Linear estimation of random fields with second-order increments and its application (Q1101057)

The purpose of this paper is to develop a mathematical model of a class of nonstationary random fields with second-order increments and to consider the estimation problem of the random field from noisy observation data obtained at scattered locations. First, a theory of random fields which are nonstationary with second-order increments is developed concerning several mathematical properties, extending the discussion to the intrinsic random field and its ergodic property. Secondly, minimum variance estimators for a state of the random field at an arbitrary location in the two-dimensional domain are considered for both cases where the information about statistical properties of the random field is a priori available and not. The estimators obtained are compared with kriging which is a useful interpolation method used in geostatistics and hydrosciences. Finally, a numerical example is presented for examining the estimators for identifying the variogram of the given random field, and the proposed estimators are tested for real meteorological data to establish a weather map.