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Bulletin of the Seismological Society of America, Vol. 104, No. 4, pp. 1976–1988, August 2014, doi: 10.1785/0120130265

Crustal Shear-Wave Velocity Models Retrieved from Rayleigh-Wave Dispersion Data in Northern Canada by Dariush Motazedian and Shutian Ma

Abstract

Baffin Island is one of the several seismically active regions in the far north of Canada. In 1933, a strong earthquake with Mw 7.3 occurred in the region. On 7 July 2009, a relatively strong earthquake with M w 6.0 occurred in the same area. This earthquake was very well recorded by many modern seismic stations. We systematically organized the Rayleigh-wave displacement records, measured Rayleighwave dispersion data at 28 stations surrounding the epicenter, and retrieved the S-wave velocity models. We used a previous model for the Western Quebec seismic zone as the initial model in our analyses and found that the velocities of all models at the shallow depths (< 15 km) were obviously slower than those of the initial model. In the middle crust, the velocities in most models were close to those of the initial model. In the directions of azimuths 171° ∼ 218° and 241°, the velocities in the middle crust were faster than those of the initial model. In the directions of 263° ∼ 279°, the velocities in the middle crust were slower than those of the initial model. The slowest S-wave velocities in the top layers occurred in the directions of azimuths 90° and 218°. These findings indicate differences in the existing crustal structures.

Introduction There are several seismically active regions in the far north of Canada. On 20 November 1933, a strong earthquake with Mw 7.3 occurred in the Baffin Island region (Fig. 1). This earthquake is the largest recorded instrumentally in North America and the Arctic region (Bent, 2002). Since the 1933 earthquake, several earthquakes with magnitudes 5 or 6 have occurred in the region. Although the epicenter region is very sparsely populated, attention should be paid to the significance of the seismicity of the region. On 7 July 2009, a relatively strong earthquake with Mw 6.0 (Incorporated Research Institutions for Seismology Consortium [IRIS]) occurred in the same seismic region. Figure 1 shows the distribution of stations that had clear Rayleigh-wave records. We systematically organized the Rayleigh-wave displacement records, which were retrieved from the Geological Survey of Canada (GSC) and IRIS. From these Rayleigh-wave records, dispersion data can be obtained and used to retrieve fundamental information on the crustal structure of the region, because these Rayleigh waves traveled mainly in the crust. Several crustal models have been set up using different methodologies in northeast North America (e.g., Mereu et al., 1986; Saikia et al., 1990; Martignole and Calvert, 1996; Darbyshire et al., 2007; Bensen et al., 2009; Motazedian et al., 2013). We analyzed the Rayleigh waves and found the dominant periods were between about 8.9 and 24 s. Figure 2 shows the 28 Rayleigh-wave seismograms.

Because the surface-wave amplitude decreases exponentially with depth, according to the two-thirds rule of the wavelength and assuming a surface-wave velocity of 3:1 km=s and a period of 24 s, the wavelength would be 74 km and the penetration depth is about 50 km. The penetration depth becomes 30 km with a percentage of about 40% of the wavelength (e.g., Lowrie, 2007). Considering the longest period (29 s) analyzed, we can set an a priori penetration depth of 40 km. This depth can be confirmed by plotting the rows of the resolution matrix (Badal et al., 1996). This implies that the Rayleigh-wave dispersion data from the 7 July 2009 mainshock can provide valuable information on the crustal structures surrounding the epicenter. Taking advantage of clear Rayleigh-wave records generated by the 7 July 2009 mainshock, we estimated S-wave velocity models using the crustal Rayleigh-wave dispersion data and focused our efforts on S-wave velocity models in the crust. In the following sections, we follow a specific procedure to obtain an S-wave velocity model from one group of data (G8). We divided the stations shown in Figure 1 into 13 groups (G1–G13 in Table 1). The steps we used to divide these groups were as follows:

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1. We preliminarily performed inversions for each of the 28 carefully selected records and obtained 28 S-wave velocity models. We plotted these velocity models and arranged the plots by station azimuth.

Crustal Shear-Wave Velocity Models Retrieved from Rayleigh-Wave Dispersion Data in Northern Canada

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Table 1 Parameters for Dispersion Curve Measurement Group

G1 G2 G3

G4

Figure 1. Distribution of the selected seismic stations that recorded the 7 July 2009 M w 6.0 earthquake. These stations are divided into 13 groups. The groups are arranged approximately by station azimuth. Some groups only have one station, and others have two or more stations. The stations in the same group are connected with dashed lines. The larger solid circle shows the approximate location of the 1933 Mw 7.3 earthquake. The other two solid circles show the epicenters of the July 2009 earthquake provided by the Geological Survey of Canada (GSC) and Incorporated Research Institutions for Seismology Consortium (IRIS). The diamonds with letters show the locations of major cities: Wh, Whitehorse; V, Vancouver; C, Calgary; Ri, Regina; W, Winnipeg; Y, Yellowknife; R, Resolute; P, Pond Inlet; T, Toronto; O, Ottawa; M, Montreal; Q, Quebec City. The color version of this figure is available only in the electronic edition.

