Abstract
The systematic study of extreme geological events (such as plate collision and subduction, extreme cold and extreme hot events, biological extinction and revival, earthquakes, volcanoes, mineralization, and oil accumulation) that occurred during the evolution of the earth is essential not only for understanding the “abrupt changes in the evolution of the earth”, but also for an in-depth understanding of the co-evolution of material-life-environment of the livable earth. However, due to the temporal and spatial anomalies and complexity of extreme geological events, classical mathematical models cannot be effectively applied to quantitively describe such events. After comparative studies of many types of geological events, the author found that such extreme geological events often depict “singular” characteristics (abnormal accumulation or depletion of matter or massive release or absorption of energy in a small space or time interval). On this basis, the author proposes a unified definition of extreme geological events, a new concept of “fractal density” and a “local singularity analysis” method for quantitative description and modeling of extreme geological events. Applications of these methods to several types of extreme geological events have demonstrated that the singularity theory and methods developed in the current research can be used as general approaches for the characterization, simulation, and prediction of geological events.
Similar content being viewed by others
References
Andersen T B, Austrheim H, Deseta N, Silkoset P, Ashwal L D. 2014. Large subduction earthquakes along the fossil Moho in Alpine Corsica. Geology, 42: 395–398
Bak P, Tang C, Wiesenfeld K. 1987. Self-organized criticality: An explanation of the 1/f noise. Phys Rev Lett, 59: 381–384
Bird P. 1978. Initiation of intracontinental subduction in the Himalaya. J Geophys Res, 83: 4975–4987
Bunde A, Kropp J, Schellnhuber H J. 2002. The Science of Disasters: Climate Disruptions, Heart Attacks, and Market Crashes. Berlin: Springer. 453
Carranza E J M. 2008. Geochemical anomaly and mineral prospectivity mapping in GIS. In: Hale M, eds. Handbook of Exploration and Environmental Geochemistry. Amsterdam: Elsevier. 368
Chen G, Cheng Q. 2018. Cyclicity and persistence of Earth’s evolution over time: Wavelet and fractal analysis. Geophys Res Lett, 45: 8223–8230
Chen W P, Yang Z. 2004. Earthquakes beneath the Himalayas and Tibet: Evidence for strong lithospheric mantle. Science, 304: 1949–1952
Cheng Q. 1999. Multifractality and spatial statistics. Comput Geoscis, 25: 949–961
Cheng Q. 2002. Multifractal modeling and GIS spatial analysis of complex fault systems. GeoInformatics, 13: 46–49
Cheng Q. 2004. A new model for quantifying anisotropic scale invariance and for decomposition of mixing patterns. Math Geol, 36: 345–360
Cheng Q. 2005. Multifractal distribution of eigenvalues and eigenvectors from 2d multiplicative cascade multifractal fields. Math Geol, 37: 915–927
Cheng Q. 2007. Mapping singularities with stream sediment geochemical data for prediction of undiscovered mineral deposits in Gejiu, Yunnan Province, China. Ore Geol Rev, 32: 314–324
Cheng Q. 2008. Non-linear theory and power-law models for information integration and mineral resources quantitative assessments. Math Geosci, 40: 503–532
Cheng Q. 2012a. Multiplicative cascade processes and information integration for predictive mapping. Nonlin Processes Geophys, 19: 57–68
Cheng Q. 2012b. Singularity theory and methods for mapping geochemical anomalies caused by buried sources and for predicting undiscovered mineral deposits in covered areas. J Geochem Explor, 122: 55–70
Cheng Q. 2016. Fractal density and singularity analysis of heat flow over ocean ridges. Sci Rep, 6: 19167
Cheng Q. 2017. Singularity analysis of global zircon U-Pb age series and implication of continental crust evolution. Gondwana Res, 51: 51–63
