The Small Scale Shallow Water Tomography Based On Vertical Travel-time Sensitivity Kernel

Ocean acoustic tomography(OAT)is a method of observing physical ocean based on the effect of acoustic propagation.It is often used to retrieve physical ocean information such as velocity profile,temperature and salinity in large scale.In this paper,the wave equation is solved by the ray acoustics theory and the normal wave theory in the distance-independent marine environment.Therefore the linear relation between the velocity perturbation and the travel time perturbation is derived respectively.In the acoustic tomography based on the normal wave theory,we introduce the sensitivity kernel function which quantitatively describes the travel-time perturbation.The sensitivity kernel is a three-dimensional spatial distribution of the velocity-dependent perturbation,which is based on the first-order Born approximation of the Green's function,and converts the nonlinear relationship between the acoustic velocity perturbation and the travel time delay perturbation into linearity.By plotting the sensitivity kernels in three dimension,we can obtain a sound energy distribution diagram similar to that of the high frequency case based on the ray theory.It is found that the travel-time delay is sensitive to the velocity variation in the Fresnel zone around the acoustic line at low frequencies,rather than the speed of sound itself.In addition,it is also known that there is a positive sensitive region,that is,the acoustic line passing through the positive acoustic region has a positive acoustic velocity perturbation,which leads to a larger travel-time delay of the arrival peak.Then the acoustic tomography becomes the inverse problem of solving the observation equation.In this paper,the regularization constrained least square method is used to invert the travel-time delay perturbation.Simulations were carried out in a small-scale shallow-water environment and a shallow-water environment with small-scale vortex disturbance.The results show that the inversion precision of the vertical sensitivity kernel function is much higher than that of the ray travel time method in the small scale shallow sea low frequency environment.