G5 G6

G7 G8 G9 G10

G11 G12 G13

Average

Station Name

Distance (km)

ALE DAG SUMG LMN SCHQ ICQ KGNO VLDQ KAPO ULM MDND FCC JOSN ARVN WALA EDM HYO GDLN COKN YKW1 CTLN GALN WRAK SKAG WHY TABL INK EGAK

836 1421 1091 3301 2294 2881 3462 3026 2911 2977 3299 2031 1523 1783 3466 3017 2838 1945 1892 2118 1977 2042 3200 2987 2859 3058 2135 2654 2465

Azimuth (°)

P1 (s)

P2 (s)

11 58 89 168 170 172 185 187 194 214 218 217 218 219 236 239 238 239 245 250 256 257 263 269 270 275 281 281

8.5 7.0 7.0 11.0 11.0 13.0 11.0 12.0 12.0 7.5 7.0 7.5 6.5 7.0 8.5 8.5 8.5 7.5 8.5 10.0 8.5 8.5 9.0 8.0 8.5 11.0 9.0 8.0 8.9

29 19 25 25 25 25 26 28 28 26 23 26 23 26 22 23 23 24 23 22 21 22 25 26 23 24 25 25 24.4

The columns present the group name, station name, station distance (Dist), station azimuth (Az), and the shortest (P1) and longest (P2) periods used in the measurement. In G1, the crustal S-velocity model retrieved using the dispersion data measured at station ALE and the model at station DAG were similar; therefore, the two stations were grouped together. The other groups had the same criteria.

3. We copied the measured dispersion data files in a group into one file; and using this file for the inversion, we then obtained one velocity model for the group. In this way, we obtained 13 crustal models. We also merged the 13 models into one for practical applications, such as locating seismic events. We estimated the impact on the retrieved S-wave velocity models by the error in the source parameters and the change of the used initial model.

Figure 2.

Vertical components of the Rayleigh-wave displacement records at 28 seismic stations. These records are arranged by group and station azimuth. The top two records belong to group G1, etc. The symbol at the left side of each trace is the station name.

2. We separated the 28 models into 13 groups, based on the similarity in models obtained at several adjacent stations at similar azimuthal directions. The models from individual records in each group are similar.

Rayleigh-Wave Group Velocity Measurements Seismograms are usually dominated by trains of surface waves. These surface waves have different frequency contents, and surface waves with different frequencies have different travel speeds (dispersion phenomenon). As these surface waves’ amplitudes decrease exponentially with depth when these waves propagate through the earth, they sample different depths, that is, the surface-wave seismograms recorded at stations on the Earth’s surface carry information

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D. Motazedian and S. Ma

of the Earth’s structures. Therefore, S-wave structures can be retrieved using surface-wave dispersion information. The digital waveform records were velocity type with instrument responses. First, we removed the instrument responses with SAC2000 software (Goldstein et al., 2003) and, at the same time, converted the velocity records into displacement records. After spectral analysis to waveform records, we found the stronger amplitudes were within periods of about 2–30 s; therefore, we used a band-pass filter (1–40 s) with the records in our inversion. After we obtained the displacement records, we selected the records that contained clear Rayleigh waves in the period range of interest. Once the records were selected, we measured the group velocities using the multiple filter technique (MFT, Dziewonski et al., 1969) in a computer program package developed by Herrmann and Ammon (2002), hereafter referred to as the HA package. The MFT method is used to retrieve group velocity dispersion curves from a preprocessed waveform record (instrument corrected). In this technique, the group time for the frequency ωn is the time when the envelope of the filtered seismic signal given by equation (1) reaches the maximum. Z∝ ω−ωn 2 jFωje−α ωn coskωr − ωtdω; hn ωn ; t; r −∝

1

in which r is the epicentral distance, Fω is the Fourier ω−ωn 2 transform of the record being analyzed, and e−α ωn is the Gaussian filter centered at frequency ωn. The envelope of the filtered signal can be computed by its instantaneous amplitude through equation (2) (Båth, 1974): q gn t h2n ωn ; t h 2n ωn ; t; 2 n ; t is the Hilbert transform of hn ωn ; t (Dziein which hω wonski et al., 1969). The group velocity was obtained by dividing the epicentral distance by the group time. Herrmann and Ammon (2002) introduced the formulas they used in their programs’ manual.

Modeling Rayleigh-Wave Dispersion for S-Wave Velocity Structures Once Rayleigh-wave dispersion data are measured at a specific seismic station, these data can be used to model the S-wave velocities along the source–receiver path. We first set up an initial crustal model, and we then revised the model based on the fit between the observed Rayleigh-wave dispersion and the predicted Rayleigh-wave dispersion generated using the crustal model. The best-fitting model is the solution. Outline of the Theoretical Background for S-Wave Velocity Inversion We assumed that δUωk was the group velocity difference between the observed and synthetic waveforms at fre-

quency ωk, the crustal model had N horizontal layers on the top of a half-space, and the S-wave velocity is βn in the nth layer (n is the index for the layer). The difference at frequency ωk k 1; …; M can then be approximated using the truncated Taylor series expansion: δUωk

∂Uωk ∂Uωk ∂Uωk δβ1 δβ2 … δβN : ∂β1 ∂β2 ∂βN

3

k The partial derivatives ∂Uω ∂βn n 1; 2; …; N were calculated using the formula proposed by Rodi et al. (1975):

