JOURNAL OF GEOPHYSICAL RESEARCH: SOLID EARTH, VOL. 118, 2191–2205, doi:10.1002/jgrb.50186, 2013
Extracting surface wave attenuation from seismic noise using correlation of the coda of correlation Jian Zhang1 and Xiaoning Yang1 Received 19 July 2012; revised 5 March 2013; accepted 5 April 2013; published 15 May 2013.
[1] Extracting surface wave travel time information from the cross-correlation (CC) of
seismic ambient noise has been a great success and remains fast growing. However, it is still challenging to exploit the amplitude content of the noise CC. Although spatial average is able to constrain somewhat meaningful attenuation using noise CC amplitudes, clear bias is observed when spatially varying attenuation is estimated with the traditional noise CC calculation methods. Perhaps the key lies in the development of novel techniques that can mitigate the effect of the uneven distribution of natural noise sources. In this paper, we propose a new method to use the correlation of the coda of correlation of noise (C3) for amplitude measurement. We examine the ability of the method to retrieve surface wave attenuation using data from selected line array stations of the USArray. By comparing C3-derived attenuation coefficients with those estimated from earthquake data, we demonstrate that C3 effectively reduces bias and allows for more reliable attenuation estimates from noise. This is probably because of the fact that the coda of noise correlation contains more diffused noise energy, and thus, the C3 processing effectively makes the noise source distribution more homogeneous. When selecting auxiliary stations for C3 calculation, we find that stations closer to noise sources (near the coast) tend to yield better signal-to-noise ratios. We suggest to preprocess noise data using a transient removal and temporal flattening method, to mitigate the effect of temporal fluctuation of the noise source intensity, and to retain relative amplitudes. In this study, we focus our analysis on 18 s measurements. Citation: Zhang, J., and X. Yang (2013), Extracting surface wave attenuation from seismic noise using correlation of the coda of correlation, J. Geophys. Res. Solid Earth, 118, 2191–2205, doi:10.1002/jgrb.50186.
1.
Introduction
[2] Constructing empirical Green’s function (EGF) from the cross-correlation (CC) of seismic noise has proven a standard and successful tool for imaging Earth’s velocity structure [e.g., Shapiro et al., 2005; Sabra et al., 2005; Yao et al., 2006; Lin et al., 2007]. Although the EGF constructed from noise is usually not exact due to the uneven distribution of noise sources, bias in travel time estimates is found to be small [Yao et al., 2006; Yang et al., 2008; Yao and van der Hilst, 2009; Harmon et al., 2010]. The ability of accurately retrieving surface wave travel time from noise, in spite of the lack of full noise field diffusivity, is also demonstrated in theory [Snieder, 2004; Godin, 2009; Weaver et al., 2009; Froment et al., 2010]. [3] The EGF derived from seismic noise correlation also contains, in its amplitude, information about the Earth’s
