DOI : https://doi.org/10.18517/ijaseit.12.5.14835

Generalized Space-Time Autoregressive Modeling of the Vertical Distribution of Copper and Gold Grades with a Porphyry-Deposit Case Study

Udjianna S. Pasaribu (1), Utriweni Mukhaiyar (2), Mohamad N. Heriawan (3), Yundari Yundari (4)
(1) Statistics Division Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung,Bandung, Indonesia
(2) Statistics Division Faculty of Mathematics and Natural Sciences, Institut Teknologi Bandung,Bandung, Indonesia
(3) Earth Resources Exploration Research Group, Faculty of Mining and Petroleum Engineering, Institut Teknologi Bandung, Bandung, Indonesia
(4) Mathematics Department, Faculty of Mathematics and Natural Sciences, Universitas Tanjungpura, Pontianak, Indonesia
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How to cite (IJASEIT) :
Pasaribu, Udjianna S., et al. “Generalized Space-Time Autoregressive Modeling of the Vertical Distribution of Copper and Gold Grades With a Porphyry-Deposit Case Study”. International Journal on Advanced Science, Engineering and Information Technology, vol. 12, no. 5, Oct. 2022, pp. 2030-8, doi:10.18517/ijaseit.12.5.14835.
Citation Format :
We examined the first-order application of the generalized space-time autoregressive GSTAR (1;1) model. The autoregressive model was used and was performed simultaneously in multiple drill-hole locations. The GSTAR model was applied to data with absolute time parameter units, such as hours, days, months, or years. Here a new perspective on modeling space-time data is raised. We used the relative time parameter index as a discretization of the same drilling depth of mineralization through a porphyritic deposit. Random variables were the copper and gold grades derived from the hydrothermal fluid that passed through the rock fractures in a porphyry copper deposit in Indonesia. This research aims to model the vertical distribution of copper and gold grades through backcasting the GSTAR (1;1) model. Such results could help geologists to predict copper and gold grades in deeper zones in an ore deposit. Two spatial weight matrices were used in the GSTAR (1;1) model, and these were based on a Euclidean distance and kernel function. Both weight matrices were constructed from different perspectives. The Euclidean distance approach gave a fixed weight matrix. Meanwhile, the kernel function approach gave the possibility to be random since it is based on real observations. It is obtained that the estimated (in-sample) and predicted (out-sample) kernel weight approach was accurate. Copper and gold grades data could recommend the GSTAR (1;1) model with a spatial kernel weight for modeling the vertical continuity case.

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