Retrieval of the Green's function from cross correlation: The canonical elastic problem

Bulletin of the Seismological Society of America

Volumn 96, Issue 3, 2006, Pages 1182-1191

  Sánchez Sesma, Francisco J ^a   Campillo, Michael ^b  

^a UNIVERSIDAD NACIONAL AUTÓNOMA DE MÉXICO   (Mexico)

^b UNIVERSITÉ GRENOBLE ALPES   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CORRELATION DETECTORS; FOURIER TRANSFORMS; GREEN'S FUNCTION; SCATTERING; TENSORS; WAVE ENERGY CONVERSION;

ELASTIC ENERGY; ISOTROPIC PLANE WAVES;

SEISMIC WAVES;

CORRELATION; ELASTIC WAVE; GREEN FUNCTION; P-WAVE; S-WAVE;

EID: 33645277175     PISSN: 00371106     EISSN: None     Source Type: Journal    
DOI: 10.1785/0120050181     Document Type: Article

References (30)

1. Abramowitz, M., and I. A. Stegun (1972). Handbook of Mathematical Functions, Dover Publications Inc., New York.
2. Aki, K. (1957). Space and time spectra of stationary stochastic waves with special reference to microtremors, Bull. Earthquake Res. Inst. 35, 415-456.
3. Aki, K., and B. Chouet (1975). Origin of coda waves: source, attenuation and scattering effects, J. Geophys. Res. 80, 3322-3342.
4. Aki, K., and P. G. Richards (1980). Quantitative Seismology, W. H. Freeman and Co., San Francisco.
5. Campillo, M., and A. Paul (2003). Long range correlations in the seismic coda, Science 299, 547-549.
6. Cox, H. (1973). Spatial correlation in arbitrary noise fields with applications to ambient sea noise, J. Acoust. Soc. Am. 54, 1289-1301.
7. Derode, A., E. Larose, M. Tanter, J. de Rosny, A. Tourin, M. Campillo, and M. Fink (2003). Recovering the Green's function from field-field correlations in an open scattering medium, J. Acoust. Soc. Am. 113, 2973-2976.
8. Eagle, D. M. (1981). Diffuse waves in solid media, J. Acoust. Soc. Am. 70, 476-480.
9. Hennino, R., N. Trégourès, N. Shapiro, L. Margerin, M. Campillo, B. van Tiggelen, and R. L. Weaver (2001). Observation of equipartition of seismic waves in Mexico, Phys. Rev. Lett. 86, 3447-3450.
10. Kittel, C., and H. Kroemer (1980). Thermal Physics, W.H. Freeman and Co., San Francisco.
11. Kuperman, W. A., and F. Ingenito (1980). Spatial correlation of surface generated noise in a stratified ocean, J. Acoust. Soc. Am. 67, 1988-1996.
12. Lobkis, O. I., and R. L. Weaver (2001). On the emergence of the Green's function in the correlations of a diffuse field, J. Acoust. Soc. Am. 110, 3011-3017.
13. Paul, A., M. Campillo, L. Margerin, E. Larose, and A. Derode (2005). Empirical synthesis of time-asymmetrical Green function from the correlation of coda waves, J. Geophys. Res. 110, doi 10.1039/ 2004JB003521.
14. Roux, P., K. G. Sabra, W. A. Kuperman, and A. Roux (2005). Ambient noise cross correlation in free space: theoretical approach, J. Acoust. Soc. Am. 117, 79-84.
15. Ryzhik, L. V., G. C. Papanicolau, and J. B. Keller (1996). Transport equations for elastic and other waves in random media, Wave Motion 24, 327-370.
16. Sabra, K. G., P. Gerstoft, P. Roux, W. A. Kuperman, and M. C. Fehler (2005). Extracting time-domain Green's function estimates from ambient seismic noise, Geophys. Res. Len. 32, L03310, doi 10.1029/2004GL021862.
17. Sánchez-Sesma, F. J., and M. Campillo (1991). Diffraction of P, SV and Rayleigh waves by topographic features: a boundary integral formulation, Bull. Seism. Soc. Am. 81, 2234-2253.
18. Sánchez-Sesma, F. J., and F. Luzón (1995). Seismic response of three-dimensional alluvial valleys for incident P, S and Rayleigh waves, Bull. Seism. Soc. Am. 85, 269-284.
19. Sato, H., and M. Fehler (1998). Wave Propagation and Scattering in the Heterogeneous Earth, Springer-Verlag, New York.
20. Shapiro, N. M., and M. Campillo (2004). Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise, Geophys. Res. Lett. 31, L07614, doi 10.1029/2004GL019491.
21. Shapiro, N. M., M. Campillo, L. Margerin, S. K. Singh, V. Kostoglodov, and J. Pacheco (2000). The energy partitioning between P and S waves and the diffusive character of the seismic coda, Bull. Seism. Soc. Am. 90, 655-665.
22. Shapiro, N. M., M. Campillo, L. Stehly, and M. Ritzwoller (2005). High resolution surface wave tomography from ambient seismic noise, Science 307, 1615-1618.
23. Snieder, R. (2002). Coda wave interferometry and the equilibration of energy in elastic media, Phys. Rev. E 66, 04615-1-8.
24. Snieder, R. (2004). Extracting the Green's function from the correlation of coda waves: A derivation based on stationary phase, Phys. Rev. E 69, 046610.
25. Van Manen, D.-J., J. O. A. Robertsson, and A. Curtis (2005). Modeling of wave propagation in inhomogeneous media, Phys. Rev. Lett. 94, 164301-1-4
26. Van Tiggelen, B. A. (2003). Green function retrieval and time reversal in a disordered world, Phys. Rev. Lett. 91, 243904.
27. Wapenaar, K. (2004). Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation, Phys. Rev. Lett. 93, 254301-1-4.
28. Weaver, R. L. (1982). On diffuse waves in solid media, J. Acoust. Soc. Am 71, 1608-1609.
29. Weaver, R. L. (1990). Diffusivity of ultrasound in polycrystals, J. Mech. Phys. Solids 38, 55-86.
30. Weaver, R. L., and O. I. Lobkis (2004). Diffuse fields in open systems and the emergence of the Green's function, J. Acoust. Soc. Am. 116, 2731-2734.