An overview of the tomographic forwnrd/inverse problem

In ocean acoustic tomography, the travel time along a ray path is a weighted average of the propagation speed along the path. Because oceanographers generally have intuition about point measurements or simple averages, it has been necessary to transform travel time data into point values (maps) before communicating the results. The transformation can be done with a variety of methods, ranging from exhaustive Monte Carlo searches to Backus‐Gilbert constrained estimation. The transformation converts travel time data with more or less independent errors to point value estimates with correlated errors that may have complicated, nonlocal structure. Since the error bars usually presented with an ocean map do not include the correlations, they do not accurately reflect the information content of a tomographic dataset. In addition, it is no longer possible to distinguish between the data errors and sampling blind spots by examining the error bars (or even the error covariances). Communicating tomographic results ...