SPS Model: a significant algorithm to reduce the time and computer memory required in geostatistical simulations
الموضوعات :
Behnam Sadeghi
1
1 - Earth Byte Group, School of Geosciences, University of Sydney, NSW 2006, Sydney, Australia
تاريخ الإرسال : 14 الخميس , صفر, 1442
تاريخ التأكيد : 16 الأحد , رجب, 1442
تاريخ الإصدار : 17 الجمعة , جمادى الأولى, 1442
الکلمات المفتاحية:
Time,
scaling and projecting sample-locations (SPS) method,
Geostatistical simulation,
Memory,
Spatial uncertainty,
ملخص المقالة :
In geochemical anomaly classification, different mathematical-statistical models have been applied. The final classified map provides only one scenario. This model is not certain enough since every model provides several thresholds which are almost different from each other meaning dissimilarity and spatial uncertainty of the classified maps. Spatial uncertainty of the models could be quantified considering the difference between the associated geochemical scenarios simulated (called: ‘realizations’) by geostatistical simulation (GS) methods. However, the main problem with GS methods is that these methods are significantly time-consuming, and CPU- and memory-demanding. To improve such problems, in this research, the method of “scaling and projecting sample-locations (SPS)” is developed. Based on the SPS theory, first of all, the whole sample-locations were projected (centralized) and scaled into a box coordinated between (0,0) to (150,0) and (0,0) to (0,100), for example (they can be equal though), with the cell-size of 1 m2. Therefore, the time consumed and the memory demanded to generate a large number of realizations, for example, 1000 realizations based on the non-scaled/non-projected (NS/NP) and scaled/projected (S/P) sample locations per case-study were quantified. In this study, the turning bands simulation (TBSIM) were applied to geochemical datasets of three different case studies to take the area scales, regularity/irregularity and density of the samples into account. The comparison between NS/NP and S/P results statistically demonstrated the same results, however, the process and outputs of the S/P samples took a significantly shorter time and consumed a remarkably lower computer-memory. Therefore, experts are able to easily run this algorithm using any normal computer.
المصادر:
Afzal P, Alhoseini SH, Tokhmechi B, Kaveh Ahangaran D, Yasrebi AB, Madani N, Wetherelt A (2014) Outlining of high quality coking coal by concentration–volume fractal model and turning bands simulation in East-Parvadeh coal deposit, Central Iran, International Journal of Coal Geology 127: 88–99.
Afzal P, Fadakar Alghalandis Y, Khakzad A, Moarefvand P & Rashidnejad Omran N (2011) Delineation of mineralization zones in porphyry Cu deposits by fractal concentration–volume modelling, Journal of Geochemical Exploration 108: 220–232.
Afzal P, Harati H, Fadakar Alghalandis Y, Yasrebi AB (2013) Application of spectrum-area fractal model to identify of geochemical anomalies based on soil data in Kahang porphyry-type Cu deposit, Iran, Chemie der Erde 73: 533–543.
Afzal P, Khakzad, A, Moarefvand P, Rashidnejad Omran N, Esfandiari B, Fadakar Alghalandis, Y (2010) Geochemical anomaly separation by multifractal modeling in Kahang (GorGor) porphyry system, Central Iran, Journal of Geochemical Exploration 104: 34–46.
Afzal P, Zia Zarifi A, Sadeghi B (2013) Separation of geochemical anomalies using factor analysis and concentration-number (CN) fractal modeling based on stream sediments data in Esfordi 1: 100000 Sheet, Central Iran, Iranian Journal of Earth Sciences 5 (2): 100–110.
Agterberg FP (1994) Fractal, multifractals, and change of support. In: R. Dimitrakopoulus (Ed.), Geostatistics for the Next Century, Kluwer, Dordrecht, 223–234.
Agterberg FP (2001) Multifractal simulation of geochemical map patterns. In: D.F. Merriam, J.C. Davis (Eds.), Geologic Modeling and Simulation: Sedimentary Systems, Kluwer-Plenum Publishers, New York, 327–346.
Agterberg FP (2018) Can multifractals be used for mineral resource appraisal?, Journal of Geochemical Exploration 189: 54–63.
Agterberg FP, Bonham-Carter GF, Wright DF (1990) Statistical pattern integration for mineral exploration. In: Gaal G, Merriam DF (eds) Computer applications in resource exploration and assessment for minerals and petroleum. Pergamon, Elmsford, 1–21.