1 EES-17: Geophysics, Los Alamos National Laboratory, Los Alamos, New Mexico, USA.
Corresponding author: J. Zhang, EES-17: Geophysics, Los Alamos National Laboratory, Los Alamos, NM 87545, USA. (
[email protected]) ©2013. American Geophysical Union. All Rights Reserved. 2169-9313/13/10.1002/jgrb.50186
attenuation. In laboratory experiments and numerical simulations, Weaver and Lobkis 2001, Larose et al. [2007], Cupillard and Capdeville [2010], and Weaver [2011a] were able to extract accurate medium attenuation from acoustic ambient noise. Early efforts using seismic noise correlation to study surface wave amplitudes were also encouraging. Prieto and Beroza [2008] showed a clear correlation between the relative amplitudes of seismic noise EGF at different stations and those obtained from earthquakes. Using a line array, Matzel [2008] obtained a noise CC amplitude decay that is related to surface wave geometric spreading and attenuation. In addition, Taylor et al. [2009] developed a standing-wave method that can be used to estimate site amplifications using seismic noise. Unlike travel time, however, bias in attenuation estimates from EGF amplitudes can be significant if noise sources are unevenly distributed [Harmon et al., 2010; Cupillard and Capdeville, 2010; Tsai, 2011], which is often the case in seismology. For example, dominant sources of microseism field across southern California are multiply located, and their locations and strengths change with season [Gerstoft and Tanimoto, 2007]. [4] Therefore, to reliably extract attenuation properties of the Earth structure from seismic noise requires techniques that can reduce the bias due to uneven noise source distributions. Prieto et al. [2009, 2011] proposed an approach to estimate surface wave attenuation using the spatial coherency of the
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seismic noise field. They used azimuthal averaging to suppress the effect of noise directionality. Lawrence and Prieto [2011] extended the method to image the lateral variation of surface wave attenuation for the western United States. Although there are theoretical arguments that the conjecture of the expression of Prieto et al. [2009] may not be strictly valid in the presence of unevenly distributed noise sources [Tsai, 2011] (Weaver, personal communication), Nakahara [2012] showed that this approach is at least approximately valid for weak attenuation. Spatial averaging was examined in the time domain as well by Lin et al. [2011], showing that azimuthally averaged EGF amplitudes over a large region yields average attenuation estimates that are consistent with estimates derived from earthquakes. [5] Recently, Weaver [2011a, 2011b] established theoretically and numerically that accurate medium attenuation could be retrieved from noise CC amplitudes if noise source intensity varies smoothly as a function of location, particularly near the extension of the line linking the two stations. The CC amplitude from such a noise field depends mainly on the medium attenuation, site amplification, and noise source intensity in the direction of the interstation line, but little on noise source intensities in other directions. The result shows promise that spatially varying surface wave attenuation, site amplification, and noise source intensity may be derived from noise CC amplitudes without averaging if novel techniques can be developed to sufficiently diffuse the noise source distribution. [6] In this study, we evaluate the method of calculating the correlation of the coda of correlation (C3) in reducing the bias in attenuation estimation from noise. Because the coda of the noise CC contains further scattered energy, the effective noise sources that generate coda are presumably more diffused. The C3 method was developed by Stehly et al. [2008] to address the problem of poorly constructed EGF in some directions due to the azimuthal variation of noise sources. It has been successfully used to retrieve robust travel time estimates in situations where noise source intensity varies strongly in space [Stehly et al., 2008; Garnier and Papanicolaou, 2009; de Ridder et al., 2009; Froment et al., 2011]. To the best of our knowledge, this study is the first attempt at exploiting the noise CC coda for accurate amplitude measurement. To preprocess the data, we use a temporal flattening method suggested by Weaver [2011a], instead of traditional methods such as one bit or running absolute mean (RAM) [Bensen et al., 2007], in order to mitigate the effect of temporal fluctuation of the noise source intensity and to retain relative amplitudes. We focus our analysis on 18 s measurements near the primary microseisms peak.
2.
Data
[7] We collected 2 years (2007 and 2008) worth of continuous, long-period (one sample per second), verticalcomponent seismograms from the Transportable Array (TA) of the USArray and Southern California Seismic Network (CI). We then form line arrays of different lengths, locations, and directions from among all the stations for our analysis. We require a minimum of five stations for an array. For each array, we find an earthquake that is either located near one of the end stations of the array or along the
