Exact Reconstruction of Ocean Bottom Velocity Profiles from Monochromatic Scattering Data
Abstract
This thesis presents theoretical and computational underpinnings of a novel approach to determining the acoustic parameters of the ocean bottom using a monochromatic source. The problem is shown to be equivalent to that of the reconstruction of the potential in a Schrodinger equation from the knowledge of the plane-wave reflection coefficient as a function of vertical wavenumber, r(k sub z) for all real positive (k sub z). First, the reflection coefficient is shown to decay asymptotically at least as fast as r(1/(k sub z)sq) for large k sub z and is therefore integrable. The Gelfand-Levitan inversion procedure is extended to include the case of basement velocity higher than the velocity of sound water. Neglect of bound states is shown to be justified in both clayey silt and silty clay at the 220 Hz frequency of operation. Three numerical solution methods for the integral equation are investigated. The first is an 'Improved Born approximation' wherein the solution is given as a series expansion the first term of which is the Born approximation while the 2nd term represents a substantial and yet easy to implement improvement over Born. The other methods are based on discretization of the Gelfand-Levitan integral equation and both avoid a matrix inversion: one by using a recursive procedure, and the other by coupling the Gelfand-Levitan equation with a partial differential equation. Bounds are obtained on errors in the solution due either to discretization or to data inaccuracy.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1987
- Accession Number
- ADA225947
Entities
People
- Andre A. Merab
Organizations
- Woods Hole Oceanographic Institution