Sensitivity kernels of finite-frequency travel times in ocean acoustic tomography

Abstract

Wave theoretic modeling is applied to obtain travel-time sensitivity kernels representing the amount by which travel times are affected by localized sound-speed variations anywhere in the medium. In the ray approximation travel times are sensitive to medium changes only along the corresponding eigenrays. In the wave-theoretic approach the perturbations of peak arrival times are expressed in terms of pressure perturbations, which are further related with the underlying sound-speed perturbations using the first Born approximation. In this way, an integral representation of travel-time perturbations is obtained in terms of sound-speed perturbations; the associated kernel represents the spatial sensitivity of travel times to sound-speed perturbations. The application of the travel-time sensitivity kernel to an ocean acoustic waveguide gives a picture close to the ray-theoretic one in the high-frequency case but significantly differs at lower frequencies. Low-frequency travel times are sensitive to sound-speed changes in areas surrounding the eigenrays, but not on the eigenrays themselves, where the sensitivity is zero. Further, there are areas of positive sensitivity, where, e.g., a sound-speed increase results in a counter-intuitive increase of arrival times. These findings are confirmed by independent forward calculations.