Low frequency seabed scattering at low grazing angles

Abstract

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)].

Echo and reverberation in a Pekeris waveguide by convolution and by the product rule

“…This error becomes infinite if the angle range of integration is extended to p/2. Despite its shortcomings, the product rule remains in use both for discrete normal mode 20,22 and continuum [18][19][20][21][22] methods. The error can be corrected in a straightforward manner by introducing an additional factor cos h cos / in the product rule integrand (or summand in the case of a discrete mode sum) to cancel with the unwanted sec h sec / factor, as illustrated by Appendix B.…”

“…Despite its shortcomings, the product rule remains the basis for modern research publications. [18][19][20][21][22] An important advance was made by Harrison and Nielsen, 23 who applied a time domain convolution to derive the time dependence of the target echo in various environments, including the isovelocity case. This convolution method was extended to reverberation by Harrison and Ainslie.…”