A Critical Approach to Probability Laws in Geochemistry

Probability laws in geochemistry have been a major issue of concern over the last decades. The lognormal on the positive real line or the additive logistic normal on the simplex are two classical laws of probability to model geochemical data sets due to their association with a relative measure of difference. This fact is not fully exploited in the classical approach when viewing both the positive real line and the simplex as subsets of real space with the induced geometry. But it can be taken into account considering them as real linear vector spaces with their own structure. This approach implies using a particular geometry and a measure different from the usual ones. Therefore, we can work with the coordinates with respect to an orthonormal basis. It could be shown that the two mentioned laws are associated with a normal distribution on the coordinates. In this contribution both approaches are compared, and a real data set is used to illustrate similarities and differences.     

Anisotropic Mean Traveltime Curves: A Method to Estimate Anisotropic Parameters from 2D Transmission Tomographic Data

We present the mathematical deduction and properties of the mean traveltime curves for homogeneous elliptical anisotropic media. These curves generalize their isotropic counterparts which have been introduced in the past as a simple data quality analysis technique at the pre-inversion stage for 2D transmission experiments, allowing the inference of prior velocity models to gain stability at the tomographic inversion. Also, the anisotropy parameters (maximum velocity, anisotropic direction and ratio) are shown to affect the shape of these curves. The degree of asymmetry of the anisotropic mean traveltime curves (displacement of the mean time and standard deviation minima from the middle of the gathering line) is related to the direction of anisotropy which can then be visually estimated. Least squares’ fitting of the anisotropic theoretical models to their experimental counterparts is an effective method to estimate at the pre-inversion stage a macroscopic elliptical anisotropic velocity model, valid at the scale of the experiment, and able to match the experimental mean traveltime distribution. Sensitivity analysis has shown that the mean curve is less prone to errors than the standard deviation curve. Parameter identification from the standard deviation curve becomes unstable for noise levels higher than 5%; data errors produce smearing of the value of the estimated anisotropy ratio and wrong directions of anisotropy biased towards zero degrees. Also, identification from the mean traveltime curve becomes stable when the maximum velocity is well constrained. Finally, this methodology is illustrated with the application to the Grimsel data set. Performing MTC analysis is always recommended since it does not need high numerical requirements, and as shown in the sensibility analysis section, errors in data can be misinterpreted as geological anisotropies. J.L. Fernández Martínez is a visiting professor at UC Berkeley, Department of Civil and Environmental Eng., CA 94720-1710.     

Stability of Kerogen Classification with Regard to Image Segmentation

This paper investigates the stability of an automatic system for classifying kerogen material from images of sieved rock samples. The system comprises four stages: image acquisition, background removal, segmentation, and classification of the segmented kerogen pieces as either inertinite or vitrinite. Depending upon a segmentation parameter d, called “overlap”, touching pieces of kerogen may be split differently. The aim of this study is to establish how robust the classification result is to variations of the segmentation parameter. There are two issues that pose difficulties in carrying out an experiment. First, even a trained professional may be uncertain when distinguishing between isolated pieces of inertinite and vitrinite, extracted from transmitted-light microscope images. Second, because manual labelling of large amount of data for training the system is an arduous task, we acquired the true labels (ground truth) only for the pieces obtained at overlap d=0.5. To construct ground truth for various values of d we propose here label-inheritance trees. With thus estimated ground truth, an experiment was carried out to evaluate the robustness of the system to changes in the segmentation through varying the overlap value d. The average system accuracy across values of d spanning the range from 0 to 1 was 86.5%, which is only slightly lower than the accuracy of the system at the design value of d=0.5 (89.07%).     

