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

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Absorption and Scattering of Acoustic Waves in
NaClP. B. Price, U. C. Berkeley, February 3,
2005
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Acoustic ScatteringIn ice, it occurs at grain
boundaries. In a salt dome it also occurs at
cracks, layers of clay,anhydrite, and liquid
inclusions. Acoustic Absorptionoccurs by
relaxation mechanisms. In NaCl the thermal phonon
gas extracts energy from acoustic phonons via
anharmonic interactions.
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Conversion of ionization energy into acoustic
energy ocean, 15º ice, -51º
NaCl, 30º ltvLgt m s-1 1530
3920 4560 ltvSgt 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 ? ? ltvLgt2 ?/CP 0.153
1.12 2.87 d RMoliere 0.1 m
0.1 m 0.054 m L3Xoln(Eo/Ec)1/2 10.3 m
10.3 m 3.43m fpeak vL / 2d 7.7 kHz
20 kHz 42 kHz disk ? d/L 0.5º
0.5º 0.9º
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Scattering of acoustic wave at grain
boundaries(speed depends on crystallographic
direction)Rayleigh regime (?/4pa gt 1)
Stochastic regime (0.5 lt ?/4pa lt 1) Geometric
regime (?/4pa lt 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)
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Grain boundary scattering in Rayleigh regime
(cubic)
Grain boundary scattering in stochastic regime
(cubic)
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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
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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
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Salt evaporite beds WIPP repository contains
salt beds lt 100 m thick with gt1 water (mostly in
liquid inclusions) and separated vertically by
thin beds of clay, silt, and anhydrite
(CaSO4). Salt domes In Louisiana, several mines
have gt99 NaCl, are very dry (only 2 to 40 ppm
water), and have small (7.5 mm) grain size, which
is good.
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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)
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Liquid inclusions in salt domes They scatter
acoustic waves but are infrequent.
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3x10-8
NaCl
S.P.Station noise?
dp/df g cm-1 s-1
ice
10-8
f Hz
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Acoustic scattering and absorption in South Pole
ice and NaCl ?scatt ?abs
104 Hz 3x104 Hz 104 Hz
3x104 Hz Ice (D0.2 cm) 1650 km 20
km 7 km 7 km NaCl (D2 cm) 6 km
0.15 km 3x104 km 3300 km NaCl (D0.75
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 ?scatt
and ?abs over gt1km in salt dome!
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Optical detection NaCl has absorption
length gt100m for wavelength gt350 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