Travel-Time and Amplitude Sensitivity Kernels
SCRIPPS INSTITUTION OF OCEANOGRAPHY LA JOLLA CA
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LONG-TERM GOALS Our long-term goal is to study the sensitivity behavior of travel-time and arrival-amplitude observables due to sound-speed perturbations in low-frequency, long-range acoustic propagation in the ocean. OBJECTIVES The leading objective of this project is to rigorously study the asymptotic behavior of wave-theoretic travel-time sensitivity kernels with increasing range, as a means to explain their observed convergence towards the corresponding ray-theoretic sensitivity kernels even at low frequencies. Further objectives include the derivation and study of 2D and 3D first-order amplitude sensitivity kernels, as well as vertical sensitivity kernels for arrival amplitudes, first- and second-order. A last objective is the study of sensitivity behavior of late arrivals depending on propagation frequency and range. APPROACH Previous work has revealed a numerical convergence of wave-theoretic travel-time vertical sensitivity kernels VTSKs towards the corresponding ray-theoretic sensitivity kernels with increasing range even at low frequencies 1. To study this behavior, the asymptotic form of finite-frequency kernels with increasing range is rigorously derived here using a stationary-phase approach 2. The wave-theoretic VTSK involves an integral over frequency with a rapidly oscillating kernel, the oscillation rate increasing with propagation range. The stationary-phase approach is used to evaluate the asymptotic form of this integral and finally of the VTSK for long ranges.
- Physical and Dynamic Oceanography