Simulation of intrinsic random fields of order k with a continuous spectral algorithm

Original Paper


Intrinsic random fields of order k, defined as random fields whose high-order increments (generalized increments of order k) are second-order stationary, are used in spatial statistics to model regionalized variables exhibiting spatial trends, a feature that is common in earth and environmental sciences applications. A continuous spectral algorithm is proposed to simulate such random fields in a d-dimensional Euclidean space, with given generalized covariance structure and with Gaussian generalized increments of order k. The only condition needed to run the algorithm is to know the spectral measure associated with the generalized covariance function (case of a scalar random field) or with the matrix of generalized direct and cross-covariances (case of a vector random field). The algorithm is applied to synthetic examples to simulate intrinsic random fields with power generalized direct and cross-covariances, as well as an intrinsic random field with power and spline generalized direct covariances and Matérn generalized cross-covariance.


Non-stationary random fields Generalized direct and cross-covariances Generalized increments of order k Spectral density 



The authors acknowledge the funding by the Chilean Commission for Scientific and Technological Research (CONICYT), through Projects CONICYT/ FONDECYT/ INICIACIÓN EN INVESTIGACIÓN/ N\(^{\circ }\)11170529 (Daisy Arroyo) and CONICYT PIA Anillo ACT1407 (Xavier Emery). Two anonymous reviewers are also acknowledged for their constructive comments.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of ConcepciónConcepciónChile
  2. 2.Department of Mining EngineeringUniversity of ChileSantiagoChile
  3. 3.Advanced Mining Technology CenterUniversity of ChileSantiagoChile

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