Fractal and Multifractal Propertiesof the Spatial Distribution of Natural Fractures——Analyses and Applications

The Cantor's dust theory is applied to investigate the scaling properties of the spatial distribution of natural fractures obtained from detailed scanline surveys of 27 field sites in the Appalachian Plateau of western New York, USA. The results obtained in this study indicate: 1) fracture spacing is characterized by fractal and multifractal properties. On small scales analyses yield an average fractal dimension of 0.15, which suggests a very high degree of clustering. In contrast, on large scales, fractures tend to be more regular and evenly distributed with an average fracture dimension of 0.52; 2) fractal dimension varies with different sets in different orientations, which can be attributed to interactions between pre-existing fractures and younger ones, as well as variations of the intensity of the stresses under which the fractures were formed; 3) a time sequence of fracture set formation can be proposed based on fractal and multifractal analyses, which consists of (from old to young): N-S, NW, EN     

Correlation Fractal and Multifractal Characteristics of Seismic Activity in the Taiwan Area, China

Based on the analysis of newly collected data of plate tectonics, distribution of active faults and crustal deformation, the Taiwan area is divided into two seismic regions and six seismic belts. Then, correlation fractal dimensions of all the regions and belts are calculated, and the fractal characteristics of hypocenteral distribution can be quantitatively analyzed. Finally, multifractal dimensions Dq and f(α) are calculated by using the earthquake catalog of the past 11 years in the Taiwan area. This study indicates that (1) there exists a favorable corresponding relationship between spatial images of seismic activity described with correlation fractal dimension analysis and tectonic settings; (2) the temporal structure of earthquakes is not single but multifractal fractal, and the pattern of Dq variation with time is a good indicator for predicting strong earthquake events.     

Distribution and Influence of Iron Phases the Physico—Chemical Properties of Phyllosilicates

Clay minerals from different Cretaceous stratigraphic successions of Egypt were investigated using XRD,DTA,dissolution analysis(DCB),IR,Moessbauer and X-ray Electron Spin Resonance(ESR) spectroscopes.The purity of the samples and the degree of their structural order were determined by XRD.The location of Fe in the octahedral sheet is characterized by absorption bands at-875cm^-1 assigned as Al-OH-Fe which persist after chemical dissolution of free iron.The Moessbauer spectra of these clays show two doublets with isomer shift and quadrupole splitting typical of octahedrally coordinated Fe^3 ,in addition to third doublet with hyperfine parameter typical of Fe^2 in the spectra of Abu-Had kaolinite (H) sample.Six-lines magnetic hyperfine components which are consistent with those of hematite are confirmed in the spectra of both Isel and Rish kaolinite samples.Goethite was confirmed by both IR and DTA.Multiple nature of ESR of these clays suggested structural Fe in distorted octahedral symmetry as well as non-structural Fe.Little dispersion and low swelling indices as well as incomplete activation of the investigated montmorillonite samplas by NaCO3 appear to be due to incomplete disaggregation of montmorillonite particles.This can be explained by the ability of Fe-gel to aggregate the montmorillonite into pseudo-particles and retard the rigid-gel structure.However,extraction of this ferric amorphous compound by dithonite treatment recovers the surface properties of the montmorillonite samples.On the other hand,the amount and site occupation of Fe associated with kaolinite samples show an inverse correlation with the parameters used to describe the degree of crystallinity perfection,color,brightness and vitrification range of these kaolinite samples.     

Distribution and Influence of Iron Phases on the Physico—Chemical Properties of Phyllosilicates

