Methods of Three-part Quantitative Assessments of Undiscovered Mineral Resources: Examples from Victoria,Australia

Quantitative mineral resource assessments following the 3-part form rely on grade and tonnage models and probabilistic estimates of the number of undiscovered deposits. Assessments completed in Victoria, Australia, indicate that undiscovered mineral resources can be effectively estimated using grade and tonnage sub-models constructed using only medium- and large-tonnage deposits. Numbers of undiscovered deposits can be estimated on the basis of expert judgement or entirely by statistical means. Appropriate mathematical aggregation of individual expert views, expressed at interactive expert workshops, provides robust estimates of the number of undiscovered deposits. Underestimation of uncertainty, which is common in expert judgement, can be compensated by the statistical modification of individual interval estimates. In this study, the linear opinion pool was used as a simple and robust method of mathematical aggregation of multiple expert estimates of the number of undiscovered deposits. A general regression model, which estimates numbers of undiscovered deposits based on the size of the geologically permissive area and the median deposit tonnage, provided results generally compatible with those based on expert judgement or local deposit density models.     

Theory and Method of Mineral Resource Prediction Based on Synthetic Information

Metallogenic prognosis of synthetic information uses the geological body and the miaeral resource body as a statistical unit to interpret synthetically the information of geology, geophysics, geo-chemistry and remote sensing from the evolution of geology and puts all the information into one entire system by drawing up digitalized interpretation maps of the synthetic information. On such basis, differ-ent grades and types of mineral resource prospecting models and predictive models of synthetic informa-tion can be established. Hence, a new integrated prediction system will be formed of metallogenic prog-nosis (qualitative prediction), mineral resources statistic prediction (determining targets) and mlaeral resources prediction (determining resources amount).     

The Tau Model for Data Redundancy and Information Combination in Earth Sciences: Theory and Application

Many decision-making processes in the Earth sciences require the combination of multiple data originating from diverse sources. These data are often indirect and uncertain, and their combination would call for a probabilistic approach. These data are also partially redundant with each other or with all others taken jointly. This overlap in information arises due to a variety of reasons—because the data arises from the same geology, because they originate from the same location or the same measurement device, etc. The proposed tau model combines partially redundant data, each taking the form of a prior probability for the event being assessed to occur given that single datum. The parameters of that tau model measure the additional contribution brought by any single datum over that of all previously considered data; they are data sequence-dependent and also data value-dependent. Data redundancy depends on the sequence in which the data is considered and also on the data values themselves. However, for a given sequence, averaging the tau model parameters over all possible data values leads to exact analytical expressions and corresponding approximations and inference avenues. Information on multiple-point connectivity of permeability arrives from core data, well-test data and seismic data which are defined over varying supports with complex redundancy between these information sources. In order to compute these tau weights for determining connectivity, one needs a model of data redundancy, here expressed as a vectorial training image (Ti) constructed using a prior conceptual knowledge of geology and the physics of data measurement. From such a vectorial Ti, the tau weights can be computed exactly. Neglecting data redundancy leads to an over-compounding of individual data information and the possible risk of making extreme decisions.     

“Three-Component” Digital Prospecting Method：A New Approach for Mineral Resources Quantitative Prediction and Assessment

“Three-component” method consists of three clase-connected aspects: geological anomaly,diversity of mineralization and mineral deposit spectrum. All these three concepts are not new separately, but it is a new approach to combine these three aspects in one single concept for quantitative mineral resources prediction and assessment and it is also the first time to conduct a more detailed study in each aspect. Investigation and clarification of geological anomalies, diversity of mineralization and spectrum of mineral deposits are realized by digitization and quantification of ore forming controlling factors, oreexisting symbols or marks, characteristics of mineralization and regulation of ore-genesis and laws of distribution. These procedures lead to construction of a “digital model“ for mineral resources prediction andassessment.     

