Using deterministic ray-acoustic modeling of 1000-km propagation in the North Pacific, a depth-dependent parameter of ocean sound channels has been found to strongly influence geometrical ray propagation. This parameter is the sound speed times the second vertical derivative of sound speed divided by the square of the first derivative. Ray and wavefront timing and intensity can be influenced within realistic ocean sound channels by unpredictable wavefront triplications and caustics. These triplications are associated with large values of the parameter at ray turning points. The parameter, a relative curvature, behaves as a random variable because of ocean finestructure, causing the unpredictability. The relative curvature has a higher mean value near the sound-speed minimum for both an internal-wave model and actual data, so that this mechanism is a plausible explanation of poor multipath resolution and identifiability late in North Pacific pulse trains.