During the past forty years, in the mathematical geology domains, such as mineral resource quantitative assessment and nonlinear theory and their application in ore geology and mineral exploration, Chinese scholars have developed new theories and new methods which have advanced the relevant subjects. For example, the theory of geological anomaly quantitative prediction and mineral resource assessment, the theory of "three components" digital ore-finding, the idea of comprehensive information for mineral prognosis, the theory of mineral deposit growth at the edge of chaos, the multifractal theories and nonlinear information extraction and integration methods, such as concentration-area model (C-A) and spectrum-area model (S-A), the model of fuzzy weight of evidence (FWofE), and etc.. All these have not only advanced geomathematics but also provided new ways of applying geomathematical methods in mineral prospecting, environment and geological disaster predicting. Chinese scholars have made significant contributions to the development of mathematical geosciences, and so some of them occupied important posts of International Association for Mathematical Geosciences (IAMG). In addition, Chinese scholars also contribute to IAMG by means of our association as well as to the expertise such as serving as journal editors, conference hosts and council members. China has become one of the current international centers for research in mathematical geology.

New non-linear theory and methods of multifractal singularity are applied to map weak anomalies related to deeply buried ores and mineralization halos.The main contents of singularity theory and methodology include three main principles and models: local singularity analysis (for example Δ-analysis) for enhancing weak anomalies caused by buried ores, generalized self-similarity analysis (for example C-A and S-A models) for anomaly decomposition and for anomaly and background separation, and fractal spectrum analysis (for example mapping posterior probability) for characterizing spatial distribution of singularities and anomalies.This paper uses the local singularity analysis to map the anomalies not only in the eastern area where known mineral deposits are found but also in the western area where few mineral deposits have been found.It also uses the generalized self-similarity analysis method S-A model in integration of the principle component analysis in separating element association anomalies in both eastern and western areas.The results show that the eastern and western areas depict significant background difference and the local anomalies obtained using both local singularity model and S-A model show generalized self-similarity in eastern and western areas.Several target areas are delineated on the basis of these local anomalies.

This paper is based on several research projects conducted in Gejiu Sn and Cu mineral districts on regional mineral resource assessment, 3D mineral resource assessment and prediction of deeply buried mineral deposits.New non-linear theory and methods of multifractal singularity have been applied in these projects to map weak anomalies related to deeply buried ores and mineralization halos.The weights of evidence model with corrected posterior probability using a newly developed correction method is applied to integrate various geo-evidential layers to map mineral potentials in the Gejiu area.The binary evidential layers include two layers defined on the basis of geochemical data, with one on distance from intersection of faults and the other on Gejiu Formation.Each addition of a binary layer can be considered as a partition of the study area and redistribution of posterior probability which can be treated as a general multiplicative cascade process and the final product may show multifractal properties with multiple singularities.A power-law model was established between posterior probability and undiscovered mineral deposits for the area.

Based on a new hypothesis that sphalerites are formed in replacement of hexagonal calcites in Mississippi Valley-type (MVT) deposits, a new cellular nonlinear network (CNN) model is proposed in a hexagonal coordinate system.The simulated results show that the sphalerites formed have Liesegang band textures and the radii of the crystallites oscillating decreases from the rim of the calcite crystal inward.It also shows that the radii of sphalerites decreases from the rim in conformity with the power-law distribution.

It is difficult to discover the certainty and randomness of the law of the evolution of the underground water system by only using deterministic method or stochastic method, because the evolution of the system is not only deterministic but also stochastic, due to the effect of such factors as hydrologic geology and mine exploitation.Chaos theory combines both deterministic analysis method and stochastic analysis method.The time series of water inrush in mine are the results of the interaction between the factors of the underground water system in mine and contain the information of this dynamical system.Based on the background analysis of hydrologic geology of the second coal mine in Liuqiao, we obtained the Lyapunov index (0.1427) of the time series of water inrush by modeling and analyzing of the chaotic time series.The Lyapunov index shows that the water inrush of the second coal mine in Liuqiao is of chaotic characteristics.By using the established model, the time series of water inrush in mine from April 2004 to February 2005 was verified, and the results indicate that the chaotic time series analysis method is feasible and highly effective in predicting the water inrush in mine.

