The paper generalizes the matched field method to the flowing-medium c
ase with special reference to acoustic tomography of ocean currents. I
t is shown that by matching the nonreciprocities of acoustic fields pr
opagating toward one another in opposite directions (rather than the f
ields themselves), it is possible to separate the relatively weak effe
cts due to currents from the acoustic signal variations brought about
by variations in the sound velocity field and to determine the paramet
ers of the current under study. Extensive numerical experiments on rea
listic models close to the hydrological conditions existing in the Gul
f Stream (the deep ocean case) and in the Straits of Florida (the shal
low sea case) provide insight into the inversion stability related to
emitter-receiver positioning errors, uncertainties in knowledge of the
sound velocity field in the medium, specification of input variables
at a limited number of points, and acoustic noise. Several alternative
choices are considered for the physical quantities whose nonreciproci
ty is to be matched. It is further demonstrated that recourse to the f
ield phase nonreciprocity assures a highly accurate solution and a sta
bility toward the errors listed above, sufficient for the proposed sch
eme to be implemented in full-scale experiments.