Document Type


Date of Award

Spring 5-31-2001

Degree Name

Doctor of Philosophy in Mathematical Sciences - (Ph.D.)


Mathematical Sciences

First Advisor

Eliza Zoi-Heleni Michalopoulou

Second Advisor

David C. Stickler

Third Advisor

Jonathan H.C. Luke

Fourth Advisor

Bonnie K. Ray

Fifth Advisor

Hongya Ge

Sixth Advisor

Alex Tolstoy


This dissertation describes efficient methods developed and implemented for source localization and sound speed and bottom depth estimation using sound propagation in the ocean. The proposed inversion techniques are based on the linearization of the generally non-linear inverse problem of parameter estimation in underwater acoustics. These techniques take into account properties of the ocean environment and are accurate in their estimation results without being prohibitively computationally intensive. For the inversion, select ray paths are taken into account: the direct, first surface bounce, and first bottom bounce. Ray travel time derivatives with respect to parameters that affect path arrival times are obtained analytically. These derivatives and a first order expansion are then used to find estimates of unknown parameters through replica and true paths; replica paths are generated using ray theory for underwater sound propagation and true paths are identified from measured time series. The linearization scheme works efficiently for the estimation of geometric parameters such as the source and receiver location coordinates and the depth of the water column. It is also successful in estimating the sound speed profile in the ocean using empirical orthogonal functions. In this work, the linearization inversion technique is applied to marine mammal tracking, and it is also used with real data collected during the Haro Strait experiment for source and receiver localization. For the Haro Strait data, inversion using linearization is also compared to matched-field processing, which estimates source location and geoacoustic parameters through a full field matching approach.

Included in

Mathematics Commons



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