A High-Order, Data-Driven Framework for Joint Simulation of Categorical Variables
| Autor: | Roussos Dimitrakopoulos, Ilnur Minniakhmetov |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Computer science
0208 environmental biotechnology Approximation algorithm 02 engineering and technology Conditional probability distribution 010502 geochemistry & geophysics Grid 01 natural sciences 020801 environmental engineering Data-driven Bayes' theorem Variogram Categorical variable Spatial analysis Algorithm 0105 earth and related environmental sciences |
| Zdroj: | Geostatistics Valencia 2016 ISBN: 9783319468181 |
| DOI: | 10.1007/978-3-319-46819-8_19 |
| Popis: | Relatively recent techniques for categorical simulations are based on multipoint statistical approaches where a training image (TI) is used to derive complex spatial relationships using patterns. In these cases, simulated realizations are driven by the TI utilized, while the spatial statistics of the hard data is not used. This paper presents a data-driven, high-order simulation approach based upon the approximation of high-order spatial indicator moments. The high-order spatial statistics are expressed as functions of spatial distances similar to variogram models for two-point methods. It is shown that the higher-order statistics are connected with lower orders via boundary conditions. Using an advanced recursive B-spline approximation algorithm, the high-order statistics are reconstructed from hard data. Finally, conditional distribution is calculated using Bayes rule and random values are simulated sequentially for all unsampled grid nodes. The main advantages of the proposed technique are its ability to simulate without a training image, which reproduces the high-order statistics of hard data, and to adopt the complexity of the model to the information available in the hard data. The approach is tested with a synthetic dataset and compared to a conventional second-order method, sisim, in terms of cross-correlations and high-order spatial statistics. |
| Databáze: | OpenAIRE |
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