Aliyari F, Afzal P, Lotfi M, Shokri S, Feizi H (2020) Delineation of geochemical haloes using the developed zonality index using multivariate and fractal analysis in the Cu-Mo porphyry deposits, Applied Geochemistry 121: 104694.
An P, Moon, WM, Bonham-Carter GF (1994) Uncertainty management in integration of exploration data using the belief functions, Non-renewable Resources 3: 60–71.
Andersson M, Carlsson M, Ladenberger A, Morris G, Sadeghi M, Uhlbäck J (2014) Geochemical Atlas of Sweden, Geological Survey of Sweden (SGU), Uppsala.
Aucott JW (1987) Workshop 5: geochemical anomaly recognition, Journal of Geochemical Exploration 29: 375–376.
Bárdossy G, Fodor J (2001) Traditional and new ways to handle uncertainty in geology, Natural Resources Research 10(3): 179–187.
Bárdossy G, Fodor J (2004) Evaluation of Uncertainties and Risks in Geology. Springer Verlag.
Bonham-Carter GF, Agterberg FP, Wright DF (1988) Integration of geological datasets for gold exploration in Nova Scotia, Photogrammetric Engineering & Remote Sensing 54: 1585–1592.
Bonham-Carter GF, Agterberg FP, Wright DF (1989) Weights of evidence modeling: a new approach to mapping mineral potential. In: Agterberg, F.P., Bonham-Carter, G.F. (eds) Statistical applications in the Earth sciences: geological survey, Canada paper 89 (9): 171–183.
Caers J (2011) Modeling uncertainty in earth sciences. Wiley, Chichester.
Carranza EJM (2009) Geochemical anomaly and mineral prospectivity mapping in GIS. Handbook of Exploration and Environmental Geochemistry. 11. Elsevier, Amsterdam.
Chen Z, Cheng Q, Chen J, Xie S (2007) A novel iterative approach for mapping local singularities from geochemical data, Nonlinear Processes in Geophysics 14: 317–324.
Cheng Q (2007) Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China, Ore Geology Reviews 32: 314–324.
Cheng Q (2012) Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas, Journal of Geochemical Exploration 122: 55–70.
Cheng Q (2015) Multifractal interpolation method for spatial data with singularities, The Journal of the Southern African Institute of Mining and Metallurgy 115: 235–240.
Cheng Q, Agterberg FP, Ballantyne SB (1994) The separation of geochemical anomalies from background by fractal methods, Journal of Geochemical Exploration 51: 109–130.
Cheng Q, Xu Y, Grunsky E (1999) Integrated spatial and spectral analysis for geochemical anomaly separation. In: Lippard, S.J., Naess, A. & Sinding-Larsen, R. (Eds.), Proc. of the Conference of the International Association for Mathematical Geology, Trondheim, Norway 1: 87–92.
Chentsov NN (1957) Levy Brownian motion for several parameters and generalized white noise, Theory of Probability and its Applications 2(2): 265–266.
Chilès JP, Delfiner P (2012) Geostatistics: Modeling Spatial Uncertainty. John Wiley & Sons, Inc (Second Edition).
Chilès JP, Delfiner P (1999) Geostatistics: Modeling Spatial Uncertainty. John Wiley & Sons, Inc.
Costa JF, Koppe JC (1999) Assessing Uncertainty Associated with the Delineation of Geochemical Anomalies, Natural Resources Research 8(1): 59–67.
Daneshvar Saein LD, Rasa I, Omran NR, Moarefvand P, Afzal P, Sadeghi B (2013) Application of Number-Size (NS) Fractal Model to Quantify of the Vertical Distributions of Cu and Mo in Nowchun Porphyry Deposit (Kerman, Se Iran), Archives of Mining Sciences 58 (1): 89–105.
Davis JC (2002) Statistics and data analysis in geology, third edition. John Wiley & Sons, Inc.
Emery X (2008) A turning bands program for conditional co-simulation of cross-correlated Gaussian random fields, Computers and Geosciences 34(12): 1850–1862.
Emery X, Lantuéjoul C (2006) TBSIM: A computer program for conditional simulation of three-dimensional Gaussian random fields via the turning bands method, Computers and Geosciences 32: 1615–1628.
Fisher PF (1999) Models of uncertainty in spatial data. In: Longley, P.A., Goodchild, M.F., Maguire, D.J., Rhind, D.W. (eds). Geographical information systems: principles, techniques management and applications. Wiley, New York.
Good IJ (1950) Probability and the weighing of evidence. Griffin, London, 119 p.
