Exploring Spatially Non-stationary Relationships in the Determinants of Mineralization in 3D Geological Space
Tóm tắt
Exploring the spatial relationships between various geological features and mineralization is not only conducive to understanding the genesis of ore deposits but can also help to guide mineral exploration by providing predictive mineral maps. However, most current methods assume spatially constant determinants of mineralization and therefore have limited applicability to detecting possible spatially non-stationary relationships between the geological features and the mineralization. In this paper, the spatial variation between the distribution of mineralization and its determining factors is described for a case study in the Dingjiashan Pb–Zn deposit, China. A local regression modeling technique, geological weighted regression (GWR), was leveraged to study the spatial non-stationarity in the 3D geological space. First, ordinary least-squares (OLS) regression was applied, the redundancy and significance of the controlling factors were tested, and the spatial dependency in Zn and Pb ore grade measurements was confirmed. Second, GWR models with different kernel functions in 3D space were applied, and their results were compared to the OLS model. The results show a superior performance of GWR compared with OLS and a significant spatial non-stationarity in the determinants of ore grade. Third, a non-stationarity test was performed. The stationarity index and the Monte Carlo stationarity test demonstrate the non-stationarity of all the variables throughout the area. Finally, the influences of the degree of non-stationary of all controlling factors on mineralization are discussed. The existence of significant non-stationarity of mineral ore determinants in 3D space opens up an exciting avenue for research into the prediction of underground ore bodies.
Tài liệu tham khảo
Agterberg, F. P. (1964). Methods of trend surface analysis. Colorado School Mines,59, 111–130.
Agterberg, F. P. (1970). Multivariate prediction equations in geology. International Association for Mathematical Geology, 319–324.
Andrew, B. T., Peter, J. K., & Sharmistha, B. S. (2015). Geographic variation in male suicide rates in the United States. Applied Geography,62, 201–209.
Batisani, N., & Yarnal, B. (2009). Urban expansion in centre county Pennsylvania: spatial dynamics and landscape transformations. Applied Geography,29, 235–249.
Breetzke, G. D., & Cohn, E. G. (2012). Seasonal assault and neighborhood deprivation in South Africa: some preliminary findings. Environment and Behavior,44(5), 641–667.
Brunsdon, C., Fotheringham, A. S., & Charlton, M. E. (1996). Geographically weighted regression: a method for exploring spatial nonstationarity. Geographical Analysis,28, 281–298.
Brunsdon, C., Fotheringham, A. S., & Charlton, M. (1998). Geographically weighted regression modeling spatial non-stationarity. Statistician,47, 431–443.
Brunsdon, C., Fotheringham, A. S., & Charlton, M. (2002). Geographically weighted summary statistics - a framework for localized exploratory data analysis. Computers, Environment and Urban Systems,26, 501–524.
Casetti, E. (1972). Generating models by the expansion method: Applications to geographic research. Geographical Analysis,4, 81–91.
Chen, J. P., Wang, G. W., & Hou, C. B. (2005). Quantitative prediction and evaluation of mineral resources based on GIS: A case study in Sanjiang Region, Southwestern China. Natural Resources Research,14(4), 285–294. https://doi.org/10.1007/s11053-006-9005-6.
Chen, Y., & Wu, W. (2017). Mapping mineral prospectivity using an extreme learning machine regression. Ore Geology Reviews,80, 200–213.
Chen, Y., & Wu, W. (2019). Isolation forest as an alternative data-driven mineral prospectivity mapping method with a higher data-processing efficiency. Natural Resources Research,28(1), 31–46. https://doi.org/10.1007/s11053-018-9375-6.
Cheng, Q. (1997). Fractal/multifractal modeling and spatial analysis. Keynote Lecture in Proceedings of the International Mathematical Geology Association Conference,1, 57–72.
Cheng, Q. (1999). Multifractality and spatial statistics. Computers & Geosciences,25(949–961), 1999.
Clement, F., Orange, D., Williams, M., Mulley, C., & Epprecht, M. (2009). Drivers of afforestation in Northern Vietnam: assessing local variations using geographically weighted regression. Applied Geography,29(4), 561–576.
