Document Type

Article

Publication Date

6-12-2024

Department

Department of Geological and Mining Engineering and Sciences

Abstract

Multiple-point geostatistics (MPS) is an established tool for the uncertainty quantification of Earth systems modeling, particularly when dealing with the complexity and heterogeneity of geological data. This study presents a novel pixel-based MPS method for modeling spatial data using advanced machine-learning algorithms. Pixel-based multiple-point simulation implies the sequential modeling of individual points on the simulation grid, one at a time, by borrowing spatial information from the training image and honoring the conditioning data points. The developed methodology is based on the mapping of the training image patterns database using the t-Distributed Stochastic Neighbor Embedding (t-SNE) algorithm for dimensionality reduction, and the clustering of patterns by applying the Density-based Spatial Clustering of Applications with Noise (DBSCAN) algorithm, as an efficient unsupervised classification technique. For the automation, optimization, and input parameter tuning, multiple stages are implemented, including entropy-based determination of the template size and a k-nearest neighbors search for clustering parameter selection, to ensure the proposed method does not require the user’s interference. The proposed model is validated using synthetic two- and three-dimensional datasets, both for conditional and unconditional simulations, and runtime information is provided. Finally, the method is applied to a case study gold mine for stochastic orebody modeling. To demonstrate the computational efficiency and accuracy of the proposed method, a two-dimensional training image with 101 by 101 pixels is simulated for 100 conditional realizations in 453 s (~4.5 s per realization) using only 361 hard data points (~3.5% of the simulation grid), and the resulting average simulation has a good visual match and only an 11.8% pixel-wise mismatch with the training image.

Publisher's Statement

Copyright: © 2024 by the authors. Licensee MDPI, Basel, Switzerland. Publisher’s version of record: https://doi.org/10.3390/geosciences14060162

Publication Title

Geosciences (Switzerland)

Creative Commons License

Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Version

Publisher's PDF

Download

Share

COinS