The discussion so far has dealt with a range-independent (RI) sound channel. But the ocean certainly varies horizontally and is always range-dependent (RD); one of the chief goals of tomography is to derive its range-averaged (RA) properties.

The RD treatment will vary depending on whether the scale of the horizontal variations is larger, comparable to, or very much smaller than the ray-loop range (typically 50 km). The term “adiabatic range dependence” is defined to apply to the case of small fractional variation over a ray loop. Variations on a gyre scale can accordingly be treated by the adiabatic approximation, assuming there are no sharp frontal surfaces.

The term “loop resonance” applies to ray travel-time perturbations due to ocean perturbations with horizontal scales equal to the ray-loop scale, or to a fraction of the loop scale. This includes mesoscale activity (which accidentally has a scale comparable to the loop scale) and ranges down to the longer components in the internal wave spectrum. Cornuelle and Howe (1987) have shown that measured travel-time perturbations associated with loop resonance can provide some RD information for even a single source-receiver transmission path.

Internal waves are generally included among the small-scale processes for which the forward problem yields estimates of the variance and other statistical properties of the travel time (Flatté et al., 1979). These estimates are required for inversion of the measured data set. In turn, the measured variances can provide useful information about the small-scale structure (Flatté and Stoughton, 1986).