The Hilbert-Hankel Transform and Its Application to Shallow Water Ocean Acoustics.
Abstract
In the shallow water acoustics problem, a time-harmonic source is placed in the ocean and a hydrophone records the acoustic pressure field as a function of range from the source. In this thesis, new techniques related to the synthetic generation, acquisition, and inversion of this data are developed. A hybrid method for accurate shallow water synthetic data generation is presented. The method is based on computing the continuum portion analytically. In the related problem of extracting the reflection coefficient, it is shown that the inversion can be highly sensitive to errors in the Green's function estimate. This sensitivity can be eliminated by positioning the source and receiver above the invariant critical depth of the waveguide. The theory of a new transform, referred to as the Hilbert-Hankel transform, is developed. Its consistency with the Hankel transform leads to an approximate real-part/imaginary-part sufficiency condition for acoustic fields. An efficient reconstruction method for obtaining the complex-valued acoustic field from a single quadrature component is developed and applied to synthetic and experimental data. The Hilbert-Hankel transform is a unilateral version of the Hankel transform and its application to this problem is based on the outgoing nature of the acoustic field. The theory of this transform and its one-dimensional counterpart can be applied to a wide class of problems.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1986
- Accession Number
- ADA168509
Entities
People
- Michael S. Wengrovitz
Organizations
- Massachusetts Institute of Technology