Cross-correlation of independent, equipartitioned wavefields is a well-established method to estimate the elastic Green's function, commonly termed seismic interferometry. In this article, the sum of a wavefield recorded at two locations in a single channel is used to estimate the Green's function via the autocorrelation; the result contains some predicted artefacts. The underlying theory and hardware required to estimate the Green's function is presented and compared to traditional seismic interferometry. This technique is used to estimate the elastic Green's function between two locations on an aluminum block with surface scatterers. Wavefields excited via rapid thermoelastic expansion of the surface using a pulsed laser are detected by a dual-beam heterodyne interferometer. The detector is capable of directly recording the sum of a wavefield measured at two locations in a single channel. This method could be an effective, low cost, and non-contacting technique for structural monitoring, particularly where ambient noise has established equipartitioned wavefields in the structure.

1.
K.
Aki
, “
Space and time spectra of stationary stochastic waves, with special reference to microtremors
,”
Bull. Earth. Res. Inst.
35
,
415
456
(
1957
).
2.
M.
Campillo
and
A.
Paul
, “
Long-range correlations in the diffuse seismic coda
,”
Science
299
(
5606
),
547
549
(
2003
).
3.
R.
Snieder
and
E.
Şafak
, “
Extracting the building response using seismic interferometry: Theory and application to the Millikan Library in Pasadena, California
,”
Bull. Seismol. Soc. Am.
96
(
2
),
586
598
(
2006
).
4.
A.
Curtis
,
P.
Gerstoft
,
H.
Sato
,
R.
Snieder
, and
K.
Wapenaar
, “
Seismic interferometry: Turning noise into signal
,”
The Leading Edge
25
(
9
),
1082
1092
(
2006
).
5.
O. I.
Lobkis
and
R. L.
Weaver
, “
On the emergence of the Green's function in the correlations of a diffuse field
,”
J. Acoust. Soc. Am.
110
(
6
),
3011
3017
(
2001
).
6.
C.
Sens-Schönfelder
and
U.
Wegler
, “
Passive image interferometry and seasonal variations of seismic velocities at Merapi Volcano, Indonesia
,”
Geophys. Res. Lett.
33
(
21
),
L21302
, (
2006
).
7.
A. E.
Malcolm
,
J. A.
Scales
, and
B. A.
van Tiggelen
, “
Extracting the Green's function from diffuse, equipartitioned waves
,”
Phys. Rev. E
70
(
1
),
015601
(
2004
).
8.
T. D.
Mikesell
,
K.
van Wijk
,
T. E.
Blum
,
R.
Snieder
, and
H.
Sato
, “
Analyzing the coda from correlating scattered surface waves
,”
J. Acoust. Soc. Am.
131
(
3
),
EL275
EL281
(
2012
).
9.
K. G.
Sabra
,
P.
Roux
, and
W.
Kuperman
, “
Emergence rate of the time-domain Green's function from the ambient noise cross-correlation function
,”
J. Acoust. Soc. Am.
118
(
6
),
3524
3531
(
2005
).
10.
K.
Wapenaar
and
J.
Fokkema
, “
Green's function representations for seismic interferometry
,”
Geophysics
71
(
4
),
SI33
SI46
(
2006
).
11.
A.
Grêt
,
R.
Snieder
, and
U.
Özbay
, “
Monitoring in situ stress changes in a mining environment with coda wave interferometry
,”
Geophys. J. Int.
167
(
2
),
504
508
(
2006
).
12.
R.
Snieder
and
M.
Hagerty
, “
Monitoring change in volcanic interiors using coda wave interferometry: Application to Arenal volcano, Costa Rica
,”
Geophys. Res. Lett.
31
(
9
),
L09608
, (
2004
).
13.
R.
Snieder
,
A.
Grêt
,
H.
Douma
, and
J.
Scales
, “
Coda wave interferometry for estimating nonlinear behavior in seismic velocity
,”
Science
295
(
5563
),
2253
2255
(
2002
).