Clay minerals from different Cretaceous stratigraphic successions of Egypt were investigated using XRD,DTA,dissolution analysis(DCB),IR,Moessbauer and X-band Electron Spin Resonance(ESR) spectroscopies.The purity of the samples and the degree of structural order were determined by XRD.The location of Fe in the octahedral sheet is characterized by absorption bands at-875cm^-1 assigned as Al-OH-Fe which is present after chemical dissolution of free iron.The Moessbauer spectra of these clays sow two doublets with isomer shift and quadrupole splitting typical of octahedral coordinated Fe^3 ,in addition to third doubler with hyperfine parameter typical of Fe^2 in the spectra of Abu-Had kaolinite (H)sample.6-lines magnetic hyperfine components which are consistent with those of hematite are confirmed in the spectra of both Isel and Rish kaolinite samples.Goethite was confirmed by both IR and DTA.Multiple nature of ESR of these clays suggested structural Fe in distorted octaedral symmetry and as non-structural Fe.Little dispersion and low swelling indices as well as incomplete activaiton of investigated montmorillonite samples by NaCO3 appear to be due to incomplete disaggregation of montmorillonite particles.This can be explained by the ability of Fe-gel to aggregate the montmorillonite into pseudo-particles and retard the rigid-gel structure.However,extraction of this ferric amorphous compound by dithonite treatment recovers the surface properties of the montmorillonite samples.On the other hand,amounts and site occupation of Fe associated with kaolinite samples show a negative correlation with the parameters used to describe the degree of crystalline perfection,color,brightness and vitrification range of these kaolinite samples.     

Identification and Delineation of the Earth’s Large-Scale Closed Terrain Depressions and Their Fractal Size Distribution

Mathematical Geosciences - Closed terrain depressions are geomorphic features that show scale invariance over the wide range of scales on which they occur, from metres to thousands of kilometres....     

Applications of Error Propagation Analyses to Geochemical Calculation

Two examples are given for comparing applications and limitations of four methods which can be used to deal with error propagation in geochemical calculations.The examples indicate that the Monte Carlo method can also be employed to evaluate the effect of covariance.A special function of the method for covariance matrix shown here can reveal the correlations of middle variables relative to the independent primary variables.     

Discrimination of Natural Fractures Using Well Logging Curve Unit

It is very difficult to discriminate natural fractures using conventional well log data, especially for most of the matured oUfields in China, because the raw data were acquired with relatively obsolete tools. The raw data include only GR and SP curves, indicative of lithology, AC curves, used to calculate the porosity of the formation, and a set of logging curves from various electrode length resistivity by laterolog. On the other hand, these oilfields usually have a large amount of core data which directly display the characteristics of the formation, and enough information of injection and production. This paper describes an approach through which logging curves are calibrated in terms of the raw data, and then a prototype model of natural fractures is established based on the investigation of core data from 43 wells, totaling 4 000 m in length. A computer program has been developed according to this method. Through analysis and comparison of the features of logging curves, this paper proposes a new concept, the well logging curve unit. By strictly depicting its shape through mathematical methods, the natural facture can be discriminated. This work also suggests an equation to estimate the probability of fracture occurrence, and finally other fracture parameters are calculated using some experimental expressions. With this methodology, logging curves from 100 wells were interpreted, the results of which agree with core data and field information.     

Dielectric Properties of Minerals and Their Applications in Microwave Remote Sensing

With the advantages of all-weather operation and certain penetration microwave remote sensing has become a very important technique,Its image is a function not only of the technical parameters of the sensor but also of the geometric forms and electrical properties,such as the dielectric constants and conductivity,of the ob jects on the ground.Minerals and rocks are the most widspread objects on the earth surface,hence their dielectric properties are of fundamental significance in microwave remote sensing.     

Types, Metallogenic Environments and Characteristics of Temporal and Spatial Distribution of Copper Deposits in China

Based upon a comprehensive study of 123 copper deposits in China. this paper reaches the following conclusions: 1. The crust in China was solidified pretty late; with the accretion of the plate, the copper mineralization moved towards its margin in space and became successively younger in age. 2. The major copper ore types ever found in the world have mostly been discovered in China, in which the porphyry type seems to be the most important and the massive sulfide type in the transitional bed between marine clastic and carbonate rocks is clearly defined. 3. Carbonate strata are widespread in China and their deposition lasted for a long geological period, so the proportion of copper deposits occurring in them is large as compared with other parts of the world. 4. Seven metallogenic epochs can be recognized, in which the Mesozoic one plays the leading role and the middle(late) Palaeozoic and Cenozoic ones are next in importance. Mineralization was comparatively simple in the early geological period. and became diversified later on. In the early epochs copper deposits related to basaltic magmatism and metamorphosed marine sediments predominated, whereas in the later epochs those related to granitic magmatism and continental sedimentation were dominant. 5. There exist in China thirteen metallogenic provinces, of which the Lower Yangtze downwarping belt, Sanjiang fold system, Jiangnan axis and Xikang-Yunnan axis are of greater significance. 6. The crustal mobility in China was rather pronounced, the polycyclic evolution of the crust has resulted in such obvious phenomena as the inheritance of mineralization, the coexistence of various types and the superposition of different genetic types.     