Cheng Q. 2018a. Extrapolations of secular trends in magmatic intensity and mantle cooling: Implications for future evolution of plate tectonics. Gondwana Res, 63: 268–273
Cheng Q. 2018b. Mathematical geosciences: Local singularity analysis of nonlinear earth processes and extreme geo-events. In: Sagar B S D, Cheng Q, Agterberg F, eds. Handbook of Mathematical Geosciences, Fifty Years of IAMG. Berlin: Springer. 911
Cheng Q. 2018c. Singularity analysis of magmatic flare-ups caused by India — Asia collisions. J Geochem Explor, 189: 25–31
Cheng Q. 2021. What are mathematical geosciences and its frontiers? (in Chinese) Earth Sci Front, 28: 6–25
Cheng Q, Agterberg F P. 2009. Singularity analysis of ore-mineral and toxic trace elements in stream sediments. Comput Geoscis, 35: 234–244
Cheng Q, Agterberg F P. 1996. Multifractal modeling and spatial statistics. Math Geol, 28: 1–16
Cheng Q M, Sun H Y. 2018. Variation of singularity of earthquake-size distribution with respect to tectonic regime. Geosci Front, 9: 453–458
Cheng Q, Agterberg F P, Ballantyne S B. 1994. The separation of geochemical anomalies from background by fractal methods. J Geochem Explor, 51: 109–130
Cheng Q, Li L, Wang L. 2009. Characterization of peak flow events with local singularity method. Nonlin Processes Geophys, 16: 503–513
Cheng Q, Oberhänsli R, Zhao M. 2020. A new international initiative for facilitating data-driven Earth science transformation. Geol Soc Lond Spec Publ, 499: 225–240
Easterling D R, Meehl G A, Parmesan C, Changnon S A, Karl T R, Mearns L O. 2000. Climate extremes: Observations, modeling, and impacts. Science, 289: 2068–2074
Goswami A, Barbot S. 2018. Slow-slip events in semi-brittle serpentinite fault zones. Sci Rep, 8: 6181
Gutenberg B, Richter C F. 1944. Frequency of earthquakes in California. Bull Seismol Soc Am, 4: 185–188
Hawkesworth C, Cawood P, Kemp T, Storey C, Dhuime B. 2009. A matter of preservation. Science, 323: 49–50
Hess H H. 1962. History of ocean basins. In: Engel A E J, James H L, Leonard B F, eds. Petrologic studies: A volume in honor of A. F. Buddington. Boulder: Geological Society of America. 599–620
HYDAT CD-ROM User’s Manual. 1996. Surface water and sediment data, atmospheric environment program, version 96–1.04 User’s Manual, Environment Canada. 95 IPCC. 2012. Managing the risks of extreme events and disasters to advance climate change adaptation: A special report of working groups I and II of the intergovernmental panel on climate change. In: Field C B, Barros V, Stocker T F, Qin D H, Dokken D J, Ebi K L, Mastrandrea M D, Mach K J, Plattner G K, Allen S K, Tignor M, Midgley P M, eds. New York: Cambridge University Press. 582
Jentsch V, Kantz H, Albeverio, S. 2006. Extreme Events in Nature and Society. Berlin: Springer. 352
Kenny F M. 1997. A chromostereo enhanced digital elevation model of the Oak Ridges Moraine Area, southern Ontario and Lake Ontario Bathymetry. Geol Survey Canada, Open file 3423, scale 1:200000
Li Q, Cheng Q. 2006. VisualAnomaly: A GIS-based multifractal method for geochemical and geophysical anomaly separation in Walsh domain. Comput Geoscis, 32: 663–672
Lorenz E N. 1963. Deterministic nonperiodic flow. J Atmos Sci, 20: 130–141
Lovejoy S, Agterberg F, Carsteanu A, Cheng Q, Davidsen J, Gaonac’h H, Gupta V, L’Heureux I, Liu W, Morris S W, Sharma S, Shcherbakov R, Tarquis A, Turcotte D, Uritsky V. 2009. Nonlinear geophysics: Why we need it. Eos Trans AGU, 90: 455–456
Mandelbrot B. 1967. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science, 156: 636–638
McKenzie D P. 1967. Some remarks on heat flow and gravity anomalies. J Geophys Res, 72: 6261–6273
McPhillips L E, Chang H, Chester M V, Depietri Y, Friedman E, Grimm N B, Kominoski J S, McPhearson T, Méndez-Lázaro P, Rosi E J, Shafiei Shiva J. 2018. Defining extreme events: A cross-disciplinary review. Earths Future, 6: 441–455
National Academies of Sciences, Engineering, and Medicine. 2016. Attribution of Extreme Weather Events in the Context of Climate Change. Washington, DC: The National Academies Press