extension of the array. The earthquake also has to be recorded by the array with sufficient signal-to-noise ratios (SNRs). The selected line arrays and earthquakes are listed in Table 1. The maximum difference in azimuth between the reference end station and all other stations in an array is less than 15 . The numbers of common days when all stations in a line array have data range from 125 to 365. Except for lines 3 and 11 (Table 1), where we use surface waves from a distant earthquake along the extension of the array, the maximum distance between the earthquakes and corresponding reference stations is 33 km. Before the correlation calculation, data are band pass filteredwith a frequency do main Gaussian filter of the form exp ao2 =o20 within a frequency band and zero outside the band [Herrmann, 1973], where a is filter constant that dictates the filter width and o0 is center circular frequency. We set the filter constant to 20. Earthquake signals are filtered twice using the same filter for noise CC comparison and four times for C3 comparison. This is because noise CC calculation effectively doubles the order of the filter, and the C3 calculation doubles it again. Tests confirm that results filtered this way have consistent frequency contents. [8] We calculate daily noise CC and C3 between the reference station (colocated with, or nearest to, the selected earthquake) and the rest of the stations in an array. Seats et al. [2012] recommended dividing the data into shorter and overlapping time windows before calculating noise CC. Our tests of using 30 min window indicate little improvement in terms of the comparison between the noise- and earthquake-based attenuation estimates. We thus choose not to apply a shorter window calculation because of concerns of computation memory cost when calculating C3. We measure envelope amplitudes of both noise EGF and filtered earthquake signals for comparison. Geometric spreading isp corrected ffiffiffiffiffiffiffiffiffiffiffiffiffi by multiplying the amplitude by a distance term sinðd Þ, where d is the interstation or epicentral distance in degrees. The decay of the corrected EGF amplitude A as a function of distance r can then be used to estimate the average attenuation coefficient g along the array, through the following relationship: A(r) = exp(gr). Table 2 lists the attenuation (and velocity) estimates along with associated 95% confidence intervals from earthquakes, C3 EGF, and noise CC-derived EGF for all line array examples we present below. [9] To measure surface wave velocity from noise-derived EGF, previous studies often construct a symmetric EGF by stacking negative and positive lag components (signals that travel in opposite directions) to improve SNR. For attenuation estimation, however, we should use only the outgoing signal that travels from the end reference station to other stations. The cross-correlation between signal x at the reference station and signal y at a second station is defined as follows [Bendat and Piersol, 2000]: Z
CCxy ðtÞ ¼
xðtÞyðt þ t Þdt
(1)
Equation (1) shows that EGF at a positive lag time (t > 0), where the signal recorded by the reference station at time t is correlated with the signal recorded by the second station at a later time t + t, represents the outgoing energy from the reference station. In fact, Weaver [2011a] showed
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Array
2008/07/29 Mw5.4 33.96N 117.77W Depth: 14 km
1 2
2008/03/25 Mw4.2 44.71N 110.07W Depth: 9 km 2007/06/12 Mw4.6 37.54N 118.86W Depth: 10 km
3
2007/03/09 Mw4.7 38.43N 119.38W Depth: 9 km 2007/07/27 Mw5.1 44.39N 129.78W Depth: 10 km 2008/02/21 Mw6.0 41.19N 114.86W Depth: 8 km
4 5 6 7 8 9 10
Figure
BFS-GSC-SHO-V11A-U11A-T11A-S13A-R13A-R14A-Q14A-Q15A-P15A-P16A-O16A Figures 1, 6, and 11 BFS-SLA-FUR-U10A-GRA-S10A-S11A-R10A-R11A-Q10A-Q11A-P11A-P12AFigures 9a and 9d O11A-O12A-N11A-N12A-M12A-M13A-L12A-L13A G15A-F13A-F12A-F11A-E11A-F10A-E10A-E09A-D09A-D08A-E08A-E07A-D07A-E06AFigure 7 D06A-D05A MLAC-R05C-P05C-O05C-M02C-L02A Figure 8 MLAC-P07A-O07A-N07B-N08A-M07A-M08A-L08A-K07A-K08A-J07A-H08A-G08A-F08A MLAC-Q08A-P09A-O09A-O10A-N10A-N11A-M11A-L12A-K12A-J13A-G15A MLAC-S11A-S12A-S13A-S14A-S15A MLAC-GRA-U10A-SHO-V11A-V12A-W12A-NEE2-W13A-X13A-Y14A MLAC-CWC-LRL-RRX-BBR-SWS R06C-P08A-O09A-O10A-N10A-N11A-M11A-M12A-L12A-L13A-K13A Figures 9b and 9e
11
K04A-L07A-M08A-M09A-N11A-O12A-O13A
Figures 9c and 9f
M12A against all other TA and CI stations operated during 2008
xnumerically that negative lag EGF amplitudes decay differently than positive lag EGF amplitudes if the noise field intensity varies azimuthally due to the variation of noise energy flux at different stations in a line array. As a result, we only measure amplitudes of positive lag EGF in our analysis.
