Earth's Interior Research Articles

A mathematical model for the formation of the mineral composition of rocks removed to the surface during a volcano eruption


 
 
 The article examines the origin of chemicals obtained as a result of cooling on the Earth’s surface during a volcanic eruption. For this, we propose a mathematical model of the formation of the mineral composition of rocks brought to the surface during a volcanic eruption, depending on the crystallization temperature. To do this, we consider a certain inverse problem for the heat equation and prove its solvability under certain conditions. The proposed method can also be used in case of an earthquake. Thus, by studying the composition of rocks on the surface, we can determine at what depth the corresponding layer of rocks is located. Mathematically, this means that you need to find the unknown functions f (x) and u (x, t), where the function f (x) characterizes the source of the formation of rocks, and the function u (x, t) characterizes the crystallization of rocks depending on tem- perature because each rock has its crystallization temperature depending on temperature. We assume that the functions h (x, t), g (x, t) are known. Unknown functions f (x) and u (x, t). Using the inverse problem, we determine the function u (x, t) – the temperature in the lower layers of the earth, and knowing the temperature of crystallization of rocks, we can determine what depth the required rock is. The main purpose of the inverse problem is to determine the composition of rocks below the earth’s surface using data obtained at the earth’s surface. Experimentally, this mathematical model means that with the help of certain sensors on the surface, it is possible to give information about the subterranean depths. This information is determined by the nature of the object under study and the experimental complex used in this study. In such situations, for the diagnosis of objects and their internal structure, mathematical processing, and interpretation of observation results are required .We are talking about those tasks in which it is required to determine the causes if the consequences obtained as a result of observation are known. For example, determining the location and power of an earthquake from the vibrations measured on the earth’s surface. Or, by the structure of minerals on the surface of the earth, determining the depth of their location underground, etc. When processing the experimental data, a conclusion is made about the internal connections of the phenomenon or process. When the mathematical model of the process under study is known, the problem of identifying the mathematical model is posed. Namely, the determination of the coefficients of differential equations, their right-hand side, the boundary of the region, boundary, and initial conditions – these problems are related to inverse problems of mathematical physics. In general, inverse problems.
 
 

Multi-objective optimization of geosynthetic reinforced soil structures

Optimization models for reinforced earth structures such as foundation pads, bridge abutments, and embankments based on the Eurocode standard are presented. The developed optimization models, which take into account construction costs and environmental footprint, are used to determine an optimal design for each earth structure. The optimization model uses discrete variables, making the results more suitable for actual construction practice and fully exploiting the geotechnical and structural capacity of earth structures with geosynthetic reinforcement. The multi-objective optimization was performed to find a set of solutions that represent the best trade-off between construction cost and environmental footprint. The results show that the correct selection of geosynthetics leads to a significant reduction in costs and environmental impact. The general observation that emerges from the multi-objective optimization is that when designing the earth structures using geosynthetic reinforcements, due to the discrete set of variables, there are not so many optimal solutions that the designer can choose from. The entire optimization process is illustrated with the help of a numerical example. This study can help engineers to select earth structure and geosynthetic reinforcements that are economical and sustainable.

Oxygen Fugacity of Global Ocean Island Basalts

AbstractMantle plumes contain heterogenous chemical components and sample variable depths of the mantle, enabling glimpses into the compositional structure of Earth's interior. In this study, we evaluated ocean island basalts (OIB) from nine plume locations to provide a global and systematic assessment of the relationship between fO2 and He‐Sr‐Nd‐Pb‐W‐Os isotopic compositions. Ocean island basalts from the Pacific (Austral Islands, Hawaii, Mangaia, Samoa, Pitcairn), Atlantic (Azores, Canary Islands, St. Helena), and Indian Oceans (La Réunion) reveal that fO2 in OIB is heterogeneous both within and among hotspots. Taken together with previous studies, global OIB have elevated and heterogenous fO2 (average = +0.5 ∆FMQ; 2SD = 1.5) relative to prior estimates of global mid‐ocean ridge basalts (MORB; average = −0.1 ∆FMQ; 2SD = 0.6), though many individual OIB overlap MORB. Specific mantle components, such as HIMU and enriched mantle 2 (EM2), defined by radiogenic Pb and Sr isotopic compositions compared to other OIB, respectively, have distinctly high fO2 based on statistical analysis. Elevated fO2 in OIB samples of these components is associated with higher whole‐rock CaO/Al2O3 and olivine CaO content, which may be linked to recycled carbonated oceanic crust. EM1‐type and geochemically depleted OIB are generally not as oxidized, possibly due to limited oxidizing potential of the recycled material in the enriched mantle 1 (EM1) component (e.g., sediment) or lack of recycled materials in geochemically depleted OIB. Despite systematic offset of the fO2 among EM1‐, EM2‐, and HIMU‐type OIB, geochemical indices of lithospheric recycling, such as Sr‐Nd‐Pb‐Os isotopic systems, generally do not correlate with fO2.

