Coda Waveform Correlations

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1 Chapter 5 Coda Waveform Correlations 5.1 Cross-Correlation of Seismic Coda Introduction In the previous section, the generation of the surface wave component of the Green s function by the correlation of ambient seismic noise at two stations was investigated. The coherent information generated from many station pairs was then used for imaging the crustal structure across the Australian continent. The ambient noise field arises mainly from propagating surface waves with a broad scale sample of the outer regions of the Earth. However, the ambient seismic noise wavefield is not the only type of energy propagating within the Earth that can provide information on seismic structure. Around 15 earthquakes with magnitude above 5 occur each year, mostly in the well defined earthquake belts such as those to the north of Australia or around the Pacific rim. The recorded ground motion from each earthquake carries with it information on the seismic properties of the medium through which the waves have passed. Indeed we exploit this property in the immediate coda of P waves when we construct radial receiver functions to enhance the converted energy and provide constraints on shear wave structure. Besides the main phase arrivals from an earthquake, there is a scattered wavefield generated by the inhomogeneities in the medium. Such waves are commonly studied using ideas from stochastic wave theory with various representations used to describe scattering processes. Diffusive theory was used to describe the properties of seismic coda by Aki & Chouet (1975); Margerin et al. (1998, 1999); Wegler & Luehr (21). Here, however, we are interested in using the seismic coda as a tool to understand the nature of the structures in the neighbourhood of a seismic station, rather than focusing on the way in which the scattered energy is created. Campillo & Paul (23) were able to extract coherent information on surface waves over fairly large distances in Mexico from seismic coda on 127

2 larger events. As in the use of the ambient seismic noise wavefield, it is possible to use correlation between different sensors to extract the Green s function between two points from multiply scattered seismic waves. Although the two applications are similar, the higher amplitudes in the seismic coda allow more facets of the Green s function to emerge Coda Waves from Distant Earthquakes at the Warramunga Array Immediately following each major seismic phase arriving from an earthquake there is a complex coda that reflects the nature of the structures in the vicinity of the receiver. With an array of seismometers at close spacing (figure 5.1a) this coda has strong similarities in appearance between nearby stations, but also differences that can be exploited to understand the immediate neighbourhood of the array (figure 5.1b). 128

3 a b Figure 5.1: Coda waves following the main P wave arrival at the Warramunga array. a) -4 sec behind P. b) sec behind P. The later coda becomes more chaotic as multiply scattered waves dominate. 129

4 The Warramunga seismic array was established in the Northern Territory of Australia in 1968 with a 2-element L shaped array with short-period vertical sensors. This site has particularly low ground noise for frequencies near 1 Hz and so was able to achieve detections of small events at very large distances. In 199 the array was upgraded to its current configuration of 23 broadband vertical sensors and a 3-component broadband station (at site WB2), for its role as a primary seismic station under the Comprehensive Nuclear-Test-Ban Treaty (CTBT). The data is digitized at each sensor at 4 sample/sec and then sent by digital radio telemetry to the central recording facility. The seismic data is then sent by satellite to the International Data Centre for the CTBT in Vienna and a local copy is retained on CD. The configuration of the current array is shown in figure 5.2 along with the possible paths between station pairs. A group of 2 teleseismic events in the Western Pacific with a range of source depths were extracted from CD for the period from April to May 24. These events occur in a limited range of epicentral distances so that the expected slowness of the coherent P wave arrivals will be similar for each event. Just the 24 vertical component records were used in the coda analysis. The distribution of the events is indicated in figure 5.2, and the source parameters are shown in table 5.1. The data was not preconditioned before calculating the cross-correlations between stations to avoid modifying the spectrum. 13

5 3 o N WB WB9 WB8 WB6 WB7 WB5 WB4 WC1 WB3 WC2 WR1 WB2 WR2 WR3 WR4 WR5 WR6 WR7 WR8WR9 WC4 WB1 WC3 WR o WRA 3 o S 12 o E 15 o E 18 o W Figure 5.2: The location of Warramunga array (WRA) in Australia, the shape of the array with given interstation paths, and the locations of the teleseismic earthquakes used in this study (red dots). The cross-correlation of the coda waves from the vertical component records was carried out in a similar way that was used for Green s function retrieval from ambient seismic noise. A sequence of coda time windows was considered for constructing the cross-correlations; windows started before the event and then a sequence with varying length followed the evolution of the coda in time. The correlograms for each coda segment were then stacked to enhance the signal to noise ratio. In all, 277 cross-correlograms were computed from the records of the stations of the Warramunga array for each of the selected time periods. The theory behind the cross-correlation of seismic coda waves is very similar to the ambient seismic noise case. It is assumed that the constructive interference of the propagation from the sources along the surface V to x A and x B is sufficient to allow the construction of the Green s function between x A and x B where sources are acting as result of propagating elastic waves 131

6 Date Latitude Longitude Depth Magnitude Distance (Year-Julian Day) ( ) ( ) (km) (m b ) Table 5.1: The list of 2 teleseismic earthquakes used in coda-correlations. The epicentral distances were calculated from WB. induced by a distant earthquake. As a result the cross-correlation of the recorded wavefield at two points x A and x B will be 2R [ Ḡ lk (x A,x B, ω) ] S(ω) = 2 ρc v l (x A, ω)v k (x B, ω), (5.1) where S(ω) = s (x, ω)s(x, ω) (5.2) and c is the appropriate wavespeed. With the sequence of different portions of the seismic records we want to examine the nature of the wavefield crossing the array. In this way we can see 132

