Exploiting the fine structure of strongly scattered waves could provide a wealth of new information in seismology, ultrasonics, acoustics, and other fields that study wave propagation in heterogeneous media. Therefore, noncontacting laser-based measurements of ultrasonic surface waves propagating in a strongly disordered medium are performed in which the ratio of the dominant surface wavelength to the size of a scatterer is large, and waves that propagate through many scatterers are recorded. This allows analysis of scattering-induced dispersion and attenuation, as well as the transition from ballistic to diffusive propagation. Despite the relatively small size of the scatterers, multiple scattering strikingly amplifies small perturbations, making changes even in a single scatterer visible in the later-arriving waveforms. To understand the complexity of the measured waveforms, elastic spectral-element numerical simulations are performed. The multiple-scattering sensitivity requires precise gridding of the actual model, but once this has been accomplished, we obtain good agreement between the measured and simulated waveforms. In fact, the simulations are invaluable in analyzing subtle effects in the data such as weak precursory body-wave diffractions. The flexibility of the spectral-element method in handling media with sharp boundaries makes it a powerful tool to study surface-wave propagation in the multiple-scattering regime.

1.
K.
Aki
and
B.
Chouet
, “
Origin of coda waves: Source, attenuation, and scattering effects
,”
J. Geophys. Res.
80
,
3322
3342
(
1975
).
2.
R.
Hennino
,
N.
Trégourès
,
N. M.
Shapiro
,
L. L.
Margerin
,
M.
Campillo
,
B. A.
van Tiggelen
, and
R. L.
Weaver
, “
Observation of equipartition of seismic waves
,”
Phys. Rev. Lett.
86
(
15
),
3447
3450
(
2001
).
3.
R.
Benites
,
P.
Roberts
,
K.
Yomogida
, and
M.
Fehler
, “
Scattering of elastic waves in 2-D composite media. I. Theory and test
,”
Phys. Earth Planet. Inter.
104
,
161
173
(
1997
).
4.
R.
Snieder
,
A.
Grêt
,
H.
Douma
, and
J. A.
Scales
, “
Coda wave interferometry for estimating nonlinear behavior in seismic velocity
,”
Science
295
,
2253
2255
(
2002
).
5.
M. L.
Cowan
,
I. P.
Jones
,
J. H.
Page
, and
D. A.
Weitz
, “
Diffusing acoustic wave spectroscopy
,”
Phys. Rev. E
65
,
066605
(
2002
).
6.
G.
Poupinet
,
W.
Ellsworth
, and
J.
Frechet
, “
Monitoring velocity variations in the crust using earthquake doublets—An application to the Calaveris fault, California
,”
J. Geophys. Res.
89
,
5719
5731
(
1984
).
7.
M.
Campillo
and
A.
Paul
, “
Long-range correlations in the diffuse seismic coda
,”
Science
299
,
547
549
(
2003
).
8.
O. I.
Lobkis
and
R. L.
Weaver
, “
Ultrasonics without a source: Thermal fluctuation correlations at MHz frequencies
,”
Phys. Rev. Lett.
87
(
13
),
134301
(
2001
).
9.
R. L.
Weaver
and
O. I.
Lobkis
, “
On the emergence of the Green’s function in the correlations of a diffuse field
,”
J. Acoust. Soc. Am.
110
,
3011
3017
(
2001
).
10.
A. Malcolm, J. A. Scales, and B. A. van Tiggelen (submitted).
11.
J. A.
Scales
and
K.
van Wijk
, “
Multiple scattering attenuation and anisotropy of ultrasonic surface waves
,”
Appl. Phys. Lett.
74
,
3899
3901
(
1999
).
12.
J. A.
Scales
and
K.
van Wijk
, “
Tunable multiple-scattering system
,”
Appl. Phys. Lett.
79
,
2294
2296
(
2001
).
13.
K. van Wijk, “Multiple scattering of surface waves,” Ph.D. thesis, Colorado School of Mines, 2003; K. van Wijk, M. Maney and J. A. Scales, “1D energy transport in a stongly scattering laboratory model,” Phys Rev. E (to be published).
