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

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 cmdiam

Sc a

tter

ing

c oef

fi ci e

nt [

m-1]

Energy loss by “relaxation” processes

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

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

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

Decay of free oscillations measures acoustic absorptivity of ice

Lab experiments on mechanical relaxation of ice as function of temp. and frequency

Predicteda for -51ºC:

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

Adopt a = 9 ± 3 km.

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

Salt evaporite beds have high impurity contentWIPP repository contains salt beds < 100 m thick with >1% water (mostly in liquid inclusions), separated vertically by thin beds of clay, silt, and anhydrite (CaSO4).

Salt domes are purer and have longer absorption lengthsIn 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 domesAvery 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% have 3-10 mm

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

Scattering is negligible at subgrain boundaries.

Large-angle grain boundaries

Small-angle (<1º) boundaries

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.

Tests of acoustic attenuation theory for ice

SCATTERINGScattering in titanium (hexagonal structure like ice) agrees with theory to ± 3X. There are no measurements of scattering in pure glacial ice at low temperature.

ABSORPTIONWe 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.

Comparison of South Pole ice and NaCl for acoustic waves

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. 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.