Source ranging with minimal environmental information using a virtual receiver and waveguide invariant theory.
A method is presented for estimating the range of an unknown broadband acoustic source in a waveguide, using a vertical array and a signal sample from another broadband source at a known location relative to the array. The method requires no modeling of the acoustic field, and little to no environmental information for flat bathymetries. Waveguide invariant theory [e.g., D'Spain and Kuperman, J. Acoust. Soc. Am 106, 2454-2468 (1999)] is applied to the "virtual receiver" [Siderius et al., J. Acoust. Soc. Am. 102, 3439-3449 (1997)] to create a "virtual aperture" (VA). In effect, the method effectively converts a source at known range r(g) into a continuum of receivers lying between ranges (1 +/- alpha/beta)*r(g), where beta is a scalar parameter called the acoustic invariant, and alpha approximately 0.1. This effective displacement is achieved by correlating the known source field, measured at frequency component omega, with the unknown source field, measured at frequency component omega + omegas. When the VA output is plotted as a function of omega and omegas, the slope of the resulting correlation contours yields the unknown source range. The concept is illustrated via both simulation and analysis of data collected from a pseudo-random noise source with 75-150-Hz bandwidth during SWellEx-3, a shallow water experiment conducted off the San Diego coast. The virtual aperture can be reformulated for range-dependent environments, if adiabatic propagation assumptions are valid, and if the bathymetry surrounding the array is known.