Earth's Interior Research Articles

On the Crustal Sources of Magnetic Anomalies in the Middle Urals

The 800×500 sq km area of the the Middle Urals, Russia, lying between 56 to 60° northern latitude and 54 to 66° eastern longitude, was studied in terms of the deep crustal structure. The study was based on three-dimensional modeling of the sources of magnetic anomalies in three layers of the Earth’s crust. The studied area covers the folded region of the Urals and adjacent structures of the East European Platform and the West Siberian Plate. The sources modeled in the near-surface layer down to a depth of 5 km make it possible to clarify the position of magnetized massifs, mainly consisting of mafic-ultrabasic rocks, and to trace their connection with mafic-ultrabasic belts in the granite layer and root blocks in the lower basaltic layer of the Earth’s crust. When the sources in the upper crustal layer are compared with those in the lower crustal layer, it is apparent that many belts on the platform have deep-seated roots and are located above the basalt layer protrusions, while most of the massifs in the Urals do not have deep-seated roots. The springs located under the western slope of the Urals allow reliably determining the depth to the basement of the ancient platform and the location of the eastern border of the East European Platform in the lower layer of the Earth’s crust. There were found extended zones of subsidence of the roof of the lower magnetized layer, which probably mark the boundaries of various terrains forming the paleo-island arc sector of the Ural fold system. The most extensive subsidence of the roof of the lower layer occurs to the west of the Tyumen-Chudinovsky fault and is perhaps the eastern deep-seated dividing line between the Ural fold system and the West Siberian Plate.

Estimation of the coefficient of permeability as an example of the application of the Random Forest algorithm in Civil Engineering

A new world record for crude steel production was recorded in 2021, which increased by 3.8% over 2020. This also affected the amount of slag produced with this production. Total waste from industrial and construction production throughout the European Union accounts for as much as 48%. Therefore, waste management should provide for the recovery of as many resources as possible. European Union strategies in line with the circular economy objectives focus on ensuring policy coherence in the areas of climate, energy efficiency, construction and demolition waste management and resource efficiency. Slags are a material of interest to researchers in terms of their use in construction. Slags, on the one hand, are materials that are becoming better understood on the other hand, we are making sure of the heterogeneity of these materials. The characteristics of physical properties of slags are influenced by many factors, including the furnace split in which they are produced. This prompts the search for tools to help determine the parameters of slags based on already available data. The study aimed to verify the hypothesis that it is possible to determine the parameter of the filtration coefficient, relevant to applications in earth structures using the machine learning algorithm – Random Forest. In the study, two types of material were analysed: blast furnace slag and furnace slag. The results of the analysis yielded a high coefficient of determination (R2) – 0.84–0.92. This leads us to believe that the algorithm may prove useful in determining filtration parameters in slags.

Deep reinforcement learning for inverting earthquake focal mechanism and its potential application to marine earthquakes

Earthquake data are one of the key means by which to explore our planet. At a large scale, the layered structure of the Earth is revealed by the seismic waves of natural earthquakes that go deep into its inner core. At a local scale, seismology for exploration has successfully been employed to discover massive fossil energies. As the volume of recorded seismic data becomes greater, intelligent methods for processing such a volume of data are eagerly anticipated. In particular, earthquake focal mechanisms are important for assessing the severity of tsunamis, characterizing seismogenic faults, and investigating the stress perturbations that follow a major earthquake. Here, we report a novel deep reinforcement learning method for inverting the earthquake focal mechanism. Unlike more typical deep learning applications, which require a large training dataset, a deep reinforcement learning system learns by itself. We demonstrate the validity and efficacy of the proposed deep reinforcement learning method by applying it to the Mw 7.1 mainshock of the Ridgecrest earthquakes in southern California. In the foreseeable future, deep learning technologies may greatly contribute to our understanding of the oceanographic process. The proposed method may help us understand the mechanism of marine earthquakes.

Digital models of the deep structure of the Earth’s crust in the Eurasian Basin of the Arctic Ocean

Digital models of the deep structure of the Earth’s crust in the Eurasian Basin of the Arctic Ocean

Глубинное строение Среднего Урала по гравитационным и магнитным данным

For the Middle Urals and adjacent territories of the East European and West Siberian platforms within geographic coordinates from 56º to 60º northern latitude and from 54º to 66º east longitude, the structural features of the anomalous magnetic and gravitational fields were studied and maps of separated anomalies were constructed for three layers of the earth's crust. Using original parallel algorithms for solving forward and inverse problems of gravimetry and magnetometry, a density model of the lithosphere and sources of magnetic anomalies in the earth's crust were constructed. The results of modeling the sources of magnetic anomalies in the Earth's crust are compared with the density model in order to study the differences in the deep structure of the western paleocontinental and eastern paleo-island arc sectors of the Ural fold system, as well as the zones of junction of the orogen with the East European and West Siberian platforms.