∂Uωk Uωk Uωk ∂Cωk 2− ∂βn Cωk Cωk ∂βn 2 U ωk ∂ ∂Cω ωk 2 ; C ωk ∂ω ∂βn

4

in which Cωk is the phase velocity. Cωk , Uωk , and ∂Cωk ∂βn were obtained using standard Thomson–Haskell ma∂ ∂Cω trix calculations, and ∂ω ∂βn were obtained by numerically

k differentiating ∂Cω ∂βn (Rodi et al., 1975). If we let m δβ1 ; δβ2 ; …; δβN , d δUω1 ; k (k 1; 2; …; M; δUω2 ; …; δUωM , and Gk;n ∂Uω ∂βn n 1; 2; …; N), we obtained the linear algebraic equation system:

d Gm:

5

After solving this equation, we obtained a set of corrections to the S-wave velocities in the N layers δβ1 ; δβ2 ; …; δβN . We could then form a new model by assigning the S-wave velocity in the nth layer, βn new βn δβn . If this new model could not be used to generate a satisfied synthetic dispersion curve, then the above steps were repeated. The methods for solving equation (5) have been extensively studied and used (e.g., Kafka and Reiter, 1987; Badal et al., 1990, 1992). We used the surf96 program in the HA package to obtain our solutions. Selection of the Damping Factor Value The inversion method used in the surf96 program was the weighted damped least-squares method. In this method, the damping factor (λ) plays a key role in determining the solutions. The default λ value was 0.5 in the script we used in the HA package. We conducted the following tests to determine the λ value for our inversion. We still used two seismograms in G8 (Fig. 2) recorded at stations EDM and HYO. We set the λ value to 0.1 and performed the inversion, resulting in the predicted dispersion curve and the resolution matrix that corresponded to the inverted crustal model in the final iteration. Theoretically, the resolution matrix, whose rows are called kernels, must have a diagonal structure. The length of any kernel of this matrix fits the number of elastic layers


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Figure 3. Impact of the damping factor value on the fit between the observed and predicted dispersions. For each set of curves, the dots show the observed Rayleigh-wave dispersion data measured at stations EDM and HYO; and the solid curve shows the predicted Rayleigh-wave dispersion, generated in the inversion using the λ value indicated at the right side of the set. To plot the seven-curve sets together for comparison, the values of the group velocities were shifted. The velocities in the bottom set were shifted downward by 0:2 km=s; the set with λ 0:05 was shifted downward by 0:1 km=s; the set with λ 0:1 was not shifted. The top set was shifted upward by 0:4 km=s. The number at the left side of each set is the root mean square (rms). The color version of this figure is available only in the electronic edition. in the inverted crustal model. The value of an element in a kernel provides the resolution degree for the model elastic layer at the corresponding depth. The calculation of the resolution matrix can be easily found in the literature, for example, in the manual of the HA package. We plotted the predicted dispersion curve and the measured dispersion data at stations EDM and HYO for comparison. The set with λ 0:1 in Figure 3 shows the comparison. We also plotted the kernels of the resolution matrix in Figure 4 (upper plot) with a damping value of 0.1, thus obtaining the corresponding resolution amplitudes. The larger the values, the larger are the resolutions. We also performed the above procedure with other λ values, the results of which have also been plotted in Figures 3 and 4.

Figure 4.

Impact of the damping factor value on the resolution. In each panel, a curve shows one kernel (row) of the resolution matrix, corresponding to the inverted crustal model in the final iteration using the λ value indicated at the bottom-right corner of the panel. The measured dispersion data at stations EDM and HYO were used in the inversion. The element value in the resolution matrix at a crustal layer’s depth shows the resolution amplitude. The larger values indicate larger resolutions. The panel with λ 0:1 shows that resolutions at depths of about 35 km or deeper are still relatively larger than those with λ ≥ 0:5. The color version of this figure is available only in the electronic edition.

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Figure 5. Comparison between the observed and predicted dispersion curves. The integer at the right side of each set of curves shows the iteration number for the running of the inversion program. The decimal number at the left side of each set shows the average rms misfit between the observed and the predicted dispersions at stations EDM and HYO. To plot these four sets of curves together, the upper three sets were shifted upward by 0.1, 0.2, and 0:3 km=s, respectively. The damping factor in this test was 0.5. The color version of this figure is available only in the electronic edition. From a visual comparison, we determined that the consistency between the measured dispersion (dots) and the predicted dispersion (solid curve) in Figure 3 was good using λ 0:5. The consistency decreased when the λ values became larger. The resolution amplitudes in the panel indicated with λ 0:5 in Figure 4 are relatively larger at a depth of about 35 km. The resolution amplitudes became smaller when the factor became larger. The above comparisons show that the default damping factor (0.5) in the script we used was appropriate for our inversion. The consistency was better with λ 0:1 than when λ 0:5, however. Therefore, we selected λ 0:1 for the inversions in the 13 groups. A procedure was developed to search for an optimal factor (e.g., Chen et al., 2010; Badal et al., 2013). They showed that the best-damping factor results from a trade-off between resolution and covariance.

Convergence of the Iterative Inversion Process The inversion process we used is iterative, with the bestfitting inversion model as the one that gave the least variance between the observed and calculated group velocities. Thus, variance reduction greatly supported the convergence of the iterative inversion process and the reliability of the results. We performed the following test to confirm the convergence of the inversion program we used. We used a damping factor value of 0.5 and the dispersion data from stations EDM and HYO and ran the inversion program four times with iteration numbers of 1, 10, 15,


Figure 6.

