Diffraction Tomography Using Born Approximation

2020 ◽  
Vol 1 (1) ◽  
Keyword(s):  
Born Approximation ◽  
Diffraction Tomography

scholarly journals Estimation of reliability of seismic and electromagnetic monitoring in seismic active areas by diffraction tomography

2001 ◽  
Vol 1 (1/2) ◽  
pp. 69-73 ◽  
Author(s):  
V. N. Troyan ◽  
Yu. V. Kiselev
Keyword(s):  
Numerical Simulation ◽  
Born Approximation ◽  
Maxwell Equations ◽  
Diffraction Tomography ◽  
Seismic Parameters ◽  
First Order ◽  
The Finite Difference Method ◽  
Tomography Method ◽  
Electromagnetic Monitoring ◽  
Direct Problems

Abstract. This paper presents the algorithms and results of the numerical simulation of the solution of a 2-D inverse problem on the restoration of seismic parameters and electrical conductivity of local inhomogeneities by the diffraction tomography method based upon the first order Born approximation. The direct problems for the Lame and Maxwell equations are solved by the finite difference method. Restoration of inhomogeneities which are not very weak is implemented with the use of a small number of receivers (source-receiver pairs).

Application of diffraction tomography to fracture detection

Geophysics ◽  
1992 ◽  
Vol 57 (2) ◽  
pp. 245-257 ◽  
Author(s):  
M. Ali C. Tura ◽  
Lane R. Johnson ◽  
Ernest L. Majer ◽  
John E. Peterson
Keyword(s):  
Quadratic Programming ◽  
Born Approximation ◽  
Field Data ◽  
Granitic Rock ◽  
Back Propagation ◽  
Synthetic Data ◽  
Programming Method ◽  
Diffraction Tomography ◽  
Inversion Methods ◽  
Quadratic Programming Method

Two diffraction tomography techniques are applied to crosshole field data to detect fractures in granitic rock. The techniques used are the conventional back‐propagation method and a new quadratic programming method incorporating constraints. In this formulation, the Born approximation is used for linearization of the inverse problem. Two dimensional (2-D) pseudo spectral finite‐difference synthetic data are generated to demonstrate the inversion methods and justify use of the Born approximation. Also, using 2-D Born synthetic data, the velocity sensitivity of the inversion algorithm and reduction of fracture generated tube waves and S‐waves are investigated. The inversion methods are applied to field data from the Grimsel test site in Switzerland. The data are collected from a [Formula: see text] rectangular area where fractures are known to exist. Data acquisition with 0.5 m spacing of three component receivers and a piezoelectric source is carried out so as to obtain a nearly complete coverage of the region. Crosshole inversions are performed on data from the receiver components in the plane of the rectangular region and normal to its boundary. As the result of a separate experiment conducted in a homogeneous region of the granitic rock, a cosine function was found to best fit the source radiation pattern. A background attenuation value is estimated for the region, using a simple statistical approach, and estimates of the wavelet are found by common source gathers, common receiver gathers, and averages of all traces. The preprocessing steps are: (1) source radiation correction, (2) attenuation correction, (3) removal of the incident wavefield, (4) muting beginning of the traces and windowing the ends, (5) wavelet deconvolution, and (6) two‐and‐a‐half dimensional (2.5-D) corrections. This preprocessing is designed to enhance scattered P‐waves that are used in the inversions. Images obtained from the application of back‐propagation and quadratic programming methods to the preprocessed data show possible fracture zones that agree well at the boundaries of the region with the fracture sets observed from core samples taken from the boreholes. Although the quadratic programming method is an order of magnitude slower than the back‐propagation method, as demonstrated by the synthetic examples, it proves useful by yielding high resolution images when constraints can be imposed. Transmission ray tomography is also applied to the crosshole data, and although the resolution is not as high, general agreement with the wave equation based methods is obtained.

Image Reconstruction with Acoustic Measurement Using Distorted Born Iteration Method

1996 ◽  
Vol 18 (2) ◽  
pp. 140-156 ◽  
Author(s):  
C. Lu ◽  
J. Lin ◽  
W. Chew ◽  
G. Otto
Keyword(s):  
Cross Section ◽  
Born Approximation ◽  
Measurement Data ◽  
Arbitrary Cross Section ◽  
Ultrasonic Measurement ◽  
Diffraction Tomography ◽  
Two Dimensional ◽  
Scattering Problems ◽  
First Order ◽  
Scattered Fields

The distorted Born iterative method (DBIM) is applied to solve electromagnetics and ultrasonics inverse scattering problems. First, we use the DBIM to process the data, which are the scattered fields from two-dimensional cylinders with arbitrary cross section. From this simulation, we confirmed that the first-order Born approximation can be applied to larger objects as long as the phase change of a wave passing through the object due to its presence is smaller than a limit. Then we applied DBIM to process the ultrasonic measurement data. Images for a balloon and an egg that are immersed in water have been reconstructed and compared with those from the first-order diffraction tomography (DT).

FEASIBILITY OF GUIDED WAVE DIFFRACTION TOMOGRAPHY WITHIN THE BORN APPROXIMATION

2010 ◽  
Author(s):  
P. Belanger ◽  
P. Cawley ◽  
Donald O. Thompson ◽  
Dale E. Chimenti
Keyword(s):  
Wave Diffraction ◽  
Born Approximation ◽  
Guided Wave ◽  
Diffraction Tomography

scholarly journals Ultrasonic laboratory tests of geophysical tomographic reconstruction

Geophysics ◽  
1988 ◽  
Vol 53 (7) ◽  
pp. 947-956 ◽  
Author(s):  
Tien‐when Lo ◽  
M. Nafi Toksöz ◽  
Shao‐hui Xu ◽  
Ru‐Shan Wu
Keyword(s):  
Born Approximation ◽  
Laboratory Tests ◽  
Tomographic Reconstruction ◽  
Acoustic Properties ◽  
Diffraction Tomography ◽  
Frequency Range ◽  
Scaled Model ◽  
Surface Reflection ◽  
Rytov Approximation ◽  
Reflection Tomography

In this study, we test geophysical ray tomography and geophysical diffraction tomography by scaled model ultrasonics experiments. First, we compare the performance of these two methods under limited view‐angle conditions. Second, we compare the adaptabilities of these two methods to objects of various sizes and acoustic properties. Finally, for diffraction tomography, we compare the Born and Rytov approximations based on the induced image distortion by using these two approximation methods. Our experimental results indicate the following: (1) When the scattered field can be obtained, geophysical diffraction tomography is in general superior to ray tomography because diffraction tomography is less sensitive to the limited view‐angle problem and can image small objects of size comparable to a wavelength. (2) The advantage of using ray tomography is that reconstruction can be done using the first arrivals only, the most easily measurable quantity; and there is no restriction on the properties of the object being imaged. (3) For geophysical diffraction tomography, the Rytov approximation is valid over a wider frequency range than the Born approximation in the cross‐borehole experiment. In the VSP and the surface reflection tomography experiments, no substantial difference between the Born and Rytov approximations is observed.

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