An acoustic pulse propagating with a current travels faster than one propagating against the current. Ocean currents are typically of order 10 cm/s rms or less, except in strong western boundary currents such as the Gulf Stream, whereas ocean sound-speed perturbations are typically of order 5 m/s rms. Travel-time perturbations due to ocean currents are correspondingly one to two orders of magnitude smaller than travel-time signals due to sound-speed perturbations. It is nonetheless possible to measure ocean currents using acoustic techniques, by differencing the travel times of signals traveling in opposite directions. As was briefly summarized in chapter 1, travel-time signals due to sound-speed perturbations cancel in the difference travel time, leaving only the effect of currents.

Section 3.1 describes ray theory as applied to moving media. The presence of a current introduces anisotropy. Perturbation expressions for the sum and difference of reciprocal travel times are then presented in section 3.2. When the flow is in geostrophic balance, the current and sound-speed fields are related. In section 3.3, quantitative estimates of their relative sizes are made, confirming the rough orders of magnitude cited earlier.

Using a horizontal-slice approximation, section 3.4 shows that the averaging properties of acoustic travel times make acoustic techniques uniquely suited for measuring the fluid circulation by integrating around a closed contour. By Stokes's theorem, the circulation is equivalent to the areal-average relative vorticity. This result is then generalized to show that differential travel times are sensitive to the solenoidal component of the flow, from which relative vorticity can be mapped, but are not functions of the irrotational component of the flow between the transceivers, which is needed to map the horizontal flow divergence.