Computation and analysis of surface wave dispersion and attenuation in layered viscoelastic-vertical transversely isotropic media by the generalized R/T coefficient method

SUMMARY In this study, we propose a systematic and effective method, that is, an extended version of the generalized reflection/transmission (R/T) coefficient method, for computing the phase-velocity (${c}_r$) dispersion curves, attenuation coefficient ($\alpha $) curves, and eigenfunctions of both Rayleigh and Love waves as well as the ellipticity of Rayleigh waves in layered viscoelastic-vertical transversely isotropic (VTI) media. The numerical scheme of combining the root-searching method with the local optimization method is designed for determining the complex-valued modal solutions (i.e. complex wavenumber $k = {\omega {/ {\vphantom {\omega {{c}_r - i\alpha }}}} {{c}_r - i\alpha }}$) of surface waves. The near-surface sedimentary geological environment is taken as the model example because it is typical viscoelastic-VTI media. Besides the anisotropic-viscoelastic (AV) media, our algorithm can also compute surface waves in isotropic-elastic (IE), isotropic-viscoelastic (IV) and anisotropic-elastic (AE) media by resetting the corresponding parameters. Using the six-layer half-space models and in these four media, we verify the correctness of our algorithm by benchmarking the modal solutions against those from other methods. In the four-layer half-space model, by comparing the results of IE, IV, AE and AV media, we analyse the effects of velocity anisotropy, viscoelasticity and attenuation anisotropy on the dispersion and attenuation characteristics of both Rayleigh and Love waves in detail. Our study can provide a theoretical basis and useful tool for surface wave imaging considering the anisotropy and/or viscoelasticity of the medium, which has the potential to better investigate the solid Earth's internal structure.

STABILZED RAMMED EARTH- A REVIEW

Rammed earth construction has gained prominence as a sustainable building technique due to its eco-friendly nature and aesthetic appeal. However, ensuring the long-term durability of rammed earth structures remains a critical challenge. This paper investigates the efficacy of incorporating stabilizers, including cement, bagasse ash, and glass fibers, to address these concerns and enhance the performance of rammed earth structures. Drawing upon extensive research and experimentation, the paper examines the impact of stabilizers on material composition, structural integrity, and long-term durability. Through comparative analysis and empirical studies, the effectiveness of various stabilizers in improving compressive strength and resistance to weathering is evaluated. The role of cement as a traditional stabilizer is scrutinized, alongside emerging alternatives such as bagasse ash, a byproduct of sugarcane processing, and innovative additives like glass fibers. Furthermore, the paper investigates the influence of stabilizer incorporation on construction practices and life cycle considerations. Key factors such as cost-effectiveness, sustainability, and compatibility with traditional rammed earth methods are analyzed to provide comprehensive guidance for practitioners and researchers. The findings highlight promising avenues for enhancing the durability and compressive strength of rammed earth structures through stabilizer utilization. Practical recommendations are offered for implementing these strategies in real-world construction projects, emphasizing the potential for innovation and sustainability in contemporary architectural practice. Keywords: · Stabilized Rammed Earth · Un-Stabilized Rammed Earth

Estimation of errors of the spectral method for measuring the concentration of water vapor and moisture reserves in the surface layer of the Earth’s atmosphere

A method for passive measurements of water vapor concentration in the atmosphere in the presence of solar radiation has been proposed and tested. The location of the measurements is the northeast of the Moscow region. When processing the results of measurements carried out on a single water absorption line, a coincidence of experimental data and data obtained from direct meteorological measurements with an error of no more than ~7.5 % was revealed. It was also found that on the water absorption line in the region of 1653 nm, the interfering factor is the nearby methane absorption line, which introduces a systematic error in the measurement results, and the results turn out to be underestimated. A possible reason is that the absorption cross section of methane molecules is ~4 orders of magnitude larger than that of water vapor molecules and light radiation is absorbed to a greater extent by methane, reducing the fraction of absorption of water vapor at a wavelength close to the methane absorption line. Compensatory corrections have been introduced to determine the concentration and moisture content in the atmospheric column with an accuracy of several percent at this wavelength. The proposed technique allows both long-term monitoring of concentration and moisture content in the atmosphere and obtaining operational information in real time. The results of the measurements performed are, on average, consistent with the results of measurements obtained using radiometers operating in the ultrahigh frequency range.

