ISSN 10693513, Izvestiya, Physics of the Solid Earth, 2011, Vol. 47, No. 9, pp. 747–756. © Pleiades Publishing, Ltd., 2011. Original Russian Text © T.B. Yanovskaya, T.Yu. Koroleva, 2011, published in Fizika Zemli, 2011, No. 9, pp. 3–12.
Effect of Earthquakes on Ambient Noise CrossCorrelation Function T. B. Yanovskaya and T. Yu. Koroleva SanktPetersburg State University email:
[email protected] Received October 28, 2010
Abstract—Surface wave tomography method based on analysis of ambient noise is widely used during the last decade. It is assumed that correlated component of noise is composed of surface waves generated by sources distributed over the Earth’s surface more or less uniformly. In such a case the crosscorrelation function (CCF) at two stations may be considered as the Green’s function of surface wave. This function should be symmetric relatively to zero time. However analysis of CCF at the stations located at the EastEuropean Plat form shows that as a rule CCF is characterized with a strong asymmetry. Since “pure” noise cannot be extracted from seismic records due to superposition of earthquake signals, the method for calculation of CCF includes amplitude normalization for suppression of earthquakes that reduces signals from earthquakes to a noise level. The parts of records containing waves from earthquakes are neglected because of their short dura tion. Present study shows that this contribution turns out to be dominant at periods larger than 20–40 s. In other words, what is assumed as a “noise” in reality is a superposition of signals from earthquakes. This fact results in distortion of the Green’s function and of surface wave dispersion curve used in surface wave tomog raphy if in the time interval used for calculation of CCF many earthquakes occur within a small area apart of an extension of the interstation path (clustering). Numerical modeling shows how clusters of sources affect CCF and dispersion curve correspondingly. Means for reducing this effect are outlined. DOI: 10.1134/S1069351311090059 1
INTRODUCTION Surface wave tomography method based on analysis of ambient noise crosscorrelation functions at pairs of stations is widely used during the last decade. It is based on the fact that the crosscorrelation function (CCF) of random wave field recorded in two points determines the Green’s function between these points [Weaver and Lobkis, 2001; Larose et al., 2006; Gouedard et al., 2008]. On the assumption that the ambient noise con tains surface waves generated by sources randomly dis tributed over the surface CCF of noise enables to deter mine the Green’s function of surface wave from a source located in one station and recorded at the other one. It was shown in [Shapiro and Campillo, 2004; Sabra et al., 2005a,b; Shapiro et al., 2005] that group velocity dispersion curves determined from the Green’s functions obtained by such a way are in a good agree ment with the dispersion curves at the same paths obtained from earthquake records. This fact gave a strong stimulus for wide use of CCF of the ambient noise at pairs of stations for determination of dispersion curves at the interstation paths and for following use them in surface wave tomography on regional and glo bal scale [Brenguier et al., 2007; Moschetti et al., 2007; Stehly et al., 2009, etc.]. If the sources are distributed over the surface uni formly CCF should be symmetric relatively to zero time: for positive times it represents a signal from a
