Geoscience Reference
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waves. A dispersion curve is determined, and from that a soil profile is derived. Another
technique of analysis that relies in the surface waves composition of microtremors is the
refraction microtremor (ReMi) introduced by Louie (2001). The advantage in this case
is the use of an exploration seismograph, which is cheaper than 12 or 24 autonomous
seismographs. The array in this case is linear and the result is again a phase velocity
dispersion curve.
An additional method can be mentioned, based on the correlation of ambient noise
records. The history of the use of noise correlation followed different paths according
to the considered domain, either frequency or time. It is only recently that the publica-
tionsarebringingtogetherthetwostrands(Ch
´
avez-Garc
´
ıaandLuzon,2005).Theuseof
cross-correlationofnoiserecordstodeterminethesubsoilstructurewasproposedexactly
50 years ago by Aki (1957). He named it the SPAC (Spatial AutoCorrelation) method. If
microtremorscanbeassumedtoconsistofplanedispersivewavespropagatingwithequal
power in all directions, Aki (1957) showed that the frequency domain cross-correlation
between stations at a given distance, averaged azimuthally, took the form of a zero-order
Bessel function, where the only unknown is the phase velocity of the waves. The details
of the method have been presented several times. The method has been applied to the
analysis of volcanic tremors (Ferrazzini et al., 1991; Chouet et al., 1998). Its applica-
tion to site effects is straightforward and many papers that use it have been published
(e.g., Apostolidis et al., 2005). Recently it has been shown (Ohori et al., 2002; Okada,
2003; Ch´avez-Garc´ıa et al., 2005) that it is possible to use of the SPAC method without
the limitations imposed by the circular array. If the waves that form the microtremors
propagate homogeneously in all directions, a single station pair samples all directions of
propagation provided that temporal averaging issubstitutedfor the azimuthal averaging.
If correlations in the frequency domain are useful, then because of Fourier transform,
they should also be useful in the time domain. However, the development of correlations
intimedomaintoexplorethesubsoilhasaverydifferenthistory.Thefirstreferencesare
related to exploration seismology (e.g., Claerbout, 1968). It was rediscovered by helio-
seismologists (Duvall et al., 1993), before making its appearance in acoustics and seis-
mology. In addition, time domain correlation of ambient noise has been the object of
many theoretical studies that have been able to show its relation with the character of
ambient noise and statistical properties of diffusive media. Weaver and Lobkis (2005)
retrace briefly this history. This is a field where many publications are currently being
published because development is possible in two domains, theoretical studies and prac-
tical applications.
It has been shown that the time derivative of the cross-correlation of seismic noise
betweentwostationsisproportionaltotheGreen'sfunctionbetweenthem,undercertain
conditions.AreviewhasbeenpresentedinCampillo(2006).Resultshavebeenpublished
from very small inter-station distances (5m in Ch´avez-Garc´ıa et al., 2006) to very large
distances (thousands of km in Shapiro et al., 2005). Figure 3.6 shows, for example, a
seismic section obtained from cross-correlations of ambient noise records computed
for the vertical component recorded at different station pairs of a small linear array at