Primary Mineral Information and Depositional Models of Relevant Mineral Facies of the Early Precambrian BIF—A Preliminary Review

The primary mineral compositions of BIF are regarded as ferric oxyhydroxide or iron silicate nanoparticles (mainly greenalite and stilpnomelane ) whichcan transform into minerals like hematite, magnetite and siderite. On the basis of predominant iron minerals, three distinctive sedimentary facies are recognized in BIF: oxide facies, silicate facies and carbonate facies. Marked by the Great Oxidation Event (GOE, 2.4~2.2 Ga), sedimentary facies can be divided into two models: “anoxic and reducing” model and “stratified ocean” model. The ancient ocean was anoxic and reducing before GOE, and under this circumstance, BIF was distributed from the distal to proximal zones transforming from hematite facies through magnetite facies to carbonate facies, such as West Rand Group BIF (2.96~2.78 Ga) and Kuruman BIF (~2.46 Ga) in south Africa. However, the ancient ocean was a stratified ocean during and after GOE, which means that shallow seawater was oxidizing while deeper seawater was reducing, leading to an opposite sedimentary facies distribution compared to the former one: BIF was distributed from the distal to proximal zones transforming from carbonate facies through magnetite facies to hematite facies, such as Yuanjiacun BIF in China (~2.3 Ga) and Sokoman iron formation in Canada (~1.88 Ga). Overall, BIF is an unrepeatable formation in geological history, which can only form in specific sedimentary environment. The key point to speculate the paleo-ocean environment, namely the problems to be solved at the moment, is to identify and derive the primary mineral compositions, to make sure the genetic mechanism of sedimentary facies especially silicate facies, to restrict the sedimentary conditions and to study microbial activities contacting with BIF.     

Application of Fractal Models to Distinguish between Different Mineral Phases

Fractal modeling is demonstrated to be an effective and rapid tool to distinguish between mineral phases in rock samples. It supplements work that previously could be performed only by observing the interpenetrational or metasomatic phenomena between different minerals with the aid of mineralographic microscope. The Gejiu tin district in southwestern China was chosen as a study area for the recognition and characterization of the spatial distribution of two phases (Types I and II) of cassiterite. Vector patterns used for this study were extracted from digital photomicrographs and analyzed with the aid of MapGIS. Perimeter–area fractal dimension, cumulative number–area exponent, and shape index were determined in order to quantify geometrical irregularities and spatial cassiterite phase distribution characteristics. The results show that fractal dimensions based on area and perimeter are larger for crystals of Type I than for those of Type II. The mean shape index (SI) increases from 0.54 (Type I) to 0.64 (Type II), indicating an increase in regularity. The number–area exponent also increases from 0.88 to 1.15, indicating the smaller crystals of Type II. The cumulative number–shape index log–log plot shows two separate straight-line segments. One of these probably represents a background shape realized during the original process of natural crystallization, whereas the other likely represents anomalous shapes because of weathering or other superimposed processes. Two parallel lines can be constructed on the perimeter–area log–log plots. The upper line, with a larger intercept, represents crystals with lower SI. The lower line represents crystals with higher SI, indicating that the intercept provides a measure of the irregularity of grains. By combining the perimeter–area model with cumulative number–area plot and shape index, the two phases of cassiterite can be distinguished and characterized. One phase has fewer crystals of large size, and the other has smaller crystals. This difference can be explained by assuming that under higher-temperature conditions, the large cassiterite crystals formed earlier than the smaller crystals. Consequently, the large cassiterites underwent longer, high-intensive weathering than the small crystals so that their shapes became more irregular. The younger, more abundant small cassiterites retained their original regular shapes.     

Supply-Demand Situation and Exploration of Mineral Resources in China during 2016–2017

正During 2016-2017,both the supply and demand of China's main mineral resources continued to grow.The import of major energy resources and metal ore resources,such as iron ores,crude oil,natural gas,coal and bauxite,except for copper,has shown a substantial increase(Table1).In order to guarantee economic development needs,the     

Extended Probability Perturbation Method for Calibrating Stochastic Reservoir Models