7 the way in which the deterministic components of the wavefield associated with the P and S waves interact with the stochastic part of the wavefield arising from multiple scattering near the array. The first window is displayed for the 9 sec following the onset of the P wave for each event. The full set of cross-correlograms between the stations at WRA are shown in figure 5.3 as record sections in terms of the distance between pairs of stations. The interstation distances range from around 1 km to 25 km. In the time interval immediately following the P arrival the dominant coherent energy has an apparent velocity of 13.5 km/sec as would be expected for the teleseismic P, and this arrival is accentuated when examined in the more restricted frequency band of 1-5 Hz, when residual long-period energy is suppressed. Fortunately, in the interval where we would expect to employ a plane wave approximation for the analysis of, e.g., receiver functions, the concept of a single plane wave is well supported in the actual data. However, for later times in the coda the coherent arrivals with high apparent velocity disappear and now much slower waves become visible. The interval from 15-2 sec after the P arrival is displayed in figure 5.4 and now the stochastic part of the wavefield is evident. Surface waves with an apparent velocity of 3.5 km/sec emerge. The near surface wavespeeds for both P and S wavespeeds are high in the granites across the Warramunga array and we are clearly seeing the surface wave part of the interstation Green s function extracted from the coda signals. The variability in velocity undoubtedly reflects local variation in structure across the array, which is evident in the character of the granite exposures. In an even later interval 3-4 sec after the P arrival, the behaviour of the cross-correlograms is similar, but the amplitude of the surface wave arrivals is somewhat lower (figure 5.5). The deterministic components persist to some extent in the 1-5 Hz band in figure 5.4b. However, in the same frequency band in the later window in figure 5.5b, the apparent velocity is much reduced and corresponds to about 6.2 km/sec (for the clearer arrival at negative times). This value is just a little higher than expected for P waves traveling across the array. The slower arrival in this frequency band is a little faster than the surface waves in figure 5.5a and would correspond to S. Thus it would appear that the high scattered energy input from the energetic main P wave arrivals has been 133

8 sufficient that it has proved possible to extract the body wave components of the interstation Green s function. As a check on this result the usual procedure of constructing the crosscorrelograms and then filtering was reversed to construct figure 5.6. In this case the data for each station were filtered in the 1-5 Hz band and then cross-correlated. For shorter interstation distances the body wave arrivals are quite distinct but tend to get lost somewhat in the clutter at greater station separation. 134

9 Hz. b) Filtered with 1-5 Hz. Figure 5.3: The deterministic part of the cross-correlations extracted from the beginning of the events with 9 sec window. The coherent arrival is due to the moveout of the first arrivals with an apparent velocity of 13.5 km/sec. a) Filtered with 1 b 1 a Chapter 5. Coda Waveform Correlations

10 Figure 5.4: The stochastic part of the cross-correlations from interval of 15-2 sec after the P arrival. The coherent arrivals present in the first case disappeared and surface waves emerged. a) Filtered with.5-1 Hz. b) Filtered with 1-5 Hz. 1 b 1 a Chapter 5. Coda Waveform Correlations

11 Figure 5.5: The stochastic part of the cross-correlations from interval of 3-4 sec after the P arrival. The coherent arrivals present in the first case disappeared and surface waves emerged. a) Filtered with.5-1 Hz. b) Filtered with 1-5 Hz. 1 b 1 a Chapter 5. Coda Waveform Correlations

12 with 1-5 Hz. Figure 5.6: The stochastic part of the cross-correlations with the emerged body wave propagation in short distances. Filtered 1.24 Chapter 5. Coda Waveform Correlations

13 The very high apparent velocities in figures 5.5, 5.6 are entirely consistent with the results from recordings of small aftershocks of the 1988 Tennant Creek Earthquakes that occur about 55 km from the nearest array element. Figure 5.7 shows a display of the records across the array with weak P waves and a distinct moveout in the Rayleigh waves along the stations of the red arm with an apparent velocity of about 3.5 km/sec. B1 B9 B8 B7 B6 B5 B4 B3 B2 B1 C2 C1 C4 C3 R1 R2 R3 R4 R5 R6 R7 R8 R9 R1 Pg Sg Rg Time [s] Figure 5.7: Full Warramunga array recording of a Tennant Creek aftershock, at a depth of 2 km, about 6 km from the centre of the array. The event lies to the west of the array so the arrival times are nearly constant on sites B1-B1. The evolution of the phases can be seen on sites R1-R1 as the epicentral distance increases by 2 km. The velocity traces have been bandpass filtered from.5 to 6. Hz (Kennett, 22, p 24). With care it is therefore possible to use passive recordings of distant earth- 139

14 quakes to generate record sections for both the body wave and surface wave components of the wavefield across a dense network. The cross-correlograms allow the construction of refraction record sections that constrain the near surface wavespeeds quite well. The use of seismic coda from larger teleseismic events can thus provide a means of characterizing the seismic properties of a locality with purely passive recording, provided that broadband high-fidelity recordings of ground motion are available. The good results obtained for stations spacings of more than 5 km indicate that the individual stations in a network do not need to be as closely placed as in the Warramunga array for information to be extracted. The L shape of the Warramunga array arose from the convenience of early analogue processing, but only a span of different interstation distances is required. Indeed a more scattered array geometry is likely to be beneficial. 14

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