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| 1 | Multifractal Simulation of GeochemicalMap Patterns显示文摘Using a simple multifractal model based on the model De Wijs, various geochemical map patterns for element concentration values are being simulated. Each pattern is self-similar on the average in that a similar pattern can be derived by application of the multiplicative cascade model used to any small subarea on the pattern. In other experiments, the original, self-similar pattern is distorted by superimposing a 2-dimensional trend pattern and by mixing it with a constant concentration value model. It is investigated how such distortions change the multifractal spectrum estimated by means of the 3-step method of moments. Discrete and continuous frequency distribution models are derived for patterns that satisfy the model of De Wijs. These simulated patterns satisfy a discrete frequency distribution model that as upper bound has a continuous frequency distribution to which it approaches in form when the subdivisions of the multiplicative cascade model are repeated indefinitely. This limiting distribution is lognormal in the center and has Pareto tails. Potentially, this approach has important implications in mineral and oil resource evaluation. | Agterberg Frederik P Geological Survey of Canada, 601 Booth Street, Ottawa, K1A 0E8, Canada | 2001 | Journal of China University of Geosciences2001，12，1： | 10 |
| 2 | Fractals and Spatial Statistics of Point Patterns显示文摘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. | Frederik P Agterberg | 2013 | Journal of Earth Science2013，24，1： | 4 |
| 3 | Principles of Probabilistic Regional Mineral Resource Estimation显示文摘Five principal sources of uncertainty in quantitative mineral resource estimation are listed and illustrated by means of a simple example (mosaic model) and a case history study for large copper deposits in the Abitibi area of the Canadian Shield.Abitibi copper potential originally was estimated on the basis of 1968 estimates of production and reserves totalling 3.12 Mt Cu.This prognostication now could be evaluated on the basis of 2008 copper production and reserves totalling 9.50 Mt Cu.An earlier hindsight study performed on the basis of 1977 data (totalling 5.23 Mt Cu) showed seven new discoveries occurring either in the immediate vicinities of known deposits or on broad regional copper anomalies predicted from the 1968 inputs.By 1977,the global geographic distribution pattern of large copper deposits in the Abitibi area had stabilized.During the next 30 years,new copper was essentially found close to existing deposits,much of it deeper down in the Earths crust.In this paper,uncertainties associated with copper ore tonnage are analyzed by comparison of 2008 data with 1968 data using (a) log-log plots of size versus rank,and (b) lognormal QQ-plots.Straight lines fitted by least squares on these plots show that 1968 slopes provide good estimates of 2008 slopes but 1968 intercepts are much less than 2008 intercepts.In each linear log-weight versus log-rank plot,the slope is related to fractal dimension of a Pareto frequency distribution,and in a lognormal QQ-plot it is determined by logarithmic variance.The difference between 2008 and 1968 intercepts represents the increase in copper ore production and reserves from 1968 to 2008.The Pareto model fits actual copper and massive sulphides increase over the past 40 years better than the lognormal frequency distribution model for 10 km×10 km cells on favorable environments in the Abitibi area. | Frits Agterberg | 2011 | 地球科学(中国地质大学学报)2011，36，2： | 2 |
| 4 | Aspects of Regional and Worldwide Mineral Resource Prediction显示文摘The purpose of this contribution is to highlight four topics of regional and worldwide mineral resource prediction:(1)use of the jackknife for bias elimination in regional mineral potential assessments;(2)estimating total amounts of metal from mineral potential maps;(3)fractal/multifractal modeling of mineral deposit density data in permissive areas;and(4)worldwide and large-areas metal size-frequency distribution modeling.The techniques described in this paper remain tentative because they have not been widely researched and applied in mineral potential studies.Although most of the content of this paper has previously been published,several perspectives for further research are suggested. | Frits Agterberg | 2021 | Journal of Earth Science2021，32，2： | 2 |
| 5 | Past and Future of Mathematical Geology显示文摘This is a brief review of alternative methods of problem-solving in geoscience with emphasis on the role of mathematical geology. It is desirable to maintain a clear-cut distinction between reliable facts which can be stored in data banks and concepts that can be incorporated in the specifications of statistical models designed for specific purposes. If possible, subjective probabilities should be incorporated in hypotheses that are to be tested by statistical inference. | Frederik P Agterberg | 2003 | Journal of China University of Geosciences2003，14，3： | 2 |
| 6 | Regression models for estimating mineral resources from geological map data显示文摘 | C. F. Chung F. P. Agterberg | 1980 | Journal of the International Association for Mathematical Geology1980，，5： | 1 |
| 7 | The sepa- ration of geochemical anomalies from background by fractal methods 显示文摘 | CHENG Q AGTERBERG F P BALLANTYNE S B | 1994 | Journal of Geochemical Exploration1994，51，2： | 1 |
| 8 | Application of singularity mapping technique to identify local anomalies using stream sediment geochemical data, a case study from Gangdese, Tibet, western China显示文摘 | Renguang Zuo Qiuming Cheng F.P. Agterberg Qinglin Xia | 2008 | Journal of Geochemical Exploration2008，，3： | 1 |
| 9 | Conditional independence lest for weights-of-evidence modeling 显示文摘 | Agterberg F P Qiu-ming CHENG | 2002 | Natural Resources Research2002，11，4： | 1 |
| 10 | Computer programs for mineral exploration显示文摘 | Agterberg F P | 1989 | Science1989，245，： | 1 |
| 11 | Computer Programs for Mineral Exploration显示文摘 | Agterberg F P | 1989 | Seience1989，245，： | 1 |
| 12 | Application of singularity mapping technique to identify local anomalies using stream sediment geochemical data, a case study from Gangdese, Tibet, western China 显示文摘 | ZUO R CHENG Q AGTERBERG F P | 2009 | Journal of Geochemical Exploration2009，101，3： | 1 |
| 13 | Fractal characterization of the spatial distribution of geological point processes显示文摘 | Renguang Zuo Frederik P. Agterberg Qiuming Cheng Lingqing Yao | 2009 | International Journal of Applied Earth Observations and Geoinformation2009，，6： | 1 |
| 14 | Integration of geological datasets for gold exploration in Nova Scotia 显示文摘 | Bonham-Carter G F Agterberg F P Wright S F | 1988 | Photogrammetry and Remote Sensing1988，54，： | 1 |
| 15 | The separation of geochemical anomalied from background by fractal methods 显示文摘 | Cheng Q Agterberg F P Ballatyne S B | 1994 | Explor Geochem1994，51，： | 1 |
| 16 | Application of a hybrid method combining multilevel fuzzy comprehensive evaluation with asymmetric fuzzy relation analysis to mapping prospectivity 显示文摘 | ZUO R CHENG Q AGTERBERG F P | 2009 | Ore Geology Reviews2009，35，1： | 1 |
| 17 | The separation of geochemical anomalies from background by fractal methods显示文摘 | Cheng Q M Agterberg F P Ballantyne S B | 1994 | Journal of Geochemical Exploration1994，51，： | 1 |
| 18 | Methods of trend surface analysis显示文摘 | Agterberg FP | 1964 | Colo Sch Min Quart1964，59，4： | 1 |
| 19 | Geochro- nology and calibration of global Milankovitch cyelicity at the Cenomanian Turonian boundary显示文摘 | Prokoph A Villeneuve M Agterberg F P | 2001 | Geology2001，29，6： | 1 |
| 20 | The separation of geochemical anomalies from background by fractal methods 显示文摘 | Cheng Q Agterberg F P Ballantyne S B | 1994 | Geochem Explor1994，51，： | 1 |
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