scholarly journals Small defects reconstruction in waveguides from multifrequency one-side scattering data

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Éric Bonnetier ◽  
Angèle Niclas ◽  
Laurent Seppecher ◽  
Grégory Vial
Keyword(s):  
Born Approximation ◽  
Field Measurements ◽  
Scattering Data ◽  
Inversion Method ◽  
Local Perturbation ◽  
Fourier Domain ◽  
Fourier Inversion ◽  
Frequency Wave ◽  
Partial Data ◽  
Stable Reconstruction

<p style='text-indent:20px;'>Localization and reconstruction of small defects in acoustic or electromagnetic waveguides is of crucial interest in nondestructive evaluation of structures. The aim of this work is to present a new multi-frequency inversion method to reconstruct small defects in a 2D waveguide. Given one-side multi-frequency wave field measurements of propagating modes, we use a Born approximation to provide a <inline-formula><tex-math id="M1">\begin{document}$ \text{L}^2 $\end{document}</tex-math></inline-formula>-stable reconstruction of three types of defects: a local perturbation inside the waveguide, a bending of the waveguide, and a localized defect in the geometry of the waveguide. This method is based on a mode-by-mode spacial Fourier inversion from the available partial data in the Fourier domain. Indeed, in the available data, some high and low spatial frequency information on the defect are missing. We overcome this issue using both a compact support hypothesis and a minimal smoothness hypothesis on the defects. We also provide a suitable numerical method for efficient reconstruction of such defects and we discuss its applications and limits.</p>

scholarly journals Cramér-Rao Bound Study of Multiple Scattering Effects in Target Separation Estimation

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Edwin A. Marengo ◽  
Paul Berestesky
Keyword(s):  
Multiple Scattering ◽  
Born Approximation ◽  
Single Scattering ◽  
Scattering Data ◽  
Approximation Model ◽  
Scattering Parameters ◽  
Helmholtz Operator ◽  
Scattering Effects ◽  
Cramer Rao Bound ◽  
Multiple Scattering Effects

The information about the distance of separation between two-point targets that is contained in scattering data is explored in the context of the scalar Helmholtz operator via the Fisher information and associated Cramér-Rao bound (CRB) relevant to unbiased target separation estimation. The CRB results are obtained for the exact multiple scattering model and, for reference, also for the single scattering or Born approximation model applicable to weak scatterers. The effects of the sensing configuration and the scattering parameters in target separation estimation are analyzed. Conditions under which the targets' separation cannot be estimated are discussed for both models. Conditions for multiple scattering to be useful or detrimental to target separation estimation are discussed and illustrated.

REAL-TIME 2.5D INVERSION OF LWD RESISTIVITY MEASUREMENTS USING DEEP LEARNING FOR GEOSTEERING APPLICATIONS ACROSS FAULTED FORMATIONS

2021 ◽  
Author(s):  
Kyubo Noh ◽  
◽  
Carlos Torres-Verdín ◽  
David Pardo ◽  
◽  
...  
Keyword(s):  
Deep Learning ◽  
Real Time ◽  
Fault Plane ◽  
Synthetic Data ◽  
Field Measurements ◽  
Geological Structure ◽  
Inversion Method ◽  
Adaptive Finite Element ◽  
Resistivity Measurements ◽  
Lwd Resistivity

We develop a Deep Learning (DL) inversion method for the interpretation of 2.5-dimensional (2.5D) borehole resistivity measurements that requires negligible online computational costs. The method is successfully verified with the inversion of triaxial LWD resistivity measurements acquired across faulted and anisotropic formations. Our DL inversion workflow employs four independent DL architectures. The first one identifies the type of geological structure among several predefined types. Subsequently, the second, third, and fourth architectures estimate the corresponding spatial resistivity distributions that are parameterized (1) without the crossings of bed boundaries or fault plane, (2) with the crossing of a bed boundary but without the crossing of a fault plane, and (3) with the crossing of the fault plane, respectively. Each DL architecture employs convolutional layers and is trained with synthetic data obtained from an accurate high-order, mesh-adaptive finite-element forward numerical simulator. Numerical results confirm the importance of using multi-component resistivity measurements -specifically cross-coupling resistivity components- for the successful reconstruction of 2.5D resistivity distributions adjacent to the well trajectory. The feasibility and effectiveness of the developed inversion workflow is assessed with two synthetic examples inspired by actual field measurements. Results confirm that the proposed DL method successfully reconstructs 2.5D resistivity distributions, location and dip angles of bed boundaries, and the location of the fault plane, and is therefore reliable for real-time well geosteering applications.

