Application of Three-Dimensional Direct Least Square Method for Ellipsoid Anisotropy Fitting Model of Highly Irregular Drill Hole Patterns
Source abstract
Abstract
Ellipsoid or geometric anisotropy is a widely used method in geostatistical analysis to obtain variograms with different ranges in different directions (azimuth) and relatively similar sill variance. Ellipsoid anisotropy is indispensable in mining when a resource geologist intends to understand the spatial continuity of variables related to any geological controls of the mineralization. For example, when dealing with mineralization related to tabular deposits, a porphyritic deposit with an irregular drill hole pattern (fan drilling), three-dimensional ellipsoid anisotropy is quite challenging to model. We assume that the variables’ spatial continuity is isotropic, and we model it using a three-dimensional omnidirectional variogram. However, if the actual spatial continuity of the variables has a three-dimensional anisotropy, then assuming a three-dimensional omnidirectional variogram will generate imprecise resource estimations. This study presents a new practical three-dimensional ellipsoid model-fitting method using a three-dimensional direct least square method. We investigated a zinc (Zn) dataset from thousands of irregular drill hole patterns from a porphyritic system associated with skarn orebodies for the case study.
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Research context
OpenAlex topics: Geochemistry and Geologic Mapping · Soil Geostatistics and Mapping · Mineral Processing and Grinding
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
Affiliations
Algebra Research Group, Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung, Bandung 40132, Indonesia
University Center of Excellence on Artificial Intelligence for Vision, Natural Language Processing & Big Data Analytics (U-CoE AI-VLB), Institut Teknologi Bandung, Bandung 40132, Indonesia
Research Group of Earth Resources Exploration, Faculty of Mining and Petroleum Engineering, Institut Teknologi Bandung, Bandung 40132, Indonesia
Funding
Institute for Research and Community Services · Bandung Institute of Technology
References (11)
Show source-provided references
1. Bayesian modeling and inference for geometrically anisotropic spatial data
2. Understanding anisotropy computations10.1023/A:1007590322263 ↗
3. Budrikaite, L., and Ducinskas, K. (2006, January 7–8). Modelling of geometric anisotropic spatial variation. Proceedings of the 10th International Conference MMA2005&CMAM2, Trakai, Lithuania.
4. Anisotropy Models for Spatial Data
5. Determination of anisotropy of spatial correlation structure in a three-dimensional permeability field accompanied by shallow fault
6. Estimation of a multidimensional covariance function in case of anisotropy10.1007/BF02082761 ↗
7. Fikri, H., Heriawan, M.N., Muchtadi-Alamsyah, I., and Rachmaputri, G. (2016, January 27–28). Analysis of area of influence with ellipsoid anisotropy pattern to the result of coal resources estimation using geostatistical approach. Proceedings of the XXV Annual Professional Meeting of Indonesian Mining Professional Association 2016 (in Bahasa Indonesia only), Bandung, Indonesia.
8. Fikri, H. (2016). Analysis on The Fitting Method of Ellipsoid Anisotropy Model and Its Influence for Resources Estimation. [Bachelor’s Thesis, Bandung Institute of Technology]. unpublished.
9. Three dimensional least-squares fitting of ellipsoids and hyperboloids10.1088/1742-6596/890/1/012121 ↗
10. Heriawan, M.N., Cervantes, J.A., Setyadi, H., and Sunyoto, W. (2008, January 1–2). Spatial characteristics of Pb-Zn grades as impurity elements based on the geological domain in Grasberg mine. Proceedings of the International Symposium on Earth Science and Technology 2008, Fukuoka, Japan.
11. Timing and genetic link of porphyry Mo and skarn Pb-Zn mineralization in the Chagele deposit, Western Nyainqentanglha belt, Tibet10.1016/j.oregeorev.2020.103929 ↗