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

Udjianna S. Pasaribu, Utriweni Mukhaiyar, Mohamad N. Heriawan, Yundari Yundari


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.


Space-time model; back-casting; autoregressive; hydrothermal fluid.

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