EDGE DIFFRACTION IN AN ARBITRARY ANISOTROPIC MEDIUM. II

1967 ◽  
Vol 45 (11) ◽  
pp. 3503-3519
Author(s):  
Shalom Rosenbaum
Keyword(s):  
Anisotropic Medium ◽  
Line Source ◽  
Short Wavelength ◽  
Entire Range ◽  
Dielectric Tensor ◽  
Total Field ◽  
Reflected Waves ◽  
Edge Diffraction ◽  
Wave Numbers ◽  
Formal Solutions

Diffraction by a perfectly conducting half-plane embedded in a transversely unbounded region filled with a uniform, lossless but arbitrarily anisotropic medium characterized by a Hermitian dielectric tensor ε is studied. Excitation is by a linearly phased line source of arbitrarily polarized electric and magnetic currents. Formal solutions are obtained in terms of a two-dimensional plane-wave modal superposition (over the entire range of the transverse wave numbers representing the incident (ηn) and scattered (η) waves). The original contours of integration in both the complex ηn and η planes are deformed simultaneously into their respective paths of steepest descent, and contributions to intercepted singular points are considered. Asymptotic (short-wavelength) analysis yields results which, despite their relative complexity, are cast into invariant, ray-optical forms, amenable to distinct physical (geometric-optical) interpretation.Mode coupling at the boundary gives rise to source-excited lateral waves as well as geometric-optical (incident and reflected) waves. In the short-wavelength limit, the edge behaves as a virtual line source whose magnitude is proportional to the total field incident upon it (which is composed of direct rays emerging from the source, as well as a lateral wave propagating along the boundary, towards the edge). Both the direct and the lateral waves are diffracted by the edge (i.e., coupled to edge-excited "radial" and "secondary" lateral waves) in a manner identical with that discussed in Part I.

EDGE DIFFRACTION IN AN ARBITRARY ANISOTROPIC MEDIUM. I

1967 ◽  
Vol 45 (11) ◽  
pp. 3479-3502 ◽  
Author(s):  
Shalom Rosenbaum
Keyword(s):  
Anisotropic Medium ◽  
Short Wavelength ◽  
Dielectric Tensor ◽  
Asymptotic Results ◽  
Asymptotic Field ◽  
Lateral Field ◽  
Reflected Waves ◽  
Edge Diffraction ◽  
Diffracted Waves ◽  
Formal Solutions

Diffraction by a perfectly conducting half-plane embedded in a transversely unbounded region filled with a uniform, lossless but arbitrarily anisotropic medium characterized by a Hermitian dielectric tensor ε is studied. Formal solutions in terms of a plane-wave modal superposition (with the modal amplitudes determined via the Wiener–Hopf technique) are obtained. Asymptotic (short-wavelength) contributions (saddle-point contributions as well as contributions due to intercepted singular points) are considered. The asymptotic results are then cast into invariant, ray optical forms, amenable to a distinct physical interpretation.Mode coupling at the boundary gives rise to diffracted (lateral) waves as well as to geometric-optical (incident and reflected) waves. In addition to the "conventional" radially diffracted waves, one observes "secondary" lateral waves generated by the edge. In the short-wavelength limit the edge behaves as a virtual line source whose magnitude is proportional to the total (direct and lateral) field incident upon it. The asymptotic field solutions are valid, subject to the exclusion of some suitably defined transition regions, which are distinctly determined by the geometric-optical expressions. The various (asymptotic) wave constituents are shown to correspond to the anticipated results of geometrical optics.

Radiation Field of a Uniformly Moving Charge in an Anisotropic Medium

1974 ◽  
Vol 29 (5) ◽  
pp. 687-692
Author(s):  
G. P. Sastry ◽  
S. Datta Majumdar
Keyword(s):  
Radiation Field ◽  
Anisotropic Medium ◽  
Point Charge ◽  
Potential Distribution ◽  
Asymptotic Form ◽  
Dielectric Tensor ◽  
Arbitrary Direction ◽  
Hankel Functions ◽  
Anisotropic Fields ◽  
Set Up

Abstract Fourier integrals are set up for the field of a point charge moving uniformly in an arbitrary direction in a uniaxial medium anisotropic in ε only. The integrals break up into several parts two of which yield the ordinary and extraordinary cones with uniform azimuthal potential distribution. The remaining integrals neither contribute to the energy radiated nor affect the size and the shape of the cones, but merely distort the field within the cones. The integrals are evaluated exactly in the non-dispersive case and closed expressions for the potential are obtained. In the dispersive case, the radiation field is determined by using the asymptotic form of the Hankel functions occurring in the integrand. The resulting expressions exhibit the high azimuthal asymmetry characteristic of anisotropic fields. From the expressions derived for a pure dielectric the potential in a doubly anisotropic medium is obtained, without a fresh calculation, by making appropriate substitutions for the coordinates of the field point and the components of the dielectric tensor.

Inversion of seismic refraction and reflection data for building long-wavelength velocity models

Geophysics ◽  
2015 ◽  
Vol 80 (2) ◽  
pp. R81-R93 ◽  
Author(s):  
Haiyang Wang ◽  
Satish C. Singh ◽  
Francois Audebert ◽  
Henri Calandra
Keyword(s):  
Wave Equation ◽  
Short Wavelength ◽  
Velocity Model ◽  
Density Model ◽  
Data Set ◽  
Reflected Waves ◽  
Long Wavelength ◽  
Velocity Models ◽  
Computation Efficiency ◽  
Refracted Waves

Long-wavelength velocity model building is a nonlinear process. It has traditionally been achieved without appealing to wave-equation-based approaches for combined refracted and reflected waves. We developed a cascaded wave-equation tomography method in the data domain, taking advantage of the information contained in the reflected and refracted waves. The objective function was the traveltime residual that maximized the crosscorrelation function between real and synthetic data. To alleviate the nonlinearity of the inversion problem, refracted waves were initially used to provide vertical constraints on the velocity model, and reflected waves were then included to provide lateral constraints. The use of reflected waves required scale separation. We separated the long- and short-wavelength subsurface structures into velocity and density models, respectively. The velocity model update was restricted to long wavelengths during the wave-equation tomography, whereas the density model was used to absorb all the short-wavelength impedance contrasts. To improve the computation efficiency, the density model was converted into the zero-offset traveltime domain, where it was invariant to changes of the long-wavelength velocity model. After the wave-equation tomography has derived an optimized long-wavelength velocity model, full-waveform inversion was used to invert all the data to retrieve the short-wavelength velocity structures. We developed our method in two synthetic tests and then applied it to a marine field data set. We evaluated the results of the use of refracted and reflected waves, which was critical for accurately building the long-wavelength velocity model. We showed that our wave-equation tomography strategy was robust for the real data application.

TRANSMISSION AND REFLECTION OF RAYLEIGH WAVES BY WEDGES

Geophysics ◽  
1960 ◽  
Vol 25 (6) ◽  
pp. 1203-1214 ◽  
Author(s):  
L. Knopoff ◽  
A. F. Gangi
Keyword(s):  
Incident Wave ◽  
Line Source ◽  
Rayleigh Waves ◽  
Wave Form ◽  
Reflected Waves ◽  
Wave Shapes ◽  
Transmission And Reflection

Experimental observations have been made of the transmission and reflection of Rayleigh waves by wedges. Results are reported for Rayleigh waves in aluminum wedges. It is observed that the wave shapes of the transmitted and reflected waves differ from that of the incident wave and depend on the angle of the wedge. The change of shape is attributed to an interference between part of the incident wave‐form and the radiation from a line source placed at the vertex. A procedure is given for the calculation of the partition between the two terms.

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