Bayesian Inversion, Uncertainty Analysis and Interrogation Using Boosting Variational Inference

AbstractGeoscientists use observed data to estimate properties of the Earth's interior. This often requires non‐linear inverse problems to be solved and uncertainties to be estimated. Bayesian inference solves inverse problems under a probabilistic framework, in which uncertainty is represented by a so‐called posterior probability distribution. Recently, variational inference has emerged as an efficient method to estimate Bayesian solutions. By seeking the closest approximation to the posterior distribution within any chosen family of distributions, variational inference yields a fully probabilistic solution. It is important to define expressive variational families so that the posterior distribution can be represented accurately. We introduce boosting variational inference (BVI) as a computationally efficient means to construct a flexible approximating family comprising all possible finite mixtures of simpler component distributions. We use Gaussian mixture components due to their fully parametric nature and the ease with which they can be optimized. We apply BVI to seismic travel time tomography and full waveform inversion, comparing its performance with other methods of solution. The results demonstrate that BVI achieves reasonable efficiency and accuracy while enabling the construction of a fully analytic expression for the posterior distribution. Samples that represent major components of uncertainty in the solution can be obtained analytically from each mixture component. We demonstrate that these samples can be used to solve an interrogation problem: to assess the size of a subsurface target structure. To the best of our knowledge, this is the first method in geophysics that provides both analytic and reasonably accurate probabilistic solutions to fully non‐linear, high‐dimensional Bayesian full waveform inversion problems.

A ground-breaking Distributed fiber-optic Pressure Sensor for geohydraulic applications

Distributed fiber optic (DFO) technology has provided significant insight into various engineering problems by enabling high spatial resolution and accurate temperature and strain measurements. Recently, a novel distributed fiber-optic pressure sensor (DPS) has been developed at the University of Applied Sciences of Eastern Switzerland (OST), which may change the paradigm of monitoring geohydraulic structure monitoring. The key innovation of the sensor is its ability to measure hydrostatic pressure with high spatial resolution and over long distances.This study provides a comprehensive characterization of this novel sensor for two different applications. In the first application the DPS was tested in a water column to measure the vertical hydraulic pressure. In the second application the sensor is tested in a laboratory-scale dike (1:4). The DPS was embedded directly into the earth structures, providing real-time monitoring of pore pressure variations during saturation. For both applications, the DPS measurements were compared with conventional pressure and piezometer sensors, demonstrating good agreement.The results of these two applications illustrate the potential of the DPS to revolutionize geohydraulic monitoring and improve our understanding of dynamic processes in water-related structures. The implementation of this technology promises to improve the safety, predictability, and performance of critical infrastructure.

Temperature-dependent elastic shear modulus of a saturated lateritic clay

The thermo-mechanical behaviour of saturated clays and sands has been studied by many researchers, considering that it is useful in many geotechnical problems, such as the analysis of energy foundations and the effects of climate change on earth structures. Despite the fact that temperature is known to affect the yielding and volume change behaviour of soils, the effects of temperature on the elastic shear modulus (G0) of soils are rarely studied. In this study, a temperaturecontrolled oedometer equipped with bender elements was developed. It was used to investigate the effects of temperature on G0 of a compacted lateritic clay at saturated conditions. The G0 was measured at 5 and 40°C during loading and unloading in the stress range of 30 to 400 kPa. Four tests were conducted in which two different initial densities (95% and 85% of maximum dry density (MDD) were considered. The results will be interpreted and discussed with reference to the elastoplastic modelling of thermo-mechanical soil behaviour.