1 The article was translated by the authors.
source located at one station and recorded at the other one, and vice versa, for negative times locations of recording and source points switch places. In case of relatively small distances between stations and corre spondingly of short wavelengths—wavelength should not exceed 1/5–1/6 of distance between stations [Koroleva et al., 2009a; Bensen et al., 2007]— “sources” of surface wave in ambient noise are storm microseisms and atmospheric disturbances. In some papers [Lin et al., 2008; Bensen et al., 2007] CCF of noise in the range of relatively short periods (not exceeding 20–40 s as a rule) turn out to be almost sym metric, though in some studies [Lin et al., 2007; Yang et al., 2006; Stehly et al., 2006] CCF asymmetry is mentioned. Even season variations of such asymmetry were found [Stehly et al., 2006, Kraeva et al., 2009] that allowed to conclude on different intensity of noise sources at different sides from stations at winter and summer time, or even on changes in properties of medium [Meier et al., 2010]. It has been shown on some examples of noise records at Asian stations [Koroleva et al., 2009a,b] that also for large distances between the stations and corre spondingly for long periods (up to 100 s) CCFs reflect surface wave Green’s function, and they are valid for constructing group and phase velocity dispersion curves for the purpose to use them in surface wave tomography to estimate lateral variations of the upper mantle struc ture rather than of only the earth crust. On the basis of this inference the method was applied for tomography
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of the upper mantle below the EastEuropean Platform (EEP), where the necessary data could not be obtained from earthquake records due to absence of earthquakes at the EEP territory. At the same time an asymmetry of CCF spectra was discovered—it was found that at the interstation paths oriented approximately along latitude the noise coming from the eastern side is much more lowfrequency than that coming from the west. High frequency content of the noise from the west may be explained by predominance of storm microseisms prop agating from Atlantic, but why the noise from the east is lowfrequency and very intensive remained rather odd [Koroleva et al., 2010]. Moreover it was found that at some paths between the stations it was not succeeded to get rather “clean” Green’s function from CCF: in some cases it happened to be much noisy or even had a time shift. Such paths were excluded from the data set, and for tomography used are only the data over such paths, for which CCF was not noisy and had no time shift. Therefore from the data set of 20 stations (190 paths) it was possible to use dispersion curves only for 120 paths. Therefore it was interesting to clear up the causes of such anomalies of CCF, that leads in turn to a problem on a nature of noise sources and their distribution over the surface. As shown below, the main sources of noise at long periods are earthquakes. FEATURES OF CCF CAUSED BY A METHOD OF ITS CALCULATION Seismic record is a superposition of ambient noise and signals from earthquakes. It is impossible to remove earthquakes from the total record. But due to higher level of them relatively to the ambient noise they give predominant contribution to CCF. Therefore to reduce their influence the amplitudes of records are normal ized prior to calculation of CCF. Some methods for normalization are proposed in [Bensen et al., 2007] from which we prefer normalizing on running average. By such a way levels of selfnoise and signals from earth quakes are equalized. And because duration of signals from earthquakes is much less than that of a “quiet” background it is assumed that contribution of earth quake records to CCF is negligible. Accordingly to the methods for calculation accepted in all similar studies, individual CCFs are calculated for a time intervals of one day, then the oneday CCFs are summed over a year or even over a longer period. Such summation over time intervals is equivalent to calculation of CCF from a lot of spatially distributed sources. The first fact that leads to an idea that the contribu tion of earthquakes to CCF is rather significant is the abovementioned difference in spectral content of noise coming from the west and from the east—the noise from the east is much more intensive in the long period range (20–100 s). Relatively EEP seismicity at the east is much higher than that on the west. It is concentrated in Pacific belt
and China. But since records of surface waves from earthquakes are not eliminated completely—only their amplitudes are reduced—one may suppose that they would contribute something to CCF. If earthquake epi centers are distributed over the surface uniformly enough, then, accordingly to the theory, CCF is formed due to superposition of the wave fields only from sources located along lines extending the path between the stations in both directions. Contributions from the sources outside these lines are mutually cancelled. However, if somewhere sources are concentrated within a small area, they will contribute to CCF. If concentra tion of the sources occurs in an immediate vicinity of the line passing through the stations, the contribution to CCF rises at the side of the station outside which these sources are located, and the CCF amplitude becomes higher at the same side. Such an asymmetry of CCF does not result in distortion of dispersion properties of the Green’s functions when the “source” (one station) and the “receiver” (another one) change places. But if the cluster of epicenters is located outside this line, a contribution to CCF is remained at a time moment determined by travel time difference at the two