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Consistency and accuracy of perturbative inversion methods for group travel time data
Brian J Sperry1, B Edward McDonald, Arthur B Baggeroer
1Ocean Sciences Group, SAIC, McLean, Virginia 22102, USA.
The Journal of the Acoustical Society of America
|November 1, 2003
Summary
Perturbation theory accurately models ocean acoustic tomography when environmental changes are small. The theory
Area of Science:
- Oceanography
- Acoustics
- Geophysics
Background:
- Ocean acoustic tomography utilizes sound propagation to study oceanographic features.
- Understanding how sound speed variations affect acoustic signals is crucial for tomography.
- Perturbation theory offers a potential framework for analyzing these effects.
Purpose of the Study:
- To investigate the applicability of perturbation theory to ocean acoustic modal group speed responses.
- To analyze the inverse problem for vertical eigenmodes in ocean acoustic tomography.
- To determine the accuracy and validity range of perturbation theory for environmental perturbations.
Main Methods:
- Developed perturbation theory for ocean acoustic modal group speed.
- Formulated the inverse problem as an integral equation for each eigenmode.
- Proved the equivalence of two forms of the integral equation.
- Performed numerical inversions using four sound-speed profiles.
Main Results:
- The inversion kernel depends on the eigenfunction and its frequency derivative.
- Perturbation theory's accuracy is influenced by both the amplitude and vertical scale size of perturbations.
- Identified parameter ranges for accurate application of perturbation theory.
Conclusions:
- Perturbation theory is applicable to ocean acoustic tomography for small environmental changes.
- The vertical scale size of perturbations is as critical as their amplitude for model validity.
- Results provide guidance for applying perturbation theory in acoustic tomography studies.
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