Doppler Shift in Layered Media.

摘要

Acoustic ray tracing in media where there are velocity gradients is a standard technique for a stationary transmitter and receiver. Also, dealing with moving sources and receivers and with the ensuing Doppler shifts is common practice in the absence of velocity gradients, i.e., when sound ray paths are straight lines. Although calculation of Doppler shifts when sound ray paths are curved are implicit in that part of the literature dealing with the total sound field, some interesting relations remain hidden when the problem is considered in such general terms and only become apparent when the Doppler effect is considered on its own. Such a study was conducted, its major results being as follows: (1) It is shown that the range rate of the source can be estimated from a knowledge of the transmitted frequency and the angle of the reception of the sound. (2) When there is a vertical offset between source and receiver, the Doppler shift reaches a maximum value at some finite horizontal separation between the two. The equations governing the specific relations are given. (3) It is shown how the error may be calculated when it is assumed that the sound propagates along a straight line rather than along the actual curved ray path. The significant parameters in this calculation are the products, velocity gradients times layer depth, for each layer through which the ray travels. (Author)