Govett GJS, Goodfellow WD, Chapman A, Chork CY (1975) Exploration geochemistry-distribution of elements and recognition of anomalies, Mathematical Geology 7(5–6): 415–446.
Grunsky EC (2007) The interpretation of regional geochemical survey data, Advances in Regional-Scale Geochemical Methods 8: 139–182.
Grunsky EC (2010) The interpretation of regional geochemical survey data, Geochemistry: Exploration, Environment, Analysis 10: 27–74.
Grunsky EC, Easton RM, Thurston PC, Jensen LS (1992) Characterization and statistical classification of Archean volcanic rocks of the Superior Province using major element geochemistry in geology of Ontario. Ontario Geological Survey 4(2): 1347–1438.
Hajsadeghi S, Asghari O, Mirmohammadi M, Afzal P, Meshkani SA (2020) Uncertainty-Volume fractal model for delineating copper mineralization controllers using geostatistical simulation in Nohkouhi volcanogenic massive sulfide deposit, Central Iran, Bulletin of the Mineral Research and Exploration 161: 1–11.
Harris JR, Grunsky EC, Wilkinson L (1997) Developments in the effective use and interpretation of lithogeochemistry in regional exploration programs: application of GIS technology. In: Gubins, A.G. (Ed.), Proceedings of Exploration 97: 4th Decennial Int. Conf. Mineral Exploration, Toronto, 285–292.
Harris JR, Wilkinson L, Grunsky E, Heather K, Ayer J (1999) Techniques for analysis and visualization of lithogeochemical data with applications to the Swayze greenstone belt, Ontario, Journal of Geochemical Exploration 67(1–3): 301–334.
Hawkes HE, Webb JS (1962) Geochemistry in mineral exploration. Harper and Row, New York.
Ji H, Sun F, Chen M, Hu D, Shi Y, Pan X (2005) Geochemical evaluation for uncovered gold-bearing structures in Jiaodong area. J. Jilin Univ. (Earth Science Education) 35(3): 308–312 (in Chinese, with English abstract).
Khalajmasoumi M, Lotfi M, Memar Kochebagh A, Khakzad A, Afzal P, Sadeghi B, Ziazarifi A (2015) Delineation of the radioactive elements based on the radiometric data using concentration-area fractal method in the Saghand area, Central Iran, Arabian Journal of Geosciences 8: 6047–6062.
Khalajmasoumi M, Sadeghi B, Carranza EJM, Sadeghi M (2017) Geochemical anomaly recognition of rare earth elements using multi-fractal modeling correlated with geological features, Central Iran, Journal of Geochemical Exploration, Special issue of “Critical metals in the Middle East and North Africa - Geochemistry: Exploration and Analysis” 181: 318-332.
Kitanidis PK (1999) Introduction to geostatistics: Applications to hydrogeology. Cambridge University Press.
Kiureghian AD, Ditlevsen O (2009) Aleatory or epistemic? Does it matter? Structural Safety 31(2): 105–112.
Klir GJ, Yuan B (1995) Fuzzy sets and fuzzy logic: theory and applications. Prentice-Hall Englewood Cliffs.
Kouhestani H, Ghaderi M, Afzal P, Zaw K (2020) Classification of pyrite types using fractal and stepwise factor analyses in the Chah Zard gold-silver epithermal deposit, central Iran, Geochemistry: Exploration, Environment, Analysis 20: 496–508.
Kreuzer OP, Etheridge MA, Guj P, Maureen E, McMahon ME, Holden DJ (2008) Linking mineral deposit models to quantitative risk analysis and decision-making in exploration, Economic Geology 103: 829–850.
Madani N, Sadeghi B (2019) Capturing Hidden Geochemical Anomalies in Scarce Data by Fractal Analysis and Stochastic Modeling, Nat Resour Res 28(3): 833–847.
Mallet JL (2002) Geomodeling. Oxford University Press.
Mandelbrot BB (1983. The Fractal Geometry of Nature. W.H. Freeman, San Francisco, CA. Updated and Augmented Edition.
Mann CJ (1993) Uncertainty in Geology: Computers in Geology—25 years of Progress. Oxford University Press, New York, 241–254.
McCuaig TC, Beresford S, Hronsky J (2010) Translating the mineral systems approach into an effective targeting system, Ore Geology Reviews 38: 128–138.
McCuaig TC, Kreuzer OP, Brown WM (2007) Fooling ourselves—Dealing with model uncertainty in a mineral systems approach to exploration. Proceedings of the Ninth Biennial SGA Meeting, Dublin.