The shortest and longest periods used to measure the dispersion data for each record. The two vertical lines show the averages of the shortest and longest periods.

and 29. Figure 5 shows the comparisons between the observed dispersion data and the predicted dispersion curves for the four inversions. It can be seen that, after 10 iterations, the average root mean square (rms) misfit between the observed and predicted dispersions was small. After 29 iterations, the fit between the two sets of the dispersions was quite good. This implies that the S-wave velocity model, which we used to generate the predicted dispersion curve, is close to the crustal velocity structures along the path between the epicenter and the two seismic stations. For further discussion on the convergence and variance reduction, refer to Badal et al. (2013). Operational Procedure to Retrieve S-Wave Velocity Models We selected 28 waveform records from those retrieved from the GSC and IRIS databases. Figure 2 shows the 28 selected seismograms, and the 28 stations (Fig. 1) were separated into 13 groups. Using the do_mft program of the HA package, we measured dispersion curves from the 28 selected records around the epicenter of the 7 July 2009 earthquake. Table 1 lists the parameters used during the measuring procedure. For each record, the source parameters, station distance, station azimuth, and the shortest and longest periods were used to measure the dispersion data. Figure 6 shows the distribution of the shortest and longest periods, as well as the averages of the periods. An example of the measured group velocities from the waveform record is shown in Figure 7 (at station EDM). The curve formed by the small squares is the dispersion curve. Using the group velocity values and the surf96 inversion program, we obtained an S-wave velocity model for the path


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of these waves were about 35 km, these waves mainly traveled through the crust. This implies that the retrieved crustal model may be significant for the path between group G8 and the epicenter at depths shallower than 35 km. Below 35 km, the retrieved S-wave velocity model may be not reliable, as the resolution became smaller below that depth (Fig. 4).

Uncertainty Estimates of the Retrieved S-Wave Velocity Models Error is always a problem in inversions. In this section, we discuss the error in the retrieved crustal models related to the initial model we used and the errors in the source parameters. Error Related to the Initial Model Figure 7. Demonstration of the group velocity measurements using the do_mft program in the HA package. The curve formed by the small squares shows the measured group velocities at station EDM. In this figure, the period range is 1–40 s. The color version of this figure is available only in the electronic edition. between group G8 (stations EDM and HYO) and the epicenter. Figure 8a shows the retrieved S-wave velocity model and the initial model, which was a previously used model (Mereu et al., 1986; Ma, 2010). The thick layers in the initial model were divided into thin layers with a thickness of 1 or 2 km for the inversion. To determine if the retrieved velocity model was reasonable, we compared the consistency between the observed dispersion data and the predicted group velocity curve. Figure 8b shows the observed group velocities (dots) and the predicted group velocity curve (solid curve). The consistency between the periods of 8.5 and 23 s was good, and this shows that the modeling corresponding to this period range was appropriate. If we assume that the penetration depths

The surf96 program was used to perform our dispersion inversion. At the start of the inversion, kernels needed to be formed using partial derivatives of the phase and group velocities, with respect to the parameters in the initial model (e.g., Chang, 1997). This implies that the values of the parameters in the initial model affect the final solution. Corchete (2012) emphasized that the selection of an initial earth model is a preceding step before the inversion process. The initial model must be prepared considering all information available for the study area, with respect to the S wave, P wave, and density distributions with depth. In our inversion, just as a starting point, a typical crustal model (Fig. 9a, dashed line) for the Western Quebec seismic zone (WQSZ) was used. To estimate the error in the final model caused by the initial model, we performed the test described in the following paragraphs. We subtracted 5%, 3%, and 1% of the values of the parameters in the initial model from the initial model and added 5%, 3%, and 1% to the initial model to form six new models (Fig. 9a, solid lines). We used these six models as initial models and the same data set as that used for the

Figure 8. (a) Comparison between the retrieved S-wave velocity model (solid line) and the initial model (dashed line) in the inversion of group G8 (stations EDM and HYO). The horizontal error bars were plotted on the new model. They are too short to be inspected. (b) Comparison between the observed group velocity values (dots) and the predicted group velocity values (solid curve) generated using the new model of (a). The vertical bars show the errors in the dispersion measurements. The period range used in the inversion was 8.5–23 s. The damping factor used for this inversion test was 0.5. The color version of this figure is available only in the electronic edition.

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initial model to perform the inversions. The obtained models are plotted in Figure 9b. It can be seen that the bias with respect to the initial model at shallow depths (< 15 km), even at middle depths (< 35 km), was not large. The bias became larger with increased depth. Table 2 lists the changes in the model solutions caused by the change in the initial crustal model. The second, third, fourth, sixth, seventh, and eighth columns show the percentages of change in the solution at a determined depth, when the initial model was changed by the amount given in the column heading. For example, if we subtracted 5% from the initial model and determined a solution of 3:2706 km=s in the top layer, we obtained 3:2706 − 3:2886=3:2886 −0:55% as the first element in the second column. It is clear that the percentage increases with depth. This fact may be related to the decreased ability to control the inversion solutions as the depth increases. We were unable to estimate the absolute errors in our solutions caused by the initial model. This issue may be very complex and needs further study. In the Baffin Island region, the geological background information is not well known; therefore, the initial model was the one for the WQSZ region. To confirm that our model solutions were significant, we performed a test using the simplest crustal model (one layer on the top of a half-space, which is the GSC model used for locating events in eastern Canada) as an initial model. Figure 9c shows the results from this test. In a comparison, we found that the retrieved model from the simple model (thick line) and the retrieved model from the WQSZ initial model (thin line) were similar at shallow depths (∼ < 20 km). This may indicate that our model solutions were significant in the penetration depth range of the Rayleigh waves used as our initial model in the inversion and more realistic than a simple model. As reasonable initial models imply better inversion solutions, our solutions were significant. Error in the Retrieved Velocity Model Related to the Errors in the Source Parameters