Fotheringham, A. S., & Brunsdon, C. (1999). Local forms of spatial analysis. Geographical Analysis,31, 340–358.
Fotheringham, A. S., Brunsdon, C., & Charlton, M. (2002). Geographically weighted regression: The analysis of spatially varying relationships (1st ed.). Chichester: Wiley.
Fotheringham, A. S., Charlton, M., & Brunsdon, C. (1996). The geography of parameter space: an investigation of spatial non-stationarity. International Journal of Geographical Information Science,10, 605–627.
Fotheringham, A. S., Charlton, M., & Brunsdon, C. (1998). Geographically weighted regression: A natural evolution of the expansion method for spatial data analysis. Environment and Planning A,30, 1905–1927.
Fotheringham, A. S., Charlton, M. E., & Brunsdon, C. (2001). Spatial variations in school performance: A local analysis using geographically weighted regression. Geographical and Environmental Modelling,5, 43–66.
Gao, J. B., & Li, S. C. (2011). Detecting spatially non-stationary and scale-dependent relationships between urban landscape fragmentation and related factors using Geographically Weighted Regression. Applied Geography,31, 292–302.
Geri, F., Amici, V., & Rocchini, D. (2010). Human activity impact on the heterogeneity of a Mediterranean landscape. Applied Geography,30, 370–379.
Gilbert, A., & Chakraborty, J. (2011). Using geographically weighted regression for environmental justice analysis: Cumulative cancer risks from air toxics in Florida. Social Science Research,40(1), 273–286.
Harris, P., & Brunsdon, C. (2010). Exploring spatial variation and spatial relationships in a freshwater acidification critical load data set for Great Britain using geographically weighted summary statistics. Computers & Geosciences,36(1), 54–70.
Hope, A. C. A. (1968). A simplified Monte Carlo significance test procedure. Journal of the Royal Statistical Society. Series B: Methodological,30(3), 582–598.
Jessell, M. W., Ailleres, L., & De Kemp, E. A. (2010). Towards an integrated inversion of geoscientific data: What price of geology? Tectonophysics,490(3–4), 294–306.
Lee, K. H., & Schuett, M. A. (2014). Exploring spatial variations in the relationships between residents’ recreation demand and associated factors: A case study in Texas. Applied Geography,53, 213–222.
LeSage, J., & Pace, R. K. (2009). Introduction to spatial econometrics. CRC Press, Taylor & Francis Group, New York.
Li, N., Song, X., Li, C., & Chen, H. (2019). 3D geological modeling for mineral system approach to GIS-based prospectivity analysis: Case study of an MVT Pb–Zn deposit. Natural Resources Research,28, 995. https://doi.org/10.1007/s11053-018-9429-9.
Lin, N., Chen, Y., & Lu, L. (2019). Mineral potential mapping using a conjugate gradient logistic regression model. Natural Resources Research. https://doi.org/10.1007/s11053-019-09509-1.
Lindsay, M. D., Aillères, L., Jessell, M. W., de Kemp, E., & Betts, P. G. (2012). Locating and quantifying geological uncertainty in three-dimensional models: Analysis of the Gippsland Basin, southeastern Australia. Tectonophysics,546–547, 10–27.
Liu, Y. C., Li, Z. X., Laukamp, C., West, G., & Gardoll, S. (2013). Quantified spatial relationships between gold mineralisation and key ore genesis controlling factors, and predictive mineralisation mapping, St Ives Goldfield, Western Australia. Ore Geology Reviews,54, 157–166.
Lu, X., & Bo, T. (2014). On the determinants of UK house prices. International Journal of Economics and Research,512, 57–64.
Lu, B. B., Charlton, M., & Fotheringham, A. S. (2011). Geographically weighted regression using a non-Euclidean distance metric with a study on London House Price Data. Procedia Environmental Sciences,7(8), 92–97.
Mao, X. C., Dai, T. G., Wu, X. B., & Zou, Y. H. (2009). The stereoscopic quantitative prediction of concealed ore bodies in the deep and marginal parts of crisis mines: A case study of the Dachang tin polymetallic ore deposit in Guangxi. Geology in China,36(2), 424–435.
