Mathematical Geosciences

, Volume 48, Issue 3, pp 305–328

Anisotropy Models for Spatial Data

Special Issue

DOI: 10.1007/s11004-015-9594-x

Cite this article as:
Allard, D., Senoussi, R. & Porcu, E. Math Geosci (2016) 48: 305. doi:10.1007/s11004-015-9594-x


This work addresses the question of building useful and valid models of anisotropic variograms for spatial data that go beyond classical anisotropy models, such as the geometric and zonal ones. Using the concept of principal irregular term, variograms are considered, in a quite general setting, having regularity and scale parameters that can potentially vary with the direction. It is shown that if the regularity parameter is a continuous function of the direction, it must necessarily be constant. Instead, the scale parameter can vary in a continuous or discontinuous fashion with the direction. A directional mixture representation for anisotropies is derived, in order to build a very large class of models that allow to go beyond classical anisotropies. A turning band algorithm for the simulation of Gaussian anisotropic processes, obtained from the mixture representation, is then presented and illustrated.


Anisotropy Covariance Isotropy Spatial statistics  Turning band method Variogram 

Copyright information

© International Association for Mathematical Geosciences 2015

Authors and Affiliations

  1. 1.UR546 Biostatistique et Processus Spatiaux (BioSP)AvignonFrance
  2. 2.Departamento de MatematicaUniversidad Santa MariaValparaisoChile

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