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Absorption and Scattering of Acoustic
Waves in NaCl
P. B. Price, U. C. Berkeley, February 3, 2005
Acoustic Scattering
In ice, it occurs at grain
boundaries. In a salt dome it
also occurs at cracks, layers
of clay,anhydrite, and liquid
inclusions.
Acoustic Absorption
occurs by relaxation
mechanisms. In NaCl the
thermal phonon gas extracts
energy from acoustic
phonons via anharmonic
interactions.
Conversion of ionization energy into acoustic energy
<vL>
[m s-1]
<vS>
[m s-1]
[m3 m-3 K-1]
CP [J kg-1 K-1]
<vL>2 /CP
d ≈ RMoliere
L≈3Xoln(Eo/Ec)1/2
fpeak ≈ vL / 2d
disk = d/L
ocean, 15º
ice, -51º
NaCl, 30º
1530
n/a
25.5x10-5
3900
0.153
0.1 m
10.3 m
7.7 kHz
3920
1995
12.5x10-5
1720
1.12
0.1 m
10.3 m
20 kHz
4560
2610
11.6x10-5
839
2.87
0.054 m
3.43m
42 kHz
0.5º
0.5º
0.9º
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, cij
Ice (hexagonal): c11, c12, c13, c33, c44
NaCl (cubic): c11, c12, c44
For an isotropic solid, c11 - c12 - 2 c44 = 0
no scattering at grain boundaries.
(For glass, = 0; for NaCl, = 0.111)
Grain boundary scattering in Rayleigh regime (cubic):
5
4
3
2
a 4 (c11 c12 2c44 ) 3 v L
3
scatt
k
1
2
2 v
375
c11
S
3
4
a
f
1
1.65 10 4
m
4
1cm 10
Grain boundary scattering in stochastic regime (cubic):
4 c11 c12 2c 44 2
k a
2
525
c11
2
scatt
2
a
f
1
7.21 104
m
4
1cm 10
2f
where k
; a mean grain radius
vL
1
South Pole ice
(-51ºC)
diam
0.4 cm 0.2 cm
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.
longitudinal waves
c-axis
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
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.
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)
Liquid inclusions in salt domes
They scatter acoustic waves but are infrequent.
dp/df [g cm-1 s-1]
3x10-8
10-8
S.P.Station
noise?
NaCl
ice
f [Hz]
Acoustic scattering and absorption in South Pole ice and NaCl
scatt
104 Hz
3x104 Hz
Ice (D=0.2 cm)
1650 km 20 km
NaCl (D=2 cm)
6 km
0.15 km†
NaCl (D=0.75 cm)* 120 km 1.4 km†
*Measured for salt in Avery Island dome
†Dominant
abs
104 Hz
3x104 Hz
7 km†
3x104 km
3x104 km
7 km
3300 km
3300 km
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 scatt and abs over >1km in salt dome!
Optical detection
Bergstrom-Price
model
• 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.