scholarly journals Geomagnetic activity and local time dependence of the distribution of ultra low-frequency wave power in azimuthal wavenumbers, <i>m</i>

2017 ◽  
Vol 35 (3) ◽  
pp. 629-638 ◽  
Author(s):  
Theodore E. Sarris ◽  
Xinlin Li
Keyword(s):  
Phase Difference ◽  
Low Frequency ◽  
Field Measurements ◽  
Resonant Interaction ◽  
Total Power ◽  
Ulf Waves ◽  
Quiet Time ◽  
Frequency Wave ◽  
Drift Frequency ◽  
Diffusion Rates

Abstract. The azimuthal wavenumber m of ultra low-frequency (ULF) waves in the magnetosphere is a required parameter in the calculations of the diffusion rates of energetic electrons and protons in the magnetosphere, as electrons and protons of drift frequency ωd have been shown to radially diffuse due to resonant interaction with ULF waves of frequency ω = mωd. However, there are difficulties in estimating m, due to lack of multipoint measurements. In this paper we use magnetic field measurements at geosynchronous orbit to calculate the cross-spectrogram power and phase differences between time series from magnetometer pairs. Subsequently, assuming that ULF waves of a certain frequency and m would be observed with a certain phase difference between two azimuthally aligned magnetometers, the fraction of the total power in each phase difference range is calculated. As part of the analysis, both quiet-time and storm-time distributions of power per m number are calculated, and it is shown that during active times, a smaller fraction of total power is confined to lower m than during quiet times. It is also shown that in the dayside region, power is distributed mostly to the lowest azimuthal wavenumbers m = 1 and 2, whereas on the nightside it is more equally distributed to all m that can be resolved by the azimuthal separation between two spacecraft.

Nonlinear waveform inversion of plane‐wave seismograms in stratified elastic media

Geophysics ◽  
1991 ◽  
Vol 56 (5) ◽  
pp. 664-674 ◽  
Author(s):  
F. Kormendi ◽  
M. Dietrich
Keyword(s):  
Plane Wave ◽  
Least Squares ◽  
Wave Velocity ◽  
Generalized Least Squares ◽  
P Wave ◽  
Gradient Algorithm ◽  
Stratified Medium ◽  
Inversion Method ◽  
Inversion Algorithm ◽  
Frequency Wave

We present a method for determining the elastic parameters of a horizontally stratified medium from its plane‐wave reflectivity. The nonlinear inverse problem is iteratively solved by using a generalized least‐squares formalism. The proposed method uses the (relatively) fast convergence properties of the conjugate gradient algorithm and achieves computational efficiency through analytical solutions for calculating the reference and perturbational wavefields. The solution method is implemented in the frequency‐wave slowness domain and can be readily adapted to various source‐receiver configurations. The behavior of the algorithm conforms to the predictions of generalized least‐squares inverse theory: the inversion scheme yields satisfactory results as long as the correct velocity trends are introduced in the starting model. In practice, the inversion algorithm should be applied first in the precritical region because of the strong nonlinear behavior of postcritical data with respect to velocity perturbations. The suggested inversion strategy consists of first inverting for the density and P‐wave velocity (or P‐wave impedance) by considering plane waves in the low slowness region (near‐normal angles of incidence), then in optimizing for the S‐wave velocity by progressively including contributions from the high slowness region (steep angles of incidence). Numerical experiments performed with noise‐free synthetic data prove that the proposed inversion method satisfactorialy reconstructs the elastic properties of a stratified medium from a limited set of plane‐wave components, at a reasonable computing cost.

Born non-scattering electromagnetic media

2017 ◽  
Vol 25 (4) ◽  
Author(s):  
Tilo Arens ◽  
John Sylvester
Keyword(s):  
Born Approximation ◽  
Electromagnetic Waves ◽  
Variational Equation ◽  
Plane Waves ◽  
Transformation Optics ◽  
Local Perturbation ◽  
Detectable Change ◽  
Scattering Media ◽  
First Order

AbstractWe consider the propagation of electromagnetic waves in an anisotropic medium. A local perturbation of the vacuum media that does not produce a detectable change in the far field is called non-scattering. Through testing by plane waves, we derive a variational equation characterizing non-scattering perturbations of permittivities and permeabilities to first order, i.e. in the Born approximation. We show that these perturbations can be characterized exactly by four functions. Three of these functions correspond to linearizations of known non-scattering media constructed by diffeomorphisms in transformation optics. The role of the fourth function is not yet understood, although some analytic properties can be derived.