Estimation of the Buffer Properties of Natural Waters with Account for the Acid–Base Characteristics of Humic Substances

The influence of the acid–base properties of humic substances in natural waters on the buffer capacity value is considered. An alternative way of calculation of the ANC parameter taking into account the dual nature of the humus organic of waters is proposed. Zonal aspects of the distribution of natural waters over ANC values are evaluated, and the features affecting these parameters are singled out.     

The General Characteristics and Distribution of the Glaucophane-Schist Belts of China

On the basis of the temperature variation, the glaucophane-schist facies Gan be classified into two faciesgroups, the glaucophane-lawsonite facies group and the glaucophane-greenschist facies group, and forms vari-ous facies series with other metamorphic facies. Glaucophane-schist belts of China are of different types withregard to their average T-P gradients and tectonic environments. They are: (1) Proterozoic intracratonicglaucophane-schist belts, (2) Caledonian intracratonic glaucophane-schist belts, (3) Palaeozoic pericratonicglaucophane-schist belts along the northern margin of the Chinese Platform, and (4) Meso-Cenozoicglaucophane-schist belts related to subduction. The initiation and evolution of glaucophane-schist metamorphism are related to their tectonic environ-ments. Most glaucophane-schist belts of China were formed in sialic environments. First the crust began tobreak up and eventually oceanic crust was formed. It seems that a non-uniformitarian mechanism may be in-volved as this evolution is related to the change of the configuration of the heat flow within the crust.     

Spatial Distribution of Contourites in Global Ocean and Its Paleoclimatic Significance—The Contribution of International Ocean Drilling to the Studies of Contourites

Contourite is one of the most important type of sediments in the global ocean, which has recorded significant information on paleoclimatic changes. It is also of great importance for ocean engineering and marine hydrocarbon exploration. The development of scientific ocean drilling, especially the “Integrated Ocean Drilling Program” and the undergoing “International Ocean Discovery Program”, has made great contribution in mapping the spatial distribution of contourites and revealing contourite-related paleoclimatic information, through coring and geophysical exploration in the global ocean. It is found that the global distribution of contourites is controlled predominantly by the global deep-water circulation while its distribution in a specific region can be affected by the intensity of deep currents, tectonic activities, sediment supply, and so on. The geological changes in the global deep-water circulation is, however, further affected by tectonic activities, origins of water masses, as well as climate changes, e.g. the Cenozoic global cooling, changes in the size of the northern hemisphere ice caps, and intensity of monsoon. The main controlling factors of deep water circulation vary with different regions.     

Temporal and Spatial Distribution of Elements in a Small Catchment, and Buffer Function of Wetland in Longgan Lake, China

Wetland is the conjunction of lake and terrene where human activities are concentrated. From the viewpoints of material transport and cycling in the terrene-lake system, wetland is the buffer where sand and mud, heavy metals, pollutants and nutrients are tarried. In this paper, we provide a case study based on the temporal and spatial distribution of elements in the Wangling River catchment, a small sub-catchment of Longgan Lake in the middle reaches of the Yangtze River. We have found that wetland can buffer major heavy metals such as Cr, Cu, etc.significantly, but has a little buffer function to some active elements such as Fe and Mn, which are always transported as solutions. Human activities not only influence the distribution of elements, but also weaken the buffer function of wetland. Intensive human activities in the Longgan Lake area in the past 70 years have been recorded in stream, wetland and lake sediments, especially the human activity events such as deforesting and reclaiming on a large scale in 1958 and the 1980‘s. Human activities caused the increase of sedimentation rates since the 1950‘ s, as well as the increase of elements‘ concentrations. The extensive use of fertilizers and pesticides since the 1960‘ s have led to the increase of total P concentrations. Increasing SO2 emission accelerate the process of cation exchange in soil, and enhance the leaching of Mn out of soils. Permanent storing of water causes the soil gleyification that also intensifies the leaching of Mn.These are two major reasons for the obvious increase of manganese concentrations in recent 20 years in Longgan Lake. Intensive human activities since the 1950s‘ have intensified the population in this region and thus destroyed the buffer function of wetland.     

