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• 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 betterthan zone-refined NaCl.

Natural NaCl is probably worse than zone-refined.

S. Pole ice, 900 m

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 = B3+ + 3 OH-

(relaxation freq. ≈ 1 kHz)

MgSO4 = Mg2+ + SO42-

(relaxation freq. ≈ 100 kHz)

water+ B(OH)3

+ MgSO4

water +MgSO4

water

abs

orp

tivity

[dB

/km

]

Frequency [Hz]

Conversion of ionization energy into acoustic energy

ocean ice NaClT (ºC) 15º -51º 30º

<vL> [m s-1] 1530 3920 4560

[m3 m-3 K-1] 25.5x10-5 12.5x10-5 11.6x10-5

CP [J kg-1 K-1] 3900 1720 839

Peak frequency 7.7 kHz 20 kHz 42 kHz

= Grüneisen constant = figure of merit of the medium = <vL>2/CP 0.153 1.12 2.87

scat

teri

ng c

oeff

icie

nt [

m-1]

Scattering of sound off of air bubbles in ice is negligible:

bbub [m-1] = 2.68 x 10-10 (no/200 cm-3) (db/0.02 cm)6 (f/10 kHz)4

bub =100 km

bub =103 km

Speed of a pressure wave in a crystalline soliddepends on angle with respect to c-axis (symmetry axis).

This leads to scattering at grain boundaries.

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, cij

Ice (hexagonal): c11, c12, c13, c33, c44

NaCl (cubic): c11, c12, c44

αscatt=43πa

3

375πk4 (c11−c12−2c44)

2

c112 1+

32

vLvS

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

5⎡

⎣

⎢ ⎢

⎤

⎦

⎥ ⎥

=1.65×10−4 a1cm

⎛ ⎝ ⎜

⎞ ⎠ ⎟

3 f104

⎛ ⎝ ⎜

⎞ ⎠ ⎟

4

m−1

αscatt=4

525

c11−c12 −2c44( )2

c112 k2⟨a⟩

=7.21×10−4 ⟨a⟩1cm

⎛

⎝ ⎜

⎞

⎠ ⎟

f104

⎛ ⎝ ⎜

⎞ ⎠ ⎟

2

m−1

where k≡2πfvL

; ⟨a⟩= mean grain radius

Scattering in Rayleigh regime for NaCl:

Scattering in stochastic regime for NaCl:

Analogous expressions for ice (hexagonal)

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 cmdiam

Gr a

i n-b

ound

a ry

scat

t erin

g [ m

-1]

South Pole ice

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

Absorptivity of ice: lab measurements of decay of free oscillations

Experiments on

mechanical relaxation

of ice as fn of T and f

predict a for -51ºC:

Schiller 1958: 5.7 kmKuroiwa 1964: 8.6 kmOguro 1982: 11.7 km

Measurements at Byrd by Bentley et al. (blue circle, -28ºC; black triangle, -21ºC)

Calculated fromKuroiwa’s labmeas. of internalfriction of ice

Tests of acoustic attenuation theory for ice

SCATTERINGScattering 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.

ABSORPTIONEstimated 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.

Natural NaClEvaporite 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 mmBryan Mound, TX 2 - 40 mm; av. 8 mmBig Hill, TX 3.7 - 60 mmWest Hackberry, LA 6 - 30 mmMoss Bluff, TX av 11 mmBayou Choctaw, LA at 0 - 728 m: 10 - 20 mmZuidwending (Austria) 25% have 1-3 mm; 75% 3-10 mm

Liquid inclusions in salt domes scatter acoustic waves.

Section through polycrystalline halite from salt dome. Most grainshave recrystallized, and scattering can occur at their boundaries.

Scattering is negligible at subgrain boundaries.

Grain boundaries (up to 90º) Subgrain boundaries (<1º)

phonon-phononabsorption

expts a(f) f 2

(weak fn of T)

105 km

103 km

s

a

104 km

Summary of predictions for ice and NaCl

scatt abs

104 Hz 3x104 Hz 104 Hz 3x104 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 3x104 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

-induced cascade leads to a

pressure wave:

P vL2/Cp

<f> ≈ vL/2d

Pice/Pwater ≈ 10<f>ice/<f>water ≈ 2

Absorption and Scattering inIce and Salt

P. B. Price

(see NIM A325, 346, 1993 for my initial work on

acoustic attenuation in ice)

Equations for optical and acoustic wavesare identical.

Test predictions: a ≈ 8.8 ± 3 kms ≈ 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.

Jefferson Island salt dome, Louisiana

NaCl

Acoustic absorption -- a “relaxation” phenomenon

For acoustic waves in ice at f < 105 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 + 4π2 f 2 2)

3. Absorptivity: [m-1] = f / vT