The Maxwell field, its adjoint field and the ‘conjugate’field in anisotropic absorbing media

Suchy, K.; Altman, C.

doi:10.1017/s0022377800026064

Cited by 18 publications

(8 citation statements)

References 15 publications

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“…They are only useful for further calculations. But they can be considered as waves in a concomitant space (Suchy and Altman 1975). It is easy to prove the following bi-orthogonality relation:…”

Section: The Eigenvalue Spectrum Of the Modes And Polarization Vectorsmentioning

confidence: 99%

Mode coupling in space- and time-varying anisotropic absorbing plasmas

Sabzevari

1997

J. Plasma Phys.

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A four dimensional systematic mathematical approach for investigating propagation and coupling of wave modes in a slowly varying (in all space directions and time) anisotropic, absorbing plasma is represented. The formalism is especially useful for energy considerations of the waves. It is applicable to general cases of mode conversion in plasmas with general geometries of space-time and magnetic field configurations. A simple example of how this formalism can be applied to practical cases is given.

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Section: The Eigenvalue Spectrum Of the Modes And Polarization Vectorsmentioning

confidence: 99%

Mode coupling in space- and time-varying anisotropic absorbing plasmas

Sabzevari

1997

J. Plasma Phys.

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“…By contrast, (7.5) makes it possible to establish a rather simple relationship between modes in the one medium, using the conjugate field. Suchy & Altman (1975) defined and discussed a field 'conjugate' to a field, decomposed into modes. Presently relevant results are now summarized.…”

Section: Relation Between Scattering Matricesmentioning

confidence: 99%

“…To gather information about the original medium from the adjoint field, in § 8 a conjugate field is used, situated in the medium under consideration, and uniquely related to the adjoint field. (For its derivation and properties, see Suchy & Altman 1975). The conjugate field enables one to convert the intermediate relations into connexions between fields in the same medium, viz.…”

Section: Introductionmentioning

confidence: 99%

Reflexion and transmission theorems for characteristic waves in stratified anisotropic absorbing media

Suchy

Altman

1975

J. Plasma Phys.

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The solutions of Maxwell's equations and of their adjoint equations, being essentially different in absorbing media, are written in terms of matrizants. A relation between these is established, utilizing the constancy of the bi-linear concomitant. With this, and with the concept of the conjugate field, introduced in Suchy & Altmann (1975), a theorem, connecting the transfer matrices of the field and the conjugate field, is derived. This, in turn, leads to a corresponding theorem connecting the scattering matrices, which are composed of the refiexion and transmission matrices.

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“…The matrix propagator methods are well known techniques for treating wave propagation in stratified media: cf. Berremann (1972) in optics, Suchy & Altman (1975) in plasma physics, Kong (1972) for the geophysical electromagnetic problem in stratified media with transversal isotropy in the direction of medium changes, Griffiths & Steinke (2000) for wave propagation in locally periodic media, Kennett (1983) for seismic wave propagation, Ursin (1983) reviewing elastic and electromagnetic wave propagation, and White & Zhou (2006) for electroseismic prospecting in layered media.…”

Section: Introductionmentioning

confidence: 99%

Electromagnetic fields in planarly layered anisotropic media

Løseth

Ursin

2007

Geophysical Journal International

161

105

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S U M M A R YThis paper presents a method for calculating the electromagnetic field from a dipole source in stratified media with general anisotropy. The formulation can be applied to geophysical applications such as ground-penetrating radar and marine controlled source electromagnetic (CSEM) methods. In stratified media, the propagation of fields can be considered in the frequencywavenumber domain. The resulting set of ordinary differential equations consists of a field vector, a system matrix, and a source vector. In each piecewise homogeneous region, the system matrix is given by the material properties and the horizontal slownesses. The vertical slownesses are the eigenvalues of the system matrix. A diagonalization of the system matrix transforms the field vector into a mode-field that contains upgoing and downgoing field constituents. For system matrices that account for general anisotropy, it is shown how the electromagnetic field from any of the four basic dipole types can be calculated at any desired position in the stratified medium. It is furthermore shown how the reflection and transmission response from a stack can be calculated by a recursive scheme. Potential numerical instabilities due to using propagators are avoided by using this reflectivity method. Due to an energy-flux normalization of the eigenvector matrices, the reciprocity relations for reflection and transmission of electromagnetic fields in general anisotropic media can be derived. Several other useful relations between the reflection and transmission matrices are obtained as well. The propagator method is dependent on the ability to calculate eigenvalues and eigenvectors of the system matrix for all layers. In simple cases with isotropy or transversal isotropy in the direction of medium variation, the eigenvalue problem can be solved explicitly. These eigenvector matrices have useful properties, e.g. when processing data. The possibility to remove layers above or below the receiver layer follows from the decomposition of a field into upgoing and downgoing polarization modes. The propagator theory was implemented in order to model anisotropy in marine CSEM. A modelling study shows that responses are affected by horizontal, vertical, and dipping anisotropy in different manners. This suggests that when anisotropy is present at a survey site, careful planning and interpretation are required in order to correctly account for the responses.

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The Maxwell field, its adjoint field and the ‘conjugate’field in anisotropic absorbing media

Cited by 18 publications

References 15 publications

Mode coupling in space- and time-varying anisotropic absorbing plasmas

Mode coupling in space- and time-varying anisotropic absorbing plasmas

Reflexion and transmission theorems for characteristic waves in stratified anisotropic absorbing media

Electromagnetic fields in planarly layered anisotropic media

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