Gravity Anomalies, Fault Tectonics and Seismicity of the Terek-Caspian Trough

При изучении геологического строения глубокопогруженных нефтегазоперспективных горизонтов и изучении современной геодинамики Терско-Каспийского прогиба (ТКП) весьма актуальным является уточнение пространственного положения существующих и выделение новых разломных структур. Пространственное положение разломов устанавливается по комплексу геолого-геофизических критериев, причем геофизические признаки являются преобладающими. Цель. На основании карты аномалий силы тяжести масштаба 1:200 000 и карты магнитного поля масштабов 1:200 000 и 1:500 000 были созданы цифровые модели гравитационного и магнитного полей и составлена схема аномального гравитационного поля (Δga) западной части ТКП. Электронная база сейсмологической информации была составлена на основе сведений об исторических и инструментальных землетрясениях (1950–2020 гг.), а также макросейсмических данных. Методы работы. Трансформация исходного аномального гравитационного поля выполнена путем расчета вектора горизонтального градиента Wsz и третьей вертикальной производной Wzzz потенциала силы тяжести, с использованием компьютерной программы, реализующей метод F-аппроксимации, основанный на представлении потенциала аномального гравитационного и магнитного полей интегралом Фурье. Для анализа сейсмичности выполнен расчет сейсмической активности А10 по формуле Ю.В. Ризниченко с использованием компьютерной программы, реализующей способ суммирования с постоянной детальностью, основанный на суммировании числа землетрясений всех энергетических классов больше минимального представительного в фиксированной зоне осреднения. Результаты работы и обсуждение. По результатам обработки и интерпретации геофизических данных построена серия тематических карт по территории ТКП: карты вектора горизонтального градиента Wsz и третьей вертикальной производной Wzzz потенциала силы тяжести; карта сейсмической активности А10. На основе анализа полученных данных с привлечением существующей геологической информации уточнено положение известных разломов и выделены новые, по итогам исследований составлена карта разломов западной части ТКП When studying the geological structure of deeply submerged oil and gas promising horizons and studying the modern geodynamics of the Terek-Caspian trough (TCT), it is very important to clarify the spatial position of the existing fault structures and identify new ones. To determine the spatial position of the faults, a set of geological and geophysical criteria is established, with geophysical features prevailing. Aim. Based on the gravity anomaly map of scale 1: 200,000 and magnetic field maps of scales 1: 200,000 and 1: 500,000, digital models of gravitational and magnetic fields were created and a diagram of the anomalous gravitational field (Δga) of the western part of the TCT was drawn. The electronic database of seismological information was compiled on the basis of information about historical and instrumental earthquakes (1950–2020), as well as macroseismic data. Methods. The transformation of the initial anomalous gravitational field is performed by calculating the horizontal gradient vector Wszand the third vertical derivative Wzzzof the gravity potential using a computer program that implements the F-approximation method based on the representation of the potential of the anomalous gravitational and magnetic fields by the Fourier integral. To analyze the seismicity, the seismic activity А10 was calculated according to the formula of Yu.V. Riznichenko using a computer program that implements the summation method with constant detail, based on the summation of the number of earthquakes of all energy classes greater than the minimum representative in a fixed averaging zone. Results and discussion. Based on the results of processing and interpretation of geophysical data, a set of thematic maps was built for the TCT territory. This set includes maps of the horizontal gradient vector Wsz and the third vertical derivative Wzzz of the gravity potential; seismic activity map А10. Based on the analysis of the data obtained with the involvement of existing geological information, the position of the known faults was clarified and new ones were identified, based on the results of the research, a map of the faults for the western part of the TCT was compiled

Design and Efficiency Analysis of Closed Loop Pump Controlled Circuit Hydraulic Lifting System of Wheel Loaders Based on Gravity Self-Balancing Hydraulic Cylinder

In the hydraulic lifting systems of wheel loaders, the valve controlled systems are used to drive the hydraulic cylinder to complete frequent lifting and falling operations. The gravitational potential energy of the lifting system, accumulated in the lifting process, is converted into heat energy through the throttling port of the valve during the falling processes, which results in significant throttling loss and severe system overheating. To solve the problems, a potential energy regeneration and utilization system is proposed, where the closed loop pump controlled circuit based on the gravity self-balancing hydraulic cylinder is adopted to eliminate throttling loss, and the gravity self-balancing chamber of the cylinder is directly connected with accumulator to recycle gravity potential energy. In the research, the structure and working principle of the proposed hydraulic system is analyzed first, then the co-simulation model and the test prototype are established to investigate the working and energy characteristics of the proposed system. Test results indicate that, compared with the traditional valve controlled hydraulic system, 58.9% energy consumption reduction can be expected for the hydraulic pump by adopting the proposed system under the same working condition.

