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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.
The topological classification of geochemical elements is widely used as a reference for regional prospecting prediction. In this study, we analyze the topological correlation structures of 39 representative geochemical elements from the Nanling area of South China by implementing the complex networks theory. The topological correlation structures of geochemical elements have a high clustering coefficient (0.8120–0.8880), but the magnitude of the shortest path (1.2950–2.3600) is small. In combination with the analysis of complex networks characteristics, we report that the topological correlation structures of the geochemical elements in this area have small-world characteristics, which reveals the self-organized criticality. As shown in the topological network, two random elements have some level of associations, which present a specific community feature. Our preliminary result shows that with changing the control parameter (k) of “coarse-graining”, the topological correlation structures undergo two critical phase transitions. As the control parameter (k) reaches 0.44, the entire element system evolves into two parts. When the control parameter (k) reaches 0.63, the system forms three “communities”. It is worth noting that the three “communities” are basically consistent with the Goldschmidt’s geochemical classification of the elements, which are lithophile, siderophile, and chalcophile groups, respectively. In these “communities”, we also found that a small level of component units is nested.
The Yingshan Formation of Middle-Lower Ordovician in Tazhong uplift in Tarim is an important fracture and karst-modified carbonate reservoir. Main pore types in this reservoir include fractures , vug and caves, which mainly resulted from multi-stage epigenetic dissolution and post-stage hypogenetic excavation. The reservoir architectural systems are of extreme heterogeneity and significant compartmentalization. This study presents an architectural hierarchy for the reservoirs not controlled by facices according to the system theory. On the basis of integrated information revealed by a variety of methods, such as geophysical methods including prestack fracture prediction technology, paleo-geomorphological analysis technology, seismic-logging wave impedance inversion technology, three-dimensional seismic attribute extraction technology, and well-logging explanation, core observation etc, the four types of reservoir units including fracture-dominated, vug-dominated, cave-dominated and complex can be identified and mapped in this area, these reservoir architectural units genetically formed in epigenetic and hydrothermal karst modification, fracturing. Moreover, the genesis of some reservoir units are studied in detail.
The natural disaster chain in the form of mathematical language on the basis of the system analysis methods is defined, and its property based on the disaster chain mode is studied. This paper studies the chain-cutting disaster mitigation from the point of its inner state and the outside environments, and points out that the outside environment influence is gestation sources of disaster and disaster chain, and reveals that disaster chain exists because of the interaction of disasters. An example in view of land desertification chain is presented. The land desertification chain results from human unreasonable activities and from the deterioration of ecological environment are drawn, and chain-cutting disaster mitigation of land desertification chain by the disaster chain mode is analyzed.
With the help of complexity indices, we quantitatively studied multifractals, frequency dis-tributions, and linear and nonlinear characteristics of geochemical data for exploration of the Daijiazhuang Pb–Zn deposit. Furthermore, we derived productivity differentiation models of elements from thermodynamics and self-organized criticality of metallogenic systems. With respect to frequency distributions and multifractals, only Zn in rocks and most ele-ments except Sb in secondary media, which had been derived mainly from weathering and alluviation, exhibit nonlinear distributions. The relations of productivity to concentrations of metallogenic elements and paragenic elements in rocks and those of elements strongly leached in secondary media can be seen as linear addition of exponential functions with a characteristic weak chaos. The relations of associated elements such as Mo, Sb, and Hg in rocks and other elements in secondary media can be expressed as an exponential function, and the relations of one-phase self-organized geological or metallogenic processes can be represented by a power function, each representing secondary chaos or strong chaos. For secondary media, exploration data of most elements should be processed using nonlinear mathematical methods or should be transformed to linear distributions before processing using linear mathematical methods.
In this paper, the status quo and modeling principles of R/S analysis of non-linear theory are introduced and reviewed. Given the hydro-geological conditions of the Wutongzhuang coal mine, Hurst exponents of mine inflow for the main shaft, ventilating shaft and auxiliary shaft were obtained using R/S analysis, which are 0.772 0, 0.824 7 and 0.905 1 respectively. Since all of the three Hurst exponents are larger than 0.5, it can be concluded that the trend of mine inflow are a long-term as well as persistent problem. Based on the level of duration, the shafts can be listed in decreasing order as the auxiliary shaft, the ventilation shaft and the main shaft, which appears identical with the actual situation of the mine inflow. With R/S analysis, a new method for long-term forecasting of mine inflows is provided.
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