stations from such sources that is evidently less than a travel time difference from sources located at the extension of this line. Therefore one may expect appearance of an addi tional maximum at CCF at earlier moments. It was found that just these anomalies of CCF become percep tible rather frequently. When such a maximum is not welldefined, one may neglect existence of the addi tional anticipatory maximum for extraction of the Green’s function from the CCF and for following con struction of the dispersion curve removing this part of CCF from the further analysis. However, in some cases intensity of the additional maximum is found to exceed the “friendly” part of CCF. Such an anomaly is illus trated in Figs. 1a, 1b, where CCF and results of its nar rowband filtering are shown for pair of stations AAK (ϕ = 42.64°N, λ = 74.49°E) and DPC (ϕ = 50.36°N, λ = 16.41°E). Positive temporary delays (righthand side of the graph) correspond to sources from the side of the station DPC, and correspondingly, negative tempo rary delays correspond to the sources from the side of AAK. Fig.1a shows the results of noise analysis for the year 2000, and Fig. 1b—for 2001. CCF for 2001 is rather symmetric, while from the data for 2000 an intensive additional maximum occurs approximately by 200–300 s earlier than the main one from the side of the station AAK, as well as some not so pronounced maxima. One can explain such difference in CCFs each cal culated from oneyear data only by difference in spatial distribution of earthquake epicenters in 2000 and 2001. Since seismic records are normalized by a running aver age, the magnitudes of the earthquakes are unimpor tant, important is only their total number. Therefore the data on earthquake epicenters with M > 4 in the north ern hemisphere were taken from the IRIS catalogue separately for 2000 and 2001. Maps of conventional epi
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Fig. 1. Crosscorrelation function of noise at the stations AAK and DPC and the results of its narrowband filtering: (a) for 2000, (b) for 2001. Frequency bands in Hz are drawn at the right size of each trace. Negative time values correspond to sources to the east from the station AAK, positive values—to the west from the station DPC. IZVESTIYA, PHYSICS OF THE SOLID EARTH
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center densities were constructed in the following way. In the cells of 3° × 3° size the earthquake epicenters were picked out. Though, as mentioned above, the earth quake magnitude is insignificant, but in case of large magnitudes the surface wave records are more long and clear, so that we may expect that contribution of such signals to CCF is higher than that from weaker earth quakes. Therefore we calculated a sum of magnitude ratios of each earthquake to a “mean” magnitude, which was assumed to be equal to 5, rather than simple number of the earthquakes fallen to a given cell. In gen eral, such sums differ slightly from the total number of epicenters. Each sum of such conditional number of earthquakes was divided by cosϕ (ϕ is latitude), i.e. by a value proportional to an area of the cell. Thus deter mined was the conditional epicenter density. Maps of conditional epicenter density for 2000 and 2001 are shown in Fig. 2. It is seen from this figure that in 2000 a lot of earthquakes happened in Japan (two strong earthquakes 1/07 and 30/07 with M > 6.5 fol lowed by a large number of aftershocks). As a result of this fact, contributions to CCF from these earthquakes turned out to be predominant. Estimate of surface wave travel time difference at AAK and DPC (see Fig. 2) from these earthquakes corresponds just to a moment when the first maximum at CCF appears at negative time delays (Fig. 1a). At the same time the symmetry of CCF for 2001 seems to be strange, because seismicity is mainly dis tributed easternly from the path AAK−DPC, i.e. along the Pacific belt. However, analysis of seismicity of the whole Earth rather then only of the northern hemi sphere shows that in 2001 a set of earthquakes occurred in Chili, whose epicenters are located just at a continu
ation of the path AAK−DPC to the west. It is seen from Fig. 3, where epicenter density, the path AAK−DPC and its extension to both directions are shown for the whole globe in Mercator projection: Chilean earth quakes contribute to CCF from the west and the earth quakes from Indonesia from the east. Another example illustrating effect of earthquakes on CCF is given in Fig. 4—CCF between the stations Kislovodsk (KIV) and Tartu (TRTE). Figure 4a shows results of narrowband filtering CCF calculated for the years 2000–2001. Figure 4b represents distribution of epicenter density. In Fig. 4a the following anomalies of CCF are strik ing: firstly, it is significant asymmetry—waves from KIV side are practically absent,—secondly, a strong maxi mum appears in the vicinity of zero. Maximum of CCF near zero may be explained by arrival of waves from Japan earthquakes in 2000—their epicenters are located in the vicinity of perpendicular to the center of the path KIV−TRTE, so that the waves arrive to both stations practically simultaneously. The asymmetry is explained by influence of Mexico earth quakes occurring in a vicinity of northern continuation of the path (from the side of TRTE), whereas from the side of KIV earthquakes are practically absent. But since sources in Mexico are located not exactly on the continuation of the path, one should expect that max ima of envelopes would appear at CCF at times earlier than those corresponding to travel times along the path KIV−TRTE. Indeed, this can be seen even visually by comparing positions of CCF maxima at positive and negative times for frequency bands from 0.013–0.022 to 0.018–0.032 Hz (Fig. 4a).
