Impact of array tilt on source-range estimation in shallow water using the array invariant.

The array invariant proposed for robust source-range estimation in shallow water is based on the dispersion characteristics in ideal waveguides for broadband signals. With minimal knowledge of the environment, the approach involves plane-wave beamforming using a vertical array, utilizing multiple arrivals (i.e., eigenrays) separated in beam angle and travel time. In the presence of array tilt, however, the beam angle estimates are shifted, which potentially affects the range estimation based on the array invariant. Conversely, the array tilt could be estimated for a known source range. In this paper, the sensitivity to array tilt is analyzed theoretically and examined using simulations and data. It is found that even a small tilt angle (e.g., <2°) of a 1.2 -m long vertical array near the surface, if not compensated for, can result in a relative range error of 20% or more, for a high-frequency source (7-19 kHz) at 3-km range in approximately 100 -m deep shallow water. Moreover, the power spectrum of the time-evolving array tilt estimated for 9 min shows a dominant period of 5.6 s, which is consistent with the surface wave period concurrently measured from a waverider buoy.