Impact of Limestone Calcined Clay Concrete (LC3) in Various Aggressive Soil Environments: A Comprehensive Review

Aggressive soil environments are known for causing deterioration in concrete sub-structure and attacking the concrete of the earth structures by chemical contamination of the soil with fluoride, sulfide, and chloride. The degree of deterioration in the soil can vary from rapid dissolution to minor effects. Many construction materials placed underground are exposed to the aggressive action of the soil. Therefore, studying the impact of soil nature on the deterioration of concrete is crucial to maintaining the safety and efficiency of infrastructures. Recent research states that the conception of limestone calcined clay concrete (LC3) is different from ordinary concrete. Therefore some changes in durability and strength might occur. Hence the present study focuses on the strength and durability aspects, which are of prime importance in almost all concrete structures and permeability. This review stated that LC3, due to their dense microstructure, were chemically resistant in terms of compressive strength, surface scaling, and length change in the aggressive soil environment. These promising results escalate LC3 to be suitable for more reliable concrete earth structures. This paper discusses the properties, optimisation method, environmental impacts, strength, and durability of LC3 and ends with suggestions on subjects on which further research is required.

Численная оценка устойчивости и деформативности конструкции земляного полотна методом замены слабого грунта на слабых основаниях

A pressing issue for the railway industry is to enhance the stability and reduce the deformability of earth embankment structures constructed on weak foundations using the method of replacing weak soil. The authors determined the width of the weak soil at the base, requiring replacement, taking into account the requirements for deformability indicators that ensure the specified geometric parameters of the earth embankment under various soil foundation conditions. The numerical modeling was based on established theoretical principles in accordance with the sequence of construction stages for a high-speed railway line on weak foundations using the geotechnical software Plaxis 2D. By considering and evaluating different thicknesses of the weak soil layer to be replaced, the authors constructed a graph of the dependence of deformation on the principal stress at the point of plastic deformation development, and determined the value of the stable safety factor. The research made it possible to propose a numerical method for determining the slope stability coefficient. Analysis of current regulatory documents and calculation methods for earth structures on weak soils has confirmed the need to refine existing calculation methods.

Small-strain shear stiffness of sand-gravel mixtures

Small-strain shear stiffness (G0) is a key parameter for seismic ground response analysis and performance evaluation of various earth structures and foundations. To account for its pressure and density dependency, G0 has been conveniently correlated to mean effective stress (σm′) and void ratio (e). Such an approach is suitable for conventional uniform materials. However as found in this study, it is not always applicable to estimate the G0 of sand-gravel mixtures (SGMs), because it essentially fails to account for the combined effects of density and gravel content (GC). In this study, aimed at addressing this issue and developing a theoretical framework and empirical correlations suitable for estimating the G0 of SGMs, a series of bender element laboratory tests were carried out on selected SGMs. Specifically, SGMs were obtained by mixing two clean sands – namely New Brighton Sand (mean diameter, D50 = 0.2 mm) and Dalton River Washed Sand (D50 = 0.75 mm) – and rounded pea gravel (D50 = 5.5 mm). Shear wave velocity of specimens having GC = 0, 10, 25, 40 and 60% and prepared at a relative density (Dr) of 20, 30, 45 and 60% was measured at σm′ = 50, 100, 150 and 200 kPa. The laboratory results indicated that G0 of SGMs increases with increasing both the Dr and σm′, whereas the effect of GC would be marginal to significant depending on the limiting and threshold sand contents. To correlate G0 simultaneously with both GC and Dr, the equivalent void ratio (ef(eq)) was adopted. It is shown that the use of ef(eq) makes it possible to uniquely describe the G0 of SGMs for any combination of GC and Dr over the full range of σm′ level applied in this study.

