Mathematics and Statistics

Abstract

This chapter consists of two main parts, an introduction to adjustment techniques (Sects. 2.1, 2.2) and an overview of geostatistical methods (Sect. 2.3). The contents has many relations to other chapters of the handbook. In particular, the adjustment technology is a foundation of many data capture methods and geostatistical methods are applied in marine GIS and geology. Section 2.1 starts with an introduction to the Gauss–Markov model, discusses error propagation, and explains the role of covariance. The positional accuracy improvement, a key method for the reduction of geometrical errors present in old paper maps, is the main topic of the remainder of Sects. 2.1, 2.2. Many related topics of positional accuracy improvement are addressed such as datum and conformal transformation as well as the consideration of geometric constraints. Section 2.3 starts with an example and then describes the most common methods for processing and analysis of huge amounts of geodata, random fields and variograms. Important terms such as stationarity, intrinsic model, and ergodicity are explained. The chapter concludes with a discourse about kriging (Sect. 2.3.6), which is a common method for the interpolation of geodata in order to estimate the contents of unknown and inaccessible mineral deposits.