Effective algorithms for sourcewise approximation of geopotential fields

Abstract

A specialized class of fast algorithms for sourcewise approximation of potential fields, which is intended for mass use in the applications associated with handling large and extralarge measurement data, is developed. Pursuing the objective of the work, we included two informal requirements in the set of the criteria to be met by our algorithms: they should have a sufficiently simple mathematical structure which is transparent for the geophysicist and they should be quite easy to program. Both these requirements are dictated by the present-day practice existing in geology, when the absence of the centralized provision of program products by the geological organizations makes the interpreter create the necessary software themselves. Among the distinguishing features of the three suggested algorithms is the fact that the dimensionality of the approximating construction is not specified a priori but is determined a posteriori. Due to this, it turned out to be helpful to combine one of these algorithms with the fast wavelet transform, which enables the dimension of the future sourcewise approximation and the amount of computing resources required for the implementation of the main algorithm to be estimated a priori. The examples of the practical application of these technologies are presented. The promising paths for the future development of the algorithms for sourcewise approximation of the potential fields are outlined.