[1] We demonstrate that the coda of station-to-station Green's functions extracted from the ambient seismic field in southern California reach stability in the microseism band (5–10 s) after correlating six months of noise data. The coda stability makes it possible to retrieve Green's functions between stations that operate asynchronously through scattered waves as recorded by a network of fiducial stations. The Green's functions extracted from asynchronous and synchronous data have comparable quality as long as stable virtual coda are used, and both show good convergence to the Green's functions extracted from 1 year of seismic noise with ∼50 fiducial stations. This approach suggests that Green's functions can be extracted across seismic stations regardless of whether or not they are occupied simultaneously, which raises the prospect of a new mode for seismic experiments that seek to constrain Earth structure.

[2] The past decade has seen tremendous progress in efforts to obtain Green's functions from the background wavefield. The method has seen application in a wide variety of settings including ultrasonics [Weaver and Lobkis, 2001], ocean acoustics [Roux and Kupperman, 2005], helioseismology [Duvall et al., 1993], electromagnetic imaging [Fan et al., 2010], and building state-of-health [Sabra et al., 2007], but the most scientifically fruitful has been seismology, where cross-correlation of the ambient seismic field recorded synchronously at multiple seismic stations converges, after time-averaging, to the station-to-station Green's function. This has freed seismologists from the need to rely on natural earthquake sources, and the result has been important new information on elastic [e.g.,Shapiro et al., 2005; Yao et al., 2006; Lin et al., 2008; Ma et al., 2008], anelastic [Prieto et al., 2009; Lawrence and Prieto, 2011], and time-dependent [Brenguier et al., 2008a, 2008b] structure of the Earth.

[3] Seismologists have also shown that the scattered waves of earthquake coda contain the requisite information for retrieving the Green's function [Campillo and Paul, 2003; Paul et al., 2005]. Moreover, correlation of the coda of correlation-based ambient-noise Green's functions can themselves be used to retrieve the Green's function [Stehly et al., 2008; Garnier and Papanicolaou, 2009; Froment et al., 2011]. This latter demonstration raises the prospect that Green's functions derived at separate times, or asynchronously, could provide the information needed to reconstruct the Green's function between them. In this paper we demonstrate the feasibility of this approach using data from the Southern California Seismic Network (Figure 1). Our results suggest a new observational approach for seismic observations, in which stations are migrated sequentially in the presence of a network of fiducial stations in order to reconstruct Green's functions between all stations regardless of whether they are occupied simultaneously.

2. Correlation of Asynchronous Ambient Noise Data

[4] We used one year of continuous ambient seismic noise data (vertical component) recorded in 2007 at 155 stations in southern California (Figure 1). We followed the typical noise processing procedure [Bensen et al., 2007]. The data were down-sampled to 10 samples per second and divided into 1-hour time windows. We removed the mean and trend in each time window, converted the signal to sign-bit, and applied spectral whitening. Each time window was correlated, and the correlation was normalized to unit peak amplitude and averaged over time. The causal and anti-causal parts of the correlation were then averaged to obtain the Green's function. Finally we applied a 5–10 s band-pass filter to emphasize the coherent energy in the microseism band. This procedure gave rise to a total of 11,935 ambient-noise Green's functions for all possible station pairs in the network.

[5] The ambient-noise Green's functions show remarkable stability for not only the direct Rayleigh waves, but also for the scattered waves of the coda (Figure 2a). The Green's functions derived from January–June and from July–December are nearly identical and quite stable. In the analysis that follows, we use the coda window from 20 s after the peak of the direct Rayleigh wave until 500 s. Beyond 500 s the coda of the Green's function becomes too unstable to be useful for this dataset. Arrivals in this window consist of scattered waves at one station due to a virtual source at the other station [Stehly et al., 2008]. Small temporal changes in the virtual coda have been used to monitor velocity changes in the crust [Brenguier et al., 2008a, 2008b], and in our case the stability of the coda indicates that it contains deterministic information about the Earth structure.

[6] We demonstrate the stability of the virtual coda by showing the convergence to the coda of the Green's functions obtained by correlating one year of noise data (Figure 1). For nearly all the station pairs the virtual coda in the Green's function from correlating 6 months of noise data reaches 90% waveform similarity with the coda of the 1-year ambient-noise Green's function (Figure 1, inset). As expected, due to the noise source being predominantly in the Pacific Ocean, station pairs aligned perpendicular to the coast converge more rapidly than the pairs aligned parallel to the coast.

[7] The stability of virtual coda makes it feasible to obtain Green's functions between stations recorded asynchronously in the presence of a permanent seismic network (Figure 2b). Stehly et al. [2008] showed that when two stations (R1 and R2) record synchronously the correlation of each station with a third station in the permanent network (R3) gives rise to Green's functions (R3 – R1 and R3 – R2) as if the third station (R3) acts as a source. The correlation of coda of the Green's functions R3 – R1 and R3 – R2 when summed over all permanent stations (R3) results in the Green's function R1 – R2. This virtual coda approach is very similar to the approach of using earthquake coda where coda correlations are averaged over the earthquake sources [Campillo and Paul, 2003; Paul et al., 2005].

