Earth Science Applications Research Articles

Mechanical properties of bi- and poly-crystalline ice

A sound knowledge of fundamental mechanical properties of water ice is of crucial importance to address a wide range of applications in earth science, engineering, as well as ice sculpture and winter sports, such as ice skating, ice fishing, ice climbing, bobsleighs, and so on. Here, we report large-scale molecular dynamics (MD) simulations of mechanical properties of bi- and poly-crystalline hexagonal ice (Ih) under mechanical loads. Results show that bicrystals, upon tension, exhibit either brittle or ductile fracture, depending on the microstructure of grain boundaries (GBs), whereas they show ductile fracture by amorphization and crystallographic slips emitted from GBs under compression. Under shearing, the strength of bicrystals exhibits a characteristic plateau or sawtooth behavior drawn out the initial elastic strains. Nanograined polycrystals are destabilized by strain-induced amorphization and collective GB sliding. Their mechanical responses depend on the grain size. Both tensile and compressive strengths decrease as grain size decreases, showing inverse Hall-Petch weakening behavior. Large fraction of amorphous water structure in polycrystals with small grain size is mainly responsible for the inverse Hall-Petch softening. Dislocation nucleation and propagation are also identified in nanograined ice, which is in good agreement with experimental measurements. Beyond the elastic strain, a combination of GB sliding, grain rotation, amorphization and recrystallization, phase transformation, and dislocation nucleation dominate the plastic deformation in both bicrystals and polycrystals.

Mathematical modeling of calcium phosphate precipitation in biologically relevant systems: scoping review.

Biologically guided precipitation of calcium phosphates is important for the formation of calcified human tissues, such as bone and teeth, and is of practical significance in numerous industrial and agricultural processes, such as wastewater treatment and dairy ultrafiltration. Mineral precipitation is physicochemically complex and becomes even more complex in the presence of biological materials. The theoretical foundation of phase transition in general has been developed and is vital for many applications, such as metallurgy and weather prediction. The goal of this scoping review was to identify and evaluate established mathematical approaches developed to describe the formation of calcium precipitates in biological systems. A scoping review was conducted using MathSciNet, Scopus, and Web of Science databases to retrieve eligible mathematical modeling papers on calcium precipitates in biological systems. From the 2096 studies screened, 115 studies were included. The major biological systems of interest were tissues of the human body (49/115), water research (38/115), and agricultural and earth sciences applications (17/115). The majority of studies described precipitation of calcium phosphate (79/115), followed by calcium carbonate (22/115). Mathematical modeling of calcium precipitation was dominated by classical nucleation (64/115) and kinetic (38/115) theories. Only a minority of studies explicitly modeled chemical reactions in the aqueous phase (33/115). Biological components were explicitly described in 45/115 studies and included as physicochemical limitations in 70/115 studies. The majority of the studies (91/115) attempted to quantitatively compare the model predictions to the experimental data, with 59/115 reporting good to reasonable fit. This scoping review suggests that broad theories, such as classical nucleation and kinetic theories, may be adapted for modeling calcium precipitation in biologically relevant systems; however, detailed mathematical descriptions of biological, chemical, and physicochemical aspects of calcium precipitation are required.

Micro-positron emission tomography for measuring sub-core scale single and multiphase transport parameters in porous media

Accurate descriptions of heterogeneity in porous media are important for understanding and modeling single phase (e.g. contaminant transport, saltwater intrusion) and multiphase (e.g. geologic carbon storage, enhanced oil recovery) transport problems. Application of medical imaging to experimentally quantify these processes has led to significant progress in material characterization and understanding fluid transport behavior at laboratory scales. While widely utilized in cancer diagnosis and management, cardiology, and neurology, positron emission tomography (PET) has had relatively limited applications in earth science. This study utilizes a small-bore micro-PET scanner to image and quantify the transport behavior of pulses of a conservative aqueous radiotracer injected during single and multiphase flow experiments in two heterogeneous Berea sandstone cores. The cores are discretized into axial-parallel streamtubes, and using the reconstructed micro-PET data, expressions are derived from spatial moment analysis for calculating sub-core tracer flux and pore water velocity. Using the flux and velocity measurements, it is possible to calculate porosity and saturation from volumetric flux balance, and calculate permeability and water relative permeability from Darcy’s law. Second spatial moment analysis enables measurement of sub-core solute dispersion during both single phase and multiphase experiments. A numerical simulation model is developed to verify the assumptions of the streamtube dimension reduction technique. A variation of the reactor ratio is presented as a diagnostic metric to efficiently determine the validity of the streamtube approximation in core and column-scale experiments. This study introduces a new method to quantify sub-core permeability, relative permeability, and dispersion. These experimental and analytical methods provide a foundation for future work on experimental measurements of differences in transport behavior across scales.

