The direct scattering problem for a crack buried in a piecewise homogenous medium

2013 ◽  
Vol 54 (5) ◽  
pp. 053514 ◽  
Author(s):  
Jun Guo ◽  
Guozheng Yan ◽  
Jianguo Ye
Keyword(s):  
Scattering Problem ◽  
Direct Scattering ◽  
Homogenous Medium

The inverse elastic scattering by an impenetrable obstacle and a crack

2020 ◽  
Author(s):  
Jianli Xiang ◽  
Guozheng Yan
Keyword(s):  
Mixed Type ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Operator ◽  
Integral Equation Method ◽  
Factorization Method ◽  
Boundary Integral ◽  
Far Field ◽  
Direct Scattering ◽  
Time Harmonic

Abstract This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by a mixed-type scatterer, which is given as the union of an impenetrable obstacle and a crack. We develop the modified factorization method to determine the shape of the mixed-type scatterer from the far field data. However, the factorization of the far field operator $F$ is related to the boundary integral matrix operator $A$, which is obtained in the study of the direct scattering problem. So, in the first part, we show the well posedness of the direct scattering problem by the boundary integral equation method. Some numerical examples are presented at the end of the paper to demonstrate the feasibility and effectiveness of the inverse algorithm.

Algorithms for solving scattering problems for the Manakov model of nonlinear Schrödinger equations

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Leonid L. Frumin
Keyword(s):  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Numerical Algorithms ◽  
Scattering Problems ◽  
Block Matrices ◽  
Nonlinear Schrödinger ◽  
Direct Scattering ◽  
Vector Case ◽  
Manakov Model ◽  
Vector Variant

AbstractWe introduce numerical algorithms for solving the inverse and direct scattering problems for the Manakov model of vector nonlinear Schrödinger equation. We have found an algebraic group of 4-block matrices with off-diagonal blocks consisting of special vector-like matrices for generalizing the scalar problem’s efficient numerical algorithms to the vector case. The inversion of block matrices of the discretized system of Gelfand–Levitan–Marchenko integral equations solves the inverse scattering problem using the vector variant the Toeplitz Inner Bordering algorithm of Levinson’s type. The reversal of steps of the inverse problem algorithm gives the solution of the direct scattering problem. Numerical tests confirm the proposed vector algorithms’ efficiency and stability. We also present an example of the algorithms’ application to simulate the Manakov vector solitons’ collision.

scholarly journals About the evaluation of the results of the microseismic sounding method in their geological interpretation

2019 ◽  
Author(s):  
А.В. Горбатиков ◽  
А.А. Цуканов
Keyword(s):  
Scattering Problem ◽  
Synthetic Data ◽  
Vertical Resolution ◽  
Geological Interpretation ◽  
Microseismic Sounding ◽  
Direct Scattering ◽  
Direct Modeling ◽  
The Crimea ◽  
Geometrical Dimensions ◽  
Rayleigh Mode

