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Long-range asymptotic behavior of vertical travel-time sensitivity kernels
E K Skarsoulis1, B D Cornuelle, M A Dzieciuch
1Institute of Applied and Computational Mathematics, Foundation for Research and Technology Hellas, P.O. Box 1385, 711 10 Heraklion, Crete, Greece.
This study explains why wave-theoretic finite-frequency VTSKs match ray-theoretic kernels at long ranges. Using a stationary-phase approach, we derive an asymptotic expression for VTSKs, confirming their convergence with ray theory and estimating the range for this behavior.
Area of Science:
- Ocean acoustics
- Seismic wave propagation
Background:
- Vertical travel-time sensitivity kernels (VTSKs) model sound-speed changes in ocean acoustics.
- Wave-theoretic VTSKs approximate ray-theoretic kernels at increasing ranges.
Purpose of the Study:
- To explain the convergence of wave-theoretic VTSKs to ray-theoretic kernels at long ranges.
- To derive a long-range asymptotic expression for wave-theoretic VTSKs.
Main Methods:
- Perturbation of normal-mode representation for analytical VTSKs.
- Numerical computation of VTSKs as marginals of 2D/3D kernels.
- Application of stationary-phase approximation for asymptotic analysis.
Main Results:
- Derived a long-range asymptotic expression for wave-theoretic VTSKs.
- Asymptotic VTSKs closely match corresponding ray-theoretic sensitivity kernels.
- Identified a smoothness condition to estimate the range for asymptotic behavior.
Conclusions:
- The long-range behavior of VTSKs is explained by wave theory.
- The stationary-phase approach provides accurate asymptotic VTSKs.
- A quantitative estimate for the onset of asymptotic behavior is established.
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