McCuaig TC, Porwal A, Gessner K (2009) Fooling ourselves: recognizing uncertainty and bias in exploration targeting, Centre Explor Target Q News 2: 1–8.
Miesch AT (1981) Estimation of the geochemical threshold and its statistical significance, Journal of Geochemical Exploration 16: 49–76.
Momeni S, Shahrokhi SV, Afzal P, Sadeghi B, Farhadinejad T, Mohammad Nikzad R (2016) Delineation of the Cr mineralization based on the stream sediment data utilizing fractal modeling and factor analysis in the Khoy 1: 100,000 sheet, NW Iran, Maden Tetkik ve Arama Dergisi 152: 143–151.
Nazarpour A, Omran NR, Rostami Paydar G, Sadeghi B, Matroud F, Mehrabi Nejad A (2015a) Application of classical statistics, logratio transformation and multifractal approaches to delineate geochemical anomalies in the Zarshuran gold district, NW Iran, Chemie der Erde 75: 117–132.
Nazarpour A, Sadeghi B, Sadeghi M (2015b) Application of fractal models to characterization and evaluation of vertical distribution of geochemical data in Zarshuran gold deposit, NW Iran, Journal of Geochemical Exploration 148: 60–70.
Paravarzar S, Emery X, Madani N (2015) Comparing sequential Gaussian and turning bands algorithms for cosimulating grades in multi-element deposits, Comptes Rendus Geoscience 347: 84–93.
Park K, Caers J (2007) History Matching in Low-Dimensional ConnectivityVector Space, SCRF report 20, Stanford University.
Pourgholam MM, Afzal P, Yasrebi AB, Gholinejad M, Wetherelt A (2021) Detection of geochemical anomalies using a fractal-wavelet model in Ipack area, Central Iran, Journal of Geochemical Exploration 220: 106675.
Remy N, Boucher A, Wu J (2009) Applied geostatistics with SGeMS (A User’s Guide). Cambridge University Press, New York. P. 264.
Sadeghi B (2020a). Quantification of Uncertainty in Geochemical Anomalies in Mineral Exploration. PhD thesis, University of New South Wales.
Sadeghi B (2020b) Concentration-concentration fractal modelling: a novel insight for correlation between variables in response to changes in the underlying controlling geological-geochemical processes, Ore Geology Reviews 128 (In Press).
Sadeghi B (2021) Evaluation of geochemical anomaly classification models based on the relevant uncertainties and error propagation per class to select the most robust model(s) for the follow-up exploration, EGU General Assembly: 19–30.
Sadeghi B, Afzal P, Moarefvand P, Khoda Shenas N (2012a). Application of concentration-area fractal method for determination of Fe geochemical anomalies and the background in Zaghia area, Central Iran, 34th International Geological Congress (IGC), Brisbane, Australia, 5–10.
Sadeghi B, Moarefvand P, Afzal P, Yasrebi AB, Daneshvar Saein L (2012b) Application of fractal models to outline mineralized zones in the Zaghia iron ore deposit, Central Iran, Journal of Geochemical Exploration 122: 9–19.
Sadeghi B, Carranza EJM (2015) Improving geological logs of drill-cores by correlating with fractal models of drill-hole geochemical data, International Association for Mathematical Geosciences (IAMG) Congress, Freiberg (Saxony), Germany.
Sadeghi B, Carranza EJM, Yilmaz H, Ford A (2016) Mapping of Au anomalies in drainage sediments by multifractal modeling, 35th International Geological Congress (IGC), Cape Town, South Africa, paper number 1286.
Sadeghi B, Yilmaz H, Pirajno F (2020) Weighting of BLEG data with drainage and catchment properties to enhance Au anomalies, Geochemistry, (In Press).
Sadeghi B, Cohen D (2021) Category-based fractal modelling: A novel model to integrate the geology into the data for more effective processing and interpretation, Journal of Geochemical Exploration (In Press).
Sadeghi B, Khalajmasoumi M, Afzal P, Moarefvand P (2014). Discrimination of iron high potential zones at the zaghia iron ore deposit, bafq, using index overlay GIS method, Iranian Journal of Earth Sciences 6 (2): 91–98.
Sadeghi B, Madani N, Carranza EJM (2015) Combination of geostatistical simulation and fractal modeling for mineral resource classification, Journal of Geochemical Exploration 149: 59–73.
Sanchez F, Sadeghi B (2018) Multi-fractal modeling: a significantly useful method to recognize geochemical anomalies in large-scale sampling networks, IAMG Conference, Prague, Czech Republic.
