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Mathematical Geology

, Volume 32, Issue 1, pp 69–85 | Cite as

Dual Kriging with Local Neighborhoods: Application to the Representation of Surfaces

  • Juan Auñón
  • J. Jaime Gómez-Hernández
Article

Abstract

Ordinary kriging, in its common formulation, is a discrete estimator in that it requires the solution of a kriging system for each point in space in which an estimate is sought. The dual formulation of ordinary kriging provides a continuous estimator since, for a given set of data, only a kriging system has to be estimated and the resulting estimate is a function continuously defined in space. The main problem with dual kriging up to now has been that its benefits can only be capitalized if a global neighborhood is used. A formulation is proposed to solve the problem of patching together dual kriging estimates obtained with data from different neighborhoods by means of a blending belt around each neighborhood. This formulation ensures continuity of the variable and, if needed, of its first derivative along neighbor borders. The final result is an analytical formulation of the interpolating surface that can be used to compute gradients, cross-sections, or volumes; or for the quick evaluation of the interpolating surface in numerous locations.

continuous interpolation analytical interpolation cartography 

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REFERENCES

  1. Dubrule, O., 1983, Two methods with different objectives: Splines and kriging: Math. Geology, v. 15, no. 2, p. 24–257.Google Scholar
  2. Galli, A., and Murillo, E., 1984, Dual kriging—Its properties and its uses in direct contouring, inG. Verly and others eds., Geostatistics for Natural Resources Characterization: D. Reidel Publishing Company, v. 2, p. 621–634.Google Scholar
  3. Journel, A. G., 1989, Fundamentals of geostatistics in five lessons, Short courses in geology: American Geophysical Union, Washington DC, v. 8.Google Scholar
  4. Matheron, G., 1975, The theory of regionalised variables and its applications, English translation of Le Cahiers du Centre de Morphologie Mathématique, Fascicule 5: Ecole des Mines de Paris, Fontainebleau, 175 p.Google Scholar
  5. Matheron, G., 1980, Splines and kriging—their formal equivalence, in Merriam, D. F. ed., Down-to-earth statistics—Solutions looking for geological problems: Syracuse University Geology Contributions, p. 77–95.Google Scholar
  6. Royer, J. J., and Vieira, P. C., 1984, Dual formalism of kriging, in G. Verly and others, eds., Geostatistics for Natural Resources Characterization: D. Reidel Publishing Company, v. 2, p. 691–702.Google Scholar
  7. Zhu, H., 1992, Dual kriging: NACOG Geostat Newsletter, v. 4, p. 4–5.Google Scholar

Copyright information

© International Association for Mathematical Geology 2000

Authors and Affiliations

  • Juan Auñón
    • 1
  • J. Jaime Gómez-Hernández
    • 2
  1. 1.Dep. De Expresión Gráfica en la IngenieríaUniversidad Politécnica de ValenciaValenciaSpain
  2. 2.Dep. de Ingeniería Hidráulica y Medio AmbienteUniversidad Politénica de ValenciaValenciaSpain

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