1. Conversion of ionization energy into acoustic energy ocean iceNaCl T (ºC) 15º -51º 30º [m s -1 ] 1530 39204560  [m 3 m -3 K -1 ] 25.5x10 -5 12.5x10 -5 11.6x10 -5 C P [J kg -1 K -1 ] 3900 1720839 Peak frequency 7.7 kHz 20 kHz42 kHz Grüneisen constant = figure of merit of the medium  2  /C P 0.153 1.12 2.87

2. scattering coefficient [m -1 ] Scattering of sound off of air bubbles in ice is negligible: b bub [m -1 ] = 2.68 x 10 -10 (n o /200 cm -3 ) (d b /0.02 cm) 6 (f/10 kHz) 4

3. 1 South Pole ice In top 600 m, grain diameter ≈ 0.2 cm  at 10 kHz, acoustic scattering length ≈ 800 km at 30 kHz, acoustic scattering length ≈ 10 km 0.4 cm 0.2 cm diam Scattering coefficient [m -1 ]

4. Energy loss by “relaxation” processes For acoustic waves in ice at f < 10 5 Hz and T below -10ºC, proton reorientation dominates. 1. Relaxation time:  =  0 exp (U/kT); (U ≈ 0.58 eV) (  = characteristic transition time between two possible configurations) 2. Log decrement:  =  max 4π f  /(1 + 4π 2 f 2  2 ) 3. Absorptivity:  [m -1 ] =  f / v T

5. Acoustic wave loses energy by reorienting molecules on ice lattice: protons move from one bond site to another D L D = extra proton; L = missing proton

6. Decay of free oscillations measures acoustic absorptivity of ice

7. Lab experiments on mechanical relaxation of ice as function of temp. and frequency Predicted a for -51ºC: Schiller 1958: 5.7 km Kuroiwa 1964: 8.6 km Oguro 1982: 11.7 km Adopt a = 9 ± 3 km. Measurements at Byrd by Bentley et al. (blue circle, -28 ºC; black triangle, -21º)

8. Salt evaporite beds have high impurity content WIPP repository contains salt beds 1% water (mostly in liquid inclusions), separated vertically by thin beds of clay, silt, and anhydrite (CaSO 4 ). Salt domes are purer and have longer absorption lengths In Louisiana, several mines have >99% NaCl, are very dry (2 to 40 ppm water), and have small (7.5 mm) grain size. Grain sizes in salt domes Avery Island, LA~7.5 mm Bryan Mound, TX2 - 40 mm; av. 8 mm Big Hill, TX3.7 - 60 mm West Hackberry, LA6 - 30 mm Moss Bluff, TXav 11 mm Bayou Choctaw, LAat 0 - 728 m: 10 - 20 mm Zuidwending (Austria)25% have 1-3 mm; 75% have 3-10 mm

9. Section through polycrystalline halite from salt dome. Most grains have recrystallized, and scattering can occur at their boundaries. Scattering is negligible at subgrain boundaries. Large-angle grain boundaries Small-angle (<1º) boundaries

10. Equations for optical and acoustic waves are identical. Test predictions: a ≈ 8.8 ± 3 km s ≈ 10 km at 30 kHz, 200 m at 100 kHz, … Deploy powerful acoustic transmitter in one borehole and receiver in a borehole at various distances.

11. Tests of acoustic attenuation theory for ice SCATTERING Scattering in titanium (hexagonal structure like ice) agrees with theory to ± 3X. There are no measurements of scattering in pure glacial ice at low temperature. ABSORPTION We estimated a from experiments on internal friction of ice and from seismic reflection shooting. NEXT SEASON AT ICECUBE Plan to measure acoustic a, s, and noise as fn of f in South Pole ice.

12. Comparison of South Pole ice and NaCl for acoustic waves scatt abs 10 4 Hz 3x10 4 Hz 10 4 Hz 3x10 4 Hz Ice (D=0.2 cm) 1650 km 20 km 8-12 km 8-12 km NaCl (D=0.75 cm) 120 km 1.4 km 3x10 4 km 3300 km 1. In salt domes, clay, liquid inclusions, and other minerals will shorten scattering and absorption lengths. 2. Scattering in salt is worse than in South Pole ice because grain size is larger. 3. In ideal salt, absorption length would be far longer than in ice, but in reality, it will be reduced by heterogeneities. 4. In-situ measurements of scatt and abs must be made.