A Calculation Method of Magnetic Anomaly Field Distribution of Ellipsoid with Arbitrary Posture

The ellipsoidal magnetization model has a wide range of application scenarios. For example, in aviation magnetic field prospecting, mineral prospecting, seabed prospecting, and UXO (unexploded ordnance) detection. However, because the existing ellipsoid magnetization formula is relatively complicated, the detection model is usually replaced by a dipole. Such a model increases the error probability and poses a significant challenge for subsequent imaging and pattern recognition. Based on the distribution of ellipsoid gravity potential and magnetic potential, the magnetic anomaly field distribution equation generated by the ellipsoid is deduced by changing the aspect ratio, making the ellipsoid equivalent to a sphere. The result of formula derivation shows that the two magnetic anomaly fields are consistent. This paper uses COMSOL finite element software to model UXO, ellipsoids, and spheres and analyzes magnetic anomalies. The conclusion shows that the ellipsoid model can completely replace the UXO model when the error range of 1nT is satisfied. Finally, we established two sets of ellipsoids and calculated the magnetic anomalous field distributions on different planes using deduction formulas and finite element software. We compared the experimental results and found that the relative error of the two sets of data was within [Formula: see text]‰. Error analysis found that the error distribution is standardized and conforms to the normal distribution. The above mathematical analysis and finite element simulation prove that the calculation method is simple and reliable and provides a magnetic field distribution equation for subsequent UXO inversion.

A New Analysis of Caldera Unrest through the Integration of Geophysical Data and FEM Modeling: The Long Valley Caldera Case Study

The Long Valley Caldera, located at the eastern edge of the Sierra Nevada range in California, has been in a state of unrest since the late 1970s. Seismic, gravity and geodetic data strongly suggest that the source of unrest is an intrusion beneath the caldera resurgent dome. However, it is not clear yet if the main contribution to the deformation comes from pulses of ascending high-pressure hydrothermal fluids or low viscosity magmatic melts. To characterize the nature of the intrusion, we developed a 3D finite element model which includes topography and crust heterogeneities. We first performed joint numerical inversions of uplift and Electronic Distance Measurement baseline length change data, collected during the period 1985–1999, to infer the deformation-source size, position, and overpressure. Successively, we used this information to refine the source overpressure estimation, compute the gravity potential and infer the intrusion density from the inversion of deformation and gravity data collected in 1982–1998. The deformation source is located beneath the resurgent dome, at a depth of 7.5 ± 0.5 km and a volume change of 0.21 ± 0.04 km3. We assumed a rhyolite compressibility of 0.026 ± 0.0011 GPa−1 (volume fraction of water between 0% and 30%) and estimated a reservoir compressibility of 0.147 ± 0.037 GPa−1. We obtained a density of 1856 ± 72 kg/m3. This density is consistent with a rhyolite melt, with 20% to 30% of dissolved hydrothermal fluids.

Density contrast, deep structure, rheology and metallogeny of the crust and upper mantle of the Verkhoyano-Kolymsky region