[8] Suppose that the station R2 was recorded asynchronously with station R1 in the presence of the same permanent network. Green's functions R3 – R1 and R3 – R2 will be constructed from data recorded at different times; however, the virtual coda in the Green's function R3 – R2 in this asynchronous case should be the same as the coda in the synchronous case once stability of virtual coda is attained through sufficient time averaging. Assuming this condition holds, the Green's function R1 – R2 obtained by correlating the virtual coda will be equivalent for the synchronous and asynchronous cases. That is, the Green's function R1 – R2 can be constructed whether or not stations R1 and R2 operated at the same time.

[9] To test this hypothesis, we constructed two groups of ambient-noise Green's functions for all station pairs in the SCSN network (Figure 1): GF1 and GF2, where GF1 are the Green's functions determined by correlating the noise data recorded in January–June and GF2 are the Green's functions determined by correlating the data recorded in July–December, i.e., GF1 and GF2 used data recorded at different, non-overlapping times. This construction was motivated by the fact that virtual coda reach stability when correlating about 6 months of data in southern California (Figures 1 and 2a).

[10] If we correlate the coda of the Green's function R3 – R1 using GF1 with the coda of the Green's function R3 – R2 from GF2, the resultant Green's function for R1 – R2 is asynchronous. Similarly, asynchronous Green's functions result when we correlate the coda of GF2 with GF1. Correlation of coda of GF1 with GF1 and GF2 with GF2 gives rise to synchronous Green's functions. In the following we chose the station ADO as R1. R2 is any station other than ADO in the network. We selected 52 stations in the network (Figure 1) as permanent stations (R3).

[11] To correlate the coda we chose the coda window starting 20 s after the arrival time of the peak Rayleigh wave in the Green's functions R3 – R1 and R3 – R2. The coda window stops at 500 s, and we divided that interval into multiple overlapping 100-s windows with 90% overlap [Seats et al., 2012]. Each window was processed as described earlier. Figure 3shows the synchronous and asynchronous Green's functions constructed from the virtual coda compared with the Green's functions by correlating the entire year of data. We find excellent agreement between the synchronous and asynchronous Green's functions, even at large station-to-station distances (Figure S1 in theauxiliary material).

[12] The mean correlation coefficient between the coda Green's functions and the ambient-noise Green's functions for these station pairs (ADO – R2) is 0.77, 0.71, 0.73, and 0.77, respectively, for Green's functions 1–1, 1–2, 2–1, and 2–2. The mean correlation coefficient increases slightly to 0.84, 0.80, 0.79, and 0.84 for Green's functions 1–1, 1–2, 2–1, and 2–2 when we use all the other 153 complementary stations as the permanent stations. The asynchronous Green's functions have comparable quality to the Green's functions constructed synchronously. The small difference between the asynchronous and synchronous Green's functions is due to the differences in the virtual coda that result mainly from the different lengths of data recorded in the first and second half of the year at some stations; most stations did not have the full 6 months of data.

[13] We computed the mean correlation coefficient between Green's functions 1–2 (with the 52 fiducial stations) and Green's functions extracted from 1 year of noise data when each station acts as R1, similar to the way we treated ADO. As expected, stations in the interior of the network have a larger mean correlation coefficient than the stations near the edges (Figure 4), indicating on average a better waveform similarity of Green's functions 1–2 with the ambient-noise Green's functions in the interior. This suggests that Green's functions constructed asynchronously will have a better quality if stations are in the interior of the fiducial network, which is consistent with the requirement that the scattered waves be azimuthally distributed. The stations at the northwestern and southeastern edges of the network have the smallest correlation coefficient. The lower quality of ambient-noise Green's functions along paths parallel to the coast may also have contributed to this outcome.

3. Discussion

[14] This method raises the prospect of a new approach to structural seismology that links temporary networks deployed at different times by asynchronous Green's functions between them through a backbone, or fiducial, seismic network (Figure 5). In this scenario, all of the station-to-station Green's functions can be obtained whether or not they operate at the same time. That is, Green's functions between stations operating at different times, can be constructed. Our approach is reminiscent of US Array, where a reference backbone network is operating across the US while the Transportable and Flexible Arrays are deployed temporarily within it. Transportable and Flexible Array stations could be linked by a Reference Network using this approach. The number of possible Green's functions increases as the number of stations squared, suggesting that this approach could in some cases lead to orders of magnitude more information. This information was available all along in the scattered wavefield, of course, but its interpretation is rendered straightforward when represented as station-to-station Green's functions for a larger station set.

Acknowledgments

[15] This work was supported by NSF grant EAR-0943885. This research was also supported by the Southern California Earthquake Center. SCEC is funded by NSF Cooperative Agreement EAR-0529922 and USGS Cooperative Agreement 07HQAG0008. The SCEC contribution number for this paper is 1538. We thank two anonymous reviewers for the constructive comments and Daniel Roten for making two figures using the Generic Mapping Tools.

[16] The Editor thanks the two anonymous reviewers for their assistance in evaluating this paper.