Mao, X. C., Zhang, B., Deng, H., Zou, Y. H., & Chen, J. (2016). Three-dimensional morphological analysis method for geologic bodies and its parallel implementation. Computers & Geosciences,96, 11–22.
Mao, X. C., Zou, Y. H., Chen, J., Lai, J. Q., Peng, S. L., Shao, Y. J., et al. (2010). Three-dimensional visual prediction of concealed ore bodies in the deep and marginal parts of crisis mines: A case study of the Fenghuangshan ore field in Tongling, Anhui, China. Geological Bulletin of China,29(2–3), 401–413.
Nilsson, P. (2014). Natural amenities in urban space—A geographically weighted regression approach. Landscape Urban Plan,121, 45–54.
Schamper, C., Auken, E., & Sørensen, K. I. (2014a). Coil response inversion for very early time modeling of helicopter-borne time-domain electromagnetic data and mapping of near-surface geological layers. Geophysical Prospecting,62, 658–674.
Schamper, C., Jørgensen, F., Auken, E., & Effersø, F. (2014b). Assessment of near-surface mapping capabilities by airborne transient electromagnetic data—An extensive comparison to conventional borehole data. Geophysics,79, B187–B199.
Shao, Y., Ma, C., Mao, X. C., et al. (2010). 3-D visual prediction of Dingjiashan lead-zinc deposit. Beijing: Geological Publishing House.
Tobler, W. R. (1979). Smooth pycnophylactic interpolation for geographical regions. Journal of the American Statistical Association,74, 519–530.
Tu, J., & Xia, Z. G. (2008). Examining spatially varying relationships between land use and water quality using geographically weighted regression I: Model design and evaluation. Science of the Total Environment,407(1), 358–378.
Wang, W., Zhao, J., & Cheng, Q. (2015). GIS-based mineral exploration modeling by advanced geo-information analysis methods in southeastern Yunnan mineral district, China. Ore Geology Reviews,71, 735–748.
Yao, J., & Fotheringham, A. S. (2015). Local spatiotemporal modeling of house prices: A mixed model approach. Professional Geographer,68(2), 1–13.
Zhang, D., Cheng, Q., Agterberg, F. P., & Chen, Z. (2016). An improved solution of local window parameters setting for local singularity analysis based on excel vba batch processing technology. Computers & Geosciences,88(C), 54–66.
Zhang, D., Jia, Q., Xu, X., Yao, S., Chen, H., Hou, X., et al. (2019). Assessing the coordination of ecological and agricultural goals during ecological restoration efforts: A case study of Wuqi County, Northwest China. Land Use Policy,82, 550–562.
Zhang, B. Y., Mao, X. C., Zhou, S. G., Hu, C., & Yan, F. (2012). Spatial affecting extents limited comprehensive geo-information mineral resources quantitative prediction models: A case study of manages ore prediction in western Guangxi and southeastern Yunnan. China. Geological review,58(5), 978–989.
Zhang, D., Ren, N., & Hou, X. (2018). An improved logistic regression model based on a spatially weighted technique (ILRBSWT v1. 0) and its application to mineral prospectivity mapping. Geoscientific Model Development, 11(6), 2525–2539.
Zhang, S. G., Shi, D. F., Han, S. L., & Li, G. X. (2011). Genetic mineralogical study of pyrrhotite in the Dingjiashan Pb-Zn ore district, Fujian province. Journal of Mineralogical and Petrological Sciences,31(3), 11–17.
Zhao, J., Wang, W., & Cheng, Q. M. (2013). Investigation of spatially non-stationary influences of tectono-magmatic processes on Fe mineralization in eastern Tianshan, China with geographically weighted regression. Journal of Geochemical Exploration,134, 38–50.
Zhao, J., Wang, W., & Cheng, Q. M. (2014). Application of geographically weighted regression to identify spatially non-stationary relationships between Fe mineralization and its controlling factors in eastern Tianshan, China. Ore Geology Reviews,57, 628–638.
Zuo, R., Carranza, E. J. M., & Wang, J. (2016). Spatial analysis and visualization of exploration geochemical data. Earth-Science Reviews,158, 9–18.
Zuo, R., & Xiong, Y. (2018). Big data analytics of identifying geochemical anomalies supported by machine learning methods. Natural Resources Research,27, 5–13.