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![Page 1: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/1.jpg)
N. Shapiro
Observation of diffuse seismic waves atteleseismic distances
Observation of diffuse seismic waves atteleseismic distances
University of Colorado at Boulder
M. Campillo
L.Margerin
E. Chaljub
B. van Tiggelen
Université Joseph Fourier Grenoble, France
![Page 2: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/2.jpg)
ballistic waves diffuse field
have been traditionally used in seismology
has been used in helioseismology (Duvall et al., 1993), ultrasonics (Lobkis and Weaver, 2001),
marine acoustics (Kuperman and Roux, 2003), and regional seismology (Campillo and Paul, 2003)
• source dependent• sample only certain directions• extended sensitivity
• source independent• samples all directions• localized sensitivity
Main goal of this study is to understand:(1) if the seismic diffuse waves can be observed far from earthquakes(2) if a deterministic information about the Earth’s structure can be
extracted from those “teleseismic” diffuse waves
Main goal of this study is to understand:(1) if the seismic diffuse waves can be observed far from earthquakes(2) if a deterministic information about the Earth’s structure can be
extracted from those “teleseismic” diffuse waves
source
![Page 3: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/3.jpg)
Signals
• teleseismic coda
• ambient seismic noise
Methods
• polarization analysis (to observe the mode equipartitioning)
• field-to-field correlation
Diffuse fields at teleseismic distances:data and methods
Diffuse fields at teleseismic distances:data and methods
![Page 4: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/4.jpg)
Example of teleseismic codaExample of teleseismic coda
![Page 5: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/5.jpg)
Example of teleseismic codaExample of teleseismic coda
vertical component
![Page 6: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/6.jpg)
Example of teleseismic codaExample of teleseismic coda
Diffuse and ballistic waves in the teleseismic coda cannot be separated by simple analysis of envelopes
Diffuse and ballistic waves in the teleseismic coda cannot be separated by simple analysis of envelopes
vertical component
![Page 7: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/7.jpg)
Polarization of teleseismic codaPolarization of teleseismic coda
![Page 8: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/8.jpg)
Polarization of teleseismic codaPolarization of teleseismic coda
![Page 9: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/9.jpg)
Polarization of teleseismic codaPolarization of teleseismic coda
![Page 10: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/10.jpg)
Polarization of teleseismic codaPolarization of teleseismic coda
![Page 11: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/11.jpg)
Stabilization of the vertical-to-horizontal energy ratioStabilization of the vertical-to-horizontal energy ratio
0.01 - 0.016 Hz
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0.01 - 0.016 Hz
Stabilization of the vertical-to-horizontal energy ratioStabilization of the vertical-to-horizontal energy ratio
![Page 13: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/13.jpg)
0.01 - 0.016 Hz
Stabilization of the vertical-to-horizontal energy ratioStabilization of the vertical-to-horizontal energy ratio
![Page 14: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/14.jpg)
0.01 - 0.016 Hz
Ez
Eh~1.5
Stabilization of the vertical-to-horizontal energy ratioStabilization of the vertical-to-horizontal energy ratio
![Page 15: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/15.jpg)
ballistic field: no scattering, no energy exchange between modeshigh-Q modes dominate the late coda
ballistic field: no scattering, no energy exchange between modeshigh-Q modes dominate the late coda
main physical cause: higher Q for P waves than for S wavesmain physical cause: higher Q for P waves than for S waves
Interpretation in terms of modal contentInterpretation in terms of modal content
Toroidal modes are attenuated faster than spheroidal modes:
linear polarization of the horizontal component
long
-liv
ing
mod
essh
ort-
livi
ngm
odes
High-Q spheroidal modes have large Z/H ratios:
domination of the vertical component
![Page 16: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/16.jpg)
diffuse field scattering and energy redistribution
between modes can result inmode equipartitioning
diffuse field scattering and energy redistribution
between modes can result inmode equipartitioning
randomization of the particle motion in the horizontal plane
randomization of the particle motion in the horizontal plane
stabilization of the vertical-to-horizontal energy ratio
stabilization of the vertical-to-horizontal energy ratio
Interpretation in terms of modal contentInterpretation in terms of modal content
![Page 17: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/17.jpg)
Comparison of the observed and the predicted Ez/Eh ratiosComparison of the observed and the predicted Ez/Eh ratios
Ez/Eh ratio in an equipartitioned field
can be predicted as an average over all modes
Ez/Eh ratio in an equipartitioned field
can be predicted as an average over all modes
observation
![Page 18: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/18.jpg)
Comparison of the observed and the predicted Ez/Eh ratiosComparison of the observed and the predicted Ez/Eh ratios
Ez/Eh ratio in an equipartitioned field
can be predicted as an averageover all modes
orover some subset of modes
Ez/Eh ratio in an equipartitioned field
can be predicted as an averageover all modes
orover some subset of modes
observation
![Page 19: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/19.jpg)
Comparison of the observed and the predicted Ez/Eh ratiosComparison of the observed and the predicted Ez/Eh ratios
observation
Possible explanations:1. Preferential scattering toward Rayleigh waves in the late coda2. Unaccounted effect of the anelastic attenuation on the equipartitioning