Figure 9. Initial model tests with identical dispersion data. (a) The dashed line in the middle shows our initial model. The other six solid lines show the test models formed by subtracting or adding 1%, 3%, and 5% of the values of the parameters in the initial model from or to the initial model. (b) The dashed line in the middle shows the new model retrieved using the initial model. The other six solid lines show the retrieved models using the above six test models. (c) The thick solid line shows the retrieved model using a simple model (one layer on the top of a half-space).

Many factors contributed to the error in the retrieved velocity model. One of the major factors was the error in the station distance, because the Rayleigh-wave group velocities were obtained from the station distance divided by the Rayleigh-wave group travel time. As such, the error in the station distance directly contributed to the error in the measured group velocity. This error was thus transferred to the retrieved velocity model. To estimate the error in the retrieved velocity model generated by the error in the epicenter, we performed the test described in the following paragraphs. The distance of station EDM was 3017 km (Fig. 1), calculated by SAC2000 using the station coordinates (53.2217° N, −113:35°) and those of the epicenter (75.27° N, −72:925°). If we wanted to change the station distance, we needed to change the coordinates of the station, the epicenter, or both. For convenience, we changed the latitude


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Table 2 Changes in Model Solutions Caused by the Changes in the Initial Model Depth (km)

−5%*

−3%*

−1%*

New Model (km=s)†

+1%*

+3%*

+5%*

2 4 6 8 10 12 14 16 17 19 21 23 24 26 28 30 32 34 36 38 40 hs

−0.55 −0.56 −0.51 −0.47 −0.63 −0.68 −0.83 −1.05 −1.29 −1.57 −1.87 −2.06 −2.16 −2.25 −2.22 −2.10 −2.18 −2.08 −2.04 −2.35 −2.47 −4.91

−0.33 −0.34 −0.30 −0.28 −0.37 −0.40 −0.49 −0.62 −0.76 −0.95 −1.12 −1.24 −1.29 −1.36 −1.34 −1.26 −1.29 −1.24 −1.20 −1.38 −1.45 −2.94

−0.12 −0.12 −0.10 −0.09 −0.13 −0.13 −0.16 −0.20 −0.25 −0.31 −0.37 −0.40 −0.44 −0.45 −0.45 −0.42 −0.43 −0.41 −0.40 −0.46 −0.47 −0.97

3.2886 3.2898 3.2911 3.3015 3.4668 3.5069 3.5575 3.6101 3.6561 3.7562 3.7955 3.8080 3.7961 3.8332 3.7938 3.7447 3.9249 3.8793 3.8437 4.2067 4.1984 4.4722

0.11 0.12 0.12 0.09 0.12 0.13 0.16 0.20 0.25 0.31 0.37 0.43 0.44 0.46 0.45 0.44 0.43 0.40 0.38 0.45 0.47 0.98

0.34 0.34 0.35 0.28 0.35 0.38 0.47 0.59 0.75 0.93 1.11 1.27 1.33 1.38 1.35 1.29 1.30 1.21 1.16 1.32 1.37 2.94

0.58 0.59 0.57 0.47 0.59 0.62 0.75 0.97 1.23 1.53 1.86 2.10 2.20 2.31 2.26 2.15 2.16 2.00 1.89 2.17 2.24 4.88

*The percentages of the model change when the initial model was changed by the amount in the column heading. † The new model is the S-wave velocity model retrieved using our initial model. In the bottom row, hs refers to half-space.

Table 3 Station Distance Changes Used to Estimate the Error in the Retrieved S-Wave Velocities Ordinal Number

1 2 3 4 5 6 7 8 9

EDM Coordinates (°)*

53.5217, 53.4217, 53.3217, 53.2717, 53.2217, 53.1717, 53.1217, 53.0217, 52.9217,

113.35 113.35 113.35 113.35 113.35 113.35 113.35 113.35 113.35

Epicenter (°)†

Distance (km)‡

Distance Change (km)§

S Velocity (km=s)‖

S Velocity Change (km=s)

75.27, 72.925

2986.145 2996.504 3006.867 3012.051 3017.236 3022.422 3027.609 3037.987 3048.370

31.091 20.732 10.369 5.185 0 +5.186 +10.373 +20.751 +31.134

3.2782 3.2879 3.2975 3.3025 3.3071 3.3122 3.3169 3.3269 3.3366

0.0289 0.0192 0.0096 0.0046 0 +0.0051 +0.0098 +0.0198 +0.0295

*The latitudes in the second column were 53:5217 53:2217 0:3; 53:4217 53:2217 0:2; 53:3217 53:2217 0:1; 53:2717 53:2217 0:05; 53:1717 53:2217 − 0:05; 53:1217 53:2217 − 0:1; 53:0217 53:2217 − 0:2; 52:9217 53:2217 − 0:3. †The epicentral coordinates were the average of the epicenters obtained from the GSC and IRIS. ‡ The distances were calculated using the station coordinates in the second column and the epicenter in the third column. §The distance changes were generated by the changes in the station coordinates. ‖ The S-wave velocities are those in the first layers of the models.