Fractal and multifractal concepts have been increasingly applied in various scientific and engineering fields.The distribution patterns of different objects at different scales have attracted more and more attention as well.This paper focuses on the investigation of the spatial heterogeneity of ore-forming minerals at micro-scales.Two ore-bearing skarn samples have been selected and the corresponding light-thin sections have also been prepared.The first sample, taken from the external contact zone between the skarn and the granite, is the blackish green ore-bearing skarn, and the second is the skarn-type ore sample which was taken from the skarn contact zone.Through MATLAB platform, the pyrites have been digitally recognized from the microphotographying images of the thin sections.The box-counting dimensions, generalized fractal dimensions and multifractal spectra have been calculated to characterize the spatial structure of the pyrites.The corresponding fractal and multifractal dimensions of the first sample are relatively lower, whereas those of the second sample are higher.The results show that there is a coressponding relationship between the multifractal parameters and the ore-forming potentials of the rocks under consideration, which can provide new indication for the quantitative assessment of ore-bearing potentials of rocks.

In order to understand various anisotropic scale invariance systems, the generalized scale invariance (GSI) concept was brought forward to present a formalism stating the most general conditions under which large and small scales can be related.Two different anisotropic scale invariance quantification models were developed: the scale invariant generator (SIG) model quantifies anisotropies by estimating the GSI generator in frequency domain, a form of scale transformation defined in GSI representing how the scaling field is stratified and how it rotates, and the family of balls that best describes the scaling field; the spectrum-area (S-A) model quantifies anisotropies by estimating the anisotropic scaling exponent defined in GSI through a power-law function representing the relationship between area of the set with spectral energy density above P on the 2D frequency domain and P. S-A is not only an anisotropic scale invariance quantification technique but also a mixing data decomposition technique, which can decompose mixing data into multiple components based on anisotropic scaling properties in frequency domain.This paper introduces the GSI concept, the SIG model and S-A model systematically and proposes an idea to combine the SIG model and S-A model so that the new combined model can not only decompose mixing data into multiple components but also quantify the decomposed components' anisotropic scale invariance as well.

The study on micro-pores of soils, pore-fracture-holes of sedimentary rocks and microstructures of minerals at different scales has attracted more and more attention.Typical fractal models, including P-A and box-counting methods, have also been used for such kind of studies.Basalts from seven sections in Laochang deposit, Yunnan Province, are well developed, but their forming processes and their contributions to deposits of Sn and other metals are still in issue.Based on the GIS-based P-A and box-counting fractal models, this paper focuses on the size distribution and irregularity analysis of pyrrhotites of the basalts.Three parameters D_A (fractal dimension of area), D_PA (fractal dimension of area and perimeter) and D_P (fractal dimension of perimeter) of pyrrhotite are calculated.The results show that, from the first-section basalt to the seventh-section basalt, with the depth of rock body increasing, the values of D_A and D_P change a little, but the value of D_PA shows an increasing trend.This indicates that the shapes of pyrrhotites become more and more irregular as the depth increases, probably due to the increase of temperature and pressure.

This paper proposes two kinds of new models of weight of evidence: weighted weights of evidence and stepwise weights of evidence to reduce the influence of correlation among evidence layers when hypothesis of conditional independence is not held.In the weighted weights of evidence model, an adjustment of weight of evidence is made to reduce the influence of correlation among evidence layers.In the stepwise model, each evidence layer is added into the logistic model as if a single layer whose weight can be calculated by using the previously calculated posterior probability as a new prior probability.These two models are compared with other models through a case study of calculating posterior probability maps for Sn-Cu mineral deposits in Gejiu, Yunnan, China.The result shows that both models are effective to reduce the influence of correlations among evidence layers on delineation of Sn-Cu anomalies.

