Spheres for calibrating high-frequency broadband echo sounders

Abstract

The notion of standard-sphere broadband calibration [Dragonette et al., J. Acoust. Soc. Am. 69, 1186 (1981)] is being realized for a new echo sounding system that spans the seven-octave range 25 kHz to 3.2 MHz. Spheres formed of tungsten carbide with 6% cobalt binder, with 10- and 20-mm diameters, have been measured in the laboratory to determine their backscattering spectra over the approximate frequency ranges 0.85–1.3 MHz and 2.9–3.6 MHz. This allows exploration of the wave number radius (ka) product over the nominal ranges 18–28, 36–56, 61–75, and 122–150. Comparison with theoretical expectation, as derived from the standard modal solution using published values for the material properties, is quite good. Confidence in the computations thus enables favorable regions of the backscattering spectra to be sought and exploited in choosing optimal diameters, as has earlier been the case with spheres for calibrating resonant transducers. In the course of checking computations, it was discovered that two independently developed numerical codes yield values for the backscattering cross section that agree to within 1 part in 10 000 to better than one part in 1 000 000 for ka of the order of 100. [Partial support of the EU through RTD Contract No. MAS3-CT95-0031 is acknowledged.]