3. Typical Bias Due to Uneven Noise Source Distribution [10] When comparing noise CC amplitude decay with that from earthquake data, we often observe a typical bias as an underestimate of the attenuation. Figure 1 presents such an example using a line array (line array 1 in Table 1). The noise is preprocessed following traditional procedures involving instrument response correction, filtering, RAM normalization, and spectral whitening [e.g., Bensen et al., 2007]. We use a filter with the center period of 18 s in the filtering. We calculate the noise CC using daylong signals and stack the outputs over the days for which all stations in the array have data. Since all noise CCs are calculated with the same data length, we do not divide the stacked signals by the data length. To illustrate the bias introduced by symmetric EGF in attenuation estimates, we also include symmetric EGF measurements in this example.
Figure 3
[11] For this line array, although clear EGF signal is constructed (Figure 1b), EGF amplitudes yield a much smaller attenuation coefficient (1.8E-4) than that from the earthquake data (7.9E-4), and the bias is even larger (4.7E-4 versus 7.9E-4) when the symmetric EGF component is used (Figure 1c). The underestimation of attenuation from noise EGF can be explained by the existence of a directionally unsmooth or discrete distribution of noise source intensity. An extreme scenario is a discrete and focused noise source located along the extension of the line array, i.e., the source region is much smaller than the distance between the source and the line array. In this case, the source behaves like a point source. The geometricp spreading term of ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi the EGF p amplitude for such a source is sin ð D þ d Þ , inffiffiffiffiffiffiffiffiffiffiffiffiffi stead of sinðd Þ , where D is the distance in degrees between the source and the reference station of the line array, and d is the interstation distance in degrees [Cupillard and Capdeville, If ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi we correct EGF amplitudes using pffiffiffiffiffiffiffiffiffiffiffiffiffi 2010]. p sinðd Þ instead of sinðD þ d Þ, the resulting amplitudes differ from the correct amplitudes by a factor pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi sinðd Þ= sinðD þ d Þ , which decreases with increasing d. The end result is that amplitudes corrected for geometric pffiffiffiffiffiffiffiffiffiffiffiffiffi spreading using sinðd Þ will decay slower than the amplitude decay due to attenuation, which is what we see in Figure 1c.
Table 2. Velocity and Attenuation Estimates with 95% Confidence Interval from Peak Envelope Amplitudes of Earthquakes and Noise EGFs Attenuation Coefficient (104 km1)
Velocity (km/s) Line
EQ
1 2 3 4 5 6 7 8 9 10 11 1 (8 s)
2.9 0.1 2.9 0.1 2.8 0.1 2.5 0.6 2.7 0.2 3.0 0.3 2.7 0.3 3.0 0.2 2.5 0.2 2.9 0.1 2.9 0.2 2.9 0.2
C 3.0 2.8 2.8 2.8 2.9 2.8 2.8 3.0 2.7 2.9 3.1 2.8
3
0.2 0.1 0.2 0.8 0.5 0.1 0.6 0.7 0.5 0.1 1.0 0.3
CCFlattening
CCRAM
EQ
C3
CCFlattening
CCRAM
3.0 0.2 2.8 0.1 N/A N/A 2.9 0.2 2.9 0.1 2.8 0.3 3.1 0.4 2.8 0.3 2.9 0.1 2.8 0.3 2.8 0.3
3.0 0.2 2.8 0.1 N/A N/A 2.9 0.2 2.9 0.1 2.8 0.3 3.1 0.3 2.9 0.2 2.9 0.1 2.8 0.3 2.8 0.3
8.4 3.4 5.9 3.8 9.1 7.0 17.5 5.5 4.9 4.8 4.8 5.0 1.1 7.5 5.1 9.9 7.1 29 5.7 5.7 8.2 12 11.1 11
8.1 6.1 6.2 7.1 10.5 8.7 10.9 22 4.5 9.0 2.9 5.8 0.8 11 4.1 16 5.1 10 3.2 10 8.8 14 11.9 12
4.1 6.5 2.5 6.6 N/A N/A 1.7 11 0.1 3.7 6.6 20 1.8 19 2.0 14 0.8 7.3 1.9 11 10.6 9.6
1.8 5.1 0.2 6.3 N/A N/A 1.7 10 2.4 3.0 0.8 18 0.3 15 4.4 8.5 2.4 7.2 2.9 5 5.7 9.6
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a)
b)
c)
Figure 1. An example of typical bias of attenuation estimates from 18 s noise. (a) Map of the western United States showing USArray stations (blue triangles), an earthquake (yellow star, EQ2008/07/29 Mw5.4 33.96N 117.77W), and a line array (red triangles). The end reference station BFS is in black. (b) Comparison of the earthquake signals (black) with the CC-derived EGFs (red). In order to better compare the amplitudes, the earthquake signals are time shifted (same for Figures 6, 7, 11, and B1). (c) Comparison of the apparent attenuation estimated from the earthquake signal amplitudes (black stars) with those from noise CC (with RAM preprocessing), measured from positive lag time (blue circles) and symmetric (magenta crosses) EGF components, respectively. Attenuation coefficients (listed in the inset) are derived by fitting the logarithms of geometric spreading corrected amplitudes with straight lines. Amplitudes of different data sets are separated by multiplying each of them with a different scaling factor. This is done to ease the comparison. Again, the same procedure is used in following figures whenever applicable.