Simulation of intrinsic random fields of order k with a continuous spectral algorithm

Intrinsic random fields of order k, defined as random fields whose high-order increments (generalized increments of order k) are second-order stationary, are used in spatial statistics to model regionalized variables exhibiting spatial trends, a feature that is common in earth and environmental sciences applications. A continuous spectral algorithm is proposed to simulate such random fields in a d-dimensional Euclidean space, with given generalized covariance structure and with Gaussian generalized increments of order k. The only condition needed to run the algorithm is to know the spectral measure associated with the generalized covariance function (case of a scalar random field) or with the matrix of generalized direct and cross-covariances (case of a vector random field). The algorithm is applied to synthetic examples to simulate intrinsic random fields with power generalized direct and cross-covariances, as well as an intrinsic random field with power and spline generalized direct covariances and Matern generalized cross-covariance.

From Photons to Pixels: Processing Data from the Advanced Baseline Imager

The Advanced Baseline Imager (ABI) is the primary Earth observing sensor on the new generation Geostationary Operational Environmental Satellites (GOES-R) series, and provides significant spectral, spatial and temporal observational enhancements compared to the legacy GOES satellites. ABI also provides enhanced capabilities for operational sensor calibration and image navigation and registration (INR) to enable observations of the Earth with high spectral fidelity as well as creating images that are accurately mapped and co-registered over time. Unlike earlier GOES Imagers, ABI has onboard calibration capability for all sixteen bands in the reflective and emissive bands. The calibration process includes periodic and routine views of the internal reflective and blackbody targets as well as views of space and the moon. Improvements in INR are made possible by having a Global Positioning System (GPS) on board the spacecraft and routine measurements of stars through the sensor’s boresight for orbit and attitude determination through a Kalman filter. This paper describes how the sensor data are processed into calibrated and geolocated radiances that enable the generation of imagery and higher level products for both meteorological and non-meteorological Earth science applications. Some examples of ABI images and calibration are presented to demonstrate the capabilities and applications of the sensor.

Conditional Latin Hypercube Simulation of (Log)Gaussian Random Fields

In earth and environmental sciences applications, uncertainty analysis regarding the outputs of models whose parameters are spatially varying (or spatially distributed) is often performed in a Monte Carlo framework. In this context, alternative realizations of the spatial distribution of model inputs, typically conditioned to reproduce attribute values at locations where measurements are obtained, are generated via geostatistical simulation using simple random (SR) sampling. The environmental model under consideration is then evaluated using each of these realizations as a plausible input, in order to construct a distribution of plausible model outputs for uncertainty analysis purposes. In hydrogeological investigations, for example, conditional simulations of saturated hydraulic conductivity are used as input to physically-based simulators of flow and transport to evaluate the associated uncertainty in the spatial distribution of solute concentration. Realistic uncertainty analysis via SR sampling, however, requires a large number of simulated attribute realizations for the model inputs in order to yield a representative distribution of model outputs; this often hinders the application of uncertainty analysis due to the computational expense of evaluating complex environmental models. Stratified sampling methods, including variants of Latin hypercube sampling, constitute more efficient sampling aternatives, often resulting in a more representative distribution of model outputs (e.g., solute concentration) with fewer model input realizations (e.g., hydraulic conductivity), thus reducing the computational cost of uncertainty analysis. The application of stratified and Latin hypercube sampling in a geostatistical simulation context, however, is not widespread, and, apart from a few exceptions, has been limited to the unconditional simulation case. This paper proposes methodological modifications for adopting existing methods for stratified sampling (including Latin hypercube sampling), employed to date in an unconditional geostatistical simulation context, for the purpose of efficient conditional simulation of Gaussian random fields. The proposed conditional simulation methods are compared to traditional geostatistical simulation, based on SR sampling, in the context of a hydrogeological flow and transport model via a synthetic case study. The results indicate that stratified sampling methods (including Latin hypercube sampling) are more efficient than SR, overall reproducing to a similar extent statistics of the conductivity (and subsequently concentration) fields, yet with smaller sampling variability. These findings suggest that the proposed efficient conditional sampling methods could contribute to the wider application of uncertainty analysis in spatially distributed environmental models using geostatistical simulation.

