title: Long-range asymptotic behavior of vertical travel-time sensitivity kernels.
abstract: Vertical travel-time sensitivity kernels (VTSKs) describe the effect of horizontally uniform sound-speed changes on travel times in range-independent ocean environments. Wave-theoretic VTSKs can be obtained either analytically, through perturbation of the normal-mode representation, or numerically, as horizontal marginals of the corresponding two-dimensional and three-dimensional travel-time sensitivity kernels. In previous works, it has been observed that wave-theoretic finite-frequency VTSKs approach the corresponding ray-theoretic sensitivity kernels as the propagation range increases. The present work is an attempt to explain this behavior. A stationary-phase approach is used to obtain a long-range asymptotic expression for the wave-theoretic VTSKs. The resulting asymptotic VTSKs are very close to the corresponding ray-theoretic ones. The smoothness condition, required for the stationary-phase approximation to hold, is used to obtain an estimate for the range beyond which the asymptotic behavior sets in.
authors.affiliation: Institute of Applied and Computational Mathematics, Foundation for Research and Technology Hellas, P.O. Box 1385, 711 10 Heraklion, Crete, Greece.
authors.forename: E K
authors.initials: EK
authors.lastname: Skarsoulis
authors.forename: B D
authors.initials: BD
authors.lastname: Cornuelle
authors.forename: M A
authors.initials: MA
authors.lastname: Dzieciuch
mesh_terms: D000162:Acoustics; D003198:Computer Simulation; D005583:Fourier Analysis; D016014:Linear Models; D009038:Motion; D009716:Numerical Analysis, Computer-Assisted; D009791:Oceanography / Q000379:methods*; D009792:Oceans and Seas; D011312:Pressure; D012623:Seawater; D013016:Sound; D013018:Sound Spectrography; D013997:Time Factors