Research subject. The Verkhoyano-Kolymsky areal of ore mineralization in the Far East of Russia.Data and methods. We used the state metallogenic map of Russia, Sc. 1: 2 500 000 (2000) and the gravity map of Russia Sc. 1: 2 500 000 (2001). Modeling was conducted by studying the deep structure of the earth’s crust and upper mantle from the anomalies of the density contrast of geological media in the intervals between the centers of density inhomogeneities and the surfaces of equivalent spheres.Results. 3D-distributions of density contrast (µz-parameter) in the crust and upper mantle of the Verkhoyano-Kolymsky region related to the rheological properties of geological media were analyzed. In the gravity models designed without attraction of external information, the structures of thrust, splitting, stretching, as well as the structures of central type (CTS) of the plume nature, were identified. In the regional stretching zone, at the border of lithospheric segments, the revealed Indigiro-Kolymsky and Verkhoyansk CTSs were described in 3D space. These structures are characterized by a mushroom-like upwelling of the asthenosphere, associated with heat flow anomalies. The identified structures differ in terms of asthenosphere depth, age and ore mineralization. The location of ore clusters and regions in the zones of CTS obeys concentric ore-magmatic zoning, typical for this type of structures. The central (trunk-like) zone of Indigiro-Kolymsky CTS features mainly high-temperature gold-quarts mineralization. On the periphery, along with gold areas, there are tin-tungsten, tin and complex ore mineralization areas. The majority of gold fields with low-temperature gold-sulfide, tin and polymetallic mineralization are attributed to the flanks of Indigiro-Kolymsky CTS. In the Verkhoyanska CTS, the majority of ore regions are characterized by multi-formation ore mineralization. In the central part of this structure, areas with mainly low-temperature tin, mercury-antimony and gold-silver ore mineralization are located. On the flanks, gold mineralization is either absent or subsidiary.Conclusions. As a result of a simple procedure, implying generalization of multiple decisions of the elementary inverse problem of gravity potential, main features of the deep structure of the Verkhyano-Kolima region were defined. In the regional stretch zone, at the boundary of lithospheric segments, the Indigiro-Kolimskaya and Verkhoyanskaya CTSs of the plume nature that control the location of ore deposits were identified and described in 3D space.

Non-integrability of a model of elastic dumbbell satellite

We study the integrability of a model of elastic satellite whose centre of mass moves in a circular Keplerian orbit around a gravity centre. The satellite is modelled by two point masses connected by an extensible massless spring that obeys Hooke’s law. It is assumed that the distance between point masses is much smaller than the radius of the orbit, so the orbital motion of the satellite is not perturbed by its rotational motion. The gravity potential of the satellite is expanded into a series with respect to its size up to quadratic terms which describe the gravity gradient torque acting on the satellite. Two cases are considered with Hooke’s centre localised in the centre of mass of the dumbbell and at an arbitrary point along a line connecting both masses. It is shown that the first case appears to be integrable and super-integrable for selected values of the parameter of the system. In the second case, model depends effectively only on one parameter and is non-integrable. In the proof, differential Galois integrability obstructions are used. For the considered sysem, these obstructions are deduced thanks to the recently developed symplectic Kovacic’s algorithm in dimension 4. According to our knowledge, this is the first application of this tool to a physical model.

Laplacian structure mirroring surface topography in determining the gravity potential by successive approximations

<p>Similarly as in other branches of engineering and mathematical physics, a transformation of coordinates is applied in treating the geodetic boundary value problem. It offers a possibility to use an alternative between the boundary complexity and the complexity of the coefficients of the partial differential equation governing the solution. In our case the Laplace operator has a relatively simple structure in terms of spherical or ellipsoidal coordinates which are frequently used in geodesy. However, the physical surface of the Earth and thus also the solution domain substantially differ from a sphere or an oblate ellipsoid of revolution, even if optimally fitted. The situation becomes more convenient in a system of general curvilinear coordinates such that the physical surface of the Earth is imbedded in the family of coordinate surfaces. Applying tensor calculus the Laplace operator is expressed in the new coordinates. However, its structure is more complicated in this case and in a sense it represents the topography of the physical surface of the Earth. The Green’s function method together with the method of successive approximations is used for the solution of the geodetic boundary value problem expressed in terms of the new coordinates. The structure of iteration steps is analyzed and if useful and possible, it is modified by means of integration by parts. Subsequently, the iteration steps and their convergence are discussed and interpreted, numerically as well as in terms of functional analysis.</p>

Developing open-source tools for reproducible inverse problems: the PyLops journey