Characterizing a GPR antenna system by near-field electric field measurements

Geophysics ◽  
2007 ◽  
Vol 72 (5) ◽  
pp. A51-A55 ◽  
Author(s):  
Rita Streich ◽  
Jan van der Kruk
Keyword(s):  
Electric Field ◽  
Field Data ◽  
Near Field ◽  
Field Measurements ◽  
Input Voltage ◽  
Antenna System ◽  
Inversion Method ◽  
Migration Imaging ◽  
Imaging Algorithms ◽  
Electric Field Measurements

A method to determine current distributions on resistively loaded Wu-King-type antennas from sparse near-field measurements of the electric field is introduced. We use a parametric formulation of current flow and invert the measured data to determine the characteristic antenna parameters and input voltage wavelets that best explain the measured electric-field data. We compare modeled and measured electric-field data to show that our inversion method yields reasonable results and that our antenna model provides a means to correct for the effects of an antenna’s finite length in migration/imaging algorithms. By modifying the description of the current distribution, our method may be adapted for various antenna types.

scholarly journals Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method

2018 ◽  
Vol 26 (4) ◽  
pp. 501-522 ◽  
Author(s):  
Dinh-Liem Nguyen ◽  
Michael V. Klibanov ◽  
Loc H. Nguyen ◽  
Michael A. Fiddy
Keyword(s):  
Experimental Data ◽  
Inverse Problem ◽  
Three Dimensional ◽  
Dielectric Constants ◽  
Scattering Data ◽  
Inversion Method ◽  
Buried Objects ◽  
Globally Convergent ◽  
Data Propagation ◽  
Analytical Result

Abstract This paper is concerned with the numerical solution to a three-dimensional coefficient inverse problem for buried objects with multi-frequency experimental data. The measured data, which are associated with a single direction of an incident plane wave, are backscatter data for targets buried in a sandbox. These raw scattering data were collected using a microwave scattering facility at the University of North Carolina at Charlotte. We develop a data preprocessing procedure and exploit a newly developed globally convergent inversion method for solving the inverse problem with these preprocessed data. It is shown that dielectric constants of the buried targets as well as their locations are reconstructed with a very good accuracy. We also prove a new analytical result which rigorously justifies an important step of the so-called “data propagation” procedure.

Explicit formula for the solution of the phaseless inverse scattering problem of imaging of nano structures

2015 ◽  
Vol 23 (2) ◽  
Author(s):  
Michael V. Klibanov ◽  
Vladimir G. Romanov
Keyword(s):  
Born Approximation ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Scattered Wave ◽  
Scattering Data ◽  
Unknown Coefficient ◽  
X Rays ◽  
Reconstruction Formula ◽  
Nano Structures ◽  
Complex Valued

AbstractImaging of nano structures is necessary for the quality control in their manufacturing. In the case when X-rays probe the medium, only the modulus of the complex valued scattered wave field can be measured. The phase cannot be measured. In the case of the Born approximation, we obtain an explicit reconstruction formula for the unknown coefficient from the phaseless scattering data.

scholarly journals Multidimensional Wave Field Signal Theory: Transfer Function Relationships

2012 ◽  
Vol 2012 ◽  
pp. 1-27 ◽  
Author(s):  
Natalie Baddour
Keyword(s):  
Transfer Function ◽  
Signal Theory ◽  
Fourier Domain ◽  
Theoretic Approach ◽  
Input Output ◽  
Coordinate Systems ◽  
Fourier Inversion ◽  
Inversion Formulas ◽  
Transmission Of Information ◽  
Physical Phenomena

The transmission of information by propagating or diffusive waves is common to many fields of engineering and physics. Such physical phenomena are governed by a Helmholtz (real wavenumber) or pseudo-Helmholtz (complex wavenumber) equation. Since these equations are linear, it would be useful to be able to use tools from signal theory in solving related problems. The aim of this paper is to derive multidimensional input/output transfer function relationships in the spatial domain for these equations in order to permit such a signal theoretic approach to problem solving. This paper presents such transfer function relationships for the spatial (not Fourier) domain within appropriate coordinate systems. It is shown that the relationships assume particularly simple and computationally useful forms once the appropriate curvilinear version of a multidimensional spatial Fourier transform is used. These results are shown for both real and complex wavenumbers. Fourier inversion of these formulas would have applications for tomographic problems in various modalities. In the case of real wavenumbers, these inversion formulas are presented in closed form, whereby an input can be calculated from a given or measured wavefield.

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