Compressional behavior of omphacite to 47 GPa

Omphacite is an important mineral component of eclogite. Single-crystal synchrotron X-ray diffraction data on natural (Ca, Na) (Mg, Fe, Al)Si₂O₆ omphacite have been collected at the Advanced Photon Source beamlines 13-BM-C and 13-ID-D up to 47 GPa at ambient temperature. Unit cell parameter and crystal structure refinements were carried out to constrain the isothermal equation of state and compression mechanism. The third-order Birch–Murnaghan equation of state (BM3) fit of all data gives V ₀ = 423.9(3) Å³, K _T0 = 116(2) GPa and K _T0′ = 4.3(2). These elastic parameters are consistent with the general trend of the diopside–jadeite join. The eight-coordinated polyhedra (M2 and M21) are the most compressible and contribute to majority of the unit cell compression, while the SiO₄ tetrahedra (Si1 and Si2) behave as rigid structural units and are the most incompressible. Axial compressibilities are determined by fitting linearized BM3 equation of state to pressure dependences of unit cell parameters. Throughout the investigated pressure range, the b-axis is more compressible than the c-axis. The axial compressibility of the a-axis is the largest among the three axes at 0 GPa, yet it quickly drops to the smallest at pressures above 5 GPa, which is explained by the rotation of the stiffest major compression axis toward the a-axis with the increase in pressure.     

Scattered Data Approximation on the Bisphere and Application to Texture Analysis

The paper deals with the approximation and optimal interpolation of functions defined on the bisphere \mathbb S²×\mathbb S²\mathbb {S}^{2}\times \mathbb {S}^{2} from scattered data. We demonstrate how the least square approximation to the function can be computed in a stable and efficient manner. The analysis of this problem is based on Marcinkiewicz–Zygmund inequalities for scattered data which we present here for the bisphere. The complementary problem of optimal interpolation is also solved by using well-localized kernels for our setting. Finally, we discuss the application of the developed methods to problems of texture analysis in material science.     

The Hilbert Transform on the Two-Sphere: A Spectral Characterization

The local analysis of signals arising on the sphere is a common task in earth sciences. On the real line the analytic signal turned out to be an important representation in local one-dimensional signal processing. Its generalization to two dimensions is the monogenic signal, and the properties of the analytic and the monogenic signal in the Fourier domain are well known. A generalization to the sphere is given by the Hilbert transform on the sphere known from Clifford analysis. To obtain a spectral characterization, the transform has to be decomposed into spherical harmonic functions. In this paper, we derive the spherical harmonic coefficients of the Hilbert transform on the sphere and give a series expansion. This will show that it acts as a differential operator on the spherical harmonic basis functions of the Laplace equation solution, analogously to the Riesz transform in two dimensions. This allows an interpretation of the Hilbert transform suitable for signal processing of signals naturally arising on the two-sphere. We show that the scale space naturally arising is a Poisson scale space in the unit ball. In addition, the obtained interpretation of the Hilbert transform is used for orientation analysis of plane waves. This representation is justified as a novel signal model on the sphere which can be used to construct intensity and rotation-invariant operators for local signal analysis in a scale-space concept.     

Textures in deforming forsterite aggregates up to 8 GPa and 1673 K

We report results from axisymmetric deformation experiments carried out on forsterite aggregates in the deformation-DIA apparatus, at upper mantle pressures and temperatures (3.1–8.1 GPa, 1373–1673 K). We quantified the resulting lattice preferred orientations (LPO) and compare experimental observations with results from micromechanical modeling (viscoplastic second-order self-consistent model—SO). Up to 6 GPa (~185-km depth in the Earth), we observe a marked LPO consistent with a dominant slip in the (010) plane with one observation of a dominant [100] direction, suggesting that [100](010) slip system was strongly activated. At higher pressures (deeper depth), the LPO becomes less marked and more complex with no evidence of a dominant slip system, which we attribute to the activation of several concurrent slip systems. These results are consistent with the pressure-induced transition in the dominant slip system previously reported for olivine and forsterite. They are also consistent with the decrease in the seismic anisotropy amplitude observed in the Earth’s mantle at depth greater than ~200 km.     

