Geodynamic Problems Research Articles

Estimating the effective elastic thickness of the Arctic lithosphere using the wavelet coherence method: Tectonic implications

Currently, knowledge of structure and tectonic evolution of the Arctic lithosphere remains limited. The effective elastic thickness of the lithosphere (Te) is a parameter that describes the lithospheric integrated strength and reflects its thermal and rheological properties, which helps to reveal intraplate tectonic process. In this study, we present a high-resolution Te model in the Arctic region (north of 67°N), which is highly heterogeneous and strongly correlated with various regional tectonic elements. To verify the recovered Te, its pattern is compared to those obtained in previous studies that used different methods and to available heat flow measurements and seismic velocity model and shows good agreement. High Te values are found in the Greenland shield, North American craton and Siberian craton, which are compatible with results from previous studies of high seismic velocity and low heat flow, suggesting that cold, thick lithosphere remains tectonically undisturbed. Low Te values occur in the Amerasia Basin, Baffin Bay, Eurasia Basin and North Atlantic Ocean where young oceanic lithosphere is created. Moreover, the areas affected by regional volcanism in the Siberian Traps and HALIP are dominated by reductions in Te, which we attribute to thermal rejuvenation triggered by the intrusion of magma. Weak lithosphere also dominates in tectonically active orogens as well, including the Alaska-Chukotka, Novaya Zemlya and Caledonides, and is related to the stress released during collisional deformation. We find that a few deep sedimentary basins are characterized by intermediate Te, which implies mechanical support of the surface sediment loads in a non-isostatic state. Our new Te model provides potentially significant insights into various tectonic and geodynamic problems of the Arctic lithosphere.

DETERMINATION OF THE VERTICAL GRADIENT OF GRAVITY FROM GRAVITY ANOMALIES

In connection with the need to use the vertical gradient in the processing of the results of gravimetric measurements and their interpretation when solving problems of geology, geophysics, geodesy, geodynamics and navigation, in addition to the urgent problems of improvement, socalled indirect methods of measuring the vertical gradient, there is an equally urgent task of developing methods for determining the vertical gradient of gravity, using dependencies between different physical fields. The article presents the development and study of a method for determining the vertical gradient from gravity anomalies using the relationship between gravity anomalies and altitude based on field data obtained in the area of the Tashtagol field on Mount Boulanger in 2019 and 2020.

An Exactly Mass Conserving and Pointwise Divergence Free Velocity Method: Application to Compositional Buoyancy Driven Flow Problems in Geodynamics

AbstractTracer methods are widespread in computational geodynamics for modeling the advection of chemical data. However, they present certain numerical challenges, especially when used over long periods of simulation time. We address two of these in this work: the necessity for mass conservation of chemical composition fields and the need for the velocity field to be pointwise divergence free to avoid gaps in tracer coverage. We do this by implementing the hybrid discontinuous Galerkin (HDG) finite element (FE) method combined with a mass conserving constrained projection of the tracer data. To demonstrate the efficacy of this system, we compare it to other common FE formulations of the Stokes system and projections of the chemical composition. We provide a reference of the numerical properties and error convergence rates which should be observed by using these various discretization schemes. This serves as a tool for verification of existing or new implementations. We summarize these data in a reproduction of a published Rayleigh‐Taylor instability benchmark, demonstrating the importance of careful choices of appropriate and compatible discretization methods for all aspects of geodynamics simulations.

Methods for interpreting grace system data for solving geodynamic monitoring problems

The study is devoted to a detailed analysis of observational data from the GRACE space system to clarify the parameters of a catastrophic earthquake with a magnitude of MW = 8.8, which occurred in the subduction zone near the coast of Chile. Digital maps of changes in the EWH parameter over the geoid contour in the investigated seismically active region of the Chilean earthquakes of 2014 and 2015 were constructed. It is shown that there is a negative correlation between the value of the geodynamic parameter H for a strong earthquake with M W = 8.8 (distance from the hypocenter to the position of the Earth-Moon barycenter) and the equivalent water height above the geoid EWH. The highest correlation coefficient between the parameters H and EWH equal to R = -0.61 was noted during the period of registration of the number of postseismic events in the region of Central Chile. In the course of further research study the representative class of earthquakes for a detailed analysis of the variability of the EWH parameter and its relationship with geodynamic processes.

