical Society.

[9]  D. F. Watson,et al.  Matheronian geostatistics—Quo vadis? , 1986 .

[10]  Michel Gevers,et al.  Identification and optimal estimation of random fields from scattered point-wise data , 1985, Autom..

[11]  W. J. Gordon,et al.  Shepard’s method of “metric interpolation” to bivariate and multivariate interpolation , 1978 .

[12]  D. F. Watson,et al.  Acord: automatic contouring of raw data , 1982 .

[13]  R. Franke.  Scattered data interpolation: tests of some methods , 1982 .

[14]  D. F. Watson.  Natural Neighbour Sorting , 1985, Aust. Comput. J..

[15]  C. L. Begovich,et al.  Variogram models for regional groundwater geochemical data , 1982 .

[16]  G M Philip,et al.  Letter to the editor comment on “comparing splines and kriging” , 1984 .

[17]  John C Davis.  Contouring Algorithms , .

[18]  O. Dubrule.  Comparing splines and kriging , 1984 .

[19]  J. R. Philip.  Issues in flow and transport in heterogeneous porous media , 1986 .

[20]  D. F. Watson,et al.  Comment on “a nonlinear empirical prescription for simultaneously interpolating and smoothing contours over an irregular grid” by F. Duggan , 1985 .

[21]  Mark Monmonier.  Computer-assisted cartography , 1982 .