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One more marked feature of CCF for this path is presence of strongly pronounced maxima of CCF at high frequencies from the side of TRTE and total absence of highfrequency signals from the side of KIV. This fact is easily explained by excitation of the high frequency noise by storm microseisms whose sources are located in Atlantic, i.e. directly outside the station TRTE. Starting from the above examples, as well as from some other ones characterized by the analogous fea tures, a question arises: how to determine the Green’s function from CCF and correspondingly group velocity dispersion curves which are the initial data for surface wave tomography? For this purpose it is necessary to study an effect of nonuniformity of source distribution typical for earth quakes on a shape of CCF and correspondingly on group velocity values. This may be done by the use of numerical modeling. RESULTS OF NUMERICAL MODELING Method for numerical modeling of CCF is described in detail in [Koroleva et al., 2009a]. CCF spectrum is calculated as a surface integral of individual CCFs from sources distributed continuously over a sur face. It has been shown that for uniform distribution of sources with equal intensity CCF is definitely symmet ric; for different intensity of sources on the right and on IZVESTIYA, PHYSICS OF THE SOLID EARTH
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the left from the path between the stations and also in case of uniform distribution CCF is symmetric in shape, but different in intensity on the right and on the left. In present study distribution of sources was assumed to be similar to realistic, if the sources are earthquakes concentrated in some epicentral zones superposed to randomly and uniformly distributed sources generating a background noise. Accordingly CCF was calculated as a sum of individual CCFs from all sources. Size of source clusters modeling earth quakes was taken in compliance with realistic one: lin ear size of such areas was assumed to be 1/5 of distance between the stations and correspondingly of an order of maximum wave length. In such a case CCFs from all sources inside such an area should be summarized prac tically inphase and intensify each other correspond ingly. Size of the area covered by the sources was taken equal to 10000 × 10000 km2, distance between stations 1000 km, size of source clusters 200 × 200 km2. Compu tations were performed for five models differing by loca tion of the clusters—from position at the extension of the interstation path (model 1) to position on the per pendicular to the center of the path (model 5). All mod els are displayed at one Fig. 5, but each model contains only one cluster. In each model 9000 sources randomly distributed over the whole area were chosen, and within the cluster the number of sources was equal to 2200. All sources had the same intensity. The clusters were No. 9
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located at the same distance from the center of the path in order that contributions from sources within the clus ters would be comparable. Correlation functions for each of the five models are shown in Fig. 6. As seen from comparison of CCF for these five mod els the largest distortion of CCF resulting in errors in group velocity estimates exists in models 2 and 3, for which contribution from additional sources superim pose to contribution from random sources. In models 4 and 5 these contributions are separated in time, and for calculation of group velocity one may ignore them using only symmetric component.
In Fig. 7 shown are CCF for models 1–5 subjected to narrowband filtering. From maxima of their envelops the group velocities were estimated, as is usually done in processing of real records. As expected, right and left parts of CCF in the model 1 differ only in intensity, but remain identical in shape due to location of additional sources along the extension of the line passing through the receivers. Shift of the clusters outside this line leads to a shift of the maximum of envelope of filtered CCF at low frequencies to lesser times, but at high frequencies CCF becomes practically symmetric. This is due to the fact that at high frequencies CCFs from different