Optimum target area (OTA) plays an important rule in mineral resource prospecting, which is not only the end production of mineral resource assessment, but also the bridge between the mineral resource assessment and exploration plan.However, it is usually ignored or simplified owing to the incomplete cognition and being lack of technique or software.In this paper, we disscuss the OTA principles based on the geology, set up the data flow for OTA and develop the GIS-based OTA model.The Gejiu, Yunnan, southwestern China, was chosen as an example to do the demonstration research.The results demonstrate that the OTA model could reflect the properties of target areas, and can enhance the efficiency of OTA.

3D property modeling is hot nowadays in geoscientific researches, the essence of which is mapping geological properties in 3D space from limited samples by interpolation or simulation methods.By extending Kriging to 3D space which evolves to the so-called 3D Kriging, a reliable method can be provided for 3D property modeling.However, one of the most difficult problems in 3D Kriging is the nested overlap of anisotropic variograms.In this paper, a simple but universal method is proposed for the nested overlap.Based on the transformation of coordinate basis, this new method takes into full consideration the difference of variation on each axis direction and puts forward the concept of anisotropy ratio.The feasibility of the new method is demonstrated and testified by a case study about 3D property modeling of groundwater quality.

With high stability, chert is widely distributed in the orogens, whose major composition is SiO₂.Affected by the orogeny, metallogenesis and recrystallization, the metamorphic processes can be well revealed by the megatectonics and microfabric characteristics.The study of the megatectonics and microfabric characteristics of the cherts of Bafangshan-Erlihe Pb-Zn ore field in the western Qinling orogen reveals that there are obvious hydrothermal sedimentary characteristics in the cherts.Because of the stresses, two types of which are extensional and compresso-shear, there are megatectonics of compresso-shear faults with EW direction and gapping faults with NNE and NNW directions.What's more, there are microfabric characteristics of microcracks and microcorrugations and stretched-out grains of quartzs.In the rocks of this ore deposit field, the dynamic metamorphism, metamorphic recrystallization and other kinds of metamorphisms are clearly revealed.The trace carbonate minerals and the stress are both important to the metallogenesis of this ore deposit, which provide the pathway and space for the metallic sulphide fluids to travel and deposit.

Gejiu ore-concentration area is one of the most important occurrences of Sn-Cu polymetallie mineralization in Southeast YunnarL Sn-Cu polymetallic system of mineralization in the area includes Sn-W greisen-quartz vein type, Cu-massive-sulfide cassiterite type, Cu-Sn altered-basic-rock type, and Sn-Pb-Zn vein types of deposits. The study of the relationship between the tectono-magmatic evolution and the Gejiu system of mineralization shows that Sn-Cu polymetal enrichment occurred in and near the contact zone between granite and wall rock through contact metamorphism, metasomatic and filling processes, when the composite granites invaded into folded limestones of Middle Triassic (Gejiu Formation). These metals may come from two reservoirs, i.e. granitic magma originated from the middle-lower crust in the Yenshan period and basalt-diabase-gabbro from the mantle in the Indo-Chinese period. Pulsatory magmatic activities are believed to be the main driving force for the formation of the hydrothermal system for the ore-forming progress. A regional model of mineralization is proposed in this study for assisting mineral exploration and prediction for new types of mineral deposits in this area.

