Absorption and Scattering of Acoustic Waves in NaCl P. B. Price, U. C. Berkeley, February 3, 2005

1. Absorption and Scattering of Acoustic Waves in NaClP. B. Price, U. C. Berkeley, February 3, 2005

2. AcousticScatteringIn ice, it occurs at grain boundaries. In a salt dome it also occurs at cracks, layers of clay,anhydrite, and liquid inclusions.AcousticAbsorptionoccurs by relaxation mechanisms. In NaCl the thermal phonon gas extracts energy from acoustic phonons via anharmonic interactions.

3. Conversion of ionization energy into acoustic energy ocean, 15º ice, -51º NaCl, 30º <vL> [m s-1] 1530 3920 4560 <vS> [m s-1] n/a 1995 2610  [m3 m-3 K-1] 25.5x10-5 12.5x10-5 11.6x10-5 CP [J kg-1 K-1] 3900 1720 839   <vL>2/CP0.153 1.12 2.87 d ≈ RMoliere0.1 m 0.1 m 0.054 m L≈3Xoln(Eo/Ec)1/2 10.3 m10.3 m 3.43m fpeak ≈ vL / 2d 7.7 kHz20 kHz 42 kHz disk = d/L 0.5º 0.5º 0.9º

4. Scattering of acoustic wave at grain boundaries(speed depends on crystallographic direction)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, cijIce (hexagonal): c11, c12, c13, c33, c44NaCl (cubic): c11, c12, c44For an isotropic solid,   c11 - c12 - 2 c44 = 0 no scattering at grain boundaries.(For glass,  = 0; for NaCl, = 0.111)

5. Grain boundary scattering in Rayleigh regime (cubic): Grain boundary scattering in stochastic regime (cubic):

6. 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 In ice with a random distribution of c-axes, scattering is a factor 2.7 higher than shown. (-51ºC) 0.4 cm 0.2 cm diam

7. For ice, acoustic absorption is due to molecular reorientations, which dominates over other modes. In South Pole ice at -51ºC with random c-axis distribution, we predict abs ≈ 1.4x10-4 m-1 and abs ≈ 7 km indep. of frequency, unlike most situations longitudinal waves  c-axis abs[

8. Salt evaporite beds WIPP repository contains salt beds < 100 m thick with >1% water (mostly in liquid inclusions) and separated vertically by thin beds of clay, silt, and anhydrite (CaSO4). Salt domes In Louisiana, several mines have >99% NaCl, are very dry (only 2 to 40 ppm water), and have small (7.5 mm) grain size, which is good.

9. Section through polycrystalline halite from salt dome. Most grains have recrystallized, and scattering can occur at their boundaries. White lines delineate subgrain boundaries with small misorientation Grain boundaries (up to 90º) Subgrain boundaries (~1º)

11. Liquid inclusions in salt domes They scatter acoustic waves but are infrequent.

12. 3x10-8 NaCl S.P.Station noise? dp/df [g cm-1 s-1] ice 10-8 f [Hz]

13. Acoustic scattering and absorption in South Pole iceand NaCl scattabs 104 Hz 3x104 Hz 104 Hz 3x104 Hz Ice (D=0.2 cm) 1650 km 20 km 7 km† 7 km NaCl (D=2 cm) 6 km 0.15 km† 3x104 km 3300 km NaCl (D=0.75 cm)* 120 km 1.4 km† 3x104 km 3300 km *Measured for salt in Avery Island dome †Dominant contribution to attenuation at peak frequency 1. But salt domes may have clay, liquid inclusions, and other minerals, which shorten scattering and absorption lengths. 2. Scattering length in salt is shorter than in South Pole ice because grain size is larger. 3. Absorption length in ideal salt is far longer than in ice, but will be reduced by heterogeneities. 4. Must measure acoustic scattandabsover >1km in salt dome!

14. Optical detection • NaCl has absorption length >100m for wavelength >350 nm  salt dome may be useful as an optical Cerenkov detector. • Isotropy of refractive index in NaCl  no scattering at grain boundaries. • To calculate scattering, measure concentration of mineral inclusions and other heterogeneities. Bergstrom-Price model