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

Performance optimization of liquid ring pumps based on Gappy POD surrogate model

To solve the problems of high calculation cost and difficult optimization caused by the complex gas–liquid two-phase flow in liquid ring pumps, an optimization method of a liquid ring pump impeller based on the proper orthogonal decomposition (POD) surrogate model was proposed. The impeller blade shape was parameterized by using the quartic Bezier curve. The sample was obtained from the uniform experimental design of blade shape design parameters. The POD surrogate model was constructed by the parameters of sample blade shape and its corresponding flow field data, which was used instead of CFD numerical simulation to predict the flow field variables under the perturbations of blade design parameters in the optimization process. And then, the gradient vector of the objective function to design variables was predicted quickly and accurately. The blade shape was updated continuously along the negative direction of the gradient vector, and then, the optimal design of the impeller was acquired. The calculation case results show that the relative error between the pressure field in the impeller predicted by the POD method and that of CFD simulation is less than 5%, and the calculation cost is only 1/8460 of CFD simulation. Compared with the original model, the flow field distribution in the optimized model is significantly improved, and the efficiency is promoted by 3.8%.

Algorithm for adaptive correction of the ship's movement along the trajectory in the presence of a sea current

В статье предложен алгоритм адаптивной коррекции движения судна по траектории при наличии морского течения. В основе предлагаемого подхода лежит алгоритм градиента вспомогательных функций. Показаны преимущества предложенного алгоритма адаптивной коррекции движения судна по траектории. Сущность предлагаемого подхода заключается в замене прямолинейного участка маршрута судна, новой виртуальной траекторией и использовании ее во вспомогательной функции и при вычислении соответствующего вектора градиента. Компьютерное моделирование подтвердило эффективность предложенного алгоритма адаптивной коррекции. Адаптивные свойства разработанного алгоритма выражаются в том, что он обеспечивает асимптотически точное движение по участкам запланированной траектории, не используя информации о скорости и направлении морского течения. Предполагается использование предложенного адаптивного алгоритма при разработке систем автоматического управления движением судна по маршруту. The article proposes an algorithm for adaptive correction of the ship's movement along the trajectory in the presence of a sea current. The proposed approach is based on the gradient algorithm of auxiliary functions. The advantages of the proposed algorithm for adaptive correction of the ship's motion along the trajectory are shown. The essence of the proposed approach is to replace the straight-line section of the ship's route with a new virtual trajectory and use it in an auxiliary function and in calculating the corresponding gradient vector. Computer simulation has confirmed the effectiveness of the proposed adaptive correction algorithm. The adaptive properties of the developed algorithm are expressed in the fact that it provides asymptotically accurate movement along sections of the planned trajectory, without using information about the speed and direction of the sea current. It is supposed to use the proposed adaptive algorithm in the development of systems for automatic control of the ship's movement along the route.

Connected components of the space of proper gradient vector fields

We show that there exist two proper gradient vector fields on $$\mathbb {R}^n$$ R n which are homotopic in the category of proper maps but not homotopic in the category of proper gradient maps.

On the General Solutions of Some Non-Homogeneous Div-Curl Systems with Riemann–Liouville and Caputo Fractional Derivatives

In this work, we investigate analytically the solutions of a nonlinear div-curl system with fractional derivatives of the Riemann–Liouville or Caputo types. To this end, the fractional-order vector operators of divergence, curl and gradient are identified as components of the fractional Dirac operator in quaternionic form. As one of the most important results of this manuscript, we derive general solutions of some non-homogeneous div-curl systems that consider the presence of fractional-order derivatives of the Riemann–Liouville or Caputo types. A fractional analogous to the Teodorescu transform is presented in this work, and we employ some properties of its component operators, developed in this work to establish a generalization of the Helmholtz decomposition theorem in fractional space. Additionally, right inverses of the fractional-order curl, divergence and gradient vector operators are obtained using Riemann–Liouville and Caputo fractional operators. Finally, some consequences of these results are provided as applications at the end of this work.

