Inverse scattering in multilayer inverse problem in the presence of damping

2006 ◽  
Vol 176 (2) ◽  
pp. 455-461
Author(s):  
F.D. Zaman ◽  
Khalid Masood ◽  
Z. Muhiameed
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering

The direct and inverse problem in Newtonian scattering

1991 ◽  
Vol 118 (1-2) ◽  
pp. 119-131 ◽  
Author(s):  
M. A. Astaburuaga ◽  
Claudio Fernández ◽  
Víctor H. Cortés
Keyword(s):  
Inverse Problem ◽  
Phase Space ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Dimensional Case ◽  
Classical Particle ◽  
Scattering Operator ◽  
One Dimensional ◽  
The One

SynopsisIn this paper we study the direct and inverse scattering problem on the phase space for a classical particle moving under the influence of a conservative force. We provide a formula for the scattering operator in the one-dimensional case and we settle the properties of the potential that can be deduced from it. We also study the question of recovering the shape of the barriers which can be seen from −∞ and ∞. An example is given showing that these barriers are not uniquely determined by the scattering operator.

Approximate linearized inversion by optimal scaling of prestack depth migration

Geophysics ◽  
2008 ◽  
Vol 73 (2) ◽  
pp. R23-R35 ◽  
Author(s):  
William W. Symes
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering ◽  
Optimal Scaling ◽  
Scale Factor ◽  
Prestack Depth Migration ◽  
Depth Migration ◽  
Acoustic Inverse Scattering

Linearized inversion provides one possible sense of image amplitude correctness. An image or bandlimited model perturbation has correct amplitudes if it is an approximate inversion, that is, if linearized modeling (demigration), with the image as input, reproduces the data approximately. The theory of linearized acoustic inverse scattering with slowly varying background or macromodel shows that an approximate inversion may be recovered from the output of prestack depth migration by a combination of scaling and filtering. The necessary filter is completely specified by the theory, and the scale factor may be estimated via filtering, linearized modeling, a second migration, and the solution of a small auxiliary inverse problem.

scholarly journals Energy- and Regularity-Dependent Stability Estimates for Near-Field Inverse Scattering in Multidimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
M. I. Isaev
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering ◽  
Near Field ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Uniform Norm ◽  
Stability Estimate ◽  
Stability Estimates ◽  
Logarithmic Stability

We prove new global Hölder-logarithmic stability estimates for the near-field inverse scattering problem in dimensiond≥3. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. In addition, a global logarithmic stability estimate for this inverse problem in dimensiond=2is also given.

Inverse Scattering Solutions by a Sinc Basis, Multiple Source, Moment Method -- Part II: Numerical Evaluations

1983 ◽  
Vol 5 (4) ◽  
pp. 376-392 ◽  
Author(s):  
Michael L. Tracy ◽  
Steven A. Johnson
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Incident Radiation ◽  
Multiple Sources ◽  
Reconstruction Quality ◽  
Ill Posed ◽  
Band Limited ◽  
Pseudo Inverse

In part I, we presented a method for solving the inverse scattering problem using multiple sources and detectors. Allowance for multiple angles of incident radiation improves the ill-posed nature of the inverse problem by improving the quality and quantity of information gathered at detector points. This paper describes implementation and numerical evaluation of the method. An 11 by 11 image reconstructed from noisy scattered field data is shown to closely match the original scattering object, and the improvement possible by constraining the reconstruction to be spatially band limited is demonstrated. Furthermore, for a somewhat simpler “pseudo-inverse problem,” we give findings on the effects that detector radius, degree of overdetermination, noise, and object contrast have on reconstruction quality.

scholarly journals ON THE USE OF THE RECIPROCITY-GAP FUNCTIONAL IN INVERSE SCATTERING FROM PLANAR CRACKS

2005 ◽  
Vol 15 (10) ◽  
pp. 1553-1574 ◽  
Author(s):  
AMEL BEN ABDA ◽  
FABRICE DELBARY ◽  
HOUSSEM HADDAR
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering ◽  
Boundary Data ◽  
Acoustic Measurements ◽  
Electromagnetic Imaging

We consider the inverse problem of determining the shape and location of planar screens inside a 3D body through acoustic or electromagnetic imaging. In order to determine the flaws we perform acoustic measurements with prescribed over-determined boundary data. The reciprocity gap concept is exploited to determine sound-hard planar screens of general shapes.

scholarly journals Multipole Theory and Algorithms for Target Support Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-15 ◽  
Author(s):  
Edwin A. Marengo
Keyword(s):  
Inverse Problem ◽  
Helmholtz Equation ◽  
Inverse Scattering ◽  
Scattered Field ◽  
Source Region ◽  
Multipole Expansion ◽  
Source Regions ◽  
Support Estimation

The inverse problem of estimating the smallest region of localization (minimum source region) of a source or scatterer that can produce a given radiation or scattered field is investigated with the help of the multipole expansion. The results are derived in the framework of the scalar Helmholtz equation. The proposed approach allows the estimation of possibly nonconvex minimum source regions. The derived method is illustrated with an example relevant to inverse scattering.

The inverse scattering problem for a discrete dirac system on the whole axis

2017 ◽  
Vol 25 (6) ◽  
Author(s):  
Hidayat M. Huseynov ◽  
Agil K. Khanmamedov ◽  
Rza I. Aleskerov
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattering Data ◽  
Sufficient Condition ◽  
Dirac System ◽  
Entire Line

AbstractThis paper investigates the inverse scattering problem for a discrete Dirac system on the entire line with coefficients that stabilize to zero in one direction. We develop an algorithm for solving the inverse problem of reconstruction of coefficients. We derive a necessary and a sufficient condition on the scattering data so that the inverse problem is uniquely solvable.

An iterative ensemble Kalman method for an inverse scattering problem in acoustics

2020 ◽  
Vol 34 (28) ◽  
pp. 2050312
Author(s):  
Zhaoxing Li
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Homogeneous Medium ◽  
Inverse Scattering Problem ◽  
Numerical Examples ◽  
Incident Waves

This paper studies an inverse problem of reconstructing a sound-soft obstacle from a homogeneous medium. We deal with it in the framework of statistical inversion and adopt an iterative ensemble Kalman algorithm to reconstruct the boundary. Some numerical examples show that the algorithm is effective and it can recover the shape of the boundary using one or several of the incident waves.

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