of the station several times to obtain different station distances. Column 1 in Table 3 lists the ordinal numbers, which were used in Figure 10, and column 2 lists the values we changed. We then used these distances to measure the dispersion curves at station EDM. Figure 10a shows nine curves. The curve (dashed line) in the middle was obtained using the real coordinates of station EDM (number 5 in Table 3). The other

curves correspond to latitude changes of 0:3°, 0:2°, 0:1°, and 0:05°, respectively. It can be seen that these curves had similar shapes, implying that the retrieved crustal models had similar features. Figure 10b shows five S-wave velocity models retrieved using the curves in the above panel indicated by numbers 1, 4, 6, and 9, as well as the dashed curve, which corresponded

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to the real station coordinates. It can be clearly seen that these models were similar, except for the absolute values, which were consistent with the station distances. As expected, the error in the S-wave velocity models was proportional to the error in the station distance. Figure 10c shows the linear relationship between the error in the station distance and the error in the S-wave velocity models. In our test, the station distance was ∼3000 km. If the error in the station distance was 30 km, the relative error would be 1%. This was on a similar order as that of the retrieved S-wave velocity, that is 3:3071 − 3:2782=3:3071 0:74% (Table 3). The average distance from the stations we used was 2465 km (Table 1). If the epicenter had an error that generated a 30 km distance error, then the error in the S-wave velocity models would be in the order of 30=2465 ∼ 1:2%. Ma et al. (2013) performed a similar test using a local station distance (∼60 km) and a smaller epicentral error (to generate a distance error of ∼2 km). The conclusion was similar to the above. The focal depth of the event we used was at most 30 km, because it was a crustal event. The focal depth contribution to the path length was very small. The shortest station–epicenter distance we used was 825 km. The distance from the hypocenter was 825.55 km. The relative error in the S-wave velocity was in the order of 825:55 − 825= 825 ∼ 0:06% (∼0:002 km=s), which was the maximum relative error caused by the focal depth in this case, as all other station distances were longer than 825 km. The impact of this factor on the inverted velocity model was negligible. Chen et al. (2010) gave an estimation of less than 0:03 km=s when analyzing the problem of source mislocation. The origin times were 2009/07/07 19:11:45 from IRIS, 2009/07/07 19:11:45 from the GSC, 2009/07/07 19:11:45.58 in the U.S. Geological Survey (USGS) moment tensor solution, and 2009/07/07 19:11:49.4 from the Global Centroid Moment Tensor (CMT) project (Harvard University). If we assume the maximum error in the origin time was 5 s and the average Rayleigh-wave velocity was 3:0 km=s, we could determine the travel time to be 825 km=3 km=s 275 s. We added 5 s and obtained the travel time of 280 s; therefore, the velocity was 825=280 2:95 km=s. The error in the velocity was 3:0 − 2:95 0:05 km=s. This was the maximum error caused by the error in the origin time, as other station distances were longer than 825 km. Surface waves, especially those recorded at telestations, are mainly generated by the major rupture of an earthquake. Using the Global CMT origin time to retrieve dispersion data may be better than using the conventional origin time, which refers to the rupture start time. Figure 10.

S-Wave Velocity Models Following the above procedure, we processed 13 groups and retrieved 13 velocity models. For practical uses, such as earthquake location, we also calculated the average model surrounding the epicenter. For all the above tests, a damping

Distance error test for the error in the retrieved Swave velocity model, generated by the error in the station distance (epicentral error). (a) The dispersion curves measured at different station distances (Table 3) using the Rayleigh-wave record at station EDM (the line numbers are consistent with the ordinal number). (b) The S-wave velocity models retrieved using the dispersion curves in (a) (the model numbers are consistent with the curve number above). (c) The tilted line shows the relation between the error in the S-wave velocity model and the error in the station distance.


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Figure 11. Retrieved S-wave velocity models at 13 azimuthal directions and the average velocity model. In the upper-left panel, the initial model is indicated with ‘initial’. For all panels, the initial model is identical. For each panel, the station names are at the upper-right corner, and the group name and azimuth are at the bottom-left corner (e.g., G1, 34 indicates group G1 at azimuth 34°—the average of the azimuths of stations ALE and DAG). The bottom-right panel shows the average model. The dashed lines indicate the GSC model for locating events in eastern Canada, plotted here for reference. The color version of this figure is available only in the electronic edition.

factor of 0.5 was used. For the following 13 groups, the damping factor value was 0.1.

The P-wave velocity (V P ) and the density values corresponding to the S-wave velocity (V S ) value in each layer were calculated using Poisson’s ratio (V P =V S 1:732) and the following Nafe–Drake relation (Ludwig et al., 1970):

S-Wave Velocity Models in 13 Azimuthal Directions For each group, we measured the group velocities from each seismogram, using the do_mft program, and copied the individual dispersion data files into one file for the inversion. Once the dispersion file for a group was formed, we used the file to perform the inversion using the same procedure and initial model described in the Operational Procedure to Retrieve S-Wave Velocity Models section. In this way, we obtained 13 crustal velocity models. The 13 models were plotted and are shown in Figure 11 and listed in Table 4.