A q-Gradient Descent Algorithm with Quasi-Fejér Convergence for Unconstrained Optimization Problems

We present an algorithm for solving unconstrained optimization problems based on the q-gradient vector. The main idea used in the algorithm construction is the approximation of the classical gradient by a q-gradient vector. For a convex objective function, the quasi-Fejér convergence of the algorithm is proved. The proposed method does not require the boundedness assumption on any level set. Further, numerical experiments are reported to show the performance of the proposed method.

Adoption of Snake Variable Model-Based Method in Segmentation and Quantitative Calculation of Cardiac Ultrasound Medical Images

This paper intends to explore the effect of the enhanced snake variable model in the segmentation of cardiac ultrasound images and its adoption in quantitative measurement of cardiac cavity. First, the basic principles of the traditional snake model and the gradient vector flow (GVF) snake model are explained. Then, an ellipsoid model is constructed to obtain the initial contour of the heart based on the three-dimensional volume of cardiac ultrasound image, and a discretized triangular mesh model is generated. Finally, the vortical gradient vector flow (VGVF) external force field is introduced and combined with the greedy algorithm to process the deformation of the initial ellipsoid contour of the heart. The segmentation effect is quantitatively evaluated regarding the area overlap rate (AOR) and the mean contour distance (MCD). The results show that the VGVF snake model can segment the deep recessed area of the “U-shaped map” in contrast to the traditional snake model and the GVF snake model. After being applied to ultrasonic image segmentation, the VGVF snake model obtains the segmentation result that is close to the doctor’s manual segmentation result, and the average AOR and MCD are 97.4% and 3.2, respectively. The quantitative evaluation of the cardiac cavity is carried out based on the segmentation results, and the measurement of the volume change of the left ventricle within a cardiac cycle is realized. To sum up, VGVF snake model is superior to the traditional snake and GVF snake models in terms of ultrasonic image segmentation, which realizes the three-dimensional segmentation and quantitative calculation of the cardiac cavity.

FPGA based Edge Detection using Sobel Filter

In image processing, Sobel operator is utilised especially inside algorithms of edge-detection. It is a discreet differentiation operator which calculates the gradient approximation of the function picture intensity. The outcome of the Sobel operation at each location of the image is either the appropriate gradient vector or the vector standard. The Sobel operator relies on the image being converted into horizontal and vertical with a tiny, separable and integrated valued filter. This means that the computation is quite inexpensive. PAN Poanta satellite image was used for this work using Java, Core Java in GDAL package. As compared to in built Sobel operator, the image generated for this work is very fine and sharp as a result of noise suppression to a considerable extent. Inorder to do edge detection efficiently with minimal amount of false results, a correct form of Sobel filter ( I’=√(I*X)²+(I*Y)2 ) was used instead of the approximation(I’=I*X+I*Y) for the sake of computation.

Object-Oriented Building Contour Optimization Methodology for Image Classification Results via Generalized Gradient Vector Flow Snake Model

Building boundary optimization is an essential post-process step for building extraction (by image classification). However, current boundary optimization methods through smoothing or line fitting principles are unable to optimize complex buildings. In response to this limitation, this paper proposes an object-oriented building contour optimization method via an improved generalized gradient vector flow (GGVF) snake model and based on the initial building contour results obtained by a classification method. First, to reduce interference from the adjacent non-building object, each building object is clipped via their extended minimum bounding rectangles (MBR). Second, an adaptive threshold Canny edge detection is applied to each building image to detect the edges, and the progressive probabilistic Hough transform (PPHT) is applied to the edge result to extract the line segments. For those cases with missing or wrong line segments in some edges, a hierarchical line segments reconstruction method is designed to obtain complete contour constraint segments. Third, accurate contour constraint segments for the GGVF snake model are designed to quickly find the target contour. With the help of the initial contour and constraint edge map for GGVF, a GGVF force field computation is executed, and the related optimization principle can be applied to complex buildings. Experimental results validate the robustness and effectiveness of the proposed method, whose contour optimization has higher accuracy and comprehensive value compared with that of the reference methods. This method can be used for effective post-processing to strengthen the accuracy of building extraction results.