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Sensitivity of ray travel times
I. P. Smirnov1, A. L. Virovlyansky, G. M. Zaslavsky
1Institute of Applied Physics, Russian Academy of Science, 46 Ul'yanov Street, 603950 Nizhny Novgorod, Russia.
Chaos (Woodbury, N.Y.)
|June 5, 2003
Summary
Ray travel time in waveguides, even chaotic ones, follows predictable scaling laws. This research explores how ray path topology, like turning points, influences travel time in underwater acoustic waveguides.
Area of Science:
- Physics
- Acoustics
- Waveguide Theory
Background:
- Ray trajectories in nonuniform waveguides can exhibit chaotic behavior governed by Hamiltonian systems.
- Ray travel time is a crucial characteristic providing insights into waveguide conditions.
- Understanding ray behavior is vital for applications like underwater acoustics.
Purpose of the Study:
- To investigate the scaling law of ray travel time in unperturbed and nonuniform waveguides.
- To analyze how ray path topology influences travel time in chaotic systems, particularly in underwater acoustic waveguides.
- To explore the manifestation of stickiness in ray travel times within chaotic trajectories.
Main Methods:
- Analysis of ray trajectories as Hamiltonian system trajectories.
- Derivation and application of a scaling law for ray travel time.
- Modeling of underwater acoustic waveguides, including deep ocean propagation.
- Examination of ray travel time dependencies on initial momentum, propagation range, and ray path topology (e.g., turning points).
Main Results:
- A scaling law for ray travel time was identified in unperturbed waveguides.
- Properties predicted by the scaling law persist in periodically nonuniform waveguides with chaotic ray trajectories.
- In deep ocean models, ray travel time is significantly determined by endpoint coordinates and the number of turning points, even amidst ray chaos.
- Closeness of travel times for rays with equal turning points was observed, influencing dependencies on initial momentum and observation depth.
- A gap between travel times of chaotic and regular rays was identified.
- The effect of 'stickiness' on ray travel times in chaotic trajectories was discussed.
Conclusions:
- Ray travel time in waveguides, including chaotic ones, exhibits predictable behavior related to path topology.
- The identified scaling law and topological features offer valuable insights into waveguide conditions and ray dynamics.
- Findings are particularly relevant for understanding sound propagation in complex underwater acoustic environments.
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