Random Functions and their Application in Geology

Abstract

Many regionalized variables occurring in geology may be interpreted as a realization (sample functions) of random functions (RF). The powerful tools of RF theory, therefore, may be used to describe and explain properties of geological phenomena as well as solving practical problems. Geostatistics in the strict sense are based on the variogram of a stationary (or, more generally, intrinsic) RF and imply applications in mining estimation. In the nonstationary case, universal kriging procedures give the best possible estimator of a trend (drift) and may be applied to contouring problems. This paper examines what minimal probabilistic characteristic of RF is necessary to solve a given practical problem (global or local linear estimation), and what hypothesis is required for a possible estimation of this minimal characteristic.