Effect of sound speed and sea current during propagation on Doppler shift

Underwater ultrasonic devices applying Doppler effects use a constant sound speed as the average speed. However, the sound speed in the sea varies with water depth and an assumed constant sound speed has the potential to cause measuring errors. Moreover, because the sea current, which is the moving speed of a propagating medium, substantially changes the sound speed, it also affects the measurement accuracy of the Doppler shift. Unfortunately, to the authors' knowledge, no equations of depth-dependent Doppler shift have been reported. Likewise, no effects of the sea current on the measuring error of Doppler shift have been reported. Accordingly, this paper derives the equations of Doppler shift by taking into account the sound speed and the sea current that are dependent on the propagation path. By using the derived equations, the influence of the sound speed and sea current on the Doppler effects is investigated. Furthermore, the result of model experiments is described for verifying the derived proposed equations.