ρ 1:6612V P − 0:4721V 2P 0:0671V 3P − 0:0043V 4P 0:000106V 5P :

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After looking over the model curves in Figure 11, we found that 1. the velocities of all models at the shallow depths (< 15 km) were obviously slower than those of the initial model;

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Table 4 S-Wave Velocity Models at 13 Azimuth Directions Depth

G1

G2

G3

G4

G5

G6

G7

G8

G9

G10

G11

G12

G13

Average

0 2 4 6 8 10 12 14 15 17 19 21 22 24 26 28 30 32 34 36 38 40 hs*

3.15 3.16 3.21 3.27 3.47 3.52 3.55 3.57 3.60 3.69 3.74 3.79 3.81 3.89 3.87 3.83 4.00 3.92 3.84 4.15 4.08 4.04 4.44

2.97 2.99 3.07 3.18 3.40 3.44 3.46 3.47 3.49 3.58 3.65 3.72 3.76 3.86 3.85 3.81 3.97 3.87 3.78 4.08 4.01 3.97 4.45

3.09 3.09 3.11 3.18 3.43 3.56 3.69 3.79 3.85 3.95 3.96 3.92 3.86 3.85 3.78 3.73 3.93 3.92 3.93 4.35 4.40 4.44 4.50

3.27 3.27 3.28 3.28 3.44 3.48 3.53 3.59 3.65 3.77 3.84 3.88 3.88 3.92 3.87 3.80 3.94 3.86 3.78 4.11 4.07 4.06 4.46

3.34 3.33 3.28 3.22 3.35 3.40 3.50 3.63 3.75 3.91 4.00 4.01 3.95 3.93 3.83 3.71 3.85 3.79 3.77 4.17 4.22 4.28 4.52

2.96 2.99 3.08 3.17 3.36 3.40 3.48 3.59 3.72 3.91 4.05 4.12 4.10 4.10 3.98 3.84 3.93 3.83 3.77 4.15 4.18 4.24 4.52

3.35 3.35 3.33 3.29 3.40 3.40 3.43 3.49 3.55 3.68 3.76 3.81 3.82 3.86 3.81 3.73 3.88 3.79 3.72 4.05 4.03 4.02 4.47

3.33 3.33 3.32 3.31 3.45 3.47 3.51 3.56 3.62 3.74 3.80 3.83 3.83 3.87 3.82 3.75 3.91 3.84 3.78 4.13 4.10 4.10 4.47

3.24 3.24 3.23 3.22 3.39 3.44 3.53 3.62 3.70 3.83 3.91 3.93 3.92 3.95 3.90 3.84 4.01 3.96 3.93 4.31 4.31 4.33 4.49

3.23 3.24 3.25 3.29 3.50 3.57 3.65 3.71 3.75 3.84 3.85 3.84 3.82 3.85 3.81 3.78 3.99 3.98 3.98 4.37 4.38 4.40 4.48

3.24 3.24 3.24 3.26 3.43 3.47 3.52 3.57 3.60 3.70 3.73 3.73 3.71 3.74 3.70 3.65 3.82 3.77 3.73 4.09 4.08 4.09 4.46

3.21 3.21 3.22 3.22 3.38 3.41 3.45 3.49 3.54 3.64 3.69 3.71 3.70 3.74 3.69 3.62 3.78 3.70 3.64 3.98 3.95 3.95 4.45

3.21 3.21 3.21 3.21 3.36 3.40 3.46 3.52 3.58 3.69 3.75 3.77 3.76 3.79 3.74 3.68 3.85 3.79 3.74 4.09 4.08 4.08 4.46

3.20 3.20 3.22 3.24 3.41 3.46 3.52 3.58 3.65 3.76 3.82 3.85 3.84 3.87 3.82 3.75 3.91 3.85 3.80 4.15 4.14 4.15 4.48

*The term hs refers to half-space.

2. in the middle crust, the velocities in most models were close to those of the initial model; 3. in northwest direction (groups G11, G12, and G13), the velocities in the middle crust were slower than those of the initial model; 4. in groups G3, G4, G5, and G6, the velocities in the middle crust were faster than those of the initial model; and 5. the slowest S-wave velocities in the top layers occurred in groups G2 and G6. Average Crustal Models For practical purposes, such as earthquake location using conventional methods, simplified crustal models are useful; therefore, we merged models G1–G13 into one average model. The last column in Table 4 and the bottom-right panel in Figure 11 show that, in the average model, the velocities in the shallow part (∼ < 15 km) were also obviously slower than those in the initial model. In the middle crust, the velocities were also close to those in the initial model.