Measurement-based perturbation theory and differential equation parameter estimation with applications to satellite gravimetry

The numerical integration method has been routinely used by major institutions worldwide, for example, NASA Goddard Space Flight Center and German Research Center for Geosciences (GFZ), to produce global gravitational models from satellite tracking measurements of CHAMP and/or GRACE types. Such Earth’s gravitational products have found widest possible multidisciplinary applications in Earth Sciences. The method is essentially implemented by solving the differential equations of the partial derivatives of the orbit of a satellite with respect to the unknown harmonic coefficients under the conditions of zero initial values. From the mathematical and statistical point of view, satellite gravimetry from satellite tracking is essentially the problem of estimating unknown parameters in the Newton’s nonlinear differential equations from satellite tracking measurements. We prove that zero initial values for the partial derivatives are incorrect mathematically and not permitted physically. The numerical integration method, as currently implemented and used in mathematics and statistics, chemistry and physics, and satellite gravimetry, is groundless, mathematically and physically. Given the Newton’s nonlinear governing differential equations of satellite motion with unknown equation parameters and unknown initial conditions, we develop three methods to derive new local solutions around a nominal reference orbit, which are linked to measurements to estimate the unknown corrections to approximate values of the unknown parameters and the unknown initial conditions. Bearing in mind that satellite orbits can now be tracked almost continuously at unprecedented accuracy, we propose the measurement-based perturbation theory and derive global uniformly convergent solutions to the Newton’s nonlinear governing differential equations of satellite motion for the next generation of global gravitational models. Since the solutions are global uniformly convergent, theoretically speaking, they are able to extract smallest possible gravitational signals from modern and future satellite tracking measurements, leading to the production of global high-precision, high-resolution gravitational models. By directly turning the nonlinear differential equations of satellite motion into the nonlinear integral equations, and recognizing the fact that satellite orbits are measured with random errors, we further reformulate the links between satellite tracking measurements and the global uniformly convergent solutions to the Newton’s governing differential equations as a condition adjustment model with unknown parameters, or equivalently, the weighted least squares estimation of unknown differential equation parameters with equality constraints, for the reconstruction of global high-precision, high-resolution gravitational models from modern (and future) satellite tracking measurements.

Scanning diamond NV center probes compatible with conventional AFM technology

Scanning probe microscopy using nitrogen vacancy (NV) centers in diamond has become a versatile tool with applications in physics, chemistry, life sciences, and earth and planetary sciences. However, the fabrication of diamond scanning probes with high photon collection efficiency, NV centers with long coherence times, and integrated radio frequency (RF) remains challenging due to the small physical dimensions of the probes and the complexity of the fabrication techniques. In this work, we present a simple and robust method to reliably fabricate probes that can be integrated with conventional quartz tuning fork based sensors as well as commercial silicon AFM cantilevers. An integrated RF micro-antenna for NV center spin manipulation is directly fabricated onto the probe making the design versatile and compatible with virtually all AFM instruments. This integration marks a complete sensor package for NV center-based magnetometry and opens up this scanning probe technique to the broader scientific community.

