In underwater acoustics, ray tomography is the classical method used to estimate velocity variations, but recently. Travel-Time Sensitivity Kernels (TSK) approaches have been developed. In this paper, we deal with TSK for two source-receive arrays in an acoustic waveguide for shallow water tomography. As a first step, we show that separation of the different raypaths is improved by using a recently proposed new array processing [time-delay double beamforming (DBF) algorithm]. DBF consists of changing the 3-D data space from source depth, receiver depth and time into a new 3-D space related to ray propagation expressed by the beamformed variables, source angle, receive angle and time. As a consequence, each eigenray of the multipath propagation for a source-receiver couple can be identified and separated through DBF. In this context of DBF, the TSK is no longer point-to-point as usual, but relies on all source-receiver time series. Kernels are computed using the fact that the processed signal is a linear combination of time-delayed signals between all sources and receivers. Results in simulated data and in real datasets recorded in an ultrasonic tank prove that combination of TSK and DBF increases the resolution and robustness performance of shallow-water acoustic tomography.