Phase stability of convergence zone propagation at mid-frequency.

Mid-frequency transmissions (1.5 to 7.5 kHz) from a towed source to a drifting array one convergence zone away demonstrate smoothly varying phase. Calculations of the strength and diffraction parameters Φ and Λ for a representative background environment predict partially saturated propagation. For a single convergence zone path, the evolving phase rate due to the changing internal wave field corresponds to a narrowband coherent integration time, defined by the length of a discrete Fourier transform that likely captures the signal, from ∼370 s at 10 kHz to ∼1370 s at 1 kHz in the absence of source motion. Simulated propagation with a split-step parabolic equation solver through a sound speed field with thermocline fine structure and a Garrett-Munk internal wave displacement field provides a full wave picture that is consistent with the statistical predictions. Experimental data from the Philippine Sea demonstrates signal phase that is highly correlated with source tow body vertical excursions, measured by a pressure sensor, that couple into horizontal motion. The received signal can be integrated for up to 128 s at 5.5 kHz, with the upper limit thought to be due to non-uniform source motion rather than ocean dynamics.