Types and Distribution of Geological Hazards in the South China Sea

Various types of geological hazards exist in the South China Sea. In dynamics sense, they can be categorized into 5 principal genetic types related to effects of hydraulic dynamics, gaseous activity, soil mechanics, gravity and tectonism, respectively. Integrated analyses indicate that the geological hazards associated with volcanoes, earthquakes and fractures are mainly distributed in tectonically active regions, whereas those resulting from mudflows, landslides and diapirs are usually concentrated in the region of slope, that shallow gas, high pressure gas pockets and soft intercalations are major potential geological hazards in the inner shelf, and that strong hydraulic dynamics, especially storm tide, is one of the major causes of geological hazards in the littoral areas. The geological hazards that occurred in the South China Sea are also characterized by periodicity, succession and, to a certain extent, unpredictability in addition to regionalization.     

Fractal and Multifractal Modeling of Hydrothermal Mineral Deposit Spectrum： Application to Gold Deposits in Abitibi Area, Ontario, Canada

A number of fractal/multifractal methods are introduced for quantifying the mineral de-lmsit spectrum which include a number-size, grade-tonnage model, power spectrmn model,multi-fractal model and an eigeavalue spectrmn model The first two models characterize mineral deposits spec-tra based on relationships among the measures of mineral deposits.These include the number of deposits,size of deposits,concentration and volume of mineral deposits.The last three methods that deal with the spatial-temporal spectra of mineral deposit studies are all expected to be popularized in near future.A case study of hydrothermal gold deposits from the Abitibi area,a world-class mineral district is used to demonstrate the principle as well as the applications of methods proposed in this paper,It has been shown that fractal and multifractal models are generally applicable to modeling of mineral deposits and occurrences.Clusters of mineral deposits were identified by several methods including the power spectral eral deposits in the Timmins and Kirkland Lake camps.     

Relationship Between the Geometric Parameters of Rock Fractures,the Size of Percolation Clusters and REV

Modeling fractured rocks with numerical methods requires some derived parameters, among which the fracture network connectivity and the size of the representative elementary volume (REV) are both of crucial importance. Percolation and REV analyses were made by the RepSim code. The program uses input parameters such as fractal dimension of the fracture midpoints (D _c), length exponent (E) and relative dip (α ^r) data. For percolation analysis, the relative sizes of the largest percolation clusters have been calculated by stochastic realizations of the simulated fracture networks with different parameter triplets. Furthermore, fracture networks can be classified into three major types on the basis of their (E,D _c,α ^r) parameters. For the REV calculations, the porosity of the generated fracture network was calculated. The derived REV size of a fracture network depends essentially on input parameters and shows a decreasing tendency with increasing D and E and vice versa. The method mentioned above was tested on both metamorphic samples of the Pannonian Basin and Variscan granitoid rocks of the Mórágy Complex. Percolation values predicted for the Mórágy granite are highly sensitive to alterations in the input parameters. The amphibolite bodies displayed a modeled fracture network with 80 to 90% of all fractures being interconnected, while the largest achievable percolation cluster size of gneiss is less than 10%. The REV size of the amphibolite is about 20 m as a result of connected fractures filling the whole body, while gneiss has lower porosity and higher REV (approximately 70 m).     

