ESTIMATION OF A MULTIDIMENSIONAL COVARIANCE FUNCTION IN CASE OF ANISOTROPY

A model of a multivariate covariance function with an ellipsoidal dire ctional correlation scale has been developed. The axes of the ellipsoi dal scale are related to the eigenvalues and eigenvectors of a matrix B which characterizes the ellipsoid of the range of influence. The mat rix B is found to be related to a matrix T which can be estimated dire ctly from sparse sampling data and can be used to determine estimates of the matrix B. The method has been applied to both two-dimensional a nd three-dimensional cases. The numerical results show that the satisf actory accuracy is obtained with sparse sampling data from an anisotro pic random function.