HR: 1340h
AN: S53B-1268    [Abstracts]
TI: A New Derivation of Noise Correlation and Implications for Seismic Noise Tomography
AU: * Tsai, V C
EM: vtsai@fas.harvard.edu
AF: Dept. of Earth and Planetary Sciences, Harvard Univ., 20 Oxford St., Cambridge, MA 02138, United States
AU: Dalton, C A
EM: dalton@ldeo.columbia.edu
AF: Lamont-Doherty Earth Observatory, Columbia Univ., 61 Route 9W, Palisades, NY 10964, United States
AU: Dziewonski, A M
EM: dziewons@eps.harvard.edu
AF: Dept. of Earth and Planetary Sciences, Harvard Univ., 20 Oxford St., Cambridge, MA 02138, United States
AB: It has been shown that the Green's function between two receivers can be retrieved by cross-correlating time series of noise recorded at the receivers. One of the most useful and impressive applications of this noise- correlation property is the three-dimensional mapping of seismic velocities, known as seismic noise tomography. This noise-correlation property has been derived assuming that the energy in normal modes is uncorrelated and perfectly equipartitioned or that the distribution of noise sources is uniform in space. We present a simple alternative derivation that facilitates an understanding of the relationship between the noise- correlation property and seismic noise tomography efforts. This new derivation is not unlike some of the earlier derivations, but it is novel in describing the density distribution of noise sources as a function of travel-time delay and facilitates the interpretation of and calculation of the retrieved cross-correlation from arbitrary noise-source distributions. We show that the success of noise tomography follows from proper application of a two-dimensional surface- wave noise-correlation theory, rather than the assumption of noise sources distributed isotropically in three dimensions. We resolve discrepancies between various approaches in the published literature and demonstrate that certain steps, such as calculating the time derivative of the cross-correlation, are not necessary. We further demonstrate that with a non-uniform noise-source distribution or a non-uniform velocity medium, the cross- correlation includes energy originating from elastic structure away from the geometric ray connecting the two receivers. Using our alternative derivation, we are able to quantify the degree to which the sensitivity kernel is different than the geometric ray and find, for example, that the kernel width is period-dependent and that the kernel generally has maximum sensitivity not precisely on the geometric ray, even within a ray theoretical framework. In a system like the Earth, which has neither a uniform source distribution nor uniform velocities, models of seismic-wave speed produced using noise-correlation techniques may therefore, in some regions, be biased.
DE: 3270 Time series analysis (1872, 4277, 4475)
DE: 7255 Surface waves and free oscillations
DE: 7260 Theory
DE: 7270 Tomography (6982, 8180)
DE: 8180 Tomography (6982, 7270)
SC: Seismology [S]
MN: 2007 Fall Meeting