Inverse determination of the thermal-conductivity profile in steel from the thermal-wave surface data

1986 ◽  
Vol 64 (9) ◽  
pp. 1178-1183 ◽  
Author(s):  
H. J. Vidberg ◽  
J. Jaarinen ◽  
D. O. Riska
Keyword(s):  
Thermal Conductivity ◽  
Thermal Wave ◽  
Scattering Problem ◽  
Synthetic Data ◽  
Inverse Scattering Problem ◽  
Low Frequency ◽  
Wave Surface ◽  
Surface Data ◽  
Conductivity Profile

The inverse scattering problem of determining the thermal-conductivity and heat-capacity profile in steel from surface data on the thermal wave generated by a low-frequency point or line source is formulated and solved. The solution may be used for the determination of the hardening profile. The utility of the solution is demonstrated by numerical examples with synthetic data.

scholarly journals Interpretation of shallow electromagnetic instruments resistivity and magnetic susceptibility measurements using rapid 1D/3D inversion

Geophysics ◽  
2016 ◽  
Vol 81 (2) ◽  
pp. E103-E112 ◽  
Author(s):  
Christophe Benech ◽  
Michel Dabas ◽  
François-Xavier Simon ◽  
Alain Tabbagh ◽  
Julien Thiesson
Keyword(s):  
Magnetic Susceptibility ◽  
Synthetic Data ◽  
Low Frequency ◽  
Test Site ◽  
3D Inversion ◽  
Magnetic Susceptibility Data ◽  
Susceptibility Data ◽  
Surface Areas ◽  
Instrument Configuration

We have developed an inversion process of electromagnetic induction (EMI) data based on a two-step approach with 1D inversion of the entire studied surface and a fast 3D inversion applied over limited areas. This process is similar to that formerly used in resistivity prospection. For the study of soil (environmental, engineering, or archaeological explorations), low-frequency electromagnetic instruments (referred to as Slingram EMI) have highly useful specificities. They are light, are easy to move in the field, and can simultaneously measure the ground’s electric conductivity and magnetic susceptibility; they have thus been used to map these properties over large surface areas, within relatively short periods of time, and at reasonable expense. The possibility of combining several coil geometries has opened up the potential for multidepth techniques and systematic 1D inversion, which are found to be sufficiently revealing to allow larger portions of surveyed areas to be analyzed. In the “targeted areas” selected for 3D inversion, the geometries of the 3D features and the resistivity and/or susceptibility contrasts are determined. This step is based on the method of moments, where only 3D heterogeneities are meshed, and only a small number of major characteristics, such as contrast, thickness, width, etc., are sought. We first applied this process to synthetic data, then to data acquired at an experimental test site, and finally to field cases. The rapid 3D inversion complements the 1D inversion by solving a series of issues: correction for the apparent anisotropy generated by the instrument configuration, multiarched anomalies, precise location of lateral changes, and determination of the properties contrasts. Our inversion results highlighted the importance of the instrument geometry. We also have determined that apparent magnetic susceptibility data can be more appropriate for the determination of the volume of man-made features and can be highly complementary to conductivity data.

Seismic full-waveform inversion using minimization of virtual scattering sources

Geophysics ◽  
2020 ◽  
Vol 85 (3) ◽  
pp. R299-R311
Author(s):  
Donguk Lee ◽  
Sukjoon Pyun
Keyword(s):  
Newton Method ◽  
Scattering Problem ◽  
Waveform Inversion ◽  
Synthetic Data ◽  
Inverse Scattering Problem ◽  
Simulated Data ◽  
Model Space ◽  
Full Waveform Inversion ◽  
Velocity Inversion ◽  
Full Waveform

Full-waveform inversion (FWI) is a powerful tool for imaging underground structures with high resolution; however, this approach commonly suffers from the cycle-skipping issue. Recently, various FWI methods have been suggested to address this problem. Such methods are mainly classified into either data-space manipulation or model-space extension. We developed an alternative FWI method that belongs to the latter class. First, we define the virtual scattering source based on perturbation theory. The virtual scattering source is estimated by minimizing the differences between observed and simulated data with a regularization term penalizing the weighted virtual scattering source. The inverse problem for obtaining the virtual scattering source can be solved by the linear conjugate gradient method. The inverted virtual scattering source is used to update the wavefields; thus, it helps FWI to better approximate the nonlinearity of the inverse scattering problem. As the second step, the virtual scattering source is minimized to invert the velocity model. By assuming that the variation of the reconstructed wavefield is negligible, we can apply an approximated full Newton method to the velocity inversion with reasonable cost comparable to the Gauss-Newton method. From the numerical examples using synthetic data, we confirm that the proposed method performs better and more robust than the simple gradient-based FWI method. In addition, we show that our objective function has fewer local minima, which helps to mitigate the cycle-skipping problem.

scholarly journals Thermal conductivity profile determination in proton-irradiated ZrC by spatial and frequency scanning thermal wave methods

2013 ◽  
Vol 114 (13) ◽  
pp. 133509 ◽  
Author(s):  
C. Jensen ◽  
M. Chirtoc ◽  
N. Horny ◽  
J. S. Antoniow ◽  
H. Pron ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Thermal Wave ◽  
Frequency Scanning ◽  
Conductivity Profile ◽  
Wave Methods

scholarly journals Fast Localization of Small Inhomogeneities from Far-Field Pattern Data in the Limited-Aperture Inverse Scattering Problem