High pressure melt line of nickel using a generalized embedded atomic method potential

As the second most abundant metal in the Earth's core, nickel plays an important role in determining the structure and temperature of the Earth's core. Yet, the melt line of Ni at pressures corresponding to the Earth's core has not been explored in the literature. Many previous experimental and simulation efforts have reported the melting point of Ni at pressures below 100 GPa, but there exist large discrepancies, most of which have persisted due to various experimental and simulation bottlenecks in handling extreme pressure and temperature conditions. We adopted the generalized embedded atom method, which overcomes the limitations of existing interatomic potentials, to probe phase stability and phase boundaries of Ni at pressures between 50 and 500 GPa. The potential was validated by comparing the cold curves, phonon dispersion curves, and enthalpies of fusion with ab initio density functional theory calculations. Our analysis shows that face centered cubic (FCC) is stable, and the hexagonal close packed (HCP) and body centered cubic (BCC) phases are metastable close to the melt line. Melting temperatures at different pressures were obtained from two-phase co-existence simulations and take the following functional form: Tm=1969.23+19.15P−0.012P2. In contrast to iron, differences between the melting points of the stable and metastable phases of Ni are less than 250 K at 300 GPa, and the difference in melting points of the metastable BCC and HCP phases changes sign at 500 GPa, which implies that the phase transition mechanisms during solidification can be very complex.

Глибинні геологічні моделі району надглибокої cвердловини Saatly DW-1 на основі комплексу геофізичних даних

The purpose of the article is to study the reasons for the failure to achieve the scientific and geological goals set for the ultra-deep well DW-1, drilled in the Saatli region of Azerbaijan. The analysis will focus on the existing deep models built for this region, which are deemed insufficient in reflecting the truth. The paper highlights the importance of adopting a new approach to the recently created deep model and its potential benefits to the scientific community.Methodology. The technique includes a detailed comprehensive analysis of the gravitational and magnetic fields in this region, the use of local magnetic anomalies to build a model of the deep geological structure utilizing data from deep seismic sounding (DSS) and the correlation method of refracted waves (CMRW). Results. The spatial position of effusive formations in the geological section was determined using the local anomaly of the geomagnetic field in the Saatly region. At the same time, the geometric dimensions of the volcanic body were chosen in such a way that the magnetic field created by it corresponded to the observed local magnetic field. Thus, a model of the geological section up to a depth of 15 km was developed, with the display of the spatial position of the volcanic formation. In this model, unlike the previous one, the spatial position of the volcanic formation in the vertical geological section is completely different. In the newly constructed model, it turns out that there is a separate volcanic formation in the area of the Saatly DW-1. And in the previous models, it was shown that the magma came here from the Muradhanly zone, located at a distance of 25-30 km. The boundaries of the crystalline foundation and the basalt layer in the area of the DW-1 in the zone of the volcanic body are not traced. The root of the volcano narrows and goes deep into the earth. At a depth of about 15 km, the magma-producing channel has a width of 1 km. Based on the established model, it was determined that the ultra-deep well DW-1 is located on the magma-producing channel of the volcano that existed here. From the analysis of the obtained model data, it turns out that the extension of the Saatly DW-1 to depth will not allow opening the consolidated crust (crystalline foundation) and basalt layer. Because, although these layers are closer to the earth's surface in the area of the DW-1, the active volcano here has destroyed these boundaries. Orginality. Seismic survey materials were used to study the deep structures of the region, gravimagnetic data on profiles with an observation step of 250 m, and a technique was applied to construct the spatial positions of effusive formations in the geological section. Scientific novelty. It has been established that the geomagnetic field of this region is formed from three main effects - the effect of the sedimentary complex, the effect of the thickness between the basement and Curie surfaces, and the effect of local manifestations of magmatism. The sum of the first two effects quite accurately corresponds to the regional background of the observed geomagnetic field. Local positive anomalies isolated from the observed field are associated with local heterogeneities - in this region with volcanogenic formations in the sedimentary complex. Practical significance. A new geological-geophysical model was created by determining the spatial position of effusive formations in the geological section near the Saatly DW-1 well using the local anomaly of the geomagnetic field. This model has real possibilities in the direction of installation of ultra-deep wells for the study of deep layers of the earth's crust.

