| 11. |
- Kristensson, Gerhard, et al.
(författare)
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Scattering of transient electromagnetic waves in reciprocal bi-isotropic media
- 1991
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper propagation of transient electromagnetic waves in a reciprocal bi-isotropic medium is presented. The constitutive relations are convolution integrals with two susceptibility kernels that model the medium. The propagation problem is solved by the introduction of a wave-splitting technique. This wave-splitting is used to solve the propagation problem using either an imbedding approach or a Green function technique. In particular, the scattering problem of an electromagnetic wave that impinges normally on a slab of finite or infinite extent is solved. The slab is assumed to be inhomogeneous with respect to depth. The scattering problem consists of finding the reflected and the transmitted fields and the generic quantities are the reflection and the transmission kernels of the medium. Explicit expressions for the rotation and the attenuation of the wave front is presented for the inhomogeneous slab. In the special case of a homogeneous infinite slab it is proved that the reflection kernel satisfies a non-linear Volterra equation of the second kind, very suitable for numerical calculations. It is also proved that no cross polarization contribution appears for the homogeneous slab. Several numerical computations illustrate the analysis.
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| 12. |
- Kristensson, Gerhard, et al.
(författare)
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The inverse scattering problem for a homogeneous bi-isotropic slab using transient data
- 1993
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Ingår i: Inverse problems in mathematical physics / Lecture notes in physics. - 0075-8450. - 3540571957 ; 422, s. 112-125
-
Bokkapitel (övrigt vetenskapligt/konstnärligt)abstract
- Transient wave propagation in a finite bi-isotropic slab is treated. The incident field impinges normally on the slab, which can be inhomogeneous wrt depth. Dispersion and bi-isotropy are modeled by time convolutions in the constitutive relations. Outside the slab the medium is assumed to be homogeneous, non-dispersive and isotropic, and such that there is no phase velocity mismatch at the boundaries of the slab. Two alternative methods of solution to the propagation problem are given—the imbedding method and the Green function approach. The second method is used to solve the inverse problem and the first to generate synthetic data. The inverse scattering problem is to reconstruct the four susceptibility kernels of the medium using a set of finite time trace of reflection and transmission data.
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| 13. |
- Kristensson, Gerhard, et al.
(författare)
-
The inverse scattering problem for a homogeneous bi-isotropic slab using transient data
- 1992
-
Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Transient wave propagation in a finite bi-isotropic slab is treated. The incident field impinges normally on the slab, which can be inhomogeneous wrt depth. Dispersion and bi-isotropy are modeled by time convolutions in the constitutive relations. Outside the slab the medium is assumed to be homogeneous, non-dispersive and isotropic, and such that there is no phase velocity mismatch at the boundaries of the slab. Two alternative methods of solution to the propagation problem are given—the imbedding method and the Green function approach. The second method is used to solve the inverse problem and the first to generate synthetic data. The inverse scattering problem is to reconstruct the four susceptibility kernels of the medium using a set of finite time trace of reflection and transmission data.
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| 14. |
- Kristensson, Gerhard
(författare)
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Time domain inversion techniques for electromagnetic scattering problems
- 1990
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper presents a review of and a comparison between two different methods to solve an inverse scattering problem in the time domain. The problem is that of propagation of transient electromagnetic waves in spatially inhomogeneous slabs of finite length. The permittivity and conductivity profiles are assumed to vary only with depth and the scattering problem is thus onedimensional. Several algorithms to solve the direct and inverse scattering problems for continuous and discontinuous permittivity profiles are suggested. Some of these algorithms have not been published before. The aim of this paper is to compare and review these methods. More specifically, the numerical performance of the invariant imbedding approach (layer-stripping)and the Green functions formulation (downward continuation)is compared. Some new results based upon time reversal techniques for a lossless slab are presented in an appendix.
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| 15. |
- Kristensson, Gerhard
(författare)
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Transient Electromagnetic Wave Propagation in Waveguides
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper focuses on propagation of transient electromagnetic waves in waveguides of general cross section with perfectly conducting walls. The solution of the transient wave propagation problem relies on a wave splitting technique, which has been frequently used in direct and inverse scattering problems during the last decade. The field in the waveguide is represented as a time convolution of a Green function and the excitation. Some numerical computations illustrate the method. Anew way of calculating the first precursor in a Lorentz medium is presented. This method, which is not based upon the classical asymptotic methods, gives an expression of the first precursor at all depths in the medium. The excitation of the waveguide modes for time dependent sources is also addressed.