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sources within the cluster are summed up in different phases and cancel each other. But at low frequencies the whole cluster acts as a single point source, that results in appearance of a signal at CCF at the times earlier rela tively to the travel time of the wave between the receiv ers. If group velocity is estimated from the time corre sponding to maximum of the envelope of the filtered CCF on its more intensive side, then higher velocities would be obtained at low frequencies. In the models 4 and 5 the maximum of the envelope is separated from the maximum caused by random sources located at a continuation of the line passing through the receivers. If such a maximum is ignored, the group velocities are determined correctly enough from the later maximum. Figure 8 shows group velocities measured from the envelope maxima at the right and at the left as well as true (accepted in the models) group velocity dispersion curve. For all models the group velocities are in a rather good agreement with true ones at frequencies higher 0.05 Hz corresponding to the wave length 66 km, i.e. 3 times less than linear size of the cluster. This agrees also with the real data. It is seen from Fig. 1 that begin ning the frequency range 0.0375–0.0625 Hz (mean period 20 s) the signal at CCF disappears at negative times corresponding to wave arrivals from the side of AAK due to the sources in Japan. Area of concentration of sources is bounded in Fig. 9 by a rectangle, and its linear size is equal roughly to 150 km. Thus, in compli ance with numerical modeling the wave length smaller than that at which this area does not act as a concen trated source is equal to 50 km, that corresponds to period of ~17 s, and agrees with the results of numerical modeling. Consider now behavior of CCF and corresponding group velocity estimates in the model that is a superpo sition of all five models (as in Fig. 5). CCF and results of its narrowband filtering are represented in Fig. 10. Fig ure 11 shows group velocity estimates from these results. It is seen that they are in rather good agreement with the initial dispersion curve. DISCUSSION As real data and results of numerical modeling show, at low frequencies (periods > 20 s) seismic noise used in the ambient noise surface wave tomography is found to be caused mainly by earthquakes due to the method of its processing. This results in distortion of group veloci ties estimated from CCF and consequently in errors in estimates of the Earth’s structure by the method of sur face wave tomography. So a question arises: how to avoid this? Numerical modeling shows that one of the ways is to increase amount of the data for calculation of CCF. In other words, for constructing CCF it is expedient to use the data for a time interval longer than one year, as is usually done. In such a case distribution of epicenters over the surface should be more uniform. IZVESTIYA, PHYSICS OF THE SOLID EARTH
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Fig. 7. Results of narrowband filtering of CCF shown in Fig. 6. Central frequencies of the filters are indicated at the right, below numbers of the models.
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Fig. 8. Estimates of group velocity from CCF for five models in comparison with the dispersion curve accepted in the model. Stars indicate the values obtained from the righthand side of CCF, points—from the lefthand side.
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Fig. 9. Cluster of earthquakes in Japan in 2000. IZVESTIYA, PHYSICS OF THE SOLID EARTH
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Fig. 10. Crosscorrelation function and the results of its narrowband filtering calculated for superposition of all five models. Num bers at the right are central frequencies of bandpass filters.
Another way is to draw beforehand the maps of epi center density for each year and to select for each pair of stations that year, when the sources turn to be concen trated in a vicinity of the line passing through the sta tions while intensive clusters of sources shifted from this line are absent. The third way is suppression of signals from earth quakes. In the standard method a level of these signals is reduced to the noise level. But it is possible to realize stronger suppression—for example, if the running aver
age exceeds some level that indicates presence of a sig nal from earthquake, the signal in this interval should be normalized e.g. by square of the running average rather than by the running average, or even to put the signal to zero. The study was supported by RFBR grant no. 0805 00355. REFERENCES Bensen, G.D., Ritzwoller, M.H., Barmin, P., Levshin, A.L., Lin, F.C., Moschetti, M.P., Shapiro, N.M., and Yang, Y., Processing Seismic Ambient Noise Data to Obtain Reliable BroadBand Surface Wave Dispersion Measurements, Geo phys. J. Int., 2007, vol. 169, pp. 1239–1260.
Group velocity, km/s 4.0
Brenguier, F., Shapiro, N.M., Campillo, M., Nersessian, A., and Ferrazini, V., 3D Surface Wave Tomography of the Piton de la Fournaise Volcano Using Seismic Noise Correla tion, Geophys. Res. Lett., 2007, vol. 34, L02305, doi:10.1029/2006GL028586.
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Koroleva, T.Yu., Yanovskaya, T.B., and Patrusheva, S.S., Upper Mantle Structure of the EastEuropean Platform from the Ambient Noise Data, Vestnik of SPbGU, Ser. 4, 2009b, no. 2, pp. 62–71. Koroleva, T.Yu., Yanovskaya, T.B., and Patrusheva, S.S., Velocity Structure of the Upper Mantle of the East European Platform According to Seismic Noise Data, Izv. Phys. Solid Earth, 2010, vol. 46, no. 10, pp. 839–848. No. 9
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