Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Agterberg FP (1989a) Computer programs for exploration. Science 245:76–81. Medline doi:10.1126/science.245.4913.76 Agterberg FP (1989b) Systematic approach to dealing with uncertainty of geoscience information in mineral exploration. In: Weiss A (ed) Application of computers and operations in the mineral industry. Proc. 21st APCOM symp. (Las Vegas, Nevada). Colorado Society of Mining Engineers, Littleton, pp 165–178 Agterberg FP (1995) Multifractal modeling of the sizes and grades of giant and supergiant deposits. Int Geol Rev 37:1–8 Agterberg FP (2001) Multifractal simulation of geochemical map patterns. In: Merriam DF, Davis JC (eds) Geologic modeling and simulation. Sedimentary systems. Kluwer, New York, pp 327–346 Agterberg FP (2007a) New applications of the model of de Wijs in regional geochemistry. Math Geol 39:1–26. doi:10.1007/s11004-006-9063-7 Agterberg FP (2007b) Mixtures of multiplicative cascade models in geochemistry. Nonlinear Process Geophys 14:201–209 Agterberg FP, Bonham-Carter GF (1990) Deriving weights of evidence from geoscience contour maps for prediction of discrete events. In: Proc. 22nd APCOM Symp. (Berlin, Germany), Tech. Univ. Berlin, vol 2, pp 381–396 Agterberg FP, Cheng Q (2002) Conditional independence test for weights of evidence modeling. Nat Resour Res 11:249–255. doi:10.1023/A:1021193827501 Agterberg FP, Brown A, Cheng Q, Good D (1994) Multifractal modeling of fractures in Lac De Bonnet batholith, Manitoba. In: Proc of IAMG ’94, Mont-Tremblant, Quebec, October, 1994, vol 1, pp 3–8 An P, Moon WM, Rencz A (1991) Application of fuzzy set theory for integration of geological, geophysical, and remote sensing data. Can J Explor Geophys 27:1–11 Bonham-Carter GF (1994) Geographic information systems for geoscientists: modelling with GIS. Pergamon, Oxford, p 398 Bonham-Carter GF, Agterberg FP, Wright DF (1988) Integration of geological data sets for gold exploration in Nova Scotia. Photogramm Eng Remote Sensing 54:1585–1592 Chatterjee AK (1983) Metallogenic map of Nova Scotia, ver. 1, scale 1:500,000, Department of Mines and Energy, Nova Scotia, Canada Cheng Q (1989) A quantitative method for evaluating mineral resource of multivariate populations. In: Wang S, Fan J, Cheng Q (eds) Journal of Changchun Univ of Earth Sci, Special Issue (in Chinese with English abstract), vol 19, pp 50–56 Cheng Q (1997) Discrete multifractals. Math Geol 29:245–266. doi:10.1007/BF02769631 Cheng Q (1999) Multifractality and spatial statistics. Comput Geosci 25:949–961. doi:10.1016/S0098-3004(99)00060-6 Cheng Q (2000) GeoData Analysis System (GeoDAS) for mineral exploration: user’s guide and exercise manual. Material for the training workshop on GeoDAS held at York University, Nov. 1 to 3, 2000, p 204. http://www.gisworld.org/geodat Cheng Q (2003) Fractal and multifractal modeling of hydrothermal mineral deposit spectrum: application to gold deposits in the Abitibi Area, Canada. J China Univ Geosci 14:199–206 Cheng Q (2004a) Weights of evidence modeling of flowing wells in the Greater Toronto Area, Canada. Nat Resour Res 13:77–86. doi:10.1023/B:NARR.0000032645.46747.48 Cheng Q (2004b) A new model for quantifying anisotropic scale invariance and for decomposition of mixing patterns. Math Geol 36:345–360. doi:10.1023/B:MATG.0000028441.62108.8a Cheng Q (2005) Multifractal distribution of eigenvalues and eigenvectors from 2D multiplicative cascade multifractal fields. Math Geol 37:915–927. doi:10.1007/s11004-005-9223-1 Cheng Q (2006) GIS-based multifractal anomaly analysis for prediction of mineralization and mineral deposits. In: Harris J (ed) GIS for the earth sciences, Geological Association of Canada, Tri-Co Group, Ottawa, pp 285–296 Cheng Q (2007a) Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China. Ore Geol Rev 32:314–324. doi:10.1016/j.oregeorev.2006.10.002 Cheng Q (2007b) Multifractal imaging filtering and decomposition methods in space, Fourier frequency and Eigen domains. Nonlinear Process Geophys 14:293–303 Cheng Q (2007c) Log-probability model vs. logistic model for weights of evidence method. In: Zhao PD Agterberg FP Cheng Q (eds) Proceedings of IAMG’07: Geomathematics and GIS analysis of resources, environment and hazards, China, August 26–31, 2007. China University of Geosciences Printing House, Wuhan, pp 66–69 Cheng Q (2008a) A new combined model for prediction of river flow. J Hydrol 352:157–167. doi:10.1016/j.jhydrol.2008.01.017 Cheng Q (2008b) Local singularity analysis of river peak flow. Nonlinear Process Geophys (submitted) Cheng Q (2008c) Modeling local scaling properties for multi-scale mapping. Vadose Zone J (in press) Cheng Q (2008d) Comparison between Tau model and weights of evidence model. Math Geosci (submitted) Cheng Q, Agterberg FP (1996) Multifractal modeling and spatial statistics. Math Geol 