Calibrating a stochastic reservoir model on large, fine-grid to hydrodynamic data requires consistent methods to modify the petrophysical properties of the model. Several methods have been developed to address this problem. Recent methods include the Gradual Deformation Method (GDM) and the Probability Perturbation Method (PPM). The GDM has been applied to pixel-based models of continuous and categorical variables, as well as object-based models. Initially, the PPM has been applied to pixel-based models of categorical variables generated by sequential simulation. In addition, the PPM relies on an analytical formula (known as the tau-model) to approximate conditional probabilities. In this paper, an extension of the PPM to any type of probability distributions (discrete, continuous, or mixed) is presented. This extension is still constrained by the approximation using the tau-model. However, when applying the method to white noises, this approximation is no longer necessary. The result is an entirely new and rigorous method for perturbing any type of stochastic models, a modified PPM employed in similar manner to the GDM.     

Genetic Modeling of GIS-Based Cell Clusters and Its Application in Mineral Resources Prediction

This paper presents a synthetic analysis method for multi-sourced geological data from geo-graphic information system (GIS). In the previous practices of mineral resources prediction, a usually adopted methodology has been statistical analysis of cells delimitated based on thoughts of random sam-pling. That might lead to insufficient utilization of local spatial information, for a cell is treated as a point without internal structure. We now take “cell dusters“, L e. , spatial associations of cells, as basic units of statistics, thus the spatial configuration information of geological variables is easier to be detected and utilized, and the accuracy and reliability of prediction are improved. We build a linear multi-discriminating model for the dusters via genetic algorithm. Both the right-judgment rates and the in-class vs. betweewclass distance ratios are considered to form the evolutional adaptive values of the population. An application of the method in gold mineral resoerces prediction in east Xinjiang, China is presented.     

Latent Variable Modeling for Integrating Output from Multiple Climate Models

Numerical models of atmosphere–ocean circulation are widely used to understand past climate and to project future climate change. Although the same laws of physics, chemistry, and fluid dynamics govern any general circulation model, each model’s formulations and parameterizations are different, yielding different projections. Notwithstanding, models within an ensemble will have varying degrees of similarity for different outputs of interest. Multi-model ensembles have been used to increase forecast skill by using simple or weighted averages where weights have been obtained by considering factors such as estimated model bias and consensus with other models (Giorgi and Mearns, J. Clim. 15:1141–1158, 2002, Geophys. Res. Lett. 30:1629–1632, 2003; Tebaldi et al., Geophys. Res. Lett. 31:L24213, 2004, J. Clim. 18:1524–1540, 2005). This paper considers an alternative view of multi-model ensembles. For use with the North American Regional Climate Change Assessment Program (NARCCAP), multivariate statistical models are employed to characterize modes of similarity within the members of an ensemble. Specifically, we propose a spatially-correlated latent variable model which facilitates the exploration of when, where, and how regional climate models are similar, and what factors best predict observed locations of model convergence.     

The Quantitative Models of Trace Elements for Different Genetic Types of Enclaves in Granites

An attempt has been made to give an insight into the genesis of enclaves in granites by mathematically quantitative methods.After some deduction,the quantitative models of trace elements for the genetically different enclaves have been established,including those for restites,segregation schlierens,enclaves formed out of solidified margins ,and enclaves derived from the mixing of different magmas.These models have been tested and proven to be valid and reliable.The conclusions inferred from these quantitative models are consistent with field observations and petrological ,mineralogical and geochemical evidence.     

Identifying the Representative Elementary Volume for Permeability in Heterolithic Deposits Using Numerical Rock Models

Using a range of realistic 3D numerical lithofacies (dm-scale) models of ripple laminated sandstone intercalated with mudstone we evaluate how single-phase permeability varies as a function of sample support. The models represent a range of mudstone content which is typical for tidal deposits. Furthermore, the spatial distribution of flow barriers (i.e. mudstone) is not random, but governed by sedimentological rules giving a variable anisotropy ratio as a function of mudstone content. Both vertical and horizontal permeability are found to vary at small sample volumes, but these fluctuations reduce as the sample volume increases. The vertical permeability increases while the horizontal permeability is nearly constant as a function of sample support for small mudstone contents. For higher mudstone content, the horizontal permeability decreases while the vertical permeability is nearly constant as a function of sample support. We propose a criterion, based on a normalised standard deviation, to determine the Representative Elementary Volume (REV). The size of the REV is dependent on both the property measured (vertical and horizontal permeability) and the correlation lengths of the lithological elements (i.e. lithofacies). Based on this we identify three flow upscaling regimes that each require a different method for upscaling: (1) layered systems where the arithmetic and harmonic averages are appropriate, (2) systems close to the percolation threshold where a percolation model should be used, and (3) discontinuous systems where an effective medium method provides the best estimate of permeability. The work gives, by using numerical experiments on a range of heterogeneous systems, a new insight in determination of the REV for permeability at the lithofacies scale and its relation to sedimentological parameters.     

