1. 
 Karlsson, Anders, et al.
(författare)

Transient wave propagation in gyrotropic media
 1992

Ingår i: Invariant inbedding and inverse problems.  SIAM.  0898713056 ; s. 7789

Bokkapitel (övrigt vetenskapligt)abstract
 In this paper transient electromagnetic wave propagation in an inhomogeneous, cold plasma is considered. It is assumed that a constant magnetic induction is present and that the plasma is spatially inhomogeneous in the direction of the magnetic induction. Losses in the plasma are modeled with a collision frequency ν. The direct problem, which is to calculate the reflected and transmitted responses of the plasma, is considered in this paper. Special attention is paid to the precursor effects in the plasma and several examples of precursor effects in an inhomogeneous plasma are showed.


2. 
 Karlsson, Anders, et al.
(författare)

Wave splitting and imbedding equations for a spherically symmetric dispersive medium
 1992

Ingår i: Invariant inbedding and inverse problems.  SIAM.  0898713056 ; s. 103113

Bokkapitel (övrigt vetenskapligt)abstract
 The direct problem of time dependent electromagnetic scattering in the dispersive sphere is solved by a wave splitting technique. The electric field is expanded in a series involving vector spherical harmonics, leading to a system of wave equations for each term. These systems are reduced to scalar wave equations for each term, which are solved via reflection operators. Some preliminary numerical results are presented.


3. 
 Kristensson, Gerhard, et al.
(författare)

Time domain inversion techniques for electromagnetic scattering problems
 1992

Ingår i: Invariant imbedding and inverse problems.  SIAM.  0898713056 ; s. 129

Bokkapitel (övrigt vetenskapligt)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 (layerstripping)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.


4. 
 Karlsson, Anders, et al.
(författare)

Transient wave propagation in composite media:
 1992

Rapport (övrigt vetenskapligt)abstract
 A generalized Green functions technique for wave propagation of transient fields in onedimensional media is developed. The medium is partitioned into an arbitrary number of subslabs for which Green operators, that map the incident field to the internal fields, are defined. Relations between the Green operators for the entire medium and the Green operators for the subslabs are derived. The technique leads to fast numerical algorithms which are especially efficient for dispersive media. The numerical examples focus on the comparison between wave propagation in dispersive and nondispersive media.


5. 
 Björkberg, Jonas, et al.
(författare)

Threedimensional subterranean target identification by use of optimization techniques
 1991

Rapport (övrigt vetenskapligt)abstract
 The identification of a subterranean metallic ore from scattering experiments, conducted on the surface of the ground or in a bore hole, is a classic geophysical problem. In general this problem is not wellposed. However, a priori information about the shape of the target provides enough regularization to make the problem numerically stable. The problem is solved by minimizing the meansquare error between an eleven parameter model, based on the null field approach, and the data. The optimization is done with a Newton technique in which a singular value decomposition of the model Jacobian is employed. The algorithm is very stable to noise and makes good reconstructions from feasible starting guesses, for realistically noise contaminated data.


6. 
 Fridén, Jonas, et al.
(författare)

Transient Electromagnetic Wave Propagation in Anisotropic Dispersive Media
 1992

Rapport (övrigt vetenskapligt)abstract
 In this paper transient electromagnetic wave propagation in a stratified, anisotropic, dispersive medium is considered. Specifically, the direct scattering problem is addressed. The dispersive, anisotropic medium is modeled by constitutive relations (a 3 × 3 matrixvalued susceptibility operator)con taining time convolution integrals. In the general case, nine different susceptibility kernels characterize the medium. An incident plane wave impinges obliquely on a finite slab consisting of a stratified anisotropic medium. The scattered fields are obtained as time convolutions of the incident field with the scattering kernels. The scattering (reflection and transmission)k ernels are uniquely determined by the slab and are independent of the incident field. The scattering problem is solved by a wave splitting technique. Two different methods to determine the scattering kernels are presented; an imbedding and a Green functions approach. Explicit analytic expressions of the wave front are given for a special class of media. Some numerical examples illustrate the analysis.


7. 
 Fuks, Peter, et al.
(författare)

Permittivity profile reconstructions using transient electromagnetic reflection data
 1990

Rapport (övrigt vetenskapligt)abstract
 This paper is concerned with the permittivity reconstruction of inhomogeneous dielectric media. The method applies to profiles that vary with depth only, i.e. it provides a onedimensional profile reconstruction. The data are collected and analyzed in the time domain. In the first part of the paper the theory of the method is reviewed. It is showed that a finite time trace of reflection data suffices to uniquely reconstruct the permittivity profile of the medium. The latter part of the paper presents the experimental setup and contains also a thorough discussion of the errors that affect the measurements. The inverse scattering algorithm that is used is either based upon an imbedding procedure or on a Green functions approach. The input to either of these algorithms is the reflection kernel or the impulse response of the medium, i.e. the delta function response of the medium. Therefore, a deconvolution of the the measured reflected field and the incident field must be performed. This deconvolution problem is also addressed briefly in this paper.


8. 
 Karlsson, Anders, et al.
(författare)

Transient wave propagation in gyrotropic media
 1990

Rapport (övrigt vetenskapligt)abstract
 In this paper transient electromagnetic wave propagation in an inhomogeneous, cold plasma is considered. It is assumed that a constant magnetic induction is present and that the plasma is spatially inhomogeneous in the direction of the magnetic induction. Losses in the plasma are modeled with a collision frequency ν. The direct problem, which is to calculate the reflected and transmitted responses of the plasma, is considered in this paper. Special attention is paid to the precursor effects in the plasma and several examples of precursor effects in an inhomogeneous plasma are showed.


9. 
 Karlsson, Anders, et al.
(författare)

Wave splitting and imbedding equations for a spherically symmetric dispersive medium
 1991

Rapport (övrigt vetenskapligt)abstract
 The direct problem of time dependent electromagnetic scattering in the dispersive sphere is solved by a wave splitting technique. The electric field is expanded in a series involving vector spherical harmonics, leading to a system of wave equations for each term. These systems are reduced to scalar wave equations for each term, which are solved via reflection operators. Some preliminary numerical results are presented.


10. 
 Kristensson, Gerhard
(författare)

Direct and inverse scattering problems in dispersive mediaGreen's functions and invariant imbedding techniques
 1990

Rapport (övrigt vetenskapligt)abstract
 Transient electromagnetic wave propagation in a dispersive medium is reviewed. The medium is assumed to be 1) linear, 2) invariant to time translations, 3) causal, 4) continuous, and 5) isotropic. The constitutive relations are then uniquelyrepresen ted bya RiemannStieltjes integral in the time variable. The kernel in this convolution is the susceptibilityk ernel. Two explicit examples of mathematical models of the susceptibilityk ernel are given. The medium treated in this paper is assumed to varyonlywith depth. In the direct problem the reflection and transmission data are computed. The inverse scattering problem is to find the susceptibilityk ernel from known reflexion data. It is, thus, a problem of finding a function depending on the time variable. In the spatiallyhomogeneous case the inverse scattering problem is solved from reflexion data bysolving a Volterra integral equation of the second kind. This inverse problem is therefore wellposed and easyto solve.