Space–time finite element method with domain reduction techniques for dynamic soil–structure interaction problems

AbstractDesign of earth structures, such as dams, tunnels, and embankments, against the vibrational loading caused by high‐speed trains, road traffic, underground explosions, and, more importantly, earthquake motion, demands solutions of the dynamic soil–structure Interaction (SSI) problem. This paper presents a velocity‐based space–time finite element procedure, v‐ST/finite element method (FEM), to solve dynamic SSI problems. The main goal of this study is to present the computation details of implementing viscous boundary conditions of Lysmer–Kuhlemeyer to truncate the unbounded soil domain. Furthermore, additional time‐dependent boundary conditions, in terms of the free‐field response, are included to facilitate energy flow from the far field to the computation domain at the vertical truncated boundaries. In the FEM, seismic input motion is applied to an effective nodal force vector, which can be obtained explicitly in the numerical simulations. Finally, the response of a concrete gravity dam resting on an elastic half‐space to the horizontal component of earthquake motion is computed and successfully compared with the results of semidiscrete FEM using the Newmark‐ method.

A 3D computational model for ground motion simulation in Peninsular India

Due to the gradual and constant accumulation of seismic energy, Peninsular India (PI) is typically considered seismically stable with low to moderate seismicity. The seismic studies in Peninsular India always resorted to synthetic ground motion simulations, because of the limited instrumentation and hence lack of recorded data. In the absence of a well-defined medium model for PI, the usual practice is to use simple site proxies or one-dimensional velocity structures for ground motion simulations. However, the region consists of multi-scale geometric complexities, significant topography, and sedimentary basins and is surrounded by deep oceans. Thus, the radiated seismic wave field in the region is influenced by the medium properties and in the absence of a well-defined tomography model the reliable estimation of seismic hazard is a challenging problem in PI. Therefore, the seismic wave propagation in PI can be investigated using numerical simulation with reliable 3D computational model for PI, incorporating the knowledge of the underlying Earth structure. Hence, the present study attempts to develop a sophisticated three-dimensional (3D) medium model of Peninsular India for physics-based ground motion simulations for regional earthquakes. This is aided by the availability of one-dimensional (1D) velocity models and the crustal structure from the receiver function analysis which provides valuable insight into the variation of material properties in the region. In the present study, >100 s of 1D velocity profiles are collected from various literature, which is then grouped under 23 different geological regions identified in PI (as per GSI (2000)). The averaged material properties are assigned per each geological region and the information on sediment depths, basin geometry, topography, and bathymetry are incorporated. We use the spectral element method (SEM) to calibrate our 3D computational model by simulating synthetic seismograms and comparing them to recorded ground motions for two past earthquakes: the 2001 Mw 7.6 Bhuj earthquake and the 1997 Mw 5.8 Jabalpur earthquake. Further, the seismic waveforms at the near field of 2001 Mw 7.6 Bhuj event are simulated using a refined regional model. The spatial variability of associated seismic intensities and peak ground velocity (PGV) amplification are investigated. In addition, a study of the impact of model depth truncation and sphericity on ground motion is also conducted. The implemented medium model is the first of its kind for Peninsular India and can reliably be used in seismic wave propagation studies in the region. The simulated outcomes from the model are of engineering importance as these results can be used for seismic hazard assessment of the region.

Er-Doped BiVO4/BiFeO3 Nanocomposites Synthesized via Sonochemical Process and Their Piezo-Photocatalytic Application.

In this work, Er-doped BiVO4/BiFeO3 composites are prepared using the sonochemical process with a difference of rare earth loading compositions. The crystallinity and chemical and morphological structure of as-synthesized samples were investigated via X-ray diffraction, Raman scattering, and electron microscopy, respectively. The diffuse reflectance technique was used to extract the optical property and calculate the optical band gap of the composite sample. The piezo-photocatalytic performance was evaluated according to the decomposition of a Rhodamine B organic compound. The decomposition of the organic compound was achieved under ultrasonic bath irradiation combined with light exposure. The Er-doped BiVO4/BiFeO3 composite heterojunction material exhibited significant enhancement of the piezo-photocatalytic activity under both ultrasonic and light irradiation due to the improvement in charge generation and separation. The result indicates that Er dopant strongly affects the phase transformation, change in morphology, and alternation in optical band gap of the BiVO4 matrix. The incorporation of BiFeO3 in the composite form with BiVO4 doped with 1%Er can improve the photocatalytic performance of BiVO4 via piezo-induced charge separation and charge recombination retardment.

