Born approximation of the solution of the internal wave scattering problem

1984 ◽  
Vol 25 (2) ◽  
pp. 246-251 ◽  
Author(s):  
S. P. Budanov ◽  
A. S. Tibilov ◽  
V. A. Yakovlev
Keyword(s):  
Internal Wave ◽  
Born Approximation ◽  
Wave Scattering ◽  
Scattering Problem

INTEGRABLE MODELS OF FIELD THEORY AND SCATTERING ON QUANTUM HYPERBOLOIDS

1992 ◽  
Vol 07 (05) ◽  
pp. 441-446 ◽  
Author(s):  
A. ZABRODIN
Keyword(s):  
Field Theory ◽  
Symmetric Space ◽  
Quantum Group ◽  
Wave Scattering ◽  
Scattering Problem ◽  
Free Particle ◽  
Compact Quantum Group ◽  
Integrable Models ◽  
S Wave

We consider the scattering of two dressed excitations in the antiferromagnetic XXZ spin-1/2 chain and show that it is equivalent to the S-wave scattering problem for a free particle on the certain quantum symmetric space “quantum hyperboloid” related to the non-compact quantum group SU q (1, 1).

Theoretical researches on three-dimensional coda wave scattering problem

1995 ◽  
Vol 8 (1) ◽  
pp. 83-87 ◽  
Author(s):  
Yong-An Nie ◽  
Jian Zeng ◽  
De-Yi Feng
Keyword(s):  
Wave Scattering ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Coda Wave

Explicit solution of the scattering problem involving a vertical flexible membrane

2020 ◽  
Author(s):  
Srinivasa Rao Manam ◽  
Ashok Kumar ◽  
Gunasundari Chandrasekar
Keyword(s):  
Wave Scattering ◽  
Scattering Problem ◽  
Physical Problem ◽  
Plane Boundary ◽  
Water Wave Scattering ◽  
Flexible Membrane ◽  
Quarter Plane ◽  
Integral Relations ◽  
Incident Waves ◽  
Membrane Deflection

<p>The problem of normally incident water wave scattering by a flexible membrane is completely solved. The physical problem in a half-plane is reduced to a couple of equivalent quarter-plane problems by allowing incident waves from either direction of the membrane. In the same way, quarter-plane boundary value problems are posed for solid wave potentials that are solutions of the scattering problem involving a rigid structure of the same geometric configuration. Then, two novel integral relations are introduced to establish a link between the required solution wave potentials and few resolvable solid wave potentials. Explicit expressions for the scattering quantities such as the reflection and the transmission wave amplitudes are obtained. Also, the deflection of the flexible vertical membrane and the solution potentials are determined analytically. Numerical results for the scattering quantities and the membrane deflection are presented.</p>

Weak elastic‐wave scattering from massive sulfide orebodies

Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 289-299 ◽  
Author(s):  
David W. Eaton
Keyword(s):  
Numerical Modeling ◽  
Elastic Wave ◽  
Born Approximation ◽  
Wave Scattering ◽  
Shape Factor ◽  
Massive Sulfide ◽  
Ore Deposits ◽  
Elastic Wave Scattering ◽  
Weak Scattering ◽  
Scattering Response

Massive sulfide ore deposits, traditionally the target of electromagnetic or potential‐field geophysical investigations, can potentially be recognized and mapped using seismic methods based on their scattering response. To characterize the seismic expression of massive sulfide orebodies, I review formulas that describe elastic‐wave scattering from isolated inclusions in the far‐field and weak‐scattering limits (the Born approximation) and conduct a series of numerical tests. The minerals pyrite, sphalerite, and galena are used as the basis for these numerical modeling studies because they are relatively abundant and collectively span the full range of observed velocities and densities for ore rocks. The assumption of weak scattering, on which the Born approximation rests, is verified empirically in a representative example, by examining in‐situ wavefield measurements from a vertical seismic profiling experiment in northern Québec, Canada. For simplicity, orebodies are modeled as ellipsoidal inclusions in a homogeneous medium. The mathematical formalism leads to decoupling of factors for “composition” and “shape.” At seismic frequencies (∼50 Hz) and for ore deposits of sufficient size to represent economically viable targets (more than 109 kg), the shape factor effectively controls the scattering response. In this regime, negligible backscattering from spherical inclusions is predicted by the theory. In the case of flattened ellipsoids, which represent a more realistic orebody morphology, the shape‐factor effect leads to significant backscattering that is focused in the direction of specular reflection. For noisy 2-D data, numerical modeling indicates that these characteristics can cause scattering from an isolated dipping orebody to resemble reflections from a planar interface. For 3-D seismic surveys, however, isolated scattering bodies will produce a diagnostic pattern of concentric circular diffractions in unmigrated time‐slice sections.

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