14.
C. R.
Farrar
and
G. H.
James
 III
, “
System identification from ambient vibration measurements on a bridge
,”
J. Sound Vib.
205
(
1
),
1
18
(
1997
).
15.
S. C.
Stähler
,
C.
Sens-Schönfelder
, and
E.
Niederleithinger
, “
Monitoring stress changes in a concrete bridge with coda wave interferometry
,”
J. Acoust. Soc. Am.
129
(
4
),
1945
1952
(
2011
).
16.
U.
Wegler
,
B.-G.
Lühr
,
R.
Snieder
, and
A.
Ratdomopurbo
, “
Increase of shear wave velocity before the 1998 eruption of Merapi Volcano (Indonesia)
,”
Geophys. Res. Lett.
33
(
9
),
L09303
, (
2006
).
17.
R.
Weaver
and
O.
Lobkis
, “
On the emergence of the Green's function in the correlations of a diffuse field: Pulse-echo using thermal phonons
,”
Ultrasonics
40
(
1
),
435
439
(
2002
).
18.
S.
Hitchman
,
K.
van Wijk
,
N.
Broderick
, and
L.
Adam
, “
Heterodyne interferometry for the detection of elastic waves: A tutorial and open-hardware project
,”
Eur. J. Phys.
36
(
3
),
035011
(
2015
).
19.
C. B.
Scruby
and
L. E.
Drain.
,
Laser Ultrasonics: Techniques and Applications
(
Taylor and Francis
,
New York
,
1990
).
20.
S.
Hitchman
,
K.
van Wijk
, and
Z.
Davidson
, “
Monitoring attenuation and the elastic properties of an apple with laser ultrasound
,”
Postharvest Biol. Technol.
121
,
71
77
(
2016
).
21.
N.
Muramatsu
,
N.
Sakurai
,
N.
Wada
,
R.
Yamamoto
,
K.
Tanaka
,
T.
Asakura
,
Y.
Ishikawa-Takano
, and
D. J.
Nevins
, “
Remote sensing of fruit textural changes with a laser Doppler vibrometer
,”
J. Am. Soc. Hortic. Sci.
125
(
1
),
120
127
(
2000
).
22.
T. E.
Blum
,
L.
Adam
, and
K.
van Wijk
, “
Noncontacting benchtop measurements of the elastic properties of shales
,”
Geophysics
78
(
3
),
C25
C31
(
2013
).
23.
Y.
Fujino
,
K.
Kaito
, and
M.
Abe
, “
Detection of structural damage by ambient vibration measurement using laser Doppler vibrometer
,” in
6th Annual International Symposium on NDE for Health Monitoring and Diagnostics
, International Society for Optics and Photonics (
2001
), pp.
167
178
.
24.
D.
Siringoringo
,
Y.
Fujino
,
T.
Nagayama
, and
H.
Wenzel
, “
Vibration characteristics of an overpass bridge during full-scale destructive testing
,”
Procedia Eng.
14
,
777
784
(
2011
).
25.
J. L.
Johnson
,
K.
van Wijk
, and
M.
Sabick
, “
Characterizing phantom arteries with multi-channel laser ultrasonics and photo-acoustics
,”
Ultrasound Med. Biol.
40
(
3
),
513
520
(
2014
).
26.
M.
Morant
,
J.
Pérez
, and
R.
Llorente
, “
Polarization division multiplexing of ofdm radio-over-fiber signals in passive optical networks
,”
Adv. Opt. Technol.
2014
,
269524
(
2014
)
27.
S.
Haykin
,
Communication Systems
(
Wiley
,
Hoboken, NJ
,
2009
).
28.
J. L.
Johnson
,
H.
tom Wörden
, and
K.
van Wijk
, “
PLACE an open-source python package for laboratory automation, control, and experimentation
,”
J. Lab. Autom.
20
(
1
),
10
16
(
2015
).
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