Using Sequential Self-Calibration Method to Identify Conductivity Distribution: Conditioning on Tracer Test data

An iterative inverse method, the sequential self-calibration method, is developed for mapping spatial distribution of a hydraulic conductivity field by conditioning on nonreactive tracer breakthrough curves. A streamline-based, semi-analytical simulator is adopted to simulate solute transport in a heterogeneous aquifer. The simulation is used as the forward modeling step. In this study, the hydraulic conductivity is assumed to be a deterministic or random variable. Within the framework of the streamline-based simulator, the efficient semi-analytical method is used to calculate sensitivity coefficients of the solute concentration with respect to the hydraulic conductivity variation. The calculated sensitivities account for spatial correlations between the solute concentration and parameters. The performance of the inverse method is assessed by two synthetic tracer tests conducted in an aquifer with a distinct spatial pattern of heterogeneity. The study results indicate that the developed iterative inverse method is able to identify and reproduce the large-scale heterogeneity pattern of the aquifer given appropriate observation wells in these synthetic cases.     

Automated Kerogen Classification in Microscope Images of Dispersed Kerogen Preparation

We develop the classification part of a system that analyses transmitted light microscope images of dispersed kerogen preparation. The system automatically extracts kerogen pieces from the image and labels each piece as either inertinite or vitrinite. The image pre-processing analysis consists of background removal, identification of kerogen material, object segmentation, object extraction (individual images of pieces of kerogen) and feature calculation for each object. An expert palynologist was asked to label the objects into categories inertinite and vitrinite, which provided the ground truth for the classification experiment. Ten state-of-the-art classifiers and classifier ensembles were compared: Naïve Bayes, decision tree, nearest neighbour, the logistic classifier, multilayered perceptron (MLP), support vector machines (SVM), AdaBoost, Bagging, LogitBoost and Random Forest. The logistic classifier was singled out as the most accurate classifier, with an accuracy greater than 90. Using a 10 times 10-fold cross-validation provided within the Weka software, we found that the logistic classifier was significantly better than five classifiers (p<0.05) and indistinguishable from the other four classifiers. The initial set of 32 features was subsequently reduced to 6 features without compromising the classification accuracy. A further evaluation of the system alerted us to the possible sensitivity of the classification to the ground truth that might vary from one human expert to another. The analysis also revealed that the logistic classifier made most of the correct classifications with a high certainty.     

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.     

Group Time Delay in the Reflection of P-Polarized Electromagnetic Plane Waves at a Stratigraphic Interface

The group time delay (GTD) formulae of quasi-total reflection of inhomogeneous P-polarized electromagnetic waves (P-PEW, whose electric field parallels to the plane of incidence), caused by the Goos–Hänchen effect, is derived by the phase shift of the wave. A numerical example where the frequency equals to 1 GHz is given. The curves of calculating results show that there are three discontinuous points at the critical angle of phase shift vector, the critical angle of attenuation vector and 90^○. When the angle of incidence is equal to one of these three angles, the GTD will become infinite, and the electromagnetic wave will propagate along the interface. The GTD will be very large, when the angle of incidence is close to one of these three angles. The results indicate that there is an important relationship between the two critical angles and the conductivity and permittivity of the two strata, and that the GTD has an important relationship with the angle of incidence. These results can be used to determine the lithology of the strata and to delimit the interfaces of strata more effectively. It is suggested that this research may prove useful in electromagnetic logging analysis and, perhaps, in the design of logging instruments.     

Change of Support for Estimating Local Block Grade Distributions

An important aspect in mineral resource evaluation is the reduction of variance when post-processing the grade distributions defined on the support (volume) of the available data into distributions defined on the support of the proposed selective mining units. Although the volume-variance relationship is well understood for the estimation of global grade distributions, it is still an unsolved issue for local estimation studies based on non-parametric geostatistical methods, such as indicator kriging, for which the support correction is not inherent to the method. To clarify this relationship, the local change of support problem is examined in the scope of two parametric models (multi-Gaussian and discrete Gaussian models). It is shown that the variance reduction factor between point and block-support local distributions depends on the block being considered and is less than the global variance reduction factor. As a consequence, post-processing the local point-support grade distributions on the basis of the latter systematically understates the importance of the change of support at the local scale and makes selective mining appear more economically attractive than it really is. In the light of these results, a methodology is proposed to post-process the local point-support distributions obtained via non-parametric (indicator) methods into block-support distributions. An application to simulated data indicates that this methodology provides an accurate estimation at the block support when dealing with diffusion-type random fields.     