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| 16. |
- Kristensson, Gerhard, et al.
(författare)
-
Transient wave propagation in reciprocal bi-isotropic media at oblique incidence
- 1992
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In this paper a new wave splitting is suggested that simplifies the analysis of wave propagation in reciprocal bi-isotropic media. Two different methods to solve the scattering problem are analyzed; the invariant imbedding and the Green function approach. The medium is modeled by constitutive relations in the time domain (time convolutions) and the slab is assumed to be inhomogeneous with respect to the depth. It is showed that the cross-polarized contribution to the reflected field at normal incidence is zero for the general reciprocal inhomogeneous slab. Moreover, the rotation and the attenuation of the wave front are calculated explicitly in the general inhomogeneous slab case. Special attention is paid to normal incidence and to the homogeneous semi-infinite medium.
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| 17. |
- Malmqvist, Lennart, et al.
(författare)
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Electromagnetic fields in boreholes-measurements and theory in three dimensions
- 1990
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- A comparison between experimental measurements of the electromagnetic field in boreholes and a mathematical model is made. The transmitting antenna is a rectangular wire loop on the ground and the three orthogonal components of the magnetic field are measured below the ground in the borehole. In the mathematical model the ground is assumed to be a stratified half space with a rectangular wire antenna on the ground. Excellent agreement was found between the experimental results and the theoretical ones in most cases and where deviations were found, the assumption of a stratified ground was inaccurate due to present conductive inhomogeneities. The method presented in this paper is capable of determining an ore body within a radius of 100 m from the borehole. The position (direction and distance) of the target can be estimated from the measurements in the borehole. The impact on the economical effectiveness of a drilling programme is considerable when a prediction of the location of additional boreholes can be made. In the case of reconnaissance drilling of a geological structure or trend the distance between adjacent boreholes can be considerably enlarged.
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| 18. |
- Olsson, Peter, et al.
(författare)
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Wave splitting of the Timoshenko beam equation in the time domain
- 1993
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- In recent years, wave splitting in conjunction with invariant imbedding and Green’s function techniques has been applied with great success to a number of interesting inverse and direct scattering problems. The aim of the present paper is to derive a wave splitting for the Timoshenko equation, a fourth order PDE of importance in beam theory. An analysis of the hyperbolicity of the Timoshenko equation and its, in a sense, less physical relatives—the Euler-Bernoulli and the Rayleigh equations—is also provided.
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| 19. |
- Åberg, Ingegerd, et al.
(författare)
-
Propagation of transient electromagnetic waves in time-varying media - Direct and inverse scattering problems
- 1994
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- Wave propagation of transient electromagnetic waves in time-varying media is considered. The medium, which is assumed to be inhomogeneous and dispersive, lacks invariance under time translations. The spatial variation of the medium is assumed to be in the depth coordinate, i.e., it is stratified. The constitutive relations of the medium is a time integral of a generalized susceptibility kernel and the field. The generalized susceptibility kernel depends on one spatial and two time coordinates. The concept of wave splitting is introduced. The direct and inverse scattering problems are solved by the use of an imbedding or a Green functions approach. The direct and the inverse scattering problems are solved for a homogeneous semi-infinite medium. Explicit algorithms are developed. In this inverse scattering problem, a function depending on two time coordinates is reconstructed. Several numerical computations illustrate the performance of the algorithms.
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| 20. |
- Åberg, Ingegerd, et al.
(författare)
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Transient waves in non-stationary media
- 1994
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Rapport (övrigt vetenskapligt/konstnärligt)abstract
- This paper treats propagation of transient waves in non-stationary media, which has many applications in e.g. electromagnetics and acoustics. The underlying hyperbolic equation is a general, homogeneous, linear, first order 2×2 system of equations. The coefficients in this system depend only on one spatial coordinate and time. Furthermore, memory effects are modeled by integral kernels, which, in addition to the spatial dependence, are functions of two different time coordinates. These integrals generalize the convolution integrals, frequently used as a model for memory effects in the medium. Specifically, the scattering problem for this system of equations is addressed. This problem is solved by a generalization of the wave splitting concept, originally developed for wave propagation in media which are invariant under time translations, and by an imbedding or a Green functions technique. More explicitly, the imbedding equation for the reflection kernel and the Green functions (propagator kernels) equations are derived. Special attention is paid to the problem of non-stationary characteristics. A few numerical examples illustrate this problem.
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