TY - JOUR
T1 - On the correlation of non-isotropically distributed ballistic scalar diffuse waves
AU - Weaver, Richard
AU - Froment, Berenice
AU - Campillo, Michel
N1 - Funding Information:
The authors thank the Ministry of Oil and Gas of the Sultanate of Oman, Petroleum Development of Oman, and Shell Research for permission to use the data. One of the authors (B.F.) acknowledges the support from Shell Research. R.L.W. thanks the Laboratoire de Géophysique Interne et Tectonophysique for support while he was in residence in Grenoble where much of this work was done.
PY - 2009
Y1 - 2009
N2 - Theorems indicating that a fully equipartitioned random wave field will have correlations equivalent to the Green's function that would be obtained in an active measurement are now legion. Studies with seismic waves, ocean acoustics, and laboratory ultrasound have confirmed them. So motivated, seismologists have evaluated apparent seismic travel times in correlations of ambient seismic noise and tomographically constructed impressive maps of seismic wave velocity. Inasmuch as the random seismic waves used in these evaluations are usually not fully equipartitioned, it seems right to ask why it works so well, or even if the results are trustworthy. The error, in apparent travel time, due to non-isotropic specific intensity is evaluated here in a limit of large receiver-receiver separation and for the case in which the source of the noise is in the far field of both receivers. It is shown that the effect is small, even for cases in which one might have considered the anisotropy to be significant, and even for station pairs separated by as little as one or two wavelengths. A formula is derived that permits estimations of error and corrections to apparent travel time. It is successfully compared to errors seen in synthetic waveforms.
AB - Theorems indicating that a fully equipartitioned random wave field will have correlations equivalent to the Green's function that would be obtained in an active measurement are now legion. Studies with seismic waves, ocean acoustics, and laboratory ultrasound have confirmed them. So motivated, seismologists have evaluated apparent seismic travel times in correlations of ambient seismic noise and tomographically constructed impressive maps of seismic wave velocity. Inasmuch as the random seismic waves used in these evaluations are usually not fully equipartitioned, it seems right to ask why it works so well, or even if the results are trustworthy. The error, in apparent travel time, due to non-isotropic specific intensity is evaluated here in a limit of large receiver-receiver separation and for the case in which the source of the noise is in the far field of both receivers. It is shown that the effect is small, even for cases in which one might have considered the anisotropy to be significant, and even for station pairs separated by as little as one or two wavelengths. A formula is derived that permits estimations of error and corrections to apparent travel time. It is successfully compared to errors seen in synthetic waveforms.
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U2 - 10.1121/1.3203359
DO - 10.1121/1.3203359
M3 - Article
C2 - 19813796
AN - SCOPUS:70350510524
SN - 0001-4966
VL - 126
SP - 1817
EP - 1826
JO - Journal of the Acoustical Society of America
JF - Journal of the Acoustical Society of America
IS - 4
ER -