<p>Inverse problems lie at the core of many geophysical algorithms, from earthquake and exploration seismology, all the way to electromagnetics and gravity potential methods.</p><p>In 2018, we open-sourced PyLops, a Python-based framework for large-scale inverse problems. By leveraging the concept of matrix-free linear operators – together with the efficiency of numerical libraries such as NumPy, SciPy, and Numba – PyLops solves computationally intensive inverse problems with high-level code that is highly readable and resembles the underlying mathematical formulation. While initially aimed at researchers, its parsimonious software design choices, large test suite, and thorough documentation render PyLops a reliable and scalable software package easy to run both locally and in the cloud.</p><p>Since its initial release, PyLops has incorporated several advancements in scientific computing leading to the creation of an entire ecosystem of tools: operators can now run on GPUs via CuPy, scale to distributed computing through Dask, and be seamlessly integrated into PyTorch’s autograd to facilitate research in machine-learning-aided inverse problems. Moreover, PyLops contains a large variety of inverse solvers including least-squares, sparsity-promoting algorithms, and proximal solvers highly-suited to convex, possibly nonsmooth problems. PyLops also contains sparsifying transforms (e.g., wavelets, curvelets, seislets) which can be used in conjunction with the solvers. By offering a diverse set of tools for inverse problems under one unified framework, it expedites the use of state-of-the-art optimization methods and compressive sensing techniques in the geoscience domain.</p><p>Beyond our initial expectations, the framework is currently used to solve problems beyond geoscience, including astrophysics and medical imaging. Likewise, it has inspired the development of the occamypy framework for nonlinear inversion in geophysics. In this talk, we share our experience in building such an ecosystem and offer further insights into the needs and interests of the EGU community to help guide future development as well as achieve wider adoption.</p>

Optic-fiber gravity frequency transfer network

<p>According to<strong> </strong>Einstein’s general relativity theory (GRT), a clock at a position with higher potential runs faster than a clock at a position with lower potential. Hence, inversely, one can determine the gravity potential (geopotential) and orthometric height based on precise clocks. If a clock with an accuracy of 10<sup>-18</sup> is used, the geopotential difference between two points can be determined with an accuracy of centimeters level.<strong> </strong>With the rapid development of science and technology, optical clocks achieve 10<sup>-18</sup> stability, which opens up opportunity for scientists to practically determine geopotential as well as orthometric height using optical clocks. One of the challenges of classical geodesic in the long time has been the unification of local hight systems. To complete this task is very difficult because each country has a regional high system. This problem can be solved if using a clock network, which overcomes the weaknesses of the spirit leveling method. Here we provide a formulation to establish a model of a network using optical clocks linked together by optical fibers for the purpose of determining the geopotential and establishing a unified world hight system at centimeter accuracy level. This study is supported by National Natural Science Foundation of China (NSFC) (grant Nos. 41721003, 42030105, 41631072, 41874023, 41804012), and Space Station Project (2020)228.</p><p><strong>Key words:</strong><strong> </strong>GRT, optical clocks network, frequency transfer, geopotential, orthometric height</p>

Investigation of a Coupled Deterministic Inversion for the Interior of the Earth by using Gravity-Anomaly, Acoustic-Wavefield and Geodetic Velocity measurements

<div> <div> <div> <p>Conventionally, exploration in geology involves distinct research groups, each looking at a different observable and performing separate inversions for subsurface structure. In this work we discuss the advantages and performance of a combined inversion coupling gravity-anomaly, acoustic-wavefield and surface velocities as observables in one single framework. The gravity potential, which varies across the Earth, is sensitive to density anomalies at depth and can be obtained by solving a Poisson type equation. Its inversion is ill-posed since its solutions are non-unique in the depth and the density of the inverted anomaly. We also consider the surface displacement caused by a compressible wave as a consequence of an earthquake at depth. This inversion results in a wavespeed reconstruction but lacks interpretability, i.e. whether the anomaly is thermal or chemical in origin. The surface velocity, caused by the motion of highly viscous rocks in the subsurface, is the third observable. It can be modelled by the (nonlinear) Stokes equations, which account for the density and viscosity of a subsurface anomaly.</p> <p>All three equations and their adjoints are implemented in one single Python framework using the finite element library FeNICS. To investigate the shape of the cost function, a grid search in the parameter space for three geological settings is presented. Additionally, the performance of gradient-based inversions for each observable separately or in combination, respectively, is presented. We further investigate the performance of a shape-optimizing inversion method, assuming the material parameters are known, while the shape is unknown.</p> </div> </div> </div>