Research on core and mantle dynamics based on the electrical conductivity of materials of the Earth and planetary interior

Research on core and mantle dynamics based on the electrical conductivity of materials of the Earth and planetary interior

ФОРТЕЦІ ЛІВОБЕРЕЖНОЇ УКРАЇНИ ЯК СИРОВИННА БАЗА ДЛЯ СЕЛІТРОВАРІННЯ У 18 СТОЛІТТІ

The article is devoted to the study of the history of saltpeter mining on the territory of the Left Bank of Ukraine and the fate of the earth defense structures of the Cossack fortresses in this process. Nitrate production in the territory of the Left Bank of Ukraine was a fairly widespread industry. The development of artillery and firearms in early modern armies was one of the reasons for the increase in saltpeter production. In the 17th century, mounds of barrows and ramparts of ancient fortifications were used for its extraction, where saltpeter was naturally concentrated. But this method depended on the coincidence of many factors. From the second half of the 17th century on the territory of the Hetman Oblast and the Slobozhan Oblast, the on-board method of saltpeter mining is increasingly spreading. The appearance of saltpeter plants, which worked with artificial edges, greatly simplified the process of saltpeter production, but also required finding places for their location. At this time, saltpeter workers paid attention to the abandoned fortresses built in the 17th century, which had a convenient location and soil reserves for the construction of artificial banks. During the 18th century, the role of fortresses in the defense of Left Bank Ukraine is gradually changing. At the beginning of the century, they were an important component of defense, but over time their influence gradually decreases. Some of them are falling into disrepair, and the rest are turning into rural settlements. The territory of the abandoned fortresses was a convenient location for saltpeter workshops, and the defensive structures served as a raw material base for saltpeter mining. If in the first half of the 18th century the hetman's administration followed the preservation of fortresses, then in the second half of the century this process became widespread even without the restoration of the ramparts. The final destruction of defensive structures by saltpeter’s took place at the end of the century and was connected with the re-planning of cities.

Vertical electrical sounding techniques training on frozen multilayer soils in a cold laboratory

This paper presents a comprehensive plan for teaching the method of Vertical Electrical Sounding in the cold laboratory of the Geography Department of MSU on model-prepared frozen multilayer soils. Vertical electrical sounding (VES) is the definitive method for studying the structure of the Earth's crust. It does this by measuring the electrical resistance of rocks at different depths. A four-electrode setup is used for VES (AB is the supply electrode, and MN is the receiving electrode). The process involves measuring the current in AB and the potential difference at MN, calculating the apparent resistivity, and increasing the AB differences. The results are presented in the form of a RES curve and a transect. We will consider typical transects and VES curves (two-layer curves with ρ1 < ρ2 and ρ1 > ρ2). We will now interpret the bilayer section (sediment-granites). This allows you to master both the theory and practice of the VES method under conditions that mirror those in the field. VES, model soils, frozen soils, multilayer soils, training

ОБРАБОТКА РЕЗУЛЬТАТОВ GPS-МОНИТОРИНГА ПРИ ИНТЕНСИВНЫХ ДВИЖЕНИЯХ ЗЕМНОЙ КОРЫ В СЕЙСМОАКТИВНЫХ РЕГИОНАХ КАЗАХСТАНА

The article presents the results of GPS-monitoring studies in the zone of major tectonic faults on the territory of Almaty. It has been established that monitoring the movement of the Earth's crust is necessary to understand the processes preceding earthquakes and to develop forecasting models. Knowledge of the movement of the Earth's crust is important to ensure the safety of infrastructure such as roads, bridges and residential buildings. The results of the study can be useful for conducting scientific research (when monitoring, analyzing and predicting the movement of the Earth's crust in regions with increased seismic activity) related to the structure of the Earth's crust and the tectonics of the region.