14.
D.
Komatitsch
and
J.
Tromp
, “
Introduction to the spectral-element method for 3-D seismic wave propagation
,”
Geophys. J. Int.
139
,
806
822
(
1999
).
15.
O.
Nishizawa
,
T.
Satoh
,
X.
Lei
, and
Y.
Kuwahara
, “
Laboratory studies of seismic wave propagation in inhomogeneous media using a laser Doppler vibrometer
,”
Bull. Seismol. Soc. Am.
87
(
4
),
809
823
(
1997
).
16.
P.
Carpena
,
V.
Gasparian
, and
M.
Ortuño
, “
Energy spectra and level statistics of Fibonacci and Thue–Morse chains
,”
Phys. Rev. B
51
(
18
),
12813
12816
(
1995
).
17.
W.
Gellermann
,
M.
Kohmoto
,
B.
Sutherland
, and
P. C.
Taylor
, “
Localization of light waves in Fibonacci dielectric multilayers
,”
Phys. Rev. Lett.
72
,
633
(
1994
).
18.
L.
Dal Negro
,
C. J.
Oton
,
Z.
Gaburro
,
L.
Pavesi
,
P.
Johnson
,
A.
Lagendijk
,
R.
Righini
,
M.
Colocci
, and
D. S.
Wiersma
, “
Light transport through the band-edge states of Fibonacci quasicrystals
,”
Phys. Rev. Lett.
90
(
5
),
055501
(
2003
).
19.
E.
Priolo
,
J. M.
Carcione
, and
G.
Seriani
, “
Numerical simulations of interface waves by high-order spectral modeling techniques
,”
J. Acoust. Soc. Am.
95
,
681
693
(
1994
).
20.
E.
Faccioli
,
F.
Maggio
,
R.
Paolucci
, and
A.
Quarteroni
, “
2D and 3D elastic wave propagation by a pseudo-spectral domain decomposition method
,”
J. Seismol.
1
,
237
251
(
1997
).
21.
D.
Komatitsch
and
J. P.
Vilotte
, “
The spectral-element method: An efficient tool to simulate the seismic response of 2D and 3D geological structures
,”
Bull. Seismol. Soc. Am.
88
,
368
392
(
1998
).
22.
D.
Komatitsch
and
J.
Tromp
, “
Spectral-element simulations of global seismic wave propagation. I. Validation
,”
Geophys. J. Int.
150
,
390
412
(
2002
).
23.
D.
Komatitsch
,
J.
Ritsema
, and
J.
Tromp
, “
The spectral-element method, Beowulf computing, and global seismology
,”
Science
298
,
1737
1742
(
2002
).
24.
D.
Komatitsch
,
J. P.
Vilotte
,
R.
Vai
,
J. M.
Castillo-Covarrubias
, and
F. J.
Sánchez-Sesma
, “
The spectral element method for elastic wave equations—Application to 2-D and 3-D seismic problems
,”
Int. J. Numer. Methods Eng.
45
,
1139
1164
(
1999
).
25.
T. D. Rossing and N. H. Fletcher, Principles of Vibration and Sound (Springer, New York, 1995).
26.
H. C. van de Hulst, Light Scattering by Small Particles (Wiley, New York, 1957).
27.
A. C.
Chang
and
J. R.
Cleary
, “
Precursors to PKKP
,”
Bull. Seismol. Soc. Am.
68
(
4
),
1059
1078
(
1978
).
28.
P. S.
Earle
and
P. M.
Shearer
, “
Observations of PKKP precursors used to estimate small-scale topography on the core–mantle boundary
,”
Science
277
,
667
670
(
1997
).
29.
A. C.
Chang
and
J. R.
Cleary
, “
Scattered PKKP: Further evidence for scattering at a rough core–mantle boundary
,”
Phys. Earth Planet. Inter.
24
,
15
29
(
1981
).
This content is only available via PDF.
You do not currently have access to this content.