[12] To illustrate the variation of noise source distribution, we perform a beamforming [Gerstoft and Tanimoto, 2007] (Appendix A) using seismic noise recorded at the CI component of USArray stations (Figure 2a). Figure 2b plots the beamforming outputs in terms of spectral power in dB. The major energy of fundamental mode Rayleigh wave (the high energy at ~0.3 s/km) as a function of azimuth serves as a proxy for the directional distribution of the noise source intensity. Clearly, the noise source intensity is anisotropic a)
and temporally varying. At all four sample periods, noise sources tend to spread more during winter, coming from both Pacific and North Atlantic, while in summer times, sources from South Pacific seem dominant. The figure shows that the noise sources may not be smooth and sometimes appear strongly localized (e.g., 16 s summer and 18 s winter). In cases where noise sources are localized, attenuation derived from noise EGF would likely be biased low, according to the point source scenario discussed above.
b)
0
normalized power
1
Figure 2. An illustration of noise source distribution for noise recorded in the western United States from beamforming. (a) Map of the western United States showing a subset of USArray stations (red triangles) used for beamforming. (b) Beamforming outputs as a function of slowness (radial coordinate) and azimuth at periods of 8, 10, 16, and 18 s for winter (December 2006 to February 2007) and summer (June–August 2007), respectively. Power of each output is normalized to the scale of 0–1. 2194
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4. Azimuthally and Spatially Averaged Attenuation Coefficient Estimates From Noise [13] Following Lin et al. [2011], we investigate whether an azimuthally and spatially averaged attenuation estimate determined from noise-derived EGF agrees with the estimate using an earthquake. For all USArray stations that recorded the 2008/02/21 earthquake (Table 1), we calculate noise CC between station M12A (approximately colocated with the earthquake) and all other stations (Figure 3a). We preprocess data using the RAM normalization [Bensen et al., 2007] as what Lin et al. [2011] did, and perform duration correction by normalizing noise CC amplitudes with the length of the data used in the stacking. We then use the criteria of SNR > 2 and a distance range of 200–1000 km to select amplitude measurements for analysis. Here SNR is defined as the peak envelope amplitude of the EGF divided by the standard deviation of 1000 s noise CC coda. We measure EGF envelope amplitudes from both positive lag and symmetric components. After geometric-spreading correction, we compare the average amplitude decay of noise EGF for all stations with that of the earthquake signal at multiple periods between 6 and 25 s. [14] Figure 3 shows the comparison result. Overall, the spatially averaged EGF amplitudes yield attenuation coefficient estimates that are similar to those from the earthquake across the whole microseism band. Most of the estimates from noise EGF are within 95% confidence intervals of corresponding earthquake estimates. In addition, EGF estimates for secondary microseism periods (6–10 s) are less consistent with the earthquake-based estimates than those for primary microseism periods (14–20 s), and average attenuation coefficients determined by using the positive lag EGF component agree slightly better with the earthquake-derived results. Figure 3c also shows that EGF amplitudes are more scattered than earthquake amplitudes. [15] Our observations confirm Lin et al.’s [2011] conclusion that ambient seismic noise clearly contains meaningful anelasticity information of the Earth, and spatially averaged estimate could serve as a constraint for higher-resolution imaging. However, to image spatially varying attenuations from noise, it is still necessary to explore feasible processing methods that can reduce bias due to an inhomogeneous noise source distribution.