ОЦЕНКА ТЕМПЕРАТУРНОГО ШУМА СВОБОДНОЙ ТЕПЛОВОЙ КОНВЕКЦИИ В ВОДОНАПОЛНЕННЫХ БУРОВЫХ СКВАЖИНАХ ПО ЭКСПЕРИМЕНТАЛЬНЫМ ДАННЫМ

Актуальность. Температурные исследования в скважинах используются для решения широкого круга разведочных, промыслово-геофизических, экологических, гидрогеологических, геодинамических задач. Появление новых температурных датчиков и систем регистрации существенно расширяет возможности скважинной термометрии, одновременно предъявляя повышенные требования к точности измерений, которые часто не могут быть удовлетворены в реальных скважинных условиях вследствие влияния температурного шума, вызываемого свободной тепловой конвекцией жидкости. Эффективное планирование аппаратуры и методик температурных измерений в скважинах требует оценки амплитуды температурного шума. Цель: обоснование математических моделей, позволяющих оценивать уровень температурного шума, вызываемого свободной тепловой конвекцией. Методы: статистический анализ данных, полученных с помощью лабораторных экспериментов, в ходе температурного каротажа и мониторинга температуры в реальных скважинах. Результаты. Обоснован оптимальный параметр оценки уровня температурного шума – среднеквадратическое отклонение температурных колебаний. Разработаны модели различной сложности, позволяющие оценивать амплитуду конвективного шума в зависимости от геотермического градиента, внутреннего радиуса скважины и числа Рэлея. Предложенные модели позволяют более эффективно обосновать выбор аппаратуры и методики температурного каротажа и температурного мониторинга скважин в зависимости от соотношения «полезный сигнал/температурный шум».

Optimized approximate inverse Laplace transform for geo-deformation computation in viscoelastic Earth model

SUMMARY Integral transformations, especially the inverse Laplace transform, are powerful techniques for resolving a wide range of geophysical and geodynamic simulation problems in viscoelastic materials. The exact location or distribution range of poles of the image function in a complex plane is usually necessary for applying numerical algorithms such as contour integration. Unfortunately, there are innumerable poles (such as those of post-seismic deformations) in a realistic Earth model with continuous stratification, finite compressibility and self-gravitation. Here, an optimized method to effectively calculate the inverse Laplace transform is presented. First, the integral kernel is approximated as a rational function with two parameters (a and m). Thereafter, the residue theorem is analytically applied to the approximated integrand. Finally, a series formula of the inverse Laplace transform sampling of image functions along a contour line parallel to the image axis is obtained. The proposed approximate scheme of the inverse Laplace transform is discussed by some common geophysical signals and the optimized selection of two parameters (a = 6 and m = 4) is conducted after a detailed analysis. The proposed method is anticipated as being able to help performing certain theoretical studies related to geodynamic problems with viscoelastic deformations.

Використання геоінформаційних технологій для дослідження зсувних процесів

Виконано аналіз методів дослідження динаміки зсувних процесів. Проаналізовано причини виникнення зсувів, основними з яких є перезволоження ґрунту та збільшення навантаження на схил внаслідок забудови схилу та руху транспорту. Визначено роль рельєфу та його геоморфологічного стану у формуванні зсувів. Описано методи боротьби зі зсувами. Проаналізовано наявні методи спостережень на зсувних схилах, які забезпечують вирішення завдань із вивчення механізму та динаміки зсувного процесу. Виконано опис геодезичних методів дослідження зсувів, які передбачають створення геодезичної основи на зсувонебезпечних схилах, закріплення геодезичної основи спеціальними марками та періодичні вимірювання їх координат і висот високоточними електронними геодезичними приладами, ГНСС-приймачами. Запропоновано визначати просторово-часові характеристики зсувів геоінформаційними методами. За даними топографічного знімання з допомогою пакету програм Surfer створено тривимірну цифрову модель зсувного схилу та карту крутизни схилу. За даними зміщень геодезичних марок між двома циклами спостережень створено карти ізозміщень ґрунту по висоті та визначено межі зсуву. За геологічними даними складено карту ізопотужностей зсувного тіла, яка дає змогу визначити його об'єм. За даними повторних вимірювань створено карту швидкостей зсуву. Порівняння даних з різних циклів дає змогу проаналізувати динаміку зсувного процесу, розробити прогноз його розвитку та запроектувати відповідні протизсувні заходи. Запропоновано застосовувати геоінформаційні технології для створення просторово-часових моделей зсувних процесів. Розроблені карти є основою для створення інших геодинамічних карт: суміщених карт горизонтальних та вертикальних ізозміщень, карт прискорень ізозміщень та ін. Разом вони формують банк даних інформації, що дає змогу здійснювати ефективний моніторинг зсувних процесів.