A computationally efficient approach to modeling contact problems and fracture closure using superposition method

The shape of fractures in an elastic medium under different stress distributions have been well studied in the literature, however, the fracture closure process during unloading has not been investigated thoroughly. The fracture surface is normally assumed to be perfectly smooth so that only the width and stress intensity at the fracture tip are critical in the analysis. In reality, the creation of a fracture in a rock seldom produces smooth surfaces and the resulting asperities on the fracture surfaces can impact fracture closure. Correctly modeling this fracture closure behavior has numerous applications in structural engineering and earth sciences. In this article, we present an approach to model fracture closure behavior in a 2D and 3D elastic media. The fracture surface displacements under arbitrary normal load are derived using superposition method. The contact stress, deformation, and fracture volume evolution are estimated in a computationally efficient manner for various fracture surface properties. When compared with the traditional integral transform methods used to model fracture closure, the superposition method presented in this study produces comparable results with significant less computation time. In addition, with the aid of parallel computation, large scale fracture closure and contact problems can be successfully simulated using our proposed dynamic fracture closure model (DFCM) with very modest computation times.

Guest Editorial Computational Imaging for Earth Sciences

The papers in this special section focused on computational imaging for the earth sciences market. From the core of the earth to the farthest reaches of our planets magnetic fields, the earth sciences are concerned with all aspects of monitoring, exploring, explaining, and exploiting of natural events and resources in the geosphere. Revolutions in computational imaging over the past two decades have had profound implications across this field, bringing new modalities into common use and impacting application domains from weather monitoring and prediction, subsurface sensing, seismic imaging and exploration, to the production of minerals, oil and gas. In all these areas, reliable information extraction by collecting and processing sensor data increasingly hinges on integrated sensor design, system modeling, and efficient computational methods. The scope of such models and methods have more recently integrated statistical pattern recognition nd machine learning systems to account for variability that cannot be completely captured by physical models or simulation. Enabling most all of these processing methods are concomitant developments in optimization theory both in Euclidean spaces as well as on more general manifolds. This special issue solicited relevant contributions from researchers in signal and image processing, inverse problems, machine learning, and related areas as applied to problems of image formation and analysis arising in the context of earth science applications covering the wide range of application domains.

Origin of Magnetism in Hydrothermally Aged 2-Line Ferrihydrite Suspensions.

As an iron oxyhydroxide, nanosized ferrihydrite (Fh) is important in Earth science, biology, and industrial applications. However, its basic structure and origin of its magnetism have long been debated. We integrate synchrotron-based techniques to explore the chemical structures of 2-line ferrihydrite and to determine the origin of its magnetism during hydrothermal aging in air. Our results demonstrate that both the magnetism and X-ray magnetic circular dichroism (XMCD) signal of 2-line ferrihydrite are enhanced with aging time, and that XMCD spectral patterns resemble that of maghemite (γ-Fe2O3) rather than magnetite (Fe3O4). Fe L-edge and K-edge X-ray absorption spectroscopy (XAS) further indicate formation of both maghemite and hematite (α-Fe2O3) with increasing concentrations with longer hydrothermal aging time. Thus, magnetic enhancement with longer hydrothermal aging time is attributed to increasing maghemite concentration instead of a magnetically ordered ferrihydrite as previously reported. Moreover, L-edge and K-edge XAS spectra with different probing depths yield different ratios of these Fe oxides, which suggest the formation of a core (ferrihydrite-rich)-shell (with a mixture of both allotropes; α-Fe2O3 and γ-Fe2O3) structure during hydrothermal aging. Our results provide insights into the chemical evolution of 2-line ferrihydrite that reveal unambiguously the origin of its magnetism.