Stability Analysis and Numerical Simulation of Differential Frost Heave

Differential frost heave is often implicated in the formation of patterned ground in regions subject to recurrent freezing and thawing. A linear stability analysis (LSA) indicates that a continuum model of frost heave is linearly unstable under typical natural freezing conditions of silty-clay soils. A two-dimensional non-linear numerical analysis corroborates the frozen time LSA results, and also indicates the importance of non-linear and time-dependent terms that ultimately lead to a preferred mode, which the LSA fails to predict. Instability of the one-dimensional solution occurs at shallow freezing depths and near-zero surface loads when positive perturbations in the ice content at the freezing front lead to a concomitant increase in thermomolecular pressure and upward ice velocity. Differential frost heave can then occur because of the increased heat flux from the perturbed surfaces. A three-dimensional model using random initial surface perturbations indicates that regular surface patterns will evolve with a length scale in the order of 2–4 meters, which corresponds quite closely with naturally-occurring non-sorted patterned ground.     

Non-Linear Theory and Power-Law Models for Information Integration and Mineral Resources Quantitative Assessments

Singular physical or chemical processes may result in anomalous amounts of energy release or mass accumulation that, generally, are confined to narrow intervals in space or time. Singularity is a property of different types of non-linear natural processes including cloud formation, rainfall, hurricanes, flooding, landslides, earthquakes, wildfires, and mineralization. The end products of these non-linear processes can be modeled as fractals or multifractals. Hydrothermal processes in the Earth’s crust can result in ore deposits characterized by high concentrations of metals with fractal or multifractal properties. Here we show that the non-linear properties of the end products of singular mineralization processes can be applied for prediction of undiscovered mineral deposits and for quantitative mineral resource assessment, whether for mineral exploration or for regional, national and global planning for mineral resource utilization. In addition to the general theory and framework for the non-linear mineral resources assessment, this paper focuses on several power-law models proposed for characterizing non-linear properties of mineralization and for geoinformation extraction and integration. The theories, methods, and computer system discussed in this paper were validated using a case study dealing with hydrothermal Au mineral potential in southern Nova Scotia, Canada.     

Inversely-Mapped Analytical Solutions for Flow Patterns around and within Inclined Elliptic Inclusions in Fluid-Saturated Rocks

In this paper, an inverse mapping is used to transform the previously-derived analytical solutions from a local elliptical coordinate system into a conventional Cartesian coordinate system. This enables a complete set of exact analytical solutions to be derived rigorously for the pore-fluid velocity, stream function, and excess pore-fluid pressure around and within buried inclined elliptic inclusions in pore-fluid-saturated porous rocks. To maximize the application range of the derived analytical solutions, the focal distance of an ellipse is used to represent the size of the ellipse, while the length ratio of the long axis to the short one is used to represent the geometrical shape of the ellipse. Since the present analytical solutions are expressed in a conventional Cartesian coordinate system, it is convenient to investigate, both qualitatively and quantitatively, the distribution patterns of the pore-fluid flow and excess pressure around and within many different families of buried inclined elliptic inclusions. The major advantage in using the present analytical solution is that they can be conveniently computed in a global Cartesian coordinate system, which is widely used in many scientific and engineering computations. As an application example, the present analytical solutions have been used to investigate how the dip angle of an inclined elliptic inclusion affects the distribution patterns of the pore-fluid flow and excess pore-fluid pressure when the permeability ratio of the elliptic inclusion is of finite but nonzero values.     

The qualitative zoning record of minerals. A method for determining the duration of metamorphic events?

