Sensitivity of ray theory to input data

Abstract

Acoustic propagation problems which are solved using ray theory require certain input data. In particular, the source and receiver locations, sound-velocity field and bottom and surface conditions are required. Frequently, this data is known only to within certain confidence limits. Ray calculations are performed assuming that the input data is known to the required accuracy. A theory is presented which indicates the sensitivity of the calculations to small variations in the input data. The ray equation is characterized by a second-order ordinary differential equation; the intensity can be calculated along the particular ray directly. The necessity of having twice continuously differentiable velocity, surface and bottom profiles is clearly demonstrated in the theory. Specific examples are provided for specialized velocity profiles.