Ab initio determination of melting and sound velocity of neon up to the deep interior of the Earth.

The thermophysical properties and elemental abundances of the noble gases in terrestrial materials can provide unique insights into the Earth's evolution and mantle dynamics. Here, we perform extensive abinitio molecular dynamics simulations to determine the melting temperature and sound velocity of neon up to 370GPa and 7500K to constrain its physical state and storage capacity, together with to reveal its implications for the deep interior of the Earth. It is found that solid neon can exist stably under the lower mantle and inner core conditions, and the abnormal melting of neon is not observed under the entire temperature (T) and pressure (P) region inside the Earth owing to its peculiar electronic structure, which is substantially distinct from other heavier noble gases. An inspection of the reduction for sound velocity along the Earth's geotherm evidences that neon can be used as a light element to account for the low-velocity anomaly and density deficit in the deep Earth. A comparison of the pair distribution functions and mean square displacements of MgSiO3-Ne and Fe-Ne alloys further reveals that MgSiO3 has a larger neon storage capacity than the liquid iron under the deep Earth condition, indicating that the lower mantle may be a natural deep noble gas storage reservoir. Our results provide valuable information for studying the fundamental behavior and phase transition of neon in a higher T-P regime, and further enhance our understanding for the interior structure and evolution processes inside the Earth.

Evaluation of natural radioactivity and radiological hazards in water sample of Tounsa Sharif, South Punjab, Pakistan

Radioactive material, especially Uranium, is very dangerous for human beings, creatures, and plants. It has been documented that the groundwater of the Dera Ghazi Khan Division in Punjab is contaminated with 238U. In this communication, the groundwater of the Tehsil Taunsa located at Indus River has been investigated. 144 samples of drinking water were collected from 48 villages/towns located in the area of about 500 km2 of the city. The samples were collected in the month of June, August and November, to concentrate on the temperature impact over the Uranium concentration. All samples were analyzed for 238U concentration using a fluorometric technique. The fluorometric technique was applied after pre-treatment of the sample. The analysis of the result revealed that groundwater obtained from this region contains a high value of 238U contents. Among the 48 trials, 26 samples were found below the permissible limit, while the remaining samples contained 238U contents above the permissible level. The sample collected from areas like, Qarim Wala, Jhoke Jamki, Basti peer, Tibi Qaisrani, Pehar Adda & Malana contained even up to the alarming level (30 μg l−1 to 54 μg l−1). In addition, it was observed that the sampling period had a significant effect on the contents, which were most prominent in June. This area being almost annually flooded by water from Rodh Kohi, who originated from Koh-e-Suleiman, may lead to such a high concentration of 238U. The additional reason could be the topographical and geological structure of the earth from which the samples were collected.

Morphological characteristics and relationship with spreading rates in Mid-Ocean ridges

Mid-ocean Ridges is where plate spreads, serving as a window to explore the interior earth and its dynamics. This research investigates the morphological characteristics of mid-ocean ridges and their relationship with spreading rates, magma activity, and magma supply. The study reveals that the morphology of mid-ocean ridges is closely related to the stability and adequacy of magma supply. Mid-ocean ridges with rapid spreading exhibit relatively stable and uniform crustal thickness, thus developing axial high and smoother morphology. While those with slow and ultra-slow spreading have a cold thermal structure and thick brittle/plastic layers where fluctuations between segments are obvious and deeper axial valley shapes within segment. Additionally, the slope variation of mid-ocean ridges is associated with fluctuations in magma activity, with regions of higher magma activity often having steeper slopes. The study also finds a positive correlation between slope and axial depth, with faster spreading rates corresponding to greater axial depth.

The KISS Network in 2015–2016: Catalogs and Comparison of the Processing Results with Operational Estimates from the Permanent Network

As part of the international collaboration of several research groups from Russia, France, and Germany, 77 temporary seismic stations were installed in the summer of 2015 for one-year period to conduct a detailed study of the deep structure of the Earth’s crust and upper mantle in the region of the Klyuchevskoi Volcano Group (KGV) in the Kamchatka Peninsula. One of the results of the KISS experiment (Klyuchevskoi Investigation – Seismic Structure of an extraordinary volcanic system) was the final catalog of the joint data from the temporary stations and the permanent network of the Kamchatka Branch of the Geophysical Survey of the Russian Academy of Sciences (KB GS RAS). The catalog comprises 2136 events, including 560 for which the permanent network catalog lacked sufficient data for correct processing. The catalog in .xlsx format and the station bulletin in .isf format are presented in the supplementary material to the paper. A comparative analysis was conducted on the joint solutions of two catalogs: one obtained solely from the data of the KB GS RAS permanent network stations and another from a denser seismic network integrated with KISS stations.