Summary The efficacy of ion exchange in petrological systems, for example the Fe-Mg exchange between garnet and biotite, is a function of grainsize, temperature, rates of temperature change and diffusion parameters. The combination of these variables determines the final zoning profile of minerals. Therefore, zoning profiles may be used to derive one of these variables if the others are known. For example, a mineral grain that experienced a short thermal event may still preserve a zoning profile characteristic of the heating path. In contrast, if that grain experienced a long thermal event it may develop a zoning profile typical of the cooling path. Conversely, for the same temperature-time cycle, large grains may not completely equilibrate at the metamorphic peak, and in smaller grains any previous record may have been erased. This is commonly observed in natural rocks where different grains within one thin section preserve often qualitatively different zoning profiles. Thus, a critical grainsize,l _crit, may exist that separates grains with qualitatively different zoning profiles so that grains of sizel > l _crit still retain zoning information about the heating path and grains of sizel <l _crit contain only information about the cooling path. If the critical grainsize can be measured and an independent estimate for the peak metamorphic temperature exists, the duration of the thermal event may, in principle, be estimated.The applicability of this method to natural garnets is hampered by a range of uncertainties. However, a parameterisation of the critical grain size may be used to illustrate the relative importance of grain size, temperature and event duration to the equilibration of minerals. In this paper, the critical grainsize is parameterized for various temperature-time cycles and its dependence on diffusion parameters is discussed. It is shown that, for Barrovian conditions,l _crit between 0.1 and 1 mm separates garnets retaining prograde information from garnets retaining cooling path information. For illustration, we compare the results with the critical grainsize of garnets from two metamorphic terranes, the Prydz Bay region (Antarctica) and the Koralm complex (Eastern Alps). Despite the large range of uncertainties attached to the method, it is shown that the critical grainsize of garnets in both terranes is consistent with a very short duration of the last thermal event that affected the two regions.

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Die qualitative Form von Zonierungsprofilen in Mineralen. Information über die Dauer metamorpher Ereignisse?

Zusammenfassung Zonierungsprofile von Paragenesen im Ionenaustausch, zum Beispiel das Fe-Mg Austauschsgleichgewicht zwischen Granat und Biotit, sind eine Funktion von (i) Korngröße, (ii) Temperatur, (iii) Kühl- und Heizgeschwindigkeit sowie (iv) den Diffusionskonstanen. Es sollte daher möglich sein, Zonierungsprofile dazu zu verwenden, einen dieser Parameter zu bestimmen, wenn die anderen bekannt sind. Zonierungsprofile von Kristallen die ein kurzes thermisches Ereignis erfahren haben, mögen daher prograde Information beinhalten, wogegen derselbe Kristall ein retrogrades Profil aufweisen mag, wenn er einem langlebigen thermischen Ereignis unterlag (prograd und retrograd ist hier als: bei ansteigender Temperatur und bei abfallender Temperatur definiert). In Kristallen die dem gleichen Temperatur-Zeitpfad unterworfen waren, könnten kleine Körner nur die Kühlgeschichte dokumentieren, wogegen große noch Zonierungsinformation vom Heizpfad aufweisen. In natürlichen Gesteinen wird das oft dadurch beobachtet, daß verschiedene Körner auseinem Dünnschliff qualitativ verschiedene Zonierungsprofile aufweisen. Es ist daher möglich eine kritische Korngöße,l _crit, zu definieren, die Korngrößen mit qualitativ verschiedenen Zonierungsprofilen voneinander trennt. Körner mit einem Durchmesserl > l _crit haben, zumindest teilweise, noch prograde Profile, wogegen Körner mitl <l _crit nur retrograde Information dokumentieren. Wenn man diese kritische Korngröße messen kann, sollte sie dazu benutzt werden können, etwas über die Dauer des thermischen Ereignisses auszusagen.Die Anwendbarkeit dieser Methode ist durch eine Reihe von Fehlern limitiert. Nichtsdestotrotz, ist eine Parameterisierung der kritischen Korngröße nützlich um die relative Wichtigkeit von Korngröße, Temperatur und Zeit, für die Entwicklung von Zonierungsprofilen, zu illustrieren. Unser Modell kann dazu benutzt werden, um die Größenordnung von Granaten abzuschätzen, die noch prograde Information dokumentieren können. Die Abhängigkeit der kritischen Korngröße von Diffusionsparametern und der Form des Temperatur-Zeit Pfades wird ebenfalls diskutiert. Es wird gezeigt, daß für Metamorphose in der mittleren Grünschiefer und Amphibolit fazies,l _crit zwischen 0.1 and 1 mm prograd zonierte von retrograd zonierten Granaten trennt. Um das Modell zu illustrieren, werden die Ergebnisse auf die Prydz Bay Region (Antarktis) und den Koralm Komplex (Ostalpen) angewendet. Trotz der großen Fehlergrenzen der Methode glauben wir zeigen zu können, daß die kritische Korngröße beider Terrains andeutet, daß das letzte thermische Ereignis in beiden Gebieten kurzlebig war.

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With 5 Figures