Half-tapering strategy for conditional simulation with large datasets

Gaussian conditional realizations are routinely used for risk assessment and planning in a variety of Earth sciences applications. Assuming a Gaussian random field, conditional realizations can be obtained by first creating unconditional realizations that are then post-conditioned by kriging. Many efficient algorithms are available for the first step, so the bottleneck resides in the second step. Instead of doing the conditional simulations with the desired covariance (F approach) or with a tapered covariance (T approach), we propose to use the taper covariance only in the conditioning step (half-taper or HT approach). This enables to speed up the computations and to reduce memory requirements for the conditioning step but also to keep the right short scale variations in the realizations. A criterion based on mean square error of the simulation is derived to help anticipate the similarity of HT to F. Moreover, an index is used to predict the sparsity of the kriging matrix for the conditioning step. Some guides for the choice of the taper function are discussed. The distributions of a series of 1D, 2D and 3D scalar response functions are compared for F, T and HT approaches. The distributions obtained indicate a much better similarity to F with HT than with T.

EARTH SCIENCE APPLICATIONS IN THE FIELD OF ARCHAEOLOGY: THE HELIKE EXAMPLE

Earth science applications are widely used in the field of archaeology today. The Helike Project made use of such applications at a time when archaeology in Greece was mostly limited to traditional methodology only. Thus Helike constitutes a pioneer study case of such investigations and of their usefulness in the field of archaeology. In searching for Ancient Helike, our team since 1988 combined extensively traditional archaeological research methods and geophysical and geological exploration. The results of this multidisciplinary approach were in most cases successful beyond expectations. In this paper, I present and discuss the most significant archaeological discoveries in the area of Helike based primarily on data from our geological and geophysical investigations the last 20 years.

An introduction of Markov chain Monte Carlo method to geochemical inverse problems: Reading melting parameters from REE abundances in abyssal peridotites

Markov chain Monte Carlo (MCMC) simulation is a powerful statistical method in solving inverse problems that arise from a wide range of applications. In Earth sciences applications of MCMC simulations are primarily in the field of geophysics. The purpose of this study is to introduce MCMC methods to geochemical inverse problems related to trace element fractionation during mantle melting. MCMC methods have several advantages over least squares methods in deciphering melting processes from trace element abundances in basalts and mantle rocks. Here we use an MCMC method to invert for extent of melting, fraction of melt present during melting, and extent of chemical disequilibrium between the melt and residual solid from REE abundances in clinopyroxene in abyssal peridotites from Mid-Atlantic Ridge, Central Indian Ridge, Southwest Indian Ridge, Lena Trough, and American-Antarctic Ridge. We consider two melting models: one with exact analytical solution and the other without. We solve the latter numerically in a chain of melting models according to the Metropolis–Hastings algorithm. The probability distribution of inverted melting parameters depends on assumptions of the physical model, knowledge of mantle source composition, and constraints from the REE data. Results from MCMC inversion are consistent with and provide more reliable uncertainty estimates than results based on nonlinear least squares inversion. We show that chemical disequilibrium is likely to play an important role in fractionating LREE in residual peridotites during partial melting beneath mid-ocean ridge spreading centers. MCMC simulation is well suited for more complicated but physically more realistic melting problems that do not have analytical solutions.

The replacement of a carbonate rock by fluorite: Kinetics and microstructure

Understanding the mechanism and kinetics of the replacement of carbonates by fluorite has application in Earth sciences and engineering. Samples of Carrara marble were reacted with an ammonium fluoride (NH4F) solution for different reaction times and temperatures. The microstructure of the product phase (fluorite) was analyzed using SEM. The kinetics of replacement was monitored using Rietveld analysis of X-ray powder diffraction patterns of the products. After reaction, all samples preserved their size and external morphology (a pseudomorphic replacement). The grain boundaries of the original marble were preserved although each calcite grain was replaced by multiple fine crystals of fluorite creating inter-crystal porosity. The empirical activation energy Ea (kJ/mol) of the replacement reaction was determined by both model-fitting and model-free methods. The isoconversional method yielded an empirical activation energy of 41 kJ/mol, and a statistical approach applied to the model-fitting method revealed that the replacement of Carrara marble by fluorite is better fitted to a diffusion-controlled process. These results suggest that the replacement reaction is dependent on the ion diffusion rate in the fluid phase through the newly formed porosity.