Scheidt C, Caers J (2007) A workflow for Spatial Uncertainty Quantification using Distances and Kernels, SCRF report 20, Stanford University.
Scheidt C, Li L, Caers J (2018) Quantifying Uncertainty in Subsurface Systems. American Geophysical Union – Wiley. P. 279.
Shamseddin Meigooni M, Lotfi M, Afzal P, Nezafati N, Kargar Razi M (2020) Detection of rare earth element anomalies in Esfordi phosphate deposit of Central Iran, using geostatistical-fractal simulation, Geopersia (In Press).
Sinclair AJ (1974) Selection of threshold values in geochemical data using probability graphs, Journal of Geochemical Exploration 3(2): 129–149.
Sinclair AJ (1983) Univariate analysis. In: R.J. Howarth (Ed.). Statistics and Data Analysis in Geochemical Prospecting, Handbook of Exploration Geochemistry, Vol. 2, Elsevier, Amsterdam, 59–81.
Sinclair AJ (1991) A fundamental approach to threshold estimation in exploration geochemistry, Probability plots revisited, Journal of Geochemical Exploration 41: 1–22.
Singer DA (2010) Progress in integrated quantitative mineral resource assessments, Ore Geology Reviews 38: 242–250.
Singer DA, Menzie WD (2010) Quantitative Mineral Resource Assessments-An Integrated Approach. Oxford University Press.
Soltani F, Moarefvand P, Alinia F, Afzal P (2020) Detection of Main Rock Type for Rare Earth Elements (REEs) Mineralization Using Staged Factor and Fractal Analysis in Gazestan Iron-Apatite Deposit, Central Iran, Geopersia 10(1): 89–99.
Stanley CR, Sinclair AJ (1989) Comparison of probability plots and gap statistics in the selection of threshold for exploration geochemistry data, Journal of Geochemical Exploration 32: 355–357.
Suzuki S, Caers J (2006) History matching with an uncertain geological scenario, SPE Annual Technical Conference and Exhibition, SPE 102154.
Tennant CB, White ML (1959) Study of the distribution of some geochemical data, Economic Geology 54(7): 1281–1290.
Tukey JW (1977) Exploratory Data Analysis, Addison-Wesley, Reading.
Walker WE, Harremoës P, Rotmans J, van der Sluijs JP, van Asselt MBA, Janssen P (2003) Defining uncertainty: a conceptual basis for uncertainty management in model-based decision support, Integrated Assessment 4(1): 5–17.
Wang J, Zuo R (2015) A MATLAB-based program for processing geochemical data using fractal/multi-fractal modelling, Earth Science Informatics 8(4): 937–947.
Xiao F, Chen J, Zhang Z, Wang C, Wu G, Agterberg FP (2012) Singularity mapping and spatially weighted principal component analysis to identify geochemical anomalies associated with Ag and Pb–Zn polymetallic mineralization in Northwest Zhejiang, China, Journal of Geochemical Exploration 122: 101–112.
Zhao J, Chen S, Zuo R, Carranza EJM (2011) Mapping complexity of spatial distribution of faults using fractal and multifractal models: vectoring towards exploration targets, Computers and Geosciences 37: 1958–1966.
Zissimos AM, Cohen DR, Christoforou IC, Sadeghi B, Rutherford NF (2020). Controls on soil geochemistry fractal characteristics in Lemesos (Limassol), Cyprus, Journal of Geochemical Exploration. (In Press).
Zuo R (2011) Identifying geochemical anomalies associated with Cu and Pb–Zn skarn mineralization using principal component analysis and spectrum–area fractal modeling in the Gangdese Belt, Tibet (China), Journal of Geochemical Exploration 111: 13–22.
Zuo R, Cheng Q (2008) Mapping singularities – a technique to identify potential Cu mineral deposits using sediment geochemical data, an example for Tibet, west China, Mineralogical Magazine 72: 531–534.
Zuo R, Cheng Q, Agterberg FP, Xia Q (2009) Application of singularity mapping technique to identification local anomalies using stream sediment geochemical data, a case study from Gangdese, Tibet, Western China, Journal of Geochemical Exploration 101: 225–235.
Zuo R, Xia Q, Zhang D (2013) A comparison study of the C–A and S–A models with singularity analysis to identify geochemical anomalies in covered areas, Applied Geochemistry 33: 165–172.
Zhao J, Chen S, Zou R, Carranza EMJ (2011) Mapping complexity of spatial distribution of faults using fractal and multifractal models: vectoring towards exploration targets, Computers & Geosciences 37: 1958-1966.