Analysis of the results of the surveying and geodetic observations at the Pyt-Yakh geodynamic site

The article is devoted to a generalization of the obtained empirical material on modern geodeformation processes. For this, we used the basic methods of analysis and interpretation of the received information. In addition, we show the possibility of using the results of geodynamic monitoring in order to ensure industrial safety of urban development facilities in Pyt-Yakh from the harmful effects of the development of the Mamontovskoye oil field. The main conceptual scheme of interpretation of the obtained data is reduced to solving the inverse problems of modern fault geodynamics and identifying the sources of formation of local anomalies of stress-strain state of the subsoil. Geometric leveling of class II accuracy, high-precision satellite observations, high-precision gravimetry and satellite radar interferometry were used as the main methods of analysis.

Small shaking table testing and numerical analysis of free-field site response and soil-structure oscillation under seismic loading

In this study, the accuracy level of geometric scaling factor (herein, λ = 45) selected for the shaking table test model represents the actual site conditions as discussed by comparing the results of both experimental data and numerical analysis obtained from the soil-structure oscillation and free-field response under seismic loads. The difficulty to be overcome in this experimental campaign was to investigate the limited soil size considered for this complex geodynamic problem due to the small capacity of the shaking table having payload of 2.5 kN and the geometry of testing platform of 1 m × 1 m, respectively. The superstructure used in the analysis of the soil-structure interaction is specified as six story building structure with height of 30 m resting on a silty sand soil with a shear wave velocity of 536 m/s. Within the frame of this work, the underlying soil is handled as a homogeneous single layer on the top of rigid bedrock. The diameter of the ground specimen and the bedrock depth were considered to be 26.23 m and 10 m, respectively. Special cylindrical flexible testing equipment was designed to hold the excavated soil volume in the container without deforming the experimental setup. In order to examine the seismic responses at the control points of the scaled test models under the nonlinear supporting effects, 2-D finite element analyses of the soil-structure system have been executed by using the PLAXIS simulation program. It is obviously seen that the soil layer parameters have significantly increased the free-field site response compared with the bedrock response under different seismic excitations. Based on the comparison of calculated results with experimental recordings, it is suitable to mention that small capacity shaking table experiments with appropriate scaled test models provides an alternative means of laboratory investigations even for such complex soil-structure coupling problems.

Comprehensive Assessment of the Geoecological Situation of Mining Areas (on the Example of Solikam Urban District)

The methods for the complex assessment of the geoenviromental situation in a mining region based on the integration of open data from the ROSREESTR (The Federal Service For State Registration, Cadastre And Cartography), the ROSPRIRODNADZOR (Federal Service for Supervision of Natural Resources), Google Earth, scientific publications and other sources, in particular, related to the analysis of neotectonic and geodynamic problems in the region are considered. The conclusions are made as a result of the analysis of the geoenviromental situation on the example of the Solikamsk urban district and the recommendations are proposed: a land management program and the formation of geoecological data in the Unified State Register of Real Estate quarters (polluted, degraded and disturbed lands) - as an information basis for the regional model of spatial planning of mining regions.