5.
Transient Removal and Temporal Flattening
[16] Normalization such as one bit or RAM is often applied in traditional noise CC calculations [Bensen et al., 2007], which accelerates the EGF convergence efficiently for extracting travel time information. However this may not be appropriate for extracting attenuation as the relative amplitude information is lost during the nonlinear operation. Although one-bit preprocessing may still recover attenuation in the case of a uniform distribution of noise sources [Cupillard et al., 2011], simulations have shown that it fails for nonuniformly distributed noise sources [Cupillard and Capdeville, 2010; Weaver, 2011a], which is likely the case when dealing with real seismic data. In order to retain amplitude information, we employ a different preprocessing method in this analysis. We first remove transient signals from sources such as earthquakes and instrument glitches
after band-pass filtering the data. We then use a temporal flattening technique suggested by Weaver [2011a] to reduce the effect of temporal fluctuation of noise intensity and to retain relative amplitudes. We note, however, that neither of these preprocessing techniques is aimed at smoothing the noise source distribution in space. Figure 4 gives an example illustrating the effects of the methods on the seismograms. [17] For transient removal, we first calculate a daily median amplitude level (A1 day), i.e., the median of the envelope amplitudes of each daylong data trace, which represents the daily noise amplitude level, assuming that most of data are noise with scarce transients. We then step through consecutive 10 min long windows and calculate the mean of the envelope amplitude for each window (A10 min). Transients are identified as those 10 min window data with A10 min > 2A1 day. They are then replaced with zeros. We test using 1 month long data to calculate the average noise amplitude level, and the result is similar. Figure 4b shows that the method we use along with the parameters we choose adequately removes significant transient signals. We find that the amount of data removed constitutes less than 15% of the total data, which has little effects on the convergence of noise EGF. [18] The transient-removed noise amplitudes can still vary with time (Figure 4b), both seasonally (high in winter and low in summer across the western United States) and occasionally (e.g., due to strong storms). Strong noise off the strike direction of a station pair could cause spurious noise CC arrivals and/or decelerate the convergence of EGF. To reduce the temporal variation of noise field intensity, we then apply the temporal flattening technique to the transient-removed data, in which we normalize each daylong trace by a global noise amplitude level for that day. We calculate the global noise level as the quadratic mean (square root of the mean of squares) of noise standard deviations at all stations in an array (and coda stations defined in section 6) after transients are removed. The flattened and transientremoved noise data (Figure 4d) allow rapid convergence of EGF, while relative amplitude information between stations is retained. Slight improvement from temporal flattening can be seen in Figure 6c for the line array in Figure 6a (the same array shown in Figure 1a), where temporal flattening results in an average attenuation coefficient of 4.1E-4, which is closer to the earthquake-derived attenuation coefficient (8.4E-4) compared with either one-bit (2.2E-4) or RAM (1.8E-4) normalization results.
6.
