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Orthogonal representations of random fields and an application to geophysics data

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

M. D. Ruiz-Medina  and
M. J. Valderrama
M. D. Ruiz-Medina*
Affiliation:
University of Granada
M. J. Valderrama*
Affiliation:
University of Granada
*
∗Postal address: Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain.
∗Postal address: Department of Statistics and Operations Research, University of Granada, 18071 Granada, Spain.
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Abstract

We present a brief summary of some results related to deriving orthogonal representations of second-order random fields and its application in solving linear prediction problems. In the homogeneous and/or isotropic case, the spectral theory provides an orthogonal expansion in terms of spherical harmonics, called spectral decomposition (Yadrenko 1983). A prediction formula based on this orthogonal representation is shown. Finally, an application of this formula in solving a real-data problem related to prospective geophysics techniques is presented.

Keywords

ORTHOGONAL KARHUNEN-LOÈVE EXPANSIONLAPLACE RANDOM FIELDMINIMUM-SQUARE LINEAR PREDICTIONSPECTRAL TECHNIQUES

MSC classification

Primary: 60G60: Random fields 60G12: General second-order processes
Type
Research Article
Information
Journal of Applied Probability , Volume 34 , Issue 2 , June 1997 , pp. 458 - 476
Copyright
Copyright © Applied Probability Trust 1997 

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