6 - THE INVERSE PROBLEM: DATA-ORIENTED

Summary

Introduction

The preceding chapters have demonstrated that a variety of measurable acoustic features, including ray travel time, amplitude, and inclination, mode group velocity, and carrier phase, are integral functions of the oceanic sound-speed field. As discussed in previous chapters, sound-speed is intimately related to the oceanic density field, which is, in turn, a dynamic variable related to the oceanic flow field. Under many circumstances, knowledge of the density field alone is adequate to compute the oceanic flow field to a high degree of approximation. Reciprocal tomographic measurements are direct weighted averages of the flow field in the plane of the source and receiver. Thus, determinations of C and u carry immediate implications for the ocean circulation and must be consistent with known physics.

The forward problem has been presented in detail: Given C (or S) and u, and the characteristics of a sound source, compute the detailed structure of the signal as recorded at a receiver of known characteristics. This problem is labeled “forward” mainly as a reflection of its connection to the classic problem of finding solutions to the wave equation.

The “inverse” problem demands calculation of the ocean properties, C and/or u, given the measured properties of the arriving signal. At this stage, the problem becomes a matter of intense oceanographic interest.

Oceanographers are mostly familiar with point value data (e.g., a current meter reading or a thermometer measurement). In contrast, tomographic data are weighted integrals through the oceanic field.