Application of Multiple Point Geostatistics to Non-stationary Images

Simulation of flow and solute transport through aquifers or oil reservoirs requires a precise representation of subsurface heterogeneity that can be achieved by stochastic simulation approaches. Traditional geostatistical methods based on variograms, such as truncated Gaussian simulation or sequential indicator simulation, may fail to generate the complex, curvilinear, continuous and interconnected facies distributions that are often encountered in real geological media, due to their reliance on two-point statistics. Multiple Point Geostatistics (MPG) overcomes this constraint by using more complex point configurations whose statistics are retrieved from training images. Obtaining representative statistics requires stationary training images, but geological understanding often suggests a priori facies variability patterns. This research aims at extending MPG to non-stationary facies distributions. The proposed method subdivides the training images into different areas. The statistics for each area are stored in separate frequency search trees. Several training images are used to ensure that the obtained statistics are representative. The facies probability distribution for each cell during simulation is calculated by weighting the probabilities from the frequency trees. The method is tested on two different object-based training image sets. Results show that non-stationary training images can be used to generate suitable non-stationary facies distributions.     

A scalable cyberinfrastructure solution to support big data management and multivariate visualization of time-series sensor observation data

This paper reports our research in developing a cyberinfrastructure platform to support multivariate visualization of data collected from distributed sensor network. Three new techniques were introduced in this platform: (1) a hybrid data caching strategy that takes advantages of a scalable and distributed time series database, OpenTSDB, to realize efficient data retrieval; (2) a hyper-dimensional data cube is established to map and translate multivariate and heterogeneous sensor data into a common data structure to support location-aware visual analysis; and (3) a data-driven visualization module is implemented to support interactive and dynamic visualization on a simulated virtual globe. A series of experiments were conducted to demonstrate the good runtime performance of the proposed system. We expect this work to make a major contribution to both the visualization building block development in cyberinfrastructure research and the advancement of visual presentation and analysis of sensor data in domain sciences.     

U-Pb Ages of the Late Early Cretaceous Magmatic Rocks in the Zhalantun Area of Inner Mongolia

A great deal of early-to-mid Early Cretaceous magmatic activities have been recorded in the Zhalantun area of Inner Mongolia,while the late Early to Late Cretaceous magmatic rocks have been barely reported(Guo et al.,2018;Zhang Xiangxin et al.,2017).At present,only a few Late Cretaceous magmatic activities were reported in the Arongqi area,such as volcanic rocks of the Gushanzhen Formation.However,the Gushanzhen Formation lacks accurate isotopic age,and contemporaneous intrusive rocks has not been reported yet.In this work,we collected the volcanic rocks from the Gushanzhen Formation and contemporaneous intrusive rocks in the Zhanlantun and nearby,and aim to figure out the formation ages of volcanic rocks of the Gushanzhen Formation and accompanied intrusive rocks by analyzing zircon U-Pb isotopes(Fig.1).     

New U-Pb Geochronological Constraints on Formation and Evolution of the Susong Complex Zone in the Dabie Orogen

<正>Objective The Susong complex zone(SCZ)is a relatively lowgrade metamorphic unit mostly with an epidoteamphibolite facies,located in the southernmost part of the Dabie orogen.However,its rock compositions,ages,metamorphic processes and petrogenesis are still     

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.     

Assessment of flood mitigation through riparian detention in response to a changing climate – a case study

Considering that urban areas may suffer more substantial losses than riparian farmlands during floods, diverting floodwater into riparian areas for temporal detention is expected to mitigate flood damage in downstream urban areas. In this study, an assessment has been conducted to evaluate the effect of flood mitigation through riparian detention in response to a changing climate in the Tou-Chien River basin of Taiwan. An integrated 1D–2D flow model was used to simulate the movement of flood wave in the main stream and the overbank flow inundating into the nearby lowlands. Based on the numerical simulation results, the flooding extents in the basin corresponding to different return periods of flood using existing flood prevention infrastructures were investigated. A detention strategy by lowering the levee along the riparian farmlands was proposed to avoid severe flooding in the densely populated urban areas of the basin. Research findings showed that the proposed detention measure can completely protect the downstream areas from overbank flooding when a flood having 20-yr period occurs, and can effectively alleviate the downstream flooding area from 27.4 to \(7.6\,\hbox {km}^{2}\) for a flood possessing 200-yr period.     