Mathematics ◽  
2021 ◽  
Vol 9 (17) ◽  
pp. 2087
Author(s):  
Won-Kwang Park
Keyword(s):  
Inverse Scattering ◽  
Random Noise ◽  
Scattering Problem ◽  
Synthetic Data ◽  
Inverse Scattering Problem ◽  
Mathematical Structure ◽  
Indicator Function ◽  
Field Pattern ◽  
Far Field ◽  
Far Field Pattern

In this study, we consider a sampling-type algorithm for the fast localization of small electromagnetic inhomogeneities from measured far-field pattern data in the limited-aperture inverse scattering problem. For this purpose, we designed an indicator function based on the structure of left- and right-singular vectors of a multistatic response matrix, the elements of which were measured far-field pattern data. We then rigorously investigated the mathematical structure of the indicator function in terms of purely dielectric permittivity and magnetic permeability contrast cases by establishing a relationship with an infinite series of Bessel functions of an integer order of the first kind and a range of incident and observation directions before exploring various intrinsic properties of the algorithm, including its feasibility and limitations. Simulation results with synthetic data corrupted by random noise are presented to support the theoretical results.

scholarly journals The determination of the surface impedance of an obstacle

1993 ◽  
Vol 36 (1) ◽  
pp. 1-15 ◽  
Author(s):  
Andrzej W. Kȩdzierawski
Keyword(s):  
Acoustic Waves ◽  
Surface Impedance ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Inverse Scattering Problem ◽  
Far Field ◽  
Field Patterns ◽  
Time Harmonic ◽  
Scattered Fields

The inverse scattering problem we consider is to determine the surface impedance of a three-dimensional obstacle of known shape from a knowledge of the far-field patterns of the scattered fields corresponding to many incident time-harmonic plane acoustic waves. We solve this problem by using both the methods of Kirsch-Kress and Colton-Monk.

scholarly journals Fast Imaging of Short Perfectly Conducting Cracks in Limited-Aperture Inverse Scattering Problem

Electronics ◽  
2019 ◽  
Vol 8 (9) ◽  
pp. 1050
Author(s):  
Won-Kwang Park
Keyword(s):  
Inverse Scattering ◽  
Random Noise ◽  
Scattering Problem ◽  
Synthetic Data ◽  
Inverse Scattering Problem ◽  
Singular Values ◽  
Mathematical Structure ◽  
Fast Imaging ◽  
Expansion Formula ◽  
Imaging Performance

In this paper, we consider the application and analysis of subspace migration technique for a fast imaging of a set of perfectly conducting cracks with small length in two-dimensional limited-aperture inverse scattering problem. In particular, an imaging function of subspace migration with asymmetric multistatic response matrix is designed, and its new mathematical structure is constructed in terms of an infinite series of Bessel functions and the range of incident and observation directions. This is based on the structure of left and right singular vectors linked to the nonzero singular values of MSR matrix and asymptotic expansion formula due to the existence of cracks. Investigated structure of imaging function indicates that imaging performance of subspace migration is highly related to the range of incident and observation directions. The simulation results with synthetic data polluted by random noise are exhibited to support investigated structure.

A 3D parametric inversion algorithm for triaxial induction data

Geophysics ◽  
2006 ◽  
Vol 71 (1) ◽  
pp. G1-G9 ◽  
Author(s):  
Aria Abubakar ◽  
Tarek M. Habashy ◽  
Vladimir Druskin ◽  
Leonid Knizhnerman ◽  
Sofia Davydycheva
Keyword(s):  
Jacobian Matrix ◽  
Regularization Parameter ◽  
Scattering Problem ◽  
Synthetic Data ◽  
Inverse Scattering Problem ◽  
Single Frequency ◽  
Computational Time ◽  
Inversion Algorithm ◽  
Induction Logging ◽  
Parametric Inversion

We develop a parametric inversion algorithm to determine simultaneously the horizontal and vertical resistivities of both the formation and invasion zones, invasion radius, bed boundary upper location and thickness, and relative dip angle from electromagnetic triaxial induction logging data. This is a full 3D inverse scattering problem in transversally isotropic media. To acquire sufficient sensitivity to invert for all of these parameters, we collect the data using a multicomponent, multispacing induction array. For each transmitter-receiver spacing this multicomponent tool has sets of three orthogonal transmitter and receiver coils. At each logging point single-frequency data are collected at multiple spacings to obtain information at different depths of investigation. This inversion problem is solved iteratively with a constrained regularized Gauss-Newton minimization scheme. As documented in the literature, the main computational bottleneck when solving this full 3D inverse problem is the CPU time associated with constructing the Jacobian matrix. In this study, to achieve the inversion results within a reasonable computational time, we implement a dual grid approach wherein the Jacobian matrix is computed using a very coarse optimal grid. Furthermore, to regularize the inversion process we use the so-called multiplicative regularization technique. This technique automatically determines the regularization parameter. Synthetic data tests indicate the developed inversion algorithm is robust in extracting formation and invasion anisotropic resistivities, invasion radii, bed boundary locations, relative dip, and azimuth angle from multispacing, multicomponent induction logging data.

Sign in / Sign up

Export Citation Format

Share Document