Improvement in the Empirical Green's Function Extraction Using Root Mean Square Ratio Stacking

Document Type : Research


1 M.Sc. Graduated, Department of Earth Physics, Institute of Geophysics, University of Tehran, Tehran, Iran

2 Assistant Professor, Institute of Geophysics, Polish Academy of Sciences, Warsaw, Poland


Seismic interferometry is an efficient technique to extract the Empirical Green's Function (EGF) between station pairs when the source is considered at one of the stations. The geometry and energy flux of asymmetric noise sources have unavoidable impacts on the extracted EGFs, deduced from ambient seismic noise recorded in pairs of stations. In this study, to consider these effects, three methods of noise correlation functions stacking (linear, root mean square, root mean square ratio) are investigated using synthetic and real data processing. During synthetic data processing, effects of the noise sources geometry and energy flux inside and outside the Fresnel zone are examined. After separating stationary and non-stationary sources, the results have shown that the root mean square ratio contains the least effects of non-stationary signals compared to other methods of stacking. Moreover, comparison of the EGFs from the recorded data in Azerbaijan (NW Iran), indicates that the signal retrieved by root mean square ratio is more reliable than the other stacking methods' signals (e.g., linear, root mean square).


Main Subjects

Bensen, G. D., Ritzwoller, M. H., Barmin, M. P., Levshin, A. L., Lin, F., Moschetti, M. P., Shapiro, N. M. and Yang, Y., 2007, Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements, Geophys. J. Int, 169, 1239–1260.
Derode, A., Larose, E., Tanter, M., de Rosny, J., Tourin, A., Campillo, M. and Fink, M., 2003, Recovering the Green's function from field-field correlations in an open scattering medium, J. Acoust. Soc. Am., 113, 2973–2976.
Gouédard, P., Stehly, L., Brenguier, F., Campillo, M., Colin de Verdière, Y., Larose, E., Margerin, L., Roux, P., S´anchez-Sesma, F. J., Shapiro, N. M. and Weaver, R. L., 2008, Cross-correlation of random fields: mathematical approach and applications, Geophys. Prospect, 56(3), 375–393.
Landes, M., Hubans, F., Shapiro, N. M., Paul, A. and Campillo, M., 2010, Origin of deep ocean microseisms by using teleseismic body waves, J. Geophys. Res., 115:B05302. doi:10.1029/2009JB006918.
Liu, X. and Ben-Zion, Y., 2016, Estimating correlations of neighboring frequencies in ambient seismic noise, Geophys. J. Int., 206(2), 1065–1075.
Lobkis, O. I. and Weaver, R. L., 2001, On the emergence of the Green's function in the correlations of a diffuse field, J. acoust. Soc. Am., 110, 3011–3017.
Meier, U., Shapiro, N. M. and Brenguier, F., 2010, Detecting seasonal variations in seismic velocities within Los Angeles basin from correlations of ambient seismic noise, Geophys. J. Int.,181, 985–996.
Prieto, G. A., Lawrence, J. F. and Beroza, G. C., 2009, An elastic Earth structure from the coherency of the ambient seismic field, J. Geophys. Res., 114:B07303. doi:10.1029/2008JB006067.
Roux, P., Sabra, K. G., Kuperman, W. A. and Roux, A., 2005, Ambient noise cross correlation in free space: theoretical approach, J. Acoust. Soc. Am.,117, 79–84.
Sabra, K. G., Gerstoft, P., Roux, P., Kuperman, W. A. and Fehler, M. C., 2005, Extracting time-domain Green's function estimates from ambient seismic noise, Geophys. Res. Lett., 32, L03310. doi:10.1029/2004GL021862.
Safarkhani, M. and Shirzad, T., 2017, Investigation of scattered coda correlation functions from noise correlation functions, in retrieving optimized empirical Green's functions in Azerbaijan Region, Iran, Journal of the Earth and Space Physics (in Persian with abstract in English), 43(2), 323-337. doi:10.22059/jesphys.2017.60286.