Correlation of the Coda of Correlation (C3)
[19] Line array examples (e.g., Figures 1c and 6c) show clear discrepancy between noise CC-based attenuation estimate and that from earthquake data, despite improvements from the temporal flattening. Average over space and azimuth [Lin et al., 2011] may reduce bias, yet it does not allow for a spatially varying attenuation estimate. One possible approach of accounting for the effect of uneven noise source distribution is to first accurately characterize the distribution in both space and time [e.g., Stehly et al., 2006; Gerstoft and Tanimoto, 2007; Yang and Ritzwoller, 2008]. Another approach is to somehow smooth the noise source distribution. Since noise EGF represents the signal from a virtual source at one of the two stations involved, the coda of the EGF
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a)
b)
(positive-lag) (symmetric)
c)
Figure 3. Comparison of spatially averaged attenuation coefficients from noise EGF amplitudes with those from earthquake-generated amplitudes. (a) Map of the western United States showing the locations of an earthquake (yellow star), the reference station M12A (red triangle), and other stations (blue triangles) that recorded the earthquake and used in the analysis. (b) Attenuation coefficients at different periods estimated from amplitudes of noise EGF calculated for all stations shown in the map versus those estimated from the earthquake. Error bars indicate 95% confidence intervals. (c) At different periods, the log of positive lag EGF amplitudes as a function of distance (red dots) is compared with that of the earthquake data (black dots). Black straight lines are the best fits. Numbers are the estimated attenuation coefficients. should then be signals scattered by scatterers around the two stations. Using coda of noise EGF to calculate a second CC should then produce an EGF (C3 EGF) that is the result of a more homogeneous effective noise field from scatterers. In fact, Stehly et al. [2008] have demonstrated that calculating C3 using scattered coda energy in noise CC results in an EGF with improved time symmetry and less azimuthal
dependence on the noise source distribution. Since then, a few studies [Garnier and Papanicolaou, 2009; de Ridder et al., 2009; Froment et al., 2011] have further established that the C3 method can suppress effects due to nonisotropic noise source distribution and enhance the quality of travel time estimates. In this section, we demonstrate that C3 also yields more reliable attenuation estimates.
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coda, or stacking positive and negative lag coda without flipping to calculate C3. Our conclusion is that the method we adopted yields the most accurate attenuation estimation. We provide a comparison of these different C3 calculation methods in Appendix B. [21] To compute C3 for a line array, we select multiple coda stations around the array. For station pairs in the array, we calculate C3 using each of the coda stations for each day when all stations, including coda stations, have data. We then stack these C3 over coda stations, as well as over the common operating days, to obtain the final C3 EGF for each station pair. [22] We also test the effect of selected coda stations on the resulting SNR of the C3 EGF by choosing coda stations from different regions around the line array. We find that stations closer to the coast tend to allow C3 to converge to an EGF with higher SNR, except for northwest United States, where coda stations further inland can also allow C3 EGF with high SNR. Note that for C3 EGF, we calculate SNR as the peak envelope amplitude of the EGF divided by the standard deviation of 200 s C3 coda, instead of 1000 s noise CC coda as we use for the SNR of noise CC-derived EGF. Indeed, there should be stronger noise energy near noise sources (along the coast), and thus presumably more scattered energy as well. We also find that the time symmetry feature of C3 depends little on the locations of the coda stations. As a result
a)
e-5
b)
e-6
c)
d)
time (month)
R1
Figure 4. An example illustrating data preprocessing using transient removal and temporal flattening techniques. (a) One year (2007) worth of raw seismic records at station BFS, which is shown in Figure 1a. Spikes are highamplitude transient events (earthquakes, instrument glitches, etc.). (b) Noise data shown in Figure 4a after transient removal. (c) Global noise level averaged over all stations of the line array shown in Figure 1a. (d) Noise data shown in Figure 4b after temporal flattening using the global noise level shown in Figure 4c.
S R2
CC of S and R1
coda
[20] Figure 5 is an illustration showing how we calculate C3. In order to construct C3 EGF between a pair of stations R1 and R2, we first use preprocessed data to calculate daily CC between a third station S (termed “coda station”) and R1, CCS,R1, and between S and R2, CCS,R2. We then select the coda of EGF from CCS,R1 and CCS,R2 using a 1500 s time window Tcoda. The window starts at 500 s lag time, which is well after the surface wave arrival even for the longest interstation distance (
