Retrieval of long-wave tsunami Green’s function from the cross-correlation of continuous ocean waves excited by far-field random noise sources on the basis of a first-order Born approximation
Tóm tắt
We investigate the theoretical background for the retrieval of the tsunami Green’s function from the cross-correlation of continuous ocean waves. Considering that a tsunami is a long-wavelength ocean wave described by 2-D linear long-wave equations, and that the sea-bottom topography acts as a set of point-like scatterers, we use a first-order Born approximation in deriving the tsunami Green’s function having coda waves. The scattering pattern is non-isotropic and symmetrical with respect to the forward and backward directions. We indicate a retrieval process which shows that the derivative of the cross-correlation function of wavefields at two receivers with respect to the lag time gives the tsunami Green’s function when point noise sources generating continuous ocean waves are distributed far from, and surrounding, the two receivers. Note that this relation between the cross-correlation and the Green’s function is different from the case in which uncorrelated plane-wave incidence from all directions is assumed to be continuous ocean waves. The Green’s function retrieved from continuous ocean waves will be used as a reference to examine the validity of the Green’s function obtained by numerical simulations.
Tài liệu tham khảo
Abramowits, M. and I. A. Stegun, Handbook of Mathematical Functions, Dover, Mineola, N.Y., 1972.
Campillo, M. and A. Paul, Long range correlations in the seismic coda, Science, 299, 547–549, 2003.
Fleury, C., R. Snieder, and K. Larner, General representation theorem for perturbed media and application to Green’s function retrieval for scattering problems, Geophys. J. Int., 183, 1648–1662, doi:10.1111/j.1365-246X.2010.04825.x, 2010.
Furumura, T., K. Imai, and T. Maeda, A revised tsunami source model for the 1707 Hoei earthquake and simulation of tsunami inundation of Ryujin Lake, Kyushu, Japan, J. Geophys. Res., doi:10.1029/2010JB007918, 2011.
Margerin, L. and H. Sato, Reconstruction of multiply-scattered arrivals from the cross-correlation of waves excited by random noise sources in a heterogeneous dissipative medium, Wave Motion, doi:10.1016/j.wavemoti.2010.10.001, 2011.
Nakahara, H., A systematic study of theoretical relations between spatial correlation and Green’s function in one-, two- and three-dimensional random scalar wavefields, Geophys. J. Int., 167, 1097–1105, doi:10.1111/j.1365-246X.2006.03170.x, 2006.
Nishida, K., J. P. Montagner, and H. Kawakatsu, Global surface wave tomographyusing seismic hum, Science, 326(5949), 112, 2009.
Roux, P., K. G. Sabra, W. A. Kuperman, and A. Roux, Ambient noise cross correlation in free space: Theoretical approach, J. Acoust. Soc. Am., 117, 79–84, 2005.
Saito, T. and T. Furumura, Scattering of linear long-wave tsunamis due to randomly fluctuating sea-bottom topography: Coda excitation and scattering attenuation, Geophys. J. Int., 177, 958–965, doi:10.1111/j.1365-246X.2009.03988.x, 2009.
Saito, T., K. Satake, and T. Furumura, Tsunami waveform inversion including dispersive waves: The 2004 earthquake off Kii Peninsula, Japan, J. Geophys. Res., 115, B06303, doi:10.1029/2009JB006884, 2010.
Sanchez-Sesma, F. J., J. A. Perez-Ruiz, M. Campillo, and F. Luzon, Elastodynamic 2D Green function retrieval from cross-correlation: Canonical inclusion problem, Geophys. Res. Lett., 33, L13305, doi:10.1029/2006GL026454, 2006.
Satake, K., Inversion of tsunami waveforms for the estimation of heterogeneous fault motion of large submarine earthquakes: The 1968 Tokachioki and 1983 Japan Sea earthquakes, J. Geophys, Res., 94, 5627–5636, doi:10.1029/JB094iB05p05627, 1989.
Satake, K., S. Sakai, T. Kanazawa, Y. Fujii, T. Saito, and T. Ozaki, The February 2010 Chilean tsunami recorded on bottom pressure gauges, MIS050-P05, Japan Geoscience Union Meeting 2010, 2010.
Sato, H., Retrieval of Green’s function having coda from the cross-correlation function in a scattering medium illuminated by surrounding noise sources on the basis of the first order Born approximation, Geophys. J. Int., 179, 408–412, doi:10.1111/j.1365-246X.2009.04296.x, 2009.
Shapiro, N. M., M. Campillo, L. Stehly, and M. Ritzwoller, Highresolution surface wave tomography from ambient seismic noise, Science, 307, 1615–1618, 2005.
Snieder, R., A Guided Tour of Mathematical Methods for the Physical Sciences, Cambridge Univ. Press, Cambridge, U.K., 2001.
Snieder, R., K. van Wijk, M. Haney, and R. Calvert, Cancellation of spurious arrivals in Green’s function extraction and the generalized optical theorem, Phys. Rev. E, 78, 036606, 2008.
Wapenaar, K., E. Slob, and R. Snieder, On seismic interferometry, the generalized optical theorem, and the scattering matrix of a point scatterer, Geophysics, 75, SA27–SA35, doi:10.1190/1.3374359, 2010.
Yomogida, K. and R. A. Benites, Relation between direct wave Q and coda Q: A numerical approach, Geophys. J. Int., 123, 471–483, 1995.