ГЕОДИНАМІЧНИЙ СТАН ЗАКАРПАТСЬКОГО ВНУТРІШНЬОГО ПРОГИНУ ЗА РЕЗУЛЬТАТАМИ ДЕФОРМОМЕТРИЧНИХ СПОСТЕРЕЖЕНЬ У РЕГІОНІ

Background. The relevance of the research is determined by the gradual increase in local seismicity in the region, which occupies a peculiar geographical location, through which oil, gas and product pipelines pass, and in which critical infrastructure facilities are located that may be affected by the underground natural disaster. It is important to have information on the movements of the upper layers of the Earth's crust, their kinematics and dynamics, which significantly affect the stress-strain state of rocks and the release of energy from geomechanic processes. It is also necessary to investigate the influence of the region's geodynamics on the discharge of the stress-strain state of rocks. Methods. The research methodology is to construct time-dependent crustal displacements and compare velocities and accelerations of crustal movements in the intervals of anomalous modern lateral movements of the Earth's crust. The velocities and accelerations of crustal movements are calculated, the kinematics of movements and seismicity of the region are compared. Correlation analysis of the observed series is applied. To solve the tasks, we used the results of observations of horizontal crustal movements in the Oașh deep-seated fault area using a quartz strain gauge with a base of 24.5 m mounted in the adit of the Korolevo urban-type settlement. The seismic data were obtained using digital seismometers operating at the monitoring geophysical station of the Seismicity Department of the Carpathian region of S.I. Subbotin Institute of Geophysics of the National Academy of Sciences of Ukraine. Results. The article discusses the geodynamics of the Transcarpathian Inner Trough based on observations of modern lateral movements of the Earth's crust in the Oașh deep-seated fault area, which in 2021 were represented by rock extensions of +12.61x10-7. The physical parameters of geomotion in the region were calculated, the spatiotemporal distribution of local seismicity was established, and the relationship between seismic and geodynamic states in Transcarpathia in 2021 was studied. The variations of displacements of the upper layers of the Earth's crust over the entire period of deformation monitoring observations in Korolevo urban-type settlement (1999–2021) and the temporal distribution of local underground shocks were studied. Conclusions. The analysis of the spatio-temporal distribution of local seismicity and modern lateral movements of the Earth's crust over the entire period of deformation monitoring observations in the Oașh deep-seated fault area has indicated an increase in the seismicity of the region in the intervals of intense crustal movements and the presence of periods of crustal movement fluctuations for 12 years: familiar variable processes (expansion and contraction of rocks, the total magnitude of displacement fluctuations in the region of zero movements) were detected for 2–3 years. The most relevant and important are the periods of 9–10 years following these calm intervals, since during this time earthquakes are recorded and their frequency is also found to be increasing. The intensification of seismicity in the region is observed against the background of general rock extension, which occurs due to the steady age-related crustal movements. At the present stage, the current crustal movements are in a state of rock expansion, and if this trend does not change, an increase in seismicity in the region should be expected.

ГЕОХИМИЧЕСКИЕ ОСОБЕННОСТИ ГАББРОИДОВ И ГРАНИТОИДОВ НЯТЫГРАНСКОГО КОМПЛЕКСА (БУРЕИНСКИЙ МАССИВ)

Gneissic gabbros, gabbrodiorites, granodiorites, and granites of the Late Proterozoic Nyatygransky Complex, exposed by erosion in the eastern part of the Bureya massif, form small intrusive bodies within the boundaries of the Melgin metalliferous trough, as well as around it. Analysis of chemical and trace-element compositions of rocks from the Nyatygransky Complex revealed their geochemical features. The calculated agpaitic index values for gabbroids are very low and range from 0.11 to 0.33. Granodiorites have slightly higher index values ranging from 0.5 to 0.38, and only gneiss-granites are plumasitic with agpaitic index values between 0.45 and 0.75. Both gabbroids and granitoids are assigned to calc-alkaline rocks by their agpaitic index. Gneissic gabbros, dominated by dark-colored minerals (labradorite, hornblende), show enhanced alkalinity not common to gabbros (4%); in them, the magnesium content prevails over the iron content. They are characterized by high alumina content (15–18%), reaching 20.38%. Geochemically, they are interpreted as I-type igneous rocks. Gneissic granitoids with a slight predominance of the iron content over the magnesium content are less aluminous (Al2O3 12–15%). They are interpreted as S-type (sedimentary) and I-type (igneous) granitoids, formed in sedimentary and granitic layers of the earth’s crust. According to petrochemical diagrams, the gabbroids and granitoids of the Nyatigransky Complex belong to the volcanic arcs of the active continental margin.

Organization of continuous monitoring of quarry sides

The article discusses the fundamental conceptual positions underlying the study of the significant impact of humanity on the lithosphere, which is approaching and may exceed its limits. It is noted that most surface layers of the Earth's crust are non-renewable, and the majority of chemical elements have found practical applications, yet only about oneseventh of the extracted minerals are used in the production of final products. One of the main challenges in developing open-pit mines is maintaining the stability of the pit walls. As the depth of the pit increases, this issue becomes increasingly critical. The article emphasizes the importance of enhanced study of the fundamentals of managing rock masses in mining operations and the practical application of this knowledge, as it significantly contributes to solving problems and examples related to assessing the stability of slope walls and pit benches.

