Resolution and variance in acoustic tomography

Acoustic tomography is a proposed system for large-scale remote monitoring of ocean variables, especially the sound speed, as functions of position. In such a system, a number of sources transmit pulse codes which are detected at a number of receivers, so that the volume spanned by sources and receivers is crossed by a large number of acoustic paths (including multipaths). Travel time perturbations from a known reference state must be inverted to obtain estimates of sound-speed fluctuations from that reference state. In this paper, the Backus–Gilbert method is used to study the resolution and variance of such estimates in a horizontal ocean slice. Data kernels which are singular along ray paths are ‘‘quelled’’ by integration. Estimates are interpreted as weighted local averages of the unknown function and the weighting functions, or resolution kernels, which characterize resolution at a particular point, are illustrated at representative points. Global representations of resolution are also formulated and plotted. It is shown how resolution can be compromised for the purpose of reducing the variance of estimates due to statistical error. Such trade-off relations are discussed and exemplified.