Fractals and Spatial Statistics of Point Patterns
The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley＇s K-function has advantages in comparison with the more commonly used methods of bo...
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| Vydáno v: | Journal of earth science (Wuhan, China) Ročník 24; číslo 1; s. 1 - 11 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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China University of Geosciences
China University of Geosciences
01.02.2013
Springer Nature B.V |
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| ISSN: | 1674-487X, 1867-111X |
| On-line přístup: | Získat plný text |
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| Abstract | The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley＇s K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by re- gional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong ＂roll-off＂ effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size （metal tonnage） is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling. |
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| AbstractList | The relationship between fractal point pattern modeling and statistical methods of parameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley's K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by regional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong "roll-off" effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size (metal tonnage) is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling. The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley＇s K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by re- gional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong ＂roll-off＂ effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size （metal tonnage） is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling. The relationship between fractal point pattern modeling and statistical methods of parameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley's K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by regional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong "roll-off" effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size (metal tonnage) is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling.[PUBLICATION ABSTRACT] The relationship between fractal point pattern modeling and statistical methods of parameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley’s K -function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by regional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong “roll-off” effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size (metal tonnage) is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling. |
| Author | Frederik P Agterberg |
| AuthorAffiliation | Geological Survey of Canada, 601 Booth Street, Ottawa K1A 0E8, Canada |
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| Keywords | cluster dimension spatial statistics Pareto distribution fractal point pattern roll-off effect |
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| Notes | The relationship between fractal point pattern modeling and statistical methods of pa- rameter estimation in point-process modeling is reviewed. Statistical estimation of the cluster fractal dimension by using Ripley＇s K-function has advantages in comparison with the more commonly used methods of box-counting and cluster fractal dimension estimation because it corrects for edge effects, not only for rectangular study areas but also for study areas with curved boundaries determined by re- gional geology. Application of box-counting to estimate the fractal dimension of point patterns has the disadvantage that, in general, it is subject to relatively strong ＂roll-off＂ effects for smaller boxes. Point patterns used for example in this paper are mainly for gold deposits in the Abitibi volcanic belt on the Canadian Shield. Additionally, it is proposed that, worldwide, the local point patterns of podiform Cr, volcanogenic massive sulphide and porphyry copper deposits, which are spatially distributed within irregularly shaped favorable tracts, satisfy the fractal clustering model with similar fractal dimensions. The problem of deposit size （metal tonnage） is also considered. Several examples are provided of cases in which the Pareto distribution provides good results for the largest deposits in metal size-frequency distribution modeling. fractal point pattern, spatial statistics, roll-off effect, cluster dimension, Pareto distribution. 42-1788/P SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 14 ObjectType-Article-1 ObjectType-Feature-2 content type line 23 |
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| SubjectTerms | Biogeosciences Chromium Clusters Curved Deposition Earth and Environmental Science Earth science Earth Sciences Fractal analysis Fractals Frequency distribution Geochemistry Geology Geotechnical Engineering & Applied Earth Sciences Parameter estimation Pareto optimum Statistical methods Statistics Sulfides Volcanic belts 分形维数估计 参数估计 块状硫化物 点模式 空间统计 统计方法 过程模型 频率分布模型 |
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