1. zone-refined NaCl lab-grown ice S. Pole ice, 1740 m S. Pole ice, 1690 m Cherenkov light in ice and salt South Pole ice is better than zone-refined NaCl. Natural NaCl is probably worse than zone-refined. S. Pole ice, 900 m

2. Acoustic absorption in ocean Pure water absorbs due to its viscosity. In sea water, a pressure wave shifts chemical equilibrium between a molecule and ions, taking energy from wave: B(OH) 3 = B 3+ + 3 OH - (relaxation freq. ≈ 1 kHz) MgSO 4 = Mg 2+ + SO 4 2- (relaxation freq. ≈ 100 kHz) water + B(OH) 3 + MgSO 4 water + MgSO 4 water absorptivity [dB/km] Frequency [Hz]

3. 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

4. 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 bub =100 km bub =10 3 km

5. Speed of a pressure wave in a crystalline solid depends on angle with respect to c- axis (symmetry axis). This leads to scattering at grain boundaries.

6. Scattering of acoustic wave at grain boundaries Rayleigh regime ( /4πa > 1) Stochastic regime (0.5 < /4πa < 1) Geometric regime ( /4πa < 0.5) (a = grain radius for a polycrystalline medium) Acoustic properties depend on elastic constants, c ij Ice (hexagonal): c 11, c 12, c 13, c 33, c 44 NaCl (cubic): c 11, c 12, c 44

7. Scattering in Rayleigh regime for NaCl: Scattering in stochastic regime for NaCl: Analogous expressions for ice (hexagonal)

8. 1 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 Grain-boundary scattering [m -1 ] South Pole ice

9. Acoustic wave loses energy by reorienting molecules on ice lattice: protons move from one bond site to another by motion of L and D defects D = doppel; L = leer D L

10. Absorptivity of ice: lab measurements of decay of free oscillations

11. Experiments on mechanical relaxation of ice as fn of T and f predict a for -51ºC: Schiller 1958: 5.7 km Kuroiwa 1964: 8.6 km Oguro 1982: 11.7 km Measurements at Byrd by Bentley et al. (blue circle, -28ºC; black triangle, -21ºC) Calculated from Kuroiwa’s lab meas. of internal friction of ice

12. Tests of acoustic attenuation theory for ice SCATTERING Scattering off grain boundaries 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 Estimated a from lab experiments on internal friction of ice and from seismic reflection shooting of Bentley. Must measure a, s, and noise as function of frequency in 3 IceCube boreholes. Maybe hear stick-slip at bedrock.

13. Natural NaCl Evaporite beds have high impurity content. (water inclusions, beds of clay, silt, anhydrite,…) Salt domes are purer and have longer absorption lengths. Several mines are known to have >99% NaCl and have only 2 to 40 ppm water. Grain sizes in salt domes (smaller is better) 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% 3-10 mm

14. Liquid inclusions in salt domes scatter acoustic waves.

15. Section through polycrystalline halite from salt dome. Most grains have recrystallized, and scattering can occur at their boundaries. Scattering is negligible at subgrain boundaries. Grain boundaries (up to 90º) Subgrain boundaries (<1º)

16. phonon-phonon absorption expts  a(f)  f 2 (weak fn of T) 10 5 km 10 3 km s a 10 4 km

17. Summary of predictions for ice and NaCl 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. Clay, liquid inclusions, and anhydrite in salt domes dominate scattering and absorption. 2. Scattering in salt domes is worse than in South Pole ice because grain size is larger (geometric rather than Rayleigh). 3. In ideal salt, absorptivity would be far lower than in ice; in real salt it will be worsened by heterogeneities. 4. Must measure scatt and abs in South Pole ice and salt domes

19. -induced cascade leads to a pressure wave: P   v L 2 /C p ≈ v L /2d P ice /P water ≈ 10 ice / water ≈ 2

20. Absorption and Scattering in Ice and Salt P. B. Price (see NIM A325, 346, 1993 for my initial work on acoustic attenuation in ice)

21. 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.

22. Jefferson Island salt dome, Louisiana NaCl

23. Acoustic absorption -- a “relaxation” phenomenon For acoustic waves in ice at f < 10 5 Hz and T below -10ºC, protons get reoriented. 1. Relaxation time:  =  0 exp (U/kT); (U ≈ 0.58 eV) (  = characteristic transition time between two possible configurations) 2. Logarithmic decrement:  =  max 4π f  /(1 + 4π 2 f 2  2 ) 3. Absorptivity:  [m -1 ] =  f / v T