Thesis of N.A. Shnyrev: II. Principal notes

Настоящая работа посвящена разбору на наш взгляд ошибочного метода определения удельного потока метана из болот, предложенному в диссертации Николая Андреевича Шнырева «Режимные наблюдения и оценка газообмена на границе почвы и атмосферы (на примере потоков метана болотного стационара среднетаежной зоны Западной Сибири “Мухрино”)». Ошибочность предложенного метода заключается в первую очередь в том, что он является некорректным с математической точки зрения. Некорректность является достаточно часто встречающимся свойством решаемых в естественных науках задач. Основной характеристикой таких задач является то, что неизбежно возникающие при измерениях параметров задачи погрешности приводят к существенно отличающимся от реальных результатам. Для иллюстрации этого проводится численный эксперимент, показывающий, что вычисленный с помощью предложенного Н.А. Шнырёвым метода удельный поток имеет противоположный знак и оказывается в три раза больше по модулю, чем удельный поток, исходно заданный в модельном эксперименте. Кроме того, предложенный метод не учитывает нелинейный характер коэффициента диффузии газа по профилю почвы. Аналогичный метод определения потоков в холодное время года по профилю концентрации метана в снеге также страдает рядом недостатков и приводит к разным результатам в зависимости от вида использованной модели переноса газа в снежной толще. Помимо анализа работы профильного метода, обращено внимание на некоторые не соответствующие критериям научной этики заимствования, ошибочную трактовку процесса фотоокисления метана в камере при измерениях, а также ряд других вопросов.

Major advances in microbeam analytical techniques and their applications in Earth Science

Major advances in microbeam analytical techniques and their applications in Earth Science

Robustness Assessment of Regional GNSS Geodetic Networks for Precise Applications

Over the past few decades, the surveying fieldworks were usually carried out based on classical positioning methods for establishing horizontal and vertical geodetic networks. However, these conventional positioning techniques have many drawbacks such as time-consuming, too costly, and require massive effort. Thus, the Global Navigation Satellite System (GNSS) has been invented to fulfill the quickness, increase the accuracy, and overcome all the difficulties inherent in almost every surveying fieldwork. This research assesses the accuracy of local geodetic networks using different Global Navigation Satellite System (GNSS) techniques, such as Static, Precise Point Positioning, Post Processing Kinematic, Session method, and finally Real Time Kinematic for different surveying applications. To achieve this assessment, GNSS observations were executed to highlight the characteristics for each GNSS observation technique. Furthermore, the level of accuracy which is gained from each positioning technique is enormously investigated to figure out the amount of allowable error and the suitability for different geodetic applications. In relative positioning, at least two receivers (or more) are required for timing and positioning while the Precise Point Positioning necessitates single receiver. Some of geodetic applications require about positions with centimeter level of accuracy or less. The robust geodetic networks provide accurate positions which in turn serve different earth science applications.

NASA Computational Case Study: Golomb Rulers and Their Applications

In this case study, the author describes Golomb rulers, their properties, construction algorithms, and applications in astrophysics and Earth sciences.

Trace Element Analysis of Minerals in Magmatic-Hydrothermal Ores by Laser Ablation Inductively-Coupled Plasma Mass Spectrometry: Approaches and Opportunities

Laser ablation inductively-coupled plasma mass spectrometry (LA-ICP-MS) has rapidly established itself as the method of choice for generation of multi-element datasets for specific minerals, with broad applications in Earth science. Variation in absolute concentrations of different trace elements within common, widely distributed phases, such as pyrite, iron-oxides (magnetite and hematite), and key accessory minerals, such as apatite and titanite, can be particularly valuable for understanding processes of ore formation, and when trace element distributions vary systematically within a mineral system, for a vector approach in mineral exploration. LA-ICP-MS trace element data can assist in element deportment and geometallurgical studies, providing proof of which minerals host key elements of economic relevance, or elements that are deleterious to various metallurgical processes. This contribution reviews recent advances in LA-ICP-MS methodology, reference standards, the application of the method to new mineral matrices, outstanding analytical uncertainties that impact on the quality and usefulness of trace element data, and future applications of the technique. We illustrate how data interpretation is highly dependent on an adequate understanding of prevailing mineral textures, geological history, and in some cases, crystal structure.