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A New Type of Conditioning of Stationary Fields and Its Application to the Spectral Simulation Approach in Geostatistics

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Abstract

This paper considers the problem of conditional stochastic simulation in geostatistics. A new type of conditioning method that generalizes the well-known two-step conditioning approach is introduced. The distinctive feature of the new method is that it solves the modeling problem for multiple stochastic fields in a general setup. A generalized kriging procedure is developed in the paper, using linear combinations of the simulated fields as input data instead of the commonly used separate fields’ values. Although the new conditioning method was developed initially in the framework of a particular approach to geostatistical simulation (the spectral method), it can be applied in many more general settings of conditional simulation of stationary stochastic fields of arbitrary dimension. The workings of the method and its applicability are illustrated with the results of several numerical experiments, including simulation on real oil field data.

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Acknowledgements

The authors are grateful to both referees for careful reading and their useful advice. Research was partially supported by Native Towns, a social investment program of PJSC Gazprom Neft.

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Authors and Affiliations

  1. Gazpromneft Science & Technology Centre, 75-79 D, Moika River emb., St. Petersburg, Russia, 190000

    Niyaz S. Ismagilov & Andrey A. Yakovlev

  2. Saint-Petersburg State University, University Emb. 7/9, St. Petersburg, Russia, 199034

    Mikhail A. Lifshits

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  1. Niyaz S. Ismagilov
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  2. Mikhail A. Lifshits
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  3. Andrey A. Yakovlev
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Correspondence to Niyaz S. Ismagilov.

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Ismagilov, N.S., Lifshits, M.A. & Yakovlev, A.A. A New Type of Conditioning of Stationary Fields and Its Application to the Spectral Simulation Approach in Geostatistics. Math Geosci 53, 597–621 (2021). https://doi.org/10.1007/s11004-020-09872-3

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  • DOI: https://doi.org/10.1007/s11004-020-09872-3

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