A New and Nontraditional Method to Locate Concealed Mineral Resources—Geogas Prospecting from Nuclear Analysis and Accumulation Sampling

Today,traditional methods for locating of metal re-sources at the depth of hundreds m eters are facing many diffi-culties.However,the majority of the reserves in the world islarge or super- large mineral deposits in the deep region belowthe surface. Therefore,the development of mineral resourcesin the future will depend on the nontraditional m ethod wherethe traditional ones are less successful in searching deep re-serves.Ane method based on the nuclear analysis and accumula-tion sam pling has…     

Anisotropic Scaling Models of Rock Density and the Earth’s Surface Gravity Field

In this paper we consider an anisotropic scaling approach to understanding rock density and surface gravity which naturally accounts for wide range variability and anomalies at all scales. This approach is empirically justified by the growing body of evidence that geophysical fields including topography and density are scaling over wide range ranges. Theoretically it is justified, since scale invariance is a (geo)dynamical symmetry principle which is expected to hold in the absence of symmetry breaking mechanisms. Unfortunately, to date most scaling approaches have been self-similar, i.e., they have assumed not only scale invariant but also isotropic dynamics. In contrast, most nonscaling approaches recognize the anisotropy (e.g., the strata), but implicitly assume that the latter is independent of scale. In this paper, we argue that the dynamics are scaling but highly anisotropic, i.e., with scale dependent differential anisotropy. By using empirical density statistics in the crust and a statistical theory of high Prandtl number convection in the mantle, we argue that is a reasonable model for the 3-D spectrum (K is the horizontal wavevector and K is its modulus, k _z is a vertical wavenumber), (s,H _z ) are fundamental exponents which we estimate as (5.3,3), (3,3) in the crust and mantle, respectively. We theoretically derive expressions for the corresponding surface gravity spectrum. For scales smaller than ≈100 km, the anisotropic crust model of the density (with flat top and bottom) using empirically determined vertical and horizontal density spectra is sufficient to explain the (Bouguer) g _z spectra. However, the crust thickness is highly variable and the crust-mantle density contrast is very large. By considering isostatic equilibrium, and using global gravity and topography data, we show that this thickness variability is the dominant contribution to the surface g _z spectrum over the range ≈100–1000 km. Using estimates of mantle properties (viscosity, thermal conductivity, thermal expansion coefficient, etc.), we show that the mantle contribution to the mean spectrum is strongest at ≈1000 km and is comparable to the variable crust thickness contribution. Overall, we produce a model which is compatible with both the observed (horizontal and vertical) density heterogeneity and surface gravity anomaly statistics over a range of meters to several thousand kilometers.     

Modified Markov Chain Monte Carlo Method for Dynamic Data Integration Using Streamline Approach

In this paper, the Markov Chain Monte Carlo (MCMC) approach is used for sampling of the permeability field conditioned on the dynamic data. The novelty of the approach consists of using an approximation of the dynamic data based on streamline computations. The simulations using the streamline approach allows us to obtain analytical approximations in the small neighborhood of the previously computed dynamic data. Using this approximation, we employ a two-stage MCMC approach. In the first stage, the approximation of the dynamic data is used to modify the instrumental proposal distribution. The obtained chain correctly samples from the posterior distribution; the modified Markov chain converges to a steady state corresponding to the posterior distribution. Moreover, this approximation increases the acceptance rate, and reduces the computational time required for MCMC sampling. Numerical results are presented.