Low frequency seabed scattering at low grazing angles

Low-frequency (LF) seabed scattering at low grazing angles (LGA) is almost impossible to directly measure in shallow water (SW), except through inversion from reverberation. The energy flux method for SW reverberation is briefly introduced in this paper. The closed-form expressions of reverberation in an isovelocity waveguide, derived from this method, indicate that in the three-halves law range interval multimode/ray sea bottom scattering with different incident and scattering angles in forming the reverberation may equivalently be represented by the bottom backscattering at a single range-dependent angle. This equivalent relationship is used to derive the bottom backscattering strength (BBS) as a function of angle and frequency. The LF&LGA BBS is derived in a frequency band of 200-2500 Hz and in a grazing angle range of 1.1°-14.0° from reverberation measurements at three sites with sandy bottoms. This is based on three previous works: (1) The closed-form expressions of SW reverberation Zhou, (Chinese) Acta Acustica 5, 86-99 (1980)]; (2) the effective geo-acoustic model of sandy bottoms that follows the Biot model Zhou et al., J. Acoust. Soc. Am. 125, 2847-2866 (2009)] and (3) A quality database of wideband reverberation level normalized to source level Zhou and Zhang, IEEE J. Oceanic Eng. 30, 832-842 (2005)].