Generalized Herglotz Functions And Inverse Scattering Problem In A Finite Depth Ocean

Details

• Personal Author:
  Gilbert, Robert P. ; Xu, Yongzhi.
• Corporate Authors:
  University of Delaware.
• NOAA Program & Office:
  Sea Grant ; OAR (Oceanic and Atmospheric Research)
• Sea Grant Program:
  DELU (Delaware Sea Grant)
• Description:
  In a finite depth ocean, only a finite number of modes of the scattered wave propagate; the others decrease at an exponential rate. A far-field pattern can carry only the information from the finite propagating modes. Therefore, the same far-field pattern may correspond to very different near fields. In order to recover the shape of the scatterer, which is certainly related to the near field, we need to discover the relation between the near field and the far field under certain restrictions. In a previous paper, a proper subset of the incoming waves was constructed so that the mapping from the scattered fields to the far field patterns is an injection, and an algorithm was developed. Here, an optimal solution in the orthogonal complement of the closure of the set of far field patterns is sought.
• Keywords:
  Underwater acoustics
• Series:
  DEL-SG
• Sea Grant Document Number:
  DELU-T-89-006
• Document Type:
  Technical Report
• Funding:
  Grant no. NA86AA-D-SG040
• Rights Information:
  Public Domain
• Compliance:
  Library
• Main Document Checksum:
  urn:sha256:99eba6cdb4dcff679e0366e80219b2b310a719ec08be82798614258fae212798
• Download URL:
  https://repository.library.noaa.gov/view/noaa/39471/noaa_39471_DS1.pdf
• File Type:
  [PDF - 544.96 KB ]