Inertial modes of an Earth model with a compressible fluid core and elastic mantle and inner core

We use the linear momentum description (LMD) of the dynamics of the Earth in order to investigate the effects of mantle and inner core elasticity on the frequencies of some of the inertial modes of a spherical Earth model with a liquid core. Traditionally, a liquid core with rigid boundaries is considered to study these modes. A Galerkin method is applied to solve the linear momentum and the Poisson’s equations with the relevant boundary conditions at the interfaces. To test the validity of our method, we compute the periods of some of the Earth’s other normal modes such as the Slichter modes and the spheroidal modes and compare the results with the predicted and observed (when available) values in the literature. We show that the computed dimensionless frequencies [$$\omega /(2\varOmega $$)] of the inertial modes may be significantly affected by the elasticity of the mantle and inner core. For example, the frequencies of the (2,1,1), also known as the spin-over mode (SOM), (4,1,1), (4,2,1) and (4,3,1) modes are changed from 0.5000, $$- 0.4100$$, 0.3060 and 0.8540 for a Poincare model to 0.4995, $$- 0.4208$$, 0.3150 and 0.8587, respectively. The change in the frequency of the SOM may seem small, but it is consistent with the change in the frequency of the free-core nutation, which is the same mode as the SOM of a wobbling Earth, which changes from $$\approx 0.50144$$ for an Earth model with rigid mantle and inner core to $$\approx 0.50116$$ for an elastic Earth model. We will show that a great advantage of this method is that we ensure that the frequencies are converged and that it may be generalized to solve other problems in geodynamics including the study of the Earth’s free and forced nutation/wobble.

Plate-plume tectonics as an integrated mechanism of geodynamic development of the tectonosphere of Ukraine and adjacent regions

A progress of geodynamic processes in Early Precambrian of the Ukrainian Shield (USh) has been considered. Based on the known data on plate- and plume-tectonic processes of Phanerozoic the following problems have been investigated: 1) what trajectories of material flows in Precambrian mantle might occur; 2) what was an interaction of plumes and regular mantle convection; 3) the time of existence of plumes and are they permanent or pulsating; 4) the time of beginning of Precambrian geodynamic processes comparable with Phanerozoic ones. It has been shown taking as examples the Ukrainian and the Canadian shields that present-day thermochemical and dynamic processes do not completely delete geological-geophysical features of ancient zones of subduction and plumes in solid lithosphere and adjacent areas of mesosphere preserved since Early Precambrian. The Earth crust of these shields was intensely reprocessed by granitization and basification comparable with activity of hot points that were more developed than now. Within the area of USh these processes were the most active in the interval 2,0±0,2 Ga. Two of stages of geodynamic evolution of the USh within the limits of the Bug-Middle Dnieper-Periazov and Volyn-Podolian parts, superimposed in time, have been studied. Comparison of materials of geologic-geophysical mapping of this territory with the data of deep seismic sounding (DSS) and seismography allows refining geodynamic model of the Volyn-Podolian part of the USh along the trans-sect Eurobridge-97 composed earlier. Tectonophysical justification of necessity to include pulsating plumes with which formation of the Korsun-Novomyrgorod and Korosten plutons of gabbro -anorthosites and rapakivi was particularly associated to geodynamic process has been given. Comparison of models of subduction-collision processes within the limits of the USh and the Superior Province (Canada) has shown that independent approaches to solving geodynamic problems give relative results. The materials obtained on the USh do not exhaust all the possible episodes of its Neoarhean –Proterozoic geodynamic development. Trailing of super-modern DSS geo-travers along the axial part of the USh is required for their study.

Exact formula for the horizontal-to-vertical displacement ratio of Rayleigh waves in layered orthotropic half-spaces.

This paper is concerned with the propagation of Rayleigh waves in a compressible orthotropic half-space coated by a compressible orthotropic layer. The main purpose of the paper is to establish an explicit exact formula for the H/V ratio (the horizontal-to-vertical displacement ratio) of the Rayleigh wave. This formula is derived by using the transfer matrix for an orthotropic elastic layer and by the effective boundary condition technique. The formula recovers the H/V formula by Malischewsky and Scherbaum [(2004). Wave Motion 40, 57-67] for the compressible isotropic case and the H/V formula by Love [(1911). Some Problems of Geodynamics (Cambridge University Press, Cambridge)] for the incompressible isotropic case. The effect of anisotropy on the H/V ratio's properties is examined and it is numerically shown that the anisotropy strongly affects the peak and zero frequency of the H/V ratio and its prograde domain as well. As the H/V ratio is a dimensionless quantity and it is easily experimentally measured, the obtained formula will be a useful tool for the nondestructive evaluation of mechanical properties of thin films deposited onto half-spaces. Two numerical examples are performed to show how the obtained formula can be used to extract the material properties of deposited layers from measured values of the H/V ratio.