Tuotuohe is located at the north-west section of "Sanjiang" metallogenic belt, Qinghai Province.This area boasts favorable mineralization background and great ore mineral potential.Prospecting targets for large-and/or middle-sized lead, zinc, sliver, and copper deposits have been delineated.Tuotuohe area belongs to cold grassy highland where some of the traditional geological field survey and mapping are difficult to conduct.Remote sensing technology is expected to provide low cost and efficient means to facilitate mineral exploration.Based on the spectrum information of mineral associations involved in mineralization-associated alteration zones and with the support of ENVI software, the authors used an integrated masking-principal component analysis-histogram classification (MPH) method to process the TM multi-spectral image to extract patterns related to iron stained alteration and hydroxyl alteration of mineralization form.Geological data are integrated with the results of remote sensing image processing to divide prospective districts and delineate prospecting targets.

We obtain some new cognitions of mineralizing rule, effective prospecting method and deep forecasting for the Gejiu super Sn-Cu multi-metal deposit of Yunnan Province by systemic research in recent years.Its primary mineralizing process is repeated compound alteration by hot liquid of magma.Conformation afforded transmit alleyway and deposited space for mineralization.The wall rock condition and combination zoniferous character of mineral element lead to mineralizing multiformity.Ascertainment 3D-distributing of granite, drape and faultage conformation and lithology is the key to mineralization forecasting.It proves an effective prospecting method to combine ascertainment lithology interface and deposited roomage by gravity and magnetic survey, and multifunctional electric survey, speedy ascertainment of mineralization abnormity by geochemistry survey of sap, drill and faultage.The future deep prospecting centers around the following three aspects: (1) interbedded oxidation or nervation mineral deposit in the periphery of diggings, (2) Sn-Cu multi-metal deposit in the interface of granite or basalt and marble, (3) Cu-Sn multi-metal deposit in the alterative granite.

Mineral resources quantitative assessment involves processes of constructing models of various types from conceptual model, logical model, and mathematical model to GIS model etc.. Large project like the national project for mineral resource potential assessment currently under operation by the Chinese Ministry of Land and Resources also involves interdisciplinary research teams specialized in geology, mineral deposits, mathematical model and GIS operation etc..It is essential to provide a common platform for these people to exchange ideas and make collective decisions on constructing geological concept models and quantitative models and on GIS procedures for model implementation with actual data input and output. This paper proposes a model builder technology to serve the above purpose. Sophisticated functions such as model iteration and user-machine interaction are developed and implemented in GeoDAS GIS. Case studies of information extraction, spatial analysis, prediction unit delineation and posterior probability mapping involved in gold mineral deposit prediction in Nova Scotia, Canada are covered to illustrate how model builder technology can be used in the whole processes of mineral resource assessment.

This paper explores the possibility of applying non-negative matrix factorization (NMF) to process stream sediment geochemical data for mineral exploration. The brief introduction of principle of NMF is followed by detailed comparison of the results obtained by NMF and principal component analysis (PCA) applied to a dataset of 813 samples with six trace elements from Gejiu mineral district, Yunnan, China. It is shown that the NMF is not only suitable for processing geochemical data which are usually of positive values but also provides superior results than that by PCA in the case study introduced in the paper. The example indicates that NMF might become a useful method for processing other types of geochemical data.

The geochemical anomaly recognition is the key to geochemical prospecting.Many new models are brought forward to identify and extract the geochemical weak anomalies from the complex background.How to compare the differences in aspect of the anomaly recognition effect of these different models? The authors advance the sample ranking method to discuss this problem.The gliding anomaly contrast and the local singularity analysis are applied to the Cu element data of the stream sediment samples from Gejiu area, Yunnan Province, China.The ranks for the raw data, contrast value and the local singularity exponents, denoted by RANK (Raw), RANK (CV) and RANK (Δα) respectively, are calculated by ordering the samples from the high anomaly to the low anomaly.Three ways are employed to compare the RANK (CV) and RANK (Δα) with the RANK (Raw) : (1) the characteristics of ranks for samples with the strong background and the weak background; (2) the characteristics of ranks for samples where the Cu deposits occur; and (3) the spatial correlation between the locations of Cu deposits and the cumulative area with the same thresholds of the upper rank values.The results demonstrate that the local singularity analysis is a useful model for the weak geochemical anomaly recognition, whose effect corresponds with the gliding anomaly contrast model or even better.The prospective areas delineated by means of weights of evidence method on the basis of local singularity exponents can provide new information and may be significant for the prediction of the undiscovered mineral deposits, which is significantly superior to the results on the basis of raw concentration data.The local singularity analysis has the advantage of the perspicuous principle, convenience and effective performance, and we can substitute it for the gliding contrast value method for the anomaly recognition of geochemical data.