Nicolis G, Prigogine I. 1977. Self-organization in Nonequilibrium Systems. New York: Wiley. 491
Parman S W. 2007. Helium isotopic evidence for episodic mantle melting and crustal growth. Nature, 446: 900–903
Ren F M, Trewin B, Brunet M, Dushmanta P, Walter A, Baddour O, Korber M. 2018. A research progress review on regional extreme events. Adv Clim Change Res, 9: 161–169
Sharma A S, Baker D N, Bhattacharyya A, Bunde A, Dimri V P, Gupta H K, Gupta V K, Lovejoy S, Main I G, Schertzer D, Storch H V, Watkins N W. 2012. Complexity and extreme events in geosciences: An overview. In: Sharma A S, Bunde A, Dimri V P, Baker D N, eds. Extreme Events and Natural Hazards: The Complexity Perspective. Geophys Monogr Seri, 196: 1–16
Singer S N, Cheng C K, Scafe M G. 2003. The hydrogeology of southern Ontario. 2 ed. Hydrogeology of Ontario Series, Report 1. Technical Report. Environmental Monitoring and Reporting Branch, Ministry of Environment. 200
Stein C A, Stein S. 1992. A model for the global variation in oceanic depth and heat flow with lithospheric age. Nature, 359: 123–129
Stephenson D B, Diaz H F, Murnane R J. 2008. Definition, diagnosis, and origin of extreme weather and climate events. In: Murnane R J, Diaz H F, eds. Climate Extremes and Society. Cambridge: Cambridge University Press. 11–23
Turcotte D L. 2006. Modeling geocomplexity: “A new kind of science”. In: Manduca C A, Mogk D W, eds. Earth and Mind: How Geologists Think and Learn about the Earth. Geological Society of America (GSA) Special Papers, 413
Valentine G A, Zhang D, Robinson B A. 2002. Modeling complex, nonlinear geological processes. Annu Rev Earth Planet Sci, 30: 35–64
Wang W, Cheng Q, Zhang S, Zhao J. 2018. Anisotropic singularity: A novel way to characterize controlling effects of geological processes on mineralization. J Geochem Explor, 189: 32–41
Wolfram S. 2002. A New Kind of Science. Champaign: Wolfram Media. 1197
Fan Xiao, Kaiqi Wang, Weisheng Hou, Oktay Erten. 2020. Identifying geochemical anomaly through spatially anisotropic singularity mapping: A case study from silver-gold deposit in Pangxidong district, SE China, Journal of Geochemical Exploration, 210, doi: https://doi.org/10.1016/j.gexp
Yu C. 2003. Complexity of geosystem: Basic issues of geological science (II) (in Chinese). Earth Sci, 12: 21–40
Zhao P. 1992. Theories, principles, and methods for the statistical prediction of mineral deposits. Math Geol, 24: 589–595
Acknowledgements
Part of the content of this article was exchanged at the academic seminar of the Academician Conference of the Chinese Academy of Sciences in May of 2021. The author has exchanged and discussed the academic views and thoughts in the article with many academicians of the Chinese Academy of Sciences such as Pengda ZHAO, Hongfu YIN, Zhenmin JIN, Xuanxue MO, Shuguang LI, Zhisheng AN, Wencai YANG, Zhijun JIN, Chengshan WANG, Zengqian HOU. Thanks are due to the above academicians for their constructive comments and suggestions which have helped to improve the formation and discussion of the singularity theory and the expansion of practical applications. Several graduate students, Shubin ZHOU, Molei ZHAO, Zhengjie ZHANG, Jie YANG and Pinpin ZHU are thanked for their assistances on preparations of some of the figures and the earlier draft of the manuscripts. Finally, the author thanks the three anonymous reviewers for their constructive suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 42050103), the Ministry of Science and Technology (Grant No. 2016YFC0600500), and the Ministry of Natural Resources and the China Geological Survey (Grant No. DD20160045).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Cheng, Q. Quantitative simulation and prediction of extreme geological events. Sci. China Earth Sci. 65, 1012–1029 (2022). https://doi.org/10.1007/s11430-021-9881-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11430-021-9881-2