Asymptotic behavior of vertical travel-time sensitivity kernels with increasing propagation range

Vertical travel-time sensitivity kernels (VTSKs) describe the effect of horizontally uniform sound-speed changes on travel-times in range-independent environments. Wave-theoretic VTSKs can be obtained either analytically, through perturbation of the normal-mode representation, or numerically, as horizontal marginals of the corresponding 2D and 3D travel-time sensitivity kernels. In previous works it has been observed that, as the propagation range increases, wave-theoretic VTSKs approach the corresponding ray-theoretic sensitivity kernels even for low frequencies. In the present work an asymptotic expression of the wave-theoretic finite-frequency VTSKs is obtained, using a stationary-phase approach. Numerical results show that wave-theoretic VTSKs converge with increasing range toward the asymptotic form, which in turn lies very close to the ray-theoretic VTSK. [Work supported by ONR.]