Direct solution of the inverse problem for rough surface scattering at grazing incidence

@article{Spivack1992DirectSO,
  title={Direct solution of the inverse problem for rough surface scattering at grazing incidence},
  author={Mark Spivack},
  journal={Journal of Physics A},
  year={1992},
  volume={25},
  pages={3295-3302}
}
  • M. Spivack
  • Published 7 June 1992
  • Mathematics
  • Journal of Physics A
Considers the inverse scattering problem for a scalar wavefield incident at grazing angles on a one-dimensional rough surface. The problem is formulated first as a pair of coupled integral equations in two unknown functions, knowledge of which immediately yields the surface. A method is described for the direct approximate solution of this system. Preliminary results are presented in groups of complicated rough surfaces which are closely recaptured in all details except for scale. 

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References

SHOWING 1-8 OF 8 REFERENCES
Moments of wave scattering by a rough surface
This paper gives the first two moments of a wave field scattered by grazing incidence on a moderately rough surface. The expressions are derived for normally distributed surfaces with arbitrary
Rough surface scattering using the parabolic wave equation
The accuracy of the parabolic wave equation (PE) for calculating scattering from randomly rough, pressure‐release surfaces has been examined through comparison with exact numerical results based on
A numerical approach to rough‐surface scattering by the parabolic equation method
The parabolic equation method is an effective approach when the acoustic wave field is incident at low grazing angles onto a rough surface. The method consists of an integral equation and an
THE INVERSE SCATTERING PROBLEM FOR TIME-HARMONIC ACOUSTIC WAVES*
The inverse scattering problem we are considering in this paper is to determine the shape of a sound-soft, bounded, connected obstacle from a knowledge of the time-harmonic incident wave with
rtincipb of Optics (Oxford: Pergamon
  • 1970
T?te %ory of Elecnomopctinn (Oxford: Pergamon
  • 1964