Attenuation of acoustic waves in glacial ice and salt domes

[1] Two classes of natural solid media, glacial ice and salt domes, are under consideration as media in which to deploy instruments for detection of neutrinos with energy 10 eV. Though insensitive to 10 to 10 eV neutrinos for which observatories (e.g., AMANDA and IceCube) that utilize optical Cherenkov radiation detectors are designed, radio and acoustic methods are suited for searches for the very low fluxes of neutrinos with energies >10 eV. This is because owing to the very long attenuation lengths of radio and acoustic waves produced by interactions of such neutrinos in ice and salt, detection modules can be spaced at horizontal distances 1 km, in contrast to the 0.12 km distances between strings of IceCube modules. In this paper, I calculate the absorption and scattering coefficients as a function of frequency and grain size for acoustic waves in glacial ice and salt domes and show that experimental measurements on laboratory samples and in glacial ice and salt domes are consistent with theory. For South Pole ice with grain size 0.2 cm at depths 600 m, scattering lengths are calculated to be 2000 and 25 km at frequencies 10 and 30 kHz, respectively; for grain size 0.4 cm at 1500 m (the maximum depth to be instrumented acoustically), scattering lengths are calculated to be 250 and 3 km. These are within the range of frequencies where most of the energy of the acoustic wave is concentrated. The absorption length is calculated to be 9 ± 3 km at all frequencies above 100 Hz. For NaCl (rock salt) with grain size 0.75 cm, scattering lengths are calculated to be 120 and 1.4 km at 10 and 30 kHz, and absorption lengths are calculated to be 3 10 and 3300 km at 10 and 30 kHz. Existing measurements are consistent with theory. For ice, absorption is the limiting factor; for salt, scattering is the limiting factor. Both media would be suitable for detection of acoustic waves from ultrahigh-energy neutrino interactions.