Born Approximation for Wave Scattering in Inhomogeneous Media

Author(s):  
Haruo Sato ◽  
Michael C. Fehler
Geophysics ◽  
1999 ◽  
Vol 64 (1) ◽  
pp. 289-299 ◽  
Author(s):  
David W. Eaton

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.


1987 ◽  
Vol 65 (4) ◽  
pp. 392-394
Author(s):  
Robert Cleary

The linear response to longitudinal modulations in a superconducting alloy is calculated for the general case. Extension to transverse waves, point-charge Coulomb potentials, and magnetic dipoles is trivial. All the results are limited to Born approximation, s-wave scattering by the impurities embedded in the superconductor. Derivation of the equations for linear response is the same as for clean superconductors, with the appearing correlation functions containing impurity-averaged vertex parts. Only one vertex part is evaluated here; the remaining ones are easy extensions of our calculation.


1992 ◽  
Vol 35 (5) ◽  
pp. 275-283
Author(s):  
V. V. Akhmatov ◽  
A. G. Fokin

Sign in / Sign up

Export Citation Format

Share Document