Gravimetric inversion based on model exploration with growing source bodies (Growth) in diverse earth science disciplines

<abstract> <p>Gravimetry is a discipline of geophysics that deals with observation and interpretation of the earth gravity field. The acquired gravity data serve the study of the earth interior, be it the deep or the near surface one, by means of the inferred subsurface structural density distribution. The subsurface density structure is resolved by solving the gravimetric inverse problem. Diverse methods and approaches exist for solving this non-unique and ill-posed inverse problem. Here, we focused on those methods that do not pre-constrain the number or geometries of the density sources. We reviewed the historical development and the basic principles of the Growth inversion methodology, which belong to the methods based on the growth of the model density structure throughout an iterative exploration process. The process was based on testing and filling the cells of a subsurface domain partition with density contrasts through an iterative mixed weighted adjustment procedure. The procedure iteratively minimized the data misfit residuals jointly with minimizing the total anomalous mass of the model, which facilitated obtaining compact meaningful source bodies of the solution. The applicability of the Growth inversion approach in structural geophysical studies, in geodynamic studies, and in near surface gravimetric studies was reviewed and illustrated. This work also presented the first application of the Growth inversion tool to near surface microgravimetric data with the goal of seeking very shallow cavities in archeological prospection and environmental geophysics.</p> </abstract>

Characterization and Modeling of Reinforced Earth Structures

Characterization and Modeling of Reinforced Earth Structures

Characterization of anisotropy in basin-scale subsurface using teleseismic receiver function analysis

Teleseismic receiver function (RF) analysis offers a passive-source analogue to detect impedance boundaries using the converted body waves generated by earthquakes. While the technique traditionally has targeted deep earth structures such as the Moho and transition zones, there is growing interest in assessing its applicability in basin-scale seismic characterization, ultimately aimed for onshore commercial integration as a cost-effective complement to existing active-source seismic surveys. Specifically, the conventional broadband seismometers used in global observational seismic experiments are not only logistically simple in terms of data acquisition, but they also record ground motions in three mutually orthogonal time series, enabling effective detection of shear waves and directional variations of observed signals. Here, we perform teleseismic RF analysis to detect shear-wave anisotropy and related symmetry axes orientations in a basin setting, using open-source seismic data recorded at 55 closely spaced seismic stations in the LaBarge Passive Seismic Experiment deployed in Wyoming between November 2008 and June 2009. We find that the strengths and geometry of the observed anisotropy are variable along the array. Significantly, not only can anisotropy effectively delineate subsurface fault interfaces, it can also substantiate and reveal additional interpretable signals that are otherwise disregarded. The estimated fast axes orientations compare favorably with the complex fracture systems documented in the region. Finally, we show that P-to-S amplitude variations with P incidence are systematic and modelable using existing computational tools, offering an opportunity to develop an analysis technique similar to amplitude variation with offset with the products of RF analysis.

The influence of stress-induced anisotropy in undrained yield and ultimate shear strengths in brittle loose deposited silts

The typical undrained behaviour observed in brittle non-plastic soil is ruled by the combination of density and stress levels. Some specific silty and sandy mining waste with particles morphologies that generate high smallstrain stiffness to strength ratios when increasing deviatoric stress (q) in stress paths that tend to decrease mean effective stress (p´) may drop down the deviatoric stress before reaching the frictional critical sate. The ratio between the peak (or yield) value (Su=q/2) and the corresponding p´ is usually associated with a locus in q-p´ that is commonly associated to a straight Instability Line (IL) with a unique ratio (ηL) and for an initial state parameter. However, this is not the case if an induced anisotropy is installed differently while the at rest stress ratio (hereby defined as initial, K0) is achieved by continuous rate the principal stresses consolidated in lab prior to loading with distinct values. This fabric effect is decisive for design and in stability assessment of earth structures, like dams or piles of mine tailings where non-plastic fines are dominant, even if the prevailing stress-path is in compression. In a thorough and quite complete program varying these conditions on iron ore tailings from Minas Gerais state in Brazil, reconstituted in lab with differentiated state parameters, and its relation to the induced anisotropy effect.