Time-reversal focusing in a range-dependent ocean

Shallow water time-reversal focusing has been successfully applied in ultrasonic laboratory experiments as well as in the ocean. For simplicity the ocean is usually considered as a range-independent waveguide. As a consequence, an omnidirectional vertical time-reversal array should refocus the wave not only at the source but also on a ring surrounding the array. In a real environment, the ocean bottom may be sloping. In this work, the influence of a slight inclination of the ocean bottom is studied. We show that the symmetry breaking yields an additional focusing in azimuth. We present ultrasonic experiments, which are well supported by a theoretical model based on modal decomposition and a stationary phase approach. The shape of the focal region in depth, range and azimuth is determined. The experiments are carried out in a water tank, at a central frequency of 3 MHz. The height of the waveguide ranges between 10 mm and 13.5 mm, its length is 500 mm. The inclination of the bottom is controlled by a step motor. A piezoelectric array is used to perform the TR operation. A needle hydrophone is used to check the accuracy of focusing. In the theoretical approach, the nature of the bottom can be taken into account, which is shown to significantly change the results. This is confirmed by numerical simulations performed in a realistic ocean environment.