A tribute to Bert Boekschoten – Introduction

Geologie en Mijnbouw -     

Structural evolution of hemimorphite at high pressure up to 4.2 GPa

The high-pressure structural evolution of hemimorphite, Zn₄Si₂O₇(OH)₂·H₂O, a = 8.3881(13), b = 10.7179(11), c = 5.1311(9) Å, V = 461.30(12) Å³, space group Imm2, Z = 2, was studied by single-crystal X-ray diffraction with a diamond anvil cell under hydrostatic conditions up to 4.2 GPa. In the pressure range of 0.0001–2.44 GPa, the unit-cell parameters change almost linearly. The phase transition (probably of the second order) with symmetry reduction from Imm2 (hemimorphite-I) to Pnn2 (hemimorphite-II) was found near 2.5 GPa. The structure compressibility increases somewhat above the phase transition. Namely, the initial unit-cell volume decreases by 3.6% at 2.44 GPa and by 7.2% at 4.20 GPa. The hemimorphite framework can be described as built up of secondary building units (SBU) Zn₄Si₂O₇(OH)₂. These blocks are combined to form the rods arranged along the c-axis; these rods are multiplied by basic and I-translations of orthorhombic unit cell. The symmetry reduction is caused by the rotation of the rods along their axis. In hemimorphite-I, the compression affects mainly the SBU dimensions, whereas a rectangular section of the channels having mm2 symmetry remains practically unchanged. An appreciable decrease in this section in hemimorphite-II is determined by its oblique distortion with the loss of m planes. It results from opposite rotation of adjacent SBU, which also leads into the loss of I-translation. In hemimorphite-I, the coordination of H₂O molecules is fourfold planar; the hydrogen-bonded hydroxyls and H₂O molecules form infinite ribbons along the c-axis. In hemimorphite-II, an additional short H₂O–O contact appears as a result of asymmetric deformation of the channels. The appearance of this new contact provides the possibility for re-orientation of hydrogen bonds. The planar coordination of H₂O molecules changes to tetrahedral and the ribbons are transformed to islands (OH)₂–H₂O.     

The compressibility of Fe- and Al-bearing phase D to 30 GPa

High-pressure in situ X-ray diffraction experiment of Fe- and Al-bearing phase D (Mg_0.89Fe_0.14Al_0.25Si_1.56H_2.93O₆) has been carried out to 30.5 GPa at room temperature using multianvil apparatus. Fitting a third-order Birch–Murnaghan equation of state to the P–V data yields values of V ₀ = 86.10 ± 0.05 ų; K ₀ = 136.5 ± 3.3 GPa and K′ = 6.32 ± 0.30. If K′ is fixed at 4.0 K ₀ = 157.0 ± 0.7 GPa, which is 6% smaller than Fe–Al free phase D reported previously. Analysis of axial compressibilities reveals that the c-axis is almost twice as compressible (K _c  = 93.6 ± 1.1 GPa) as the a-axis (K _a  = 173.8 ± 2.2 GPa). Above 25 GPa the c/a ratio becomes pressure independent. No compressibility anomalies related to the structural transitions of H-atoms were observed in the pressure range to 30 GPa. The density reduction of hydrated subducting slab would be significant if the modal amount of phase D exceeds 10%.     

Functional Methods for Classification of Different Petrographic Varieties by Means of Reflectance Spectra

The need for improved product quality in the aggregates industry is driving the search for greater automation in rock type identification. In practice, reflectance spectra in visible and near-infrared light may reliably be used for the classification of rock classes and their variants. Previous studies introduced statistical classification of six rock variants by means of infrared spectra. The present investigation extends these studies to cover twelve rock types and variants of worldwide economic importance. These were measured by visible and near-infrared light. Statistical classification of these spectra is highly challenging due to the high number of groups and the high dimensionality of the data. In functional data analysis, spectra are regarded as curves instead of vectors of characteristics. To obtain a compact form that is more susceptible to further analysis, the spectra are represented by a B-spline basis. Two functional versions of linear support vector machines and penalized functional discriminant analysis are considered for classification. The multiclass problem is addressed by margin trees and by considering all one-against-one classifications combined with a voting strategy for testing. Since classification error estimated by 5-fold cross-validation is very low, in particular for penalized discriminant analysis, we conclude that the rock types can be classified reliably.