On the Existence,Uniqueness and Correctness of the Fracture Diameter Distribution Given the Fracture Trace Length Distribution

Based on the fracture trace length distribution, conditions for the existence, uniqueness, and correctness of the fracture diameter distribution are given using Warburton’s fracture model. In particular, a solution for the fracture diameter distribution exists and is unique for all trace length probability density functions, h _A (y), such that \(h_{A}(y)/\sqrt{y^{2}-x^{2}}\) is Lebesgue integrable on [x,∞). This condition is met by the uniform, exponential, gamma, lognormal, and power-law trace length distributions as well as by the trace length distributions that arise from a deterministic fracture diameter or from a discontinuous fracture diameter length distribution. Exponential, gamma, lognormal, and power-law trace length distributions satisfy necessary conditions for the diameter distribution to be non-negative, and necessary and sufficient conditions for the distribution to have unit integral over the real line. Negative values of the fracture diameter distribution arise when the trace has a uniform distribution and the lower bound of the fracture trace is greater than zero.     

Properties of a Diffusive Hydrograph and the Interpretation of Its Single Parameter

The mathematical properties of the normalized diffusive hydrograph allow for easy determination of intrinsic basin characteristics. These include lag times between storm events and peak flow, recession rate, and the total, temporally integrated flow volume, all in terms of a single parameter, the basin time constant “b”. This simple function displays surprising fidelity to measured hydrographs of springs and hundreds of streams and small rivers. We explain this fidelity by showing that the curvature of the theoretical hydrograph matches that of the natural hydrographs better than several alternate models, and by demonstrating that the simple hydrograph function can be integrated over a range of time constants (0 to b _max) to represent the hierarchy of flow paths of varying lengths that exist in real watersheds. Surprisingly, the unwieldy analytical results from this integration are almost numerically indistinguishable from a simple hydrograph using a single, suitably-weighted average for the time constant. The peak flow times are shifted slightly. The accuracy with which the simple hydrograph approximates the integrated results for hierarchies of hydrographs representing individual flow paths explains why the former can realistically describe the discharge behaviors of complex natural watersheds.     

Application of the EnKF and Localization to Automatic History Matching of Facies Distribution and Production Data

The performance of the ensemble Kalman filter (EnKF) for continuous updating of facies location and boundaries in a reservoir model based on production and facies data for a 3D synthetic problem is presented. The occurrence of the different facies types is treated as a random process and the initial distribution was obtained by truncating a bi-Gaussian random field. Because facies data are highly non-Gaussian, re-parameterization was necessary in order to use the EnKF algorithm for data assimilation; two Gaussian random fields are updated in lieu of the static facies parameters. The problem of history matching applied to facies is difficult due to (1) constraints to facies observations at wells are occasionally violated when productions data are assimilated; (2) excessive reduction of variance seems to be a bigger problem with facies than with Gaussian random permeability and porosity fields; and (3) the relationship between facies variables and data is so highly non-linear that the final facies field does not always honor early production data well. Consequently three issues are investigated in this work. Is it possible to iteratively enforce facies constraints when updates due to production data have caused them to be violated? Can localization of adjustments be used for facies to prevent collapse of the variance during the data-assimilation period? Is a forecast from the final state better than a forecast from time zero using the final parameter fields?To investigate these issues, a 3D reservoir simulation model is coupled with the EnKF technique for data assimilation. One approach to enforcing the facies constraint is continuous iteration on all available data, which may lead to inconsistent model states, incorrect weighting of the production data and incorrect adjustment of the state vector. A sequential EnKF where the dynamic and static data are assimilated sequentially is presented and this approach seems to have solved the highlighted problems above. When the ensemble size is small compared to the number of independent data, the localized adjustment of the state vector is a very important technique that may be used to mitigate loss of rank in the ensemble. Implementing a distance-based localization of the facies adjustment appears to mitigate the problem of variance deficiency in the ensembles by ensuring that sufficient variability in the ensemble is maintained throughout the data assimilation period. Finally, when data are assimilated without localization, the prediction results appear to be independent of the starting point. When localization is applied, it is better to predict from the start using the final parameter field rather than continue from the final state.