An Injective Far-Field Pattern Operator And Inverse Scattering Problem In A Finite Depth Ocean

Details

• Personal Author:
  Xu, Yongzhi
• NOAA Program & Office:
  Sea Grant ; OAR (Oceanic and Atmospheric Research)
• 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:
  Underwater acoustics
• 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
• Main Document Checksum:
  urn:sha256:46e6b7a7375f9d7ceec3fcf4cdfd6c256ba84ff0ae2d0afae5abefd102819a42
• Download URL:
  https://repository.library.noaa.gov/view/noaa/39863/noaa_39863_DS1.pdf
• File Type:
  [PDF - 528.98 KB ]