Integration of Machine Learning Algorithms with Gompertz Curves and Kriging to Estimate Resources in Gold Deposits
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Original Paper
Integration of Machine Learning Algorithms with Gompertz Curves and Kriging to Estimate Resources in Gold Deposits Steven E. Zhang,2 Glen T. Nwaila ,1,6 Leon Tolmay,3 Hartwig E. Frimmel,4,5 and Julie E. Bourdeau1 Received 27 October 2019; accepted 15 September 2020
Resource estimation on gold (Au) deposits usually requires costly Au assays and is often characterized by high degree of uncertainty especially in areas with limited number of samples. This paper reports a refinement of a novel machine learning approach (GS-Pred) that incorporates network analysis for geology-based anomalous data detection and outlier removal, and adopts feature weighting using a spatial self-similarity model inspired by kriging to enhance prediction performance for in situ Au-grade estimation. In this application, machine learning algorithms are integrated with sequential-kriging block modeling for high resolution in situ grade estimation. This process is fully automatable, and it utilizes both geological data and Au assays, making it possible to also estimate Au grade in areas that only have geological descriptions. The results of our expanded GS-Pred and block modeling, using data from the auriferous conglomerates of the Witwatersrand Basin (South Africa), demonstrate improvements in the GS-Pred performance and flexibility relative to the original algorithms. Additionally, our results provide further evidence of strong sedimentological control on Au concentration within the Witwatersrand Basin, which is suitable for quantitative predictions. Our algorithms feature fast data processing, geology- and assay-based outlier detection, visualization of complex geospatial data, and they open new avenues for intelligent and automated in situ Au-grade prediction. We demonstrate that GSPred target predictions are feasible substitutes for assays for the purpose of block modeling under suitable deployment conditions. KEY WORDS: Gold, Machine learning, Gompertz function, Simple kriging, Ordinary kriging, Resource modeling.
INTRODUCTION 1
School of Geosciences, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa. 2 PG Techno Wox, 43 Patrys Avenue, Helikon Park, Randfontein 1759, South Africa. 3 Tolmay Enterprises, 150 Galena Avenue, Roodepoort 1709, South Africa. 4 Bavarian Georesources Center (BGC), Institute of Geography and Geology, University of Wu¨rzburg, Am Hubland, 97074 Wu¨rzburg, Germany. 5 Department of Geological Sciences, University of Cape Town, Rondebosch 7700, South Africa. 6 To whom correspondence should be addressed; e-mail: [email protected]
Spatial prediction in geology, geography and environmental sciences can often be challenging due to sample-density limitations of large survey areas or volumes. In geology, relatively small samples are often strongly and erroneously assumed to be representative of the large portions of physical systems, such as ore deposits. However, ore deposits are typically internally highly variable (e.g., ore nuggets, offset by faulting and intrusions) and formed
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