The results of a computer simulation of amplitude and travel-time variations in the process of a signal crossing the Strait on a number of paths to infer the intervening fine-scale variability and transverse current are discussed in this paper. The method relies on the advection of small-scale inhomogeneities across the acoustic path. These inhomogeneities produce perturbations in the amplitude and travel time of the sound and the current can be sensed by generating a time-lagged cross correlation of the full acoustic field. A linear four-element transmission array and a four-element receiving array both with equally spaced elements were used for calculations. By combining the signals from each transmitter--receiver pair in different ways, a number of different path positions were probed and a profile of the transverse current along the propagation path was retrieved. The calculations were done in the frame of the ray model of signal propagation. Analysis has shown that the stable rays, which touch the ocean surface four or five times, are stable under the influence of inhomogeneities. These rays make it possible to avoid the phase ambiguity which can arise when a signal is propagated in an inhomogeneous waveguide.