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.