Solution of problems of geological computer mapping on the basis of potential polynomials

Operating computer software for mapping in isolines by scattered data is divided into two principally different classes. The first class includes developments based on dynamic programming and operating with discrete models of surfaces - network functions (a typical example is the well-known software Surfer developed by the American company Golden Software). Examples of the second class are the software LIDA-3 developed at the Computation Center, Novosibirsk, and a software developed at the West-Siberian Geological Research Institute, Tyumen', which use the methods of function approximation and operate with bicubic splines, i.e., use continual models. This paper, also based on continual methods, proposes a new approach to the problem under consideration, which permits overcoming the known faults of discrete optimization and spline approximation. The function of several real variables, specified at the points of a finite random set, is interpolated by a generalized polynomial constructed by potentials forming a strongly-linearly independent basis system. Some basis systems have been studied, for which an almost certain solvability of the problems of finding an interpolation potential polynomial has been proved. It is shown that the free choice of basis potentials in the proposed approach permits one to obtain results satisfying different technological requirements and the developed technique may be a basis for solving both standard and nonstandard problems of computer mapping.