Research and Investigation of High Frequency Profile of Step and Touch Voltages Due to Fragmentation of the Grounding Grid

The increasing demand and the benefits of electricity energy have led to the creation of huge power plants, so high voltage substations are necessary for electrical energy. Installing different small power plants to prevent consumption in different parts of a country requires reservation units and high costs for repairs, maintenance and fueling. The necessity of these substations can be searched in the lack of uniformity of different costs, the costs of generating electrical energy, the lack of consumption centers near power plants, and generally the existence of a national grid and the possibility of timely disconnection of the faulty parts of the power grid. The priority in the rehabilitating of a strong substation is to meet the system's operation needs. In all electrical installations, especially in industrial complexes, land connectivity is one of the most important and fundamental measures to protect individuals and equipment and improve the performance of the system. The purpose of ground equipment system is to potentialize the metal body of all electrical equipment with the ground to prevent electrocution and protect personnel. This type of connection is not normally a current carrier, but if one of the phases of the device is connected to the fuselage, the fault current enters the ground through this connection and closes its path through the trans neutral or the generator connected to the ground. Earth networks due to different structures of the earth in different regions may cause problems over time, one of them is the fragmentation of the earth's network due to rot of conductors or due to overvoltage. In this research at different and high frequencies, we use 3 frequencies of 50, 100 kilos and 1 MHz, to check the ground network factors and the security of equipment and people in high voltage substations, we use CDEGS software which is a specialized program for designing and investigating the earth network. Objetivo: Research and investigation of high frequency, profile of step and touch voltajes of grounding grid. Metodología: Design and modeling with Comsol software. Resultados: As the frequency increases, both the step voltage and the touch voltage at the corner points increase more. Conclusiones: By comparing the voltage profiles based on the simulation results, it was found that by increasing the frequency of the contact voltage in each profile and mesh, it is noticeably increased. The point to consider after reviewing the simulation results is that by increasing the frequency of both step voltage and touch voltage in the corner points, they are more increased than other parts.

Benchmarking the accuracy of higher-order particle methods in geodynamic models of transient flow

Abstract. Numerical models are a powerful tool for investigating the dynamic processes in the interior of the Earth and other planets, but the reliability and predictive power of these discretized models depends on the numerical method as well as an accurate representation of material properties in space and time. In the specific context of geodynamic models, particle methods have been applied extensively because of their suitability for advection-dominated processes and have been used in applications such as tracking the composition of solid rock and melt in the Earth's mantle, fluids in lithospheric- and crustal-scale models, light elements in the liquid core, and deformation properties like accumulated finite strain or mineral grain size, along with many applications outside the Earth sciences. There have been significant benchmarking efforts to measure the accuracy and convergence behavior of particle methods, but these efforts have largely been limited to instantaneous solutions, or time-dependent models without analytical solutions. As a consequence, there is little understanding about the interplay of particle advection errors and errors introduced in the solution of the underlying transient, nonlinear flow equations. To address these limitations, we present two new dynamic benchmarks for transient Stokes flow with analytical solutions that allow us to quantify the accuracy of various advection methods in nonlinear flow. We use these benchmarks to measure the accuracy of our particle algorithm as implemented in the ASPECT geodynamic modeling software against commonly employed field methods and analytical solutions. In particular, we quantify if an algorithm that is higher-order accurate in time will allow for better overall model accuracy and verify that our algorithm reaches its intended optimal convergence rate. We then document that the observed increased accuracy of higher-order algorithms matters for geodynamic applications with an example of modeling small-scale convection underneath an oceanic plate and show that the predicted place and time of onset of small-scale convection depends significantly on the chosen particle advection method. Descriptions and implementations of our benchmarks are openly available and can be used to verify other advection algorithms. The availability of accurate, scalable, and efficient particle methods as part of the widely used open-source code ASPECT will allow geodynamicists to investigate complex time-dependent geodynamic processes such as elastic deformation, anisotropic fabric development, melt generation and migration, and grain damage.

Earth's core-mantle boundary shaped by the crystallization of a hydrous terrestrial magma ocean.

Enigmatic anomalous structures of Earth's lowermost mantle may have been incubated at the hydrous magma ocean of the Hadean eon.