Safarkhani, M. and Shirzad, T., 2019, Improving C¹ and C³ Empirical Green's Functions from ambient seismic noise in NW Iran using RMS-ratio stacking method, J. SEISMOL, doi: 10.1007/s10950-019-09834-1.
Schuster, T. G., Yu, J., Sheng, J. and Rickett, J., 2004, Interferometric/daylightseismic imaging, Geophys. J. Int.,157, 838–852.
Sens-Schönfelder, C. and Wegler, U., 2006, Passive image interferometry and seasonal variations of seismic velocities at Merapi Volcano, Indonesia, Geophys. Res. Lett.,33, L21302. doi:10.1029/2006GL027797.
Shapiro, N. M. and Campillo, M., 2004, Emergence of broadband Rayleigh waves from correlations of the ambient seismic noise, Geophys. Res. Lett., 31, L07614. doi:10.1029/2004GL019491.
Shapiro, N. M., Campillo, M., Stehly, L. and Ritzwoller, M. H., 2005, High resolution surface-wave tomography from ambient seismic noise, Science, 307, 1615–1618.
Shirzad, T. and Shomali, Z. H., 2015, Extracting Seismic Body and Rayleigh Waves from the Ambient Seismic Noise Using the rms-Stacking Method, Seismol. Res. Lett., 86(1), 173-180. doi: 10.1785/ 0220140123.
Shirzad, T. and Shomali, ZH., 2013, Shallow crustal structures of the Tehran basin in Iran resolved by ambient noise tomography, Geophys. J. Int., 196, 1162–1176. doi:10.1093/gji/ggt449.
Snieder, R., 2004, Extracting the Green's function from correlation of coda waves: a derivation based on stationary phase, Phys. Rev. E., 69, 046610. doi:
Snieder, R. and Sens-Schönfelder, C., 2015, Seismic interferometry and stationary phase at caustics, J. Geophy. Res. Solid. Earth, 120, 4333-4343.
Snieder, R., Wapenaar, K. and Larner, K., 2006, Spurious multiples in seismic interferometry of primaries, Geophysics, 71(4), SI111–SI124.
Snieder, R., Wapenaar, K. and Wegler, U., 2007, Unified Green's function retrieval by cross-correlation: connection with energy principles, Phys. Rev. E., 75, 036103. doi:10.1103/ PhysRevE. 75.036103.
Stehly, L., Campillo, M., Froment, B. and Weaver, R. L., 2008, Reconstructing Green's function by correlation of the coda of the correlation (C3) of ambient seismic noise, J. Geophys. Res.,113, B11306. doi: 10.1029/2008JB005693.
Stehly, L., Campillo, M. and Shapiro, N. M., 2006, A study of the seismic noise from its long range correlation properties, J.Geophys. Res.,111, B10306. doi:10.1029/2005JB00237.
Stutzmann, E., Schimmel, M., Patau, G. and Maggi, A., 2009, Global climate imprint on seismic noise, Geochem. Geophys. Geosyst., doi:10.1029/2009GC002619.
Tsai, V. C., 2009, On establishing the accuracy of noise tomography travel time measurements in a realistic medium, Geophys. J. Int., 178(3), 1555–1564. doi:10.1111/j.1365-246X.2009.04239.x.
Wapenaar, K., 2004, Retrieving the elastodynamic Green's function of an arbitrary inhomogeneous medium by cross correlation, Phys. Rev. Lett., 93(25), 254301. doi:10.1103/ PhysRevLett.93. 254301.
Wapenaar, K., Draganov, D., van der Neut, J. and Thorbecke, J., 2004, Seismic interferometry: a comparison of approaches, SEG. Tech. Prog. Expand. Abstr, 23, 1981–1984.
Wapenaar, K. and Fokkema, J., 2006, Green's function representations for seismic interferometry, Geophysics, 71(4), 33-46. doi:10.1190/1.2213955.
Wapenaar, K., Slob, E. and Snieder, R., 2006, Unified Green's function retrieval by cross-correlation, Phys. Rev. Lett., 97(23), 234301. doi:10.1103/ PhysRevLett.97.234301.
Weaver, R. L. and Lobkis, O. I., 2001, Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies, Phys. Rev. Lett., 87, 134-301. doi:10.1103/PhysRevLett.87.134301.
Wessel, P. and Smith, W.H.F., 1998, New, improved version of the Generic Mapping Tools released, Eos. Trans, AGU, 79, 579.