Multiple point statistics understood in Matheronian principles


Multiple point statistics understood in Matheronian principles

van den Boogaart, K. G.

In the last years the conditional simulation of geological structures with the multiple point statistics (MPS) approach has created new opportunities for a better description of the uncertainty in inference from spatial observations to knowledge and uncertainty about the geological reality. A new paradigm of geostatistics has been created based on simulation algorithms rather than on stochastic theory. The talk thus aims at discussing MPS in the light of the ideas behind Matheron’s geostatistic. Matheron simplified the problem to linear functions due to the lack of computer power. MPS now allows incorporating nonlinearities. The normal distribution assumption was a tool to teach uncertainty to the computer. MPS now allows new tools like the training image to take that role. In this perspective MPS can be seen as the extension of Matheron’s ideas to new computational possibilities. On the other hand some of the stochastic background of Matheron’s geostatistic has been lost in the fast course of development of MPS. The talk aims at rebuilding these basics. This stochastic view to MPS allows to discuss strengths and weaknesses of various MPS applications and to ask new questions potentially improving their future performance: Which of two simulation algorithms is better? Is the training image large enough to capture the uncertainty? Does the training image adequately describe the reality? Which criteria can be used to describe the performance of a conditional simulation algorithm for a specific purpose? How large should search neighborhoods be? Adding these stochastic viewpoints is a step towards not only having good algorithms, but also good tools to judge the appropriateness of an algorithm, to anticipate possible artefacts and to see MPS as the natural evolution of Materon’s geostatistic, rather than as an alternate approach.

Keywords: Multiple Point Statistics; Uncertainty Modelling

  • Invited lecture (Conferences)
    IAMG 2014, 16th conference of the international association for mathematical geosciences, 17.-20.10.2014, New Dehli, India

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Publ.-Id: 20539