THEORY OF AXIAL RAY

The theory of the ray that travels along or arbitrarily close to an axis of minimum velocity in the ocean is examined for an extremely wide class of velocity profiles in which the depth is expressed as a generalized power series in the velocity. Although the complete ray theory is intractable for this model, the range and travel time integrals can be evaluated for the axial ray. Derivatives of these integrals with respect to the ray parameter indicate whether the axial ray is faster or slower than near axial rays. The results for range, intensity anomaly, and the derivative of the group velocity with respect to the phase velocity are expressed as simple functions of σ1, the smallest exponent in the profile representation. Other ray theory results are expressed in terms of various order profile derivatives, evaluated at the axis, and the effect of discontinuities in the profile derivatives is examined. Certain range and travel time derivatives, although finite for symmetric profiles, are found to be infinite for nonsymmetric profiles. Thus, results for several symmetric profiles in common use differ considerably from the results for more realistic nonsymmetric profiles. © 1969, Acoustical Society of America. All rights reserved.