Application of Weighted-Gaussian-Quadrature Methods to Convergence-Zone Phenomena

Weighted-Gaussian-quadrature methods are applied to convergence-zone range integrals without any severe caustic or multipath anomalies. Both flat and curved earth cases are examined. It is shown that in the convergence zone the curved-earth effects are of the same order of magnitude as the thermocline effects and should be included for a meaningful calculation. Weighted-Gaussian-quadrature methods are compared to contemporary methods that approximate the sound-velocity profile with a piecewise analytic segmented profile. Gaussian-quadrature methods avoid the class of anomalies that are due to discontinuous derivatives of some finite order at the junction of two segments of the approximated profile. Illustrative numerical examples are included.