ESTIMATION OF GOLD AND SILVER PRODUCTION BY USING UNIVARIATE KRIGING AND ORDINARY KRIGING METHOD

• Main Author: FAUZAN (20114023), ACHMAD
• Format: Theses
• Language: Indonesia
• Online Access: https://digilib.itb.ac.id/gdl/view/20693
• Institution: Institut Teknologi Bandung

Kriging is a geostatistical method that used to estimate the value of a point or a block as a linear combination of the observed values which is around a point or a block which is estimated (Armstrong, 1998). As far as, this calculation only involves result value of each location, so that the predictive value from the calculation of kriging will be very 'sensitive' if the site contains outliers is obtained. Then the predictive value will be actual or in terms of having error enough. Based on that, simulated calculation was conducted using Univariate Kriging (UK) for the alternative method. UK comprises the method kriging which formulate prediction at certain location by not only involving the value of each location, but also involving a predictors/ independent variables of each location. By examining the in uence of predictors and its relation with location distance, the result found is more stable the generated value is not far deviate from the value when it is compared by Ordinary Kriging (OK). The owchart of univariate kriging are: (1) the election of the correlation function; (2) the calculation of the parameter value (ɵ) which minimizes error with a maximum likelihood estimation; (3) the calculation of the correlation matrix between locations; (4) the counting of the value of the estimator β,σ2 (5) the prediction. Selection of correlation function based on the behavior of the data at the point of origin. Meanwhile, the search for value ɵ used spiral method with 10000 times iteration. Calculation of the inverse matrix using LU decomposition and Singular Value Decomposition (SVD) is performed to minimize error calculation if the matrix that belongs an ill condition matrix. As a case studied, used the data production of gold (Aurum (Au)) in 28 location and silver (Argentum (Ag)) in 25 location from 60 mining location. Determining the location of the prediction was done by random. As for the data gold (Aurum (Au)), the response variable is influenced by silver (Argentum (Ag)) which act as the predictor, while the silver data was Affected by the lead (Stannum (Sn)) and Plumbum (Pb). Furthermore, the following data Analysis and Statistics model are also conducted: (1) the prediction of gold; (2) the prediction of silver containing outlier; (3) the prediction of silver without outliers; (4) the prediction only outlier of silver. The result of the Sum of Square Error (SSE) sequentially between OK and UK for each methods are (1) 34.969 and 27.385; (2) 71.687 and 60.113; (3) 16.851 and 13.678; (4) 1574.612 and 1175.648. Based on the calculations of each method, SSE values obtained by applying ordinary kriging is quite optimal use if only it's applied on data with less outlier, meanwhile in case of data that has many outlier, the SSE value obtained from univariate kriging method is rather smaller compared to ordinary kriging. Thus, it can be generated univariate kriging more better than ordinary kriging method.