The sine qua non of any inverse problem is an accurate treatment of the forward problem: to construct an acoustic arrival pattern given “the ocean.” If the forward problem cannot be solved, then the measured data cannot be inverted to reconstruct the ocean.

When we entered this field in 1978, it was under the impression that the forward problem had been solved and that our efforts could be directed toward the oceanographically interesting inverse problem. As it turned out, the forward problem had not been solved; oceanographic and acoustic fields had never been simultaneously measured with accuracy adequate for a critical test. When such measurements were finally made in the late 1980s as part of tomographic work, significant discrepancies were found between the measured and computed sound fields. The most dramatic discrepancy was traced to the equations of state for sea water; some of the commonly used sound-speed equations were shown to be in error.

That era of trouble with the forward problem came to an end with the so-called SLICE89 experiment. The forward problem is now sufficiently well understood to permit oceanographically useful applications of inverse methods. Some discrepancies remain; they appear to be associated with internal waves and other range-dependent phenomena (see chapter 4).

There is a hierarchy of techniques available to predict the propagation of acoustic pulses in the ocean, given the sound-speed field. The geometric-optics approximation (i.e., ray theory) is adequate to predict travel times in the majority of situations encountered in ocean acoustic tomography.