28:1–16. doi:10.1007/BF02273520 Cheng Q, Agterberg FP (1999) Fuzzy weights of evidence method and its application in mineral potential mapping. Nat Resour Res 8:27–35. doi:10.1023/A:1021677510649 Cheng Q, Agterberg FP (2008) Singularity analysis of ore-mineral and toxic trace elements in stream sediments. Comput Geosci (in press) Cheng Q, Bonham-Carter GF, Agterberg FP, Wright DF (1994a) Fractal modeling in the geosciences and implementation with GIS. In: Proc of the 6th Canadian conference on GIS, Ottawa, June 6–10, vol 1, pp 565–577 Cheng Q, Agterberg FP, Ballantyne SB (1994b) The separation of geochemical anomalies from background by fractal methods. J Geochem Explor 51:109–130. doi:10.1016/0375-6742(94)90013-2 Cheng Q, Agterberg FB, Bonham-Carter GF, Sun J (1994c) Artificial intelligence model for integrating spatial patterns for mineral potential estimation with incomplete information. In: Proc of 6th Can conf on GIS, Ottawa, June 6–10, 1994, vol 1, pp 261–274 Cheng Q, Agterberg FP, Bonham-Carter GF (1996) Fractal pattern integration method for mineral potential mapping. Nonrenew Res 5:117–130. doi:10.1007/BF02257585 Cheng Q, Xu Y, Grunsky EC (2001) Integrated spatial and spectrum analysis for geochemical anomaly separation. Nat Resour Res 9:43–51. doi:10.1023/A:1010109829861 de Wijs HJ (1951) Statistics of ore distribution, part I. Geol Mijnb 13:365–375 Harris DP (1984) Mineral resources appraisal—mineral endowment, resources, and potential supply: concepts, methods, and cases. Oxford University Press, New York, p 455 Kemp LD, Bonham-Carter GF, Raines GL, Looney CG (2001) Arc-SDM: Arcview extension for spatial data modelling using weights of evidence, logistic regression, fuzzy logic and neural network analysis. http://www.ige.unicamp.br/sdm/ Li Q, Cheng Q (2004) Fractal singular value decomposition and anomaly reconstruction. Earth Sci 29:109–118. (In Chinese with English abstract) MacDonald MA, Horne R, Corey MC, Ham L (1992) An overview of recent bedrock mapping and follow-up petrological studies of the South Mountain Batholith, Southwestern Nova Scotia. Atl Geol 2:7–28 Malamud BD, Turcotte DL, Barton CC (1996) The 1993 Mississippi river flood: a one hundred or a one thousand year event? Environ Eng Geosci II:479–486 Malamud BD, Turcotte DL, Guzzetti F, Reichenbach P (2004) Landslide inventories and their statistical properties. Earth Surf Process Landf 29:687–711. doi:10.1002/esp.1064 Mandelbrot BB (1989) Multifractal measures, especially for the geophysicist. Pure Appl Geophys 131: 5–42. doi:10.1007/BF00874478 McCammon RB, Botbol JM, Sinding-Larsen R, Bowen RW (1983) Characteristic analysis—1981: final program and a possible discovery. Math Geol 15:59–83. doi:10.1007/BF01030076 Reynolds PH, Elias P, Muecke GK, Grist AM (1987) Thermal history of the southwestern Meguma zone, Nova Scotia, from an 40Ar/39Ar and fission track dating study of intrusive rocks. Can J Earth Sci 24:1952–1965 Rogers PJ, Mills RF, Lombard PA (1987) Regional geochemical study in Nona Scotia. In: Bates JL, MacDonald DR (eds) Mines and mineral branch, report of activities 1986, vol 87-1, pp 147–154 Schertzer D, Lovejoy S (1985) The dimension and intermittency of atmospheric dynamics—multifractal cascade dynamics and turbulent intermittency. In: Launder B (ed) Turbulent shear flow. Springer, New York, pp 7–33 Schertzer D, Lovejoy S (1987) Physical modeling and analysis of rain and clouds by anisotropic scaling of multiplicative processes. J Geophys Res 92:9693–9714. doi:10.1029/JD092iD08p09693 Schertzer D, Lovejoy S, Schmitt F, Chigirinskaya Y, Marsan D (1997) Multifractal cascade dynamics and turbulent intermittency. Fractals 5:427–471. doi:10.1142/S0218348X97000371 Singer DA (1993) Basic concepts in three-part quantitative assessments of undiscovered mineral resources. Nonrenew Res 2:69–81. doi:10.1007/BF02272804 Singer DA (2008) Mineral deposit densities for estimating mineral resources. Math Geosci 40:33–46 Sornette D (2004) Critical phenomena in natural sciences: chaos, fractals, selforganization and disorder, 2nd edn. Springer, New York Turcotte DL (1997) Fractals and chaos in geology and geophysics, 2nd edn. Cambridge University Press, Cambridge Turcotte DL (2002) Fractals in petrology. Lithos 65:261–271. doi:10.1016/S0024-4937(02)00194-9 Veneziano D (2002) Multifractality of rainfall and scaling of intensity-duration-frequency curves. Water Resour Res 38:1–12 Xie S, Cheng Q, Chen G, Chen Z, Bao Z (2007) Application of local singularity in prospecting potential oil/gas targets. Nonlinear Process Geophys 14:285–292 Xu Y, Cheng Q (2001) A multifractal filter technique for geochemical data analysis from Nova Scotia, Canada. J Geochem Explor, Anal Environ 1:1–12 Zhao P (1998) Geoanomaly and mineral prediction: modern mineral resource assessment theory and method. Geological Publishing House, Beijing, p 300 (in Chinese)