Time Series Simulation and Forecasting of Borehole Assays - a Case Study from Rajasthan, India

L. Balasubramanian
Department of Earth Sciences, Indian Institute of Technology, India

Ore deposits are formed under specific physico-chemical, biological and environmental conditions and are characterised by a certain degree of continuity in the distribution of assay values, thickness of ore bodies, top and bottom boundaries of the ore bodies with the country rocks, as well as a randomness due to several unknown factors. This continuity persists even though certain structural elements may affect it on a regional scale. Hence, a strong correlation between neighbouring assay values exists. Mineral deposits are, thus, highly amenable to stochastic modelling; simulated models, once identified, estimated and checked can be used for genetic interpretations, grade forecasting, mine planning / development, etc. Parametric time series models developed by Box & Jenkins have been used successfully for geo-science problems. The present study discusses the results of simulated ARIMA (p,d,q) models for borehole data from the Rajpura-Dariba Lead-Zinc mine in Rajasthan, India. The irregularly spaced assay values were first regularised using the method of cubic spline interpolation (deBoor). These are discrete data with closure constraints inducing varying negative associations (correlations) among the different constituents of rocks and ores. This effect can be eliminated by a log (c/1-c) transformation which simultaneously converts the discrete and heteroscedastic data into continuous Normal random variables with homogeneous variances. The time series so obtained was checked for stationarity and were differenced accordingly to achieve stationarity. Models were fixed taking into consideration the principle of parsimony. The identified models were then tested using a simple chi-squared algorithm and then were used for forecasting. Models were likewise simulated for 15 boreholes.