Работа посвящена анализу результатов двумерного численного решения прямой задачи рассеяния фундаментальной моды Рэлея на двух скоростных неоднородностях, расположенных друг под другом. Данная модель позволила проанализировать некоторые случаи использования метода микросейсмического зондирования (ММЗ) в условиях сложно построенных сред. С использованием численной модели, построенной из первых принципов в прямом моделировании получены оценки вертикальной разрешающей способности метода микросейсмического зондирования. Рассмотрены случаи ряда конкретных геометрических размеров и ряда упругих параметров включений, со значениями, близкими к встречающимся в природных условиях. Выработаны и сформулированы простые практические приемы, с помощью которых можно оценивать вертикальное разрешение объектов при интерпретации разрезов микросейсмического зондирования по экспериментально полученным разрезам. Оценка вертикальной разрешающей способности ММЗ на синтетических данных состоит в том, что, если расстояние между центрами двух малых по сравнению с глубиной залегания неоднородностей, расположенных друг над другом, составляет 36 41 (или более) от длины фундаментальной моды волны Рэлея, равной R Нcenter/ 0,4, где Нcenter глубина середины между центрами неоднородностей, то изображения этих неоднородностей будут разрешены в поле случайных волн Рэлея. То есть, для разрешимости по ММЗ расстояние по вертикали между центрами малых неоднородностей должно составлять Нcenter или более. Выработанные приемы использованы для оценки разрешения горизонтально залегающих слоев в разрезах, полученных в ходе изучения зоны сочленения Таманского полуострова и Крыма при геологической интерпретации результатов микросейсмических исследований. The paper is devoted to the analysis of the results of a twodimensional numerical solution of the direct scattering problem of the fundamental Rayleigh mode on two velocity inhomogeneities located one under another. This model made it possible to analyze some cases of using the method of microseismicsounding (MMS) in conditions of complex structured media.Using the numerical model built from first principles in direct modeling, we obtained estimates of the vertical resolution of the microseismic sounding method. The cases of a number of specific geometrical dimensions and a number of elastic parameters of inclusions with values close to those encountered in natural conditions are considered.Simple practical methods have been developed and formulated, with the help of which one can estimate the vertical resolution of objects when interpreting microseismic sounding sections obtainedexperimentally.Estimation of the vertical resolution of the MMS on synthetic data is that, if the distance between the centers of two small inhomogeneities, one above the other, compared to the depth, is 36 41 (or more) of the fundamental mode of the Rayleigh wave, equal to R Hcenter/ 0.4, where Hcenter is the midpoint depth between the centers of inhomogeneities, then the images of these inhomogeneities will be resolved in the field of random Rayleigh waves. That is, to ensure the resolution of the MMS, the vertical distance between the centers of small discontinuities should be Hcenter or more. The techniques developed were used to assess the resolution of horizontallylying layers in the sections obtained during the study of the junction zone of the Taman Peninsula and the Crimea in the course of geological interpretation of microseismic research results.

scholarly journals Interior Elastic Scattering by a Non-Penetrable Partially Coated Obstacle and Its Shape Recovering

Mathematics ◽  
2021 ◽  
Vol 9 (19) ◽  
pp. 2485
Author(s):  
Angeliki Kaiafa ◽  
Vassilios Sevroglou
Keyword(s):  
Mixed Boundary ◽  
Variational Equation ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Point Of View ◽  
Inversion Algorithm ◽  
Direct Scattering ◽  
Time Harmonic ◽  
Navier Equation ◽  
Robin Boundary

In this paper, the interior elastic direct and inverse scattering problem of time-harmonic waves for a non-penetrable partially coated obstacle placed in a homogeneous and isotropic medium is studied. The scattering problem is formulated via the Navier equation, considering incident circular waves due to point-source fields, where the corresponding scattered data are measured on a closed curve inside the obstacle. Our model, from the mathematical point of view, is described by a mixed boundary value problem in which the scattered field satisfies mixed Dirichlet-Robin boundary conditions on the Lipschitz boundary of the obstacle. Using a variational equation method in an appropriate Sobolev space setting, uniqueness and existence results as well as stability ones are established. The corresponding inverse problem is also studied, and using some specific auxiliary integral operators an appropriate modified factorisation method is given. In addition, an inversion algorithm for shape recovering of the partially coated obstacle is presented and proved. Last but not least, useful remarks and conclusions concerning the direct scattering problem and its linchpin with the corresponding inverse one are given.

scholarly journals Backscatter signal model for Irkutsk Incoherent Scatter Radar

2018 ◽  
Vol 4 (2) ◽  
pp. 24-32 ◽  
Author(s):  
Виктор Ташлыков ◽  
Viktor Tashlykov ◽  
Андрей Медведев ◽  
Andrey Medvedev ◽  
Роман Васильев ◽  
...  
Keyword(s):  
Experimental Data ◽  
Scattering Problem ◽  
Incoherent Scatter Radar ◽  
Plasma Parameters ◽  
Signal Model ◽  
Backscatter Signal ◽  
Incoherent Scatter ◽  
Scatter Radar ◽  
Direct Scattering ◽  
The Monte Carlo Method

The paper presents a backscatter signal model for Irkutsk Incoherent Scatter Radar (IISR) and proposes a technique for solving the inverse problem of determining plasma temperatures from IISR data. This solution is validated by setting up the direct scattering problem and simulating it using the Monte-Carlo method. In addition, we can introduce known systematic error sources into the backscatter signal model. This enables us to determine which approaches can be used to recover temperatures correctly. The major task of this study is to identify and methodically correct the errors that can distort the obtained temperatures. We also report the results of testing of the developed technique for determining temperatures from IISR experimental data. The presented model and IISR experimental data can be used to validate techniques for determining other ionospheric plasma parameters.

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