An injective far-field pattern operator and inverse scattering problem in a finite depth ocean
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An injective far-field pattern operator and inverse scattering problem in a finite depth ocean

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Details:

  • Personal Author:
    Xu, Yongzhi
  • NOAA Program & Office:
  • Sea Grant Program:
    DELU (Delaware Sea Grant)
  • Description:
    The inverse scattering problem for acoustic waves, which consists of recovering the shape of a scatterer from the far-field pattern of the scattered field, forms the basis of a wide variety of areas in the engineering sciences; however, nearly all intensive efforts in this field are devoted to the cases of R2 and R3. In the case of homogeneous finite depth ocean, the `propagating' far-field pattern can only carry the information from the N+1 propagating modes; this loss of information makes this problem different from that in the whole space case in that the far-field pattern operator is not injective. A formulation of the corresponding direct problem, i.e., of the exterior boundary value problem for the time harmonic acoustic scattering by a soft object, is presented, followed by some properties of the far-field pattern operator. This information is used to construct an injective far-field pattern operator in a suitable subspace. Based on this construction an optimal scheme for solving the inverse scattering problem is presented using the minimizing Tikhonov functional.
  • Keywords:
  • Series:
    DEL-SG
  • Sea Grant Document Number:
    DELU-T-89-004
  • Document Type:
    Technical Report
  • Funding:
    Grant no. NA86AA-D-SG040
  • Rights Information:
    Public Domain
  • Compliance:
    Library
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