Wang,Q., Deng,J., Liu,H., Yang,L., Wan,L. and Zhang,R.(2010): Fractal models for ore reserve estimation. Ore Geology Reviews, 37, 2-14.

『埋蔵鉱量見積りについてのフラクタル・モデル』


Abstract
 Traditional geometric and geostatistic methods for reserve estimation in a single deposit are difficult to use with skewed distribution mineralization variables including grade, orebody thickness and grade-thickness, a common characteristic of most deposits, and require complex data processing. It has been shown that the skewed mineralization variables can be described by the number-size model in a fractal domain. Based on the number-size model, assuming that orebody thickness and grade-thickness are continuous variables, the fractal model for reserve estimation (FMRE) in a single deposit can be established. In the FMRE, ore tonnage can be estimated given the orebody area and the fractal parameters of orebody thickness distribution and metal tonnage can be estimated based on the orebody area and the fractal parameters of grade-thickness distribution. The reserve estimated by the FMRE can denote actual ore tonnage and metal tonnage that can be mined out of the deposit. The FRME was applied to the Dayingezhuang gold deposit in the Jiaodong gold province in China. The gold reserves via the FMRE and the traditional geometric block method are similar, with relative errors of 3.11% in ore tonnage and 0.29% in metal tonnage. Compared to traditional reserve estimation the FMRE is much easier in calculation process and is more reasonable in dealing with the skewed distribution. However, this new method fails to calculate local reserve, which can be derived via any of the traditional estimation methods.

Keywords: Ore reserves; Jiaodong gold province; Fractal modeling』

1. Introduction
 1.1. Traditional reserve estimation methods
 1.2. Fractal models in geology
 1.3. Research objective
2. Mathematical modeling
 2.1. Preliminary processing of raw data
 2.2. Block modeling
 2.3. Fractal algorithms
  2.3.1. Number-size model
  2.3.2. Fractal model for ore tonnage estimation
  2.3.3. Fractal model for metal tonnage estimation
  2.3.4. Grade estimation
 2.4. Limitations of the FMRE
  2.4.1. Exploration grid density
  2.4.2. Ore density
  2.4.3. Variable limit
 2.5. Steps in the FMRE
3. Case study
 3.1. Regional geology and deposit geology
  3.1.1. Regional geology
  3.1.2. Deposit geology
 3.2. Deposit explorations and raw data
 3.3. FMRE application
  3.3.1. Consistence test of the fractal model
  3.3.2. Reserve estimation
4. Discussion
 4.1. Estimation result
 4.2. Comparison between FMRE and traditional methods
 4.3. FMRE application scope
5. Conclusions
Acknowledgements
References


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