Half-tapering strategy for conditional simulation with large datasets

  • D. MarcotteEmail author
  • D. Allard
Original Paper


Gaussian conditional realizations are routinely used for risk assessment and planning in a variety of Earth sciences applications. Assuming a Gaussian random field, conditional realizations can be obtained by first creating unconditional realizations that are then post-conditioned by kriging. Many efficient algorithms are available for the first step, so the bottleneck resides in the second step. Instead of doing the conditional simulations with the desired covariance (F approach) or with a tapered covariance (T approach), we propose to use the taper covariance only in the conditioning step (half-taper or HT approach). This enables to speed up the computations and to reduce memory requirements for the conditioning step but also to keep the right short scale variations in the realizations. A criterion based on mean square error of the simulation is derived to help anticipate the similarity of HT to F. Moreover, an index is used to predict the sparsity of the kriging matrix for the conditioning step. Some guides for the choice of the taper function are discussed. The distributions of a series of 1D, 2D and 3D scalar response functions are compared for F, T and HT approaches. The distributions obtained indicate a much better similarity to F with HT than with T.


Wendland covariance functions Sparsity index Infill asymptotics Spectral density Covariance tapering Taper function 



We are indebted to one anonymous reviewer for his attentive and detailed review and for his numerous constructive comments. We thank Pr. Emilio Porcu from Universidad Técnica Federico Santa María in Valparaiso (Chile) for fruitful discussions and for providing us working material on generalized Wendland covariance functions and their use under fixed domain asymptotics. This research was financed in part by National Science Research Council of Canada (Grant RGPIN105603-05).


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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Département des génies civil, géologique et des minesPolytechnique MontréalMontréalCanada
  2. 2.Biostatistique et Processus Spatiaux (BioSP)INRAAvignonFrance

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