Possible explanations:1. Preferential scattering toward Rayleigh waves in the late coda2. Unaccounted effect of the anelastic attenuation on the equipartitioning
Ez/Eh ratio in an equipartitioned field
can be predicted as an averageover all modes
orover some subset of modes
Ez/Eh ratio in an equipartitioned field
can be predicted as an averageover all modes
orover some subset of modes
![Page 20: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/20.jpg)
Extracting Green functions from the diffuse wavefield by field-to-filed correlation: theoretical background
Extracting Green functions from the diffuse wavefield by field-to-filed correlation: theoretical background
anam* =δn,mF(ωn)
C(x,y,τ) = F(ωn)un(x)un(y)e−iωnτ
n∑
φ(x,t) = anun(x)eiωnt
n∑modal representation of the diffuse field:
ωn - eigenfrequencies
un - eigenfunctions
an - modal excitations, uncorrelated random variables:
F(ω) - spectral energy density
cross-correlation between points x and y :
differs only by an amplitude factor F() from an actual Green function between x and y
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Cross-correlations from teleseismic codas: dataCross-correlations from teleseismic codas: data
records at five US permanent seismic stations from 17 M≥8 earthquakes occurred between 1993 and 2002
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Cross-correlations from teleseismic codas: ANMO - CCMCross-correlations from teleseismic codas: ANMO - CCM
vertical componentstack from13 earthquakesdistance 1405 km
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Cross-correlations from teleseismic codas: ANMO - CCMCross-correlations from teleseismic codas: ANMO - CCM
distance 1405 km vertical componentstack from13 earthquakes
![Page 24: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/24.jpg)
Cross-correlations from teleseismic codas: ANMO - CCMCross-correlations from teleseismic codas: ANMO - CCM
distance 1405 km vertical componentstack from13 earthquakes
![Page 25: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/25.jpg)
Cross-correlations from teleseismic codas: ANMO - CCMCross-correlations from teleseismic codas: ANMO - CCM
distance 1405 km vertical componentstack from13 earthquakes
![Page 26: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/26.jpg)
vertical component stacks0.03 - 0.1 Hz
3 km/s - Rayleigh wave
Cross-correlations from teleseismic codas at US stationsCross-correlations from teleseismic codas at US stations
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vertical component stacks from 13 earthquakes
at long periods:
1. scattering is weaker2. telesesmic coda is
not fully diffuse3. coherent signals
disappear in cross-correlations
at long periods:
1. scattering is weaker2. telesesmic coda is
not fully diffuse3. coherent signals
disappear in cross-correlations
Cross-correlations from teleseismic codas: ANMO - CCMCross-correlations from teleseismic codas: ANMO - CCM
![Page 28: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/28.jpg)
cross-correlations from 30 days of continuous vertical component records (2002/01/10-2002/02/08)
prediction from global group velocity maps of Ritzwoller et al. (2002)
frequency-time analysis of the broadband cross-correlation
Cross-correlations from ambient seismic noise: ANMO - CCMCross-correlations from ambient seismic noise: ANMO - CCM
![Page 29: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/29.jpg)
Cross-correlations from ambient seismic noise at US stationsCross-correlations from ambient seismic noise at US stations
frequency-time analysis of broadband cross-correlations
computed from 30 days of continuous vertical component records
![Page 30: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/30.jpg)
Cross-correlation from ambient seismic noise in North-Western PacificCross-correlation from ambient seismic noise in North-Western Pacific
broadband cross-correlation computed from 30 days of
continuous vertical component records
![Page 31: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/31.jpg)
Cross-correlation from ambient seismic noise in North-Western PacificCross-correlation from ambient seismic noise in North-Western Pacific
broadband cross-correlation computed from 30 days of
continuous vertical component records
![Page 32: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/32.jpg)
Cross-correlations from ambient seismic noise in CaliforniaCross-correlations from ambient seismic noise in California
cross-correlations of vertical component continuous records (1996/02/11-1996/03/10)0.03-0.2 Hz
3 km/s - Rayleigh wave
![Page 33: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/33.jpg)
ConclusionsConclusions
Teleseismic coda1. at relatively short periods, strong multiple scattering
makes the teleseismic coda diffuse2. at long periods, the scattering is weaker and diffuse
waves do not completely dominate in the teleseismic coda
3. Observed Z/H energy ratio may indicate that the coda is dominated by scattering toward fundamental-mode Rayleigh waves
Ambient seismic noise 1. seismic noise is randomized because of the
distribution of ambient sources (oceanic microseisms and atmospheric loads)
2. coherent Rayleigh waves can be extracted from the seismic noise in a broad range of periods
![Page 34: N. Shapiro Observation of diffuse seismic waves at teleseismic distances University of Colorado at Boulder M. Campillo L.Margerin E. Chaljub B. van Tiggelen.](https://reader036.fdocuments.net/reader036/viewer/2022062517/56649f125503460f94c261a9/html5/thumbnails/34.jpg)
Potential for seismic imagingPotential for seismic imaging
1. Measurements possible for every pair of stations
2. No source related errors
3. Localized sensitivity zones
4. Measurements can be extended to shorter periods
Cross-correlations computed from the ambient seismic noise and the teleseismic coda can provide new surface-wave dispersion measurements that have numerous advantages relative to traditional measurements made from ballistic waves: