guassian conditional simulation

In this research, the optimum block size determination method and its influence on reserve estimation were investigated. For this purpose, the Kushk lead and zinc deposit data were used as case study. The database was built using borehole data and the composite samples were prepared with a 2m length. The data was transformed to Gaussian distribution by normal score transformation method. Variography was used for identification of variability and continuity of the ore, and the best variogram models and anisotropy ellipsoids were fitted. Due to ore complexity and density of boreholes in open pit and undergrounds, indicator kriging method was used for orebody modeling and ore-waste boundary determination. Considering different block size, the lead and zinc grade variability was modeled by sequential Gaussian simulation method. In each block size simulation, 20 realizations were determined and the variances between realizations were calculated. The lower variance is accordance with more similarity of realizations which was selected as a criterion of optimum block size determination. With this method, the optimum block size of Kushk deposit was determined as 10x10x7.5 m. The optimum block size is relatively accordance with the anisotropy ratio at the deposit, therefore it was chosen as suitable block size for reserve estimation of the deposit. By this optimum block size, and considering a 3% cut off grade for sum of lead and zinc, the reserve of the deposit was calculated about 39.12 million tons.

An important part of mineral deposit modeling is block modeling. In this paper, various geostatistical methods such as estimation variance, kriging efficiency and Gaussian conditional simulation have been used to select the optimal block dimensions for Surk iron ore and Esfordi phosphate mines.

Methodology and Approaches:

Statistical analysis of Surk and Esfordi iron ore data shows that the data follow an abnormal distribution. Normal Score Transform (NST) is applied for transferring data to Gaussian distribution. Variography of iron and phosphorus composite data was performed in different directions. At first, the optimal block size was determined using kriging efficiency values. In this method, the criterion for selecting the optimal dimensions was to maximize the kriging efficiency. Because the optimal dimensions obtained by kriging efficiency method are not compatible with the operating conditions and anisotropy of the deposit, in the next step, geostatistical simulation method was used. In the simulation process, 20 realizations were considered. The criterion for selecting the optimal block dimensions was to minimize the variance between the realizations in each block.

In the Gaussian conditional simulation method, with the idea that the smaller the variance between the realizations, the greater the similarity of the realizations,  the optimal dimensions were calculated for the Surk mine as 7.5×7.5×7.5 m3 and for the Esfordi mine as 10×10×7.5 m3. The dimensions obtained from Gaussian conditional simulation method are in good agreement with the anisotropic ratios of each mine.According to the optimal dimensions obtained from the Gaussian simulation method, the reserve estimation was made. Based on 20% iron cut off grade, the tonnage of Surk mine is 9.84 million tons with an average grade of 46.07%, and based on the cut off grade of 5% phosphorus, the tonnage of Esfordi mine is 11.93 million tons with an average grade of 13.85%.