Eastern Yunnan area is the important Cu-Au-PGE ore-forming perspective area in China.The factor analysis, geostatistics and multifractal S-A filtering method are applied in this paper to quantitatively extract and estimate the Pt-Cu-Au mineralization anomalies from the complicated geological background.The research shows that: (1) the results of factor analysis illustrate that there are three element associations existing in eastern Yunnan area: factor Ⅰ (Cu-Pd-Co-Pt-V-Cr-Ni), which characterizes the element association of the Permian Er'meishan basalt occurred in the Yangtz block, Similarly; factor Ⅱ (Sb-As-U-Mo), which characterizes the carbonaceous sediment formation occurred in the South China fold system and factor Ⅲ (Pb-Ag-Zn-W-Zn-As-Au), which represents the hydrothermal mineralization with the base metal mineralization as the typification; (2) the semivariation analysis illustrates that the concentrations of Pt, Cu and Au are continuous in NE trend (9°-18.6°) and the maximal ranges are about 95km.The geochemical maps obtained by the universal Kringing imply that the concentration distributions of Pt, Cu and Au are mainly controlled by the faults and magmatism; (3) the multifractal S-A filtering method characterizes the detailed information of local mineralization and extracts the conceal mineralization information.The anomaly maps delineated by the S-A method may provide important evidence for Pt-Cu-Au targeting; (4) different geological and ore-forming problems can be solved by different geomathematic methods.The linear geomathematic methods such as the factor analysis and geostatistics can be used to explore the regional ore-forming background and the regional spatial variability of the ore-forming elements and the element associations, while the nonlinear geomathematic methods such as S-A method are efficient in extracting the local ore-forming information.These methods are of benefit to the concealed ore-forming anomaly information extraction.

Mineral resource prospecting aims at providing sufficient information on mine state for further resource evaluation and production.In this process, the information technique can be utilized to increase the efficiency and quality of data analysis and processing.In this paper, the authors consider that data management and three dimensional model and virtual reality are three pivotal taches of information processing, by which we can systematically integrate the information technique for mineral resource prospecting.And the authors put forward a new 3D data structure and a new systematic method for expressing geological solid, which have already been successfully applied to multi-resource perambulation work.

In the domain of earth system, temporal-spatial and functional direct or indirect interdependent relationships between geospatial objects provide the clue for the study of complex issues.The simulation and analysis of the direct and indirect dependent relationships between these geospatial objects are always the foundation to know complex systems and make geospatial decisions.For example, in some emergencies, such as earthquakes, floods, and fire disasters, the interrelated effect and dependency among particular infrastructures and departments are usually complicated and inharmonious.Then, the potential cascading effects may cause unexpected serious consequences.Therefore, how to know more about disaster effects, and forecast corresponding cascading effects becomes quite important and fundamental to increase the capability of disaster prevention and emergency response.Based on the study on geospatial complex structure among relative objects in disasters, this paper quantifies the interrelationships between these objects, and then applies fuzzy Petri net to simulate potential cascading effects between them.Finally, an example is included to illustrate geospatial complex structure of barrier lakes coming from the Wenchuan earthquake in Sichuan Province, China.The potential cascading effects among barrier lakes are dynamically simulated, and then the vulnerable barrier lakes can be found out, which provides one specific theory and technical method to efficiently prevent secondary disasters of earthquakes.In the same way, the proposed method and technique would be used to simulate and analyze other geoscientific complex system structures as well.