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Observations of broadband sound propagation through the deep ocean, rich in sound-speed inhomogeneities, show that the double accordion acoustic wavefront pattern expected from model predictions without inhomogeneities is remarkably stable. This stability is found for propagation ranges up to 5000 km for acoustic frequencies of 28-84 Hz, and up to 1200-km range for 250 Hz. While the observed wavefront pattern is stable, the acoustic intensity along the wavefront is not. Furthermore, significant vertical extension of turning point caustics has been observed. This line of evidence suggests that the scattering is anisotropic in the sense that it is primarily along the wavefront, rather than across it. In addition, ray and parabolic equation simulations of acoustic propagation through ocean internal waves obeying the Garrett-Munk (GM) internal wave spectrum reinforce this notion of the anisotropy of the wavefront distortion. This paper presents a ray-based physical model for this phenomenon based on small angle forward scattering and provides analytic formulas to predict the wavefront distortions caused by ocean internal waves and other ocean processes. Further applications include out-of vertical-plane scattering and wavefront healing near seamounts or islands.