Estimation of a multidimensional covariance function in case of anisotropy. (English) Zbl 0970.86544
Summary: A model of a multivariate covariance function with an ellipsoidal directional correlation scale is developed. The axes of the ellipsoidal scale are related to the eigenvalues and eigenvectors of a matrix \(B\) which characterizes the ellipsoid of the range of influence. The matrix \(B\) is found to be related to a matrix \(T\) which can be estimated directly from sparse sampling data and can be used to determine estimates of the matrix \(B\). The method is applied to both two-dimensional and three-dimensional cases. The numerical results show that satisfactory accuracy is obtained with sparse sampling data from an anisotropic random function.
References:
| [1] | Christakos, G., 1992,Random Field Models in Earth Science: Academic Press, San Diego, 474 p. · Zbl 0759.60055 |
| [2] | David, M., 1977,Geostatistical Ore Reserve Estimation: Elsevier, Amsterdam, 364 p. |
| [3] | Hagan, L. R., 1982,Application of Spectral Theory and Analysis in Mining Geostatistics and Statistical Linear Wave Theory: University of Wyoming, 338 p. |
| [4] | Hogg, R., and Craig A., 1968,Introduction to Mathematical Statistics: MacMillan, New York. 383 p. |
| [5] | Isaaks, E. H., and Srivastava, R. M., 1989,Applied Geostatistics: Oxford University Press, New York, 561 p. |
| [6] | Journel, A. G., and Huijbregts, C. J., 1978,Mining Geostatistics: Academic Press. New York, 600 p. |
| [7] | Marquardt, D. W., 1963, An algorithm for least squares estimation of nonlinear parameters: Soc. Ind. Appl. Math., v. 11, p. 431–441. · Zbl 0112.10505 · doi:10.1137/0111030 |
| [8] | Taheri, S. M., 1980.Data Retrieval and Multidimensional Simulation of Mineral Resources: University of Wyoming, 316 p. |
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