1. Observation of diffuse seismic waves at teleseismic distances
N. Shapiro
University of Colorado at Boulder
M. Campillo
L.Margerin
E. Chaljub
B. van Tiggelen
Université Joseph Fourier Grenoble, France

2. Diffuse field vs. ballistic waves
source
source dependent
sample only certain directions
extended sensitivity
source independent
samples all directions
localized sensitivity
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)
Main goal of this study is to understand:
if the seismic diffuse waves can be observed far from earthquakes
if a deterministic information about the Earth’s structure can be extracted from those “teleseismic” diffuse waves

3. Diffuse fields at teleseismic distances: data and methods
Signals
teleseismic coda
ambient seismic noise
Methods
polarization analysis (to observe the mode equipartitioning)
field-to-field correlation

4. Example of teleseismic coda

5. Example of teleseismic coda
vertical component

6. Example of teleseismic coda
vertical component
Diffuse and ballistic waves in the teleseismic coda cannot be separated by simple analysis of envelopes

7. Polarization of teleseismic coda

8. Polarization of teleseismic coda

9. Polarization of teleseismic coda

10. Polarization of teleseismic coda

11. Stabilization of the vertical-to-horizontal energy ratioHz

12. Stabilization of the vertical-to-horizontal energy ratioHz

13. Stabilization of the vertical-to-horizontal energy ratioHz

14. Stabilization of the vertical-to-horizontal energy ratioHz Ez Eh
~1.5

15. Interpretation in terms of modal content
ballistic field: no scattering, no energy exchange between modes
high-Q modes dominate the late coda
Toroidal modes are attenuated faster than spheroidal modes:
linear polarization of the horizontal component
long-living
modes
short-living
High-Q spheroidal modes have large Z/H ratios:
domination of the vertical component
main physical cause: higher Q for P waves than for S waves

16. mode equipartitioning
Interpretation in terms of modal content
diffuse field
scattering and energy redistribution between modes can result in
mode equipartitioning
randomization of the particle motion in the horizontal plane
stabilization of the vertical-to-horizontal energy ratio

17. Comparison 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
observation

18. Comparison 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 or
over some subset of modes
observation

19. Comparison 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 or
over some subset of modes
observation
Possible explanations:
Preferential scattering toward Rayleigh waves in the late coda
Unaccounted effect of the anelastic attenuation on the equipartitioning

20. Extracting Green functions from the diffuse wavefield by field-to-filed correlation: theoretical background
modal representation of the diffuse field:
- eigenfunctions
- eigenfrequencies
- modal excitations, uncorrelated random variables:
- 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

21. Cross-correlations from teleseismic codas: data
records at five US permanent seismic stations from 17 M≥8 earthquakes occurred between 1993 and 2002

22. Cross-correlations from teleseismic codas: ANMO - CCM
vertical component
stack from13 earthquakes
distance 1405 km

23. Cross-correlations from teleseismic codas: ANMO - CCM
vertical component
stack from13 earthquakes
distance 1405 km

24. Cross-correlations from teleseismic codas: ANMO - CCM
vertical component
stack from13 earthquakes
distance 1405 km

25. Cross-correlations from teleseismic codas: ANMO - CCM
vertical component
stack from13 earthquakes
distance 1405 km

26. Cross-correlations from teleseismic codas at US stations
vertical component stacks Hz
3 km/s - Rayleigh wave

27. Cross-correlations from teleseismic codas: ANMO - CCM
vertical component stacks from 13 earthquakes
at long periods:
scattering is weaker
telesesmic coda is not fully diffuse
coherent signals disappear in cross-correlations

28. Cross-correlations from ambient seismic noise: ANMO - CCM
cross-correlations from 30 days of continuous vertical component records (2002/01/ /02/08)
prediction from global group velocity maps of Ritzwoller et al. (2002)
frequency-time analysis of the broadband cross-correlation

29. Cross-correlations from ambient seismic noise at US stations
frequency-time analysis of broadband cross-correlations computed from 30 days of continuous vertical component records

30. Cross-correlation from ambient seismic noise in North-Western Pacific
broadband cross-correlation computed from 30 days of continuous vertical component records

31. Cross-correlation from ambient seismic noise in North-Western Pacific
broadband cross-correlation computed from 30 days of continuous vertical component records

32. Cross-correlations from ambient seismic noise in California
cross-correlations of vertical component continuous records (1996/02/ /03/10) Hz
3 km/s - Rayleigh wave

33. Conclusions Teleseismic coda
at relatively short periods, strong multiple scattering makes the teleseismic coda diffuse
at long periods, the scattering is weaker and diffuse waves do not completely dominate in the teleseismic coda
Observed Z/H energy ratio may indicate that the coda is dominated by scattering toward fundamental-mode Rayleigh waves
Ambient seismic noise
seismic noise is randomized because of the distribution of ambient sources (oceanic microseisms and atmospheric loads)
coherent Rayleigh waves can be extracted from the seismic noise in a broad range of periods

34. Potential for seismic imaging
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:
Measurements possible for every pair of stations
No source related errors
Localized sensitivity zones
Measurements can be extended to shorter periods