Ocean bottom geophysical array studies may reveal the cause of seafloor flattening

Flattening of old seafloor as a result of the time evolution of oceanic lithosphere and asthenosphere has been studied for several decades and remains one of the unresolved fundamental problems of geodynamics. The phenomenon of seafloor flattening at ages greater than 70-80 Ma can be explained by a simple model of a cooling plate with a fixed thickness, but the physical cause of flattening is not fully understood. Here, a simple model of lithosphere rejuvenation is considered as an alternative mechanism and is also shown to represent similar features of seafloor flattening. We suggest that constraints on mantle structure from use of data such as variations of seafloor depth and heat flow are weak, but that first order differences in mantle thermal structure are introduced by these two models. This suggests that probing of the mantle by geophysical arrays on the seafloor, particularly those sensitive to mantle temperature such as magnetotelluric imaging, should be able to constrain the cause of seafloor flattening. In the present study, recent results of seafloor electromagnetic explorations are compiled and estimated depths to the high conductivity layer (HCL) are used as a proxy for 1,300°C isotherm depths. For the data obtained at sites well away from plate boundaries in the Pacific Ocean, a model of lithosphere rejuvenation was found to better explain the correlation between HCL depths and seafloor depths than a standard plate cooling model.

Efficient and practical Newton solvers for non-linear Stokes systems in geodynamic problems

Many problems in geodynamic modelling result in a non-linear Stokes problem in which the viscosity depends on the strain rate and pressure (in addition to other variables). After discretization, the resulting non-linear system is most commonly solved using a Picard fixedpoint iteration. However, it is well understood that Newton's method - when augmented by globalization strategies to ensure convergence even from points far from the solution - can be substantially more efficient and accurate than a Picard solver. In this contribution, we evaluate how a straightforward Newton method must be modified to allow for the kinds of rheologies common in geodynamics. Specifically, we show that the Newton step is not actually well posed for strain rate-weakening models without modifications to the Newton matrix. We derive modifications that guarantee well posedness and that also allow for efficient solution strategies by ensuring that the top left block of the Newton matrix is symmetric and positive definite.We demonstrate the applicability and relevance of thesemodifications with a sequence of benchmarks and a test case of realistic complexity.

UWGeodynamics: A teaching and research tool for numerical geodynamic modelling

The UWGeodynamics module facilitates development of 2D and 3D thermo-mechanical geodynamic models (Subduction, Rift, Passive Margins, Orogenic systems etc.). It is designed to be used for research and teaching, and combined the flexibility of the Under- world Application Programming Interface, (Moresi, Dufour, & Muhlhaus, 2002, Moresi, Dufour, & Muhlhaus (2003), Moresi et al. (2007)) with a structured workflow. Designing geodynamic numerical models can be a daunting task which often requires good understanding of the numerical code. UWGeodynamics provides a simple interface with examples to get you started with development of numerical models. Users can start designing their models without any pre-existing knowledge of programming. Expert users can easily modify the framework and adapt it to more specific needs. The code can be run in parallel on multiple CPUs on personal computers and/or High Performance Computing systems. Although UWGeodynamics has been primarily designed to address geodynamic problems, it can also be used to teach fluid dynamics and material mechanics. UWGeodynamics uses the flexibility of the Python language and the Jupyter Notebook environment, which allows leveraging the wide range of scientific libraries available from the Python community. It also facilitates the coupling with existing scientific Python modules such as Badlands (Salles, Ding, & Brocard, 2018). The functionalities include: • Dimensional input values, using user’s choice of physical units. • Automated and transparent scaling of dimensional values. • Sets of predefined geometries that can be combined to define the initial geometry of a model. • Handles Newtonian and non-Newtonian rheologies (Viscous, Visco-plastic and Visco-elasto-plastic). • Database of common rheologies used in geodynamics, which can be personalised / extended by users. • Simple definition of kinematic, stress, and thermal boundary conditions. • Lithostatic pressure calculation • Thermal equilibrium (steady-state) calculation. • Pseudo Isostasy using a range of kinematic or stress boundary conditions. • Partial melt calculation and associated change in viscosity / heat production. • Simple definition of passive tracers and grid of tracers. • Simple Phase changes • 2-way coupling with the surface processes model pyBadlands (Salles et al., 2018). UWGeo comes with a series of examples, benchmarks and tutorial setups that can be used as cookbook recipes. They provide a wide range of teaching materials useful to introduce numerical geodynamic modeling to students. New functionalities are constantly being added to the code and contributions are more than welcomed. You can access the full documentation online at https://uwgeodynamics. readthedocs.io

Problems of global geodynamics

Global geodynamics is determined by thermal convection in the mantle which manifests itself on the surface by movements, relief, heat flow, and volcanism. Thermal convection in the Earth is complicated by the fact that the lithosphere is broken into rigid plates, the crust is broken into six separate floating continents and a number of islands, on the mantle bottom there are two giant piles of heavy material, at high convection intensity the ascending convective flows acquire a plume shape, and phase transformations take place in the mantle. The impacts of many factors on the mantle structure have been thoroughly studied and fairly well understood. It is pertinent to reconcile the new data on phase transformations at depths of 650 to 700 km with the seismic data on the positions of these boundaries. The ultimate problem of global geodynamics has not yet been solved; the three-dimensional structure of the whole-mantle flows, consistent with the observations in geophysics, geochemistry, geology, and numerical modeling, is not known even on a semischematic level.

Эволюционные уравнения и случайные графы

На примере эволюции случайного графа обсуждается подход к стохастической динамике сложных систем на основе эволюционных уравнений. Для случая графа эти уравнения описывают временные изменения в структуре графа, связанные с процессом случайного добавления в него новых связей. Такой процесс тесно связан с коалесценцией отдельных неприводимых компонент графа и ведет к появлению сингулярностей в спектрах и их моментах в течение конечных промежутков времени. Эти сингулярности возникают вследствие появления гигантской связной компоненты, порядок которой сравним с полным порядком всего графа. В работе демонстрируется метод анализа динамики процесса эволюции случайного графа, основанный на точном решении эволюционного уравнения, которое описывает зависимость от времени производящего функционала для вероятности застать в системе заданное распределение связных компонент графа. Дан вывод нелинейного интегрального уравнения для производящей функции распределения по числу связных компонент и обрисованы методы его анализа. В заключительной части обсуждены возможности применения изложенного подхода для решения ряда эволюционных проблем статистической геодинамики.

The application of geologically-constrained 3D heat conduction models to geothermal exploration

Renewed interest in the thermal structure of the upper crust has led to the development of a new generation of tools capable of modelling the 3D heat conduction problem, incorporating the complex geology and physical properties of the crust. The numerical and resolution requirements of such models has necessitated a high performance performance computing approach, utilising massively parallel machine architecture to obtain ~10m resolution of models over a basin-scale. Here we demonstrate the application of the StGermain/Underworld geodynamic modelling framework to basin-scale geodynamic problems. The default code has been modified to incorporate importing of geometrically complex geological units, each with its own conductivity and heat production, and temperaturedependent thermal conductivity. Thermal models demonstrate the importance of incorporating 2 & 3D geometries, with large lateral variations in the subsurface temperature field and heat flow as a result of the heterogenous basin architecture. We explore the effect of lithological resolution, and identify a critical level of detail required to adequately represent basin-scale temperature variations. The regional temperature field play a dominant role in determining tenement-level subsurface temperatures, and highlight the importance of understanding regional temperature variations in geothermal exploration.

Use of the program and goal-oriented approach to observe the vertical displacements of the earth’s surface in Russia

The paper considers the problematic issues of the special aspects of solution of the problems of modern geodynamics and technogenic geomechanics in oil and gas fields based on the results of re-levelling. The disadvantages and fundamental errors traditionally made by mining and land surveyors in organizing and performing re-levelling on the territories of oil and gas fields are given. The results of high precision levelling, obtained on the territory of an oil and gas field using the program and goal-oriented approach for its formulation, are presented. The representativeness and sufficient accuracy of obtaining the results of re-levelling allowed us to establish significant speeds of geodynamic and technogenic displacements of the earth’s surface (0.4 - 3.6 mm/year) in the shortest time possible with high economic efficiency.