Mathematical Geology

, Volume 34, Issue 5, pp 479–503

Kriging of Regionalized Directions, Axes, and Orientations I. Directions and Axes

  • K. Gerald van den Boogaart
  • Helmut Schaeben

DOI: 10.1023/A:1016000826707

Cite this article as:
van den Boogaart, K.G. & Schaeben, H. Mathematical Geology (2002) 34: 479. doi:10.1023/A:1016000826707


The problem to predict a direction, axis, or orientation (rotation) from corresponding geocoded data is discussed and a general solution by virtue of embedding a sphere/hemisphere in a real vector space is presented. Its explicit justification in terms of mathematical assumptions concerning stationarity/homogeneity and isotropy is included. The data are modelled by a stationary random field, and the spatial correlation is represented by modified multivariate variograms and covariance functions. Various types of isotropy assumptions concerning invariance under translation/rotation of the data locations, the measurements, or a combination of both, can be distinguished and lead to different simplifications of the general cross-covariance function. Beyond spatial prediction a measure of confidence in the estimates is provided.

geostatistic manifolds isotropy assumptions 

Copyright information

© International Association for Mathematical Geology 2002

Authors and Affiliations

  • K. Gerald van den Boogaart
    • 1
  • Helmut Schaeben
    • 1
  1. 1.Mathematical Geology and Computer Sciences in GeologyFreiberg University of Mining and TechnologyFreibergGermany