Discussion The observed group velocities were calculated based on the station distance and the Rayleigh-wave travel time. Therefore, the error in the epicenter could have generated an error in the observed group velocities; and this error would have propagated to the retrieved S-wave velocity solutions. In northern Canada, the distribution of seismic stations is sparse; therefore, the error in the epicenter was relatively large. For

the 2009 Baffin Island earthquake, the GSC provided an epicenter of 75.19° N, −73:40° W, whereas an epicenter of 75.35° N, −72:45° W was retrieved from IRIS. The distance between the two epicenters is about 30 km. We plotted the station distributions around the epicenters and found that the Canadian stations were distributed on the southwest side, within an azimuth range of ∼90° (Fig. 12a), whereas the stations retrieved from IRIS were distributed around the epicenters (Fig. 12b). To decrease the epicenter error, we took the average of the two epicenters for our inversion. In this way, we assumed the epicenter error was 30 km. The error in the velocity models caused by the errors in the epicenter was about 1%–3%. This type of error affected the absolute values of the velocity models but had little influence on the features of the velocity distribution with depth (see Fig. 10). Both the errors in the focal depth and the origin time could also generate errors in the retrieved S-wave velocity models; they were not major factors, however, and had little influence on the features of the velocity distribution with depth. The initial model must be prepared before inversion. Based on our tests, the values of the parameters in the initial model directly impacted the solution. Therefore, the initial model should be established using known crustal structure information in the studied region. Figure 9b shows that the S-wave velocities at depths shallower than 15 km were not very affected by the used initial models. This implies that the average S-wave velocities at shallow parts were reliable. It is known that a Rayleigh wave of period 8 s does not sample depths less than 5 km well. To


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In most models, the retrieved velocity values at depths of around 20–25 km were close to those of the initial model. In the west direction, the retrieved velocity values in groups G11, G12, and G13 around the depth range of 20–25 km seemed to be systematically slower than those of the initial model, as shown in Figure 11. For groups G3, G4, G5, and G6, the retrieved velocity values at the depth range of 20–25 km were faster than those of the initial model. Table 4 shows that groups G2 and G6 had the slowest S-wave velocities in the top layers. The two groups were at different azimuthal directions; therefore, the two slowest S-wave velocities were not likely caused by the error in the epicenter. The above findings may indicate existing differences in crustal structures and may warrant further study.

Conclusion

Figure 12.

(a) Distribution of the Canadian seismic stations that recorded the 7 July 2009 Mw 6.0 earthquake. (b) Distribution of the IRIS stations that recorded the same event. The color version of this figure is available only in the electronic edition.

retrieve velocity structures in the top few kilometers, the appropriate periods of Rayleigh waves are around 1 s (Ma et al., 2013). Figure 9b also shows that, although the absolute values of the models were strongly affected by the initial models at depths below about 15 km, the shapes of the curves were similar. Figure 9c shows that, although we used a very simple initial model, a solution that had significance at depths shallower than the penetration depth could still be obtained. As the average longest period we used was approximately 24 s, the S-wave velocity models below 40 km may be not reliable as the resolution became smaller below that depth (Fig. 4). Error is always a problem in inversions. The error output from the HA package, however, is small. We consulted the author of the program (Robert Herrmann, Saint Louis University, St. Louis, Missouri) and know that a small error does not mean necessarily that the model is realistic. The larger the error in the solution, the better the resolution and vice versa. This issue depends on the trade-off between covariance and resolution (Chen et al., 2010; Badal et al., 2013). Currently, we cannot estimate absolute errors in inversion solutions.

The 2009 Baffin Island M w 6 earthquake generated crustal Rayleigh waves that were clearly recorded at many seismic stations. The dispersion data measured from these seismograms can be used to estimate crustal models surrounding the epicenter. We carefully selected 28 records, measured the Rayleigh-wave dispersion curves, and used these curves to retrieve crustal models relative to 13 azimuthal directions. In all of the retrieved models, we found the S-wave velocities at shallow depths were obviously slower than those of the initial model. Our tests showed that the error in the epicenter influenced the retrieved models. The relative errors were about 1%–3%, depending on the station distance used; the errors, however, had little impact on the shapes of the model curves. This implies that the error in the epicenter only impacted the absolute values of the retrieved crustal models. An initial model was unavoidable in our inversion and definitely had an influence on our inversion results. Our tests showed that the impacts of the changes of our initial model differed with depth. At depths where the shortest Rayleigh waves could penetrate, the change of the retrieved models caused by the change in the initial models was very small; and, the shapes of the retrieved model curves were almost independent of changes in the initial model. The shapes of the retrieved S-wave velocity model were controlled by the used Rayleigh-wave dispersion curves. Based on our tests and the analysis of the characteristics of our models, our conclusion that the retrieved S-wave velocities at shallow depths were obviously slower than those of the initial model was reliable. The features (shapes) of the retrieved S-wave velocity models were also reliable, as those features were determined by the observed Rayleighwave dispersion data. For most Rayleigh-wave records, the longest period used to measure group velocities was about 24 s; and, the corresponding penetration depth was approximately 35 ∼ 40 km. Therefore, the distinguishable feature that the velocities were slower at shallower depths than those of the initial model should be reliable.

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Data and Resources Seismograms used in this study were collected from the Geological Survey of Canada (GSC) at http:// earthquakescanada.nrcan.gc.ca/index‑eng.php (last accessed 29 August 2013) and the Incorporated Research Institutions for Seismology (IRIS) Consortium at http://www.iris.edu/hq/ (last accessed 29 August 2013).

Acknowledgments The authors gratefully acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada (NSERC). We are thankful for the constructive comments and significant suggestions of Editor Diane I. Doser, reviewers José Badal at the University of Zaragoza, Zaragoza, Spain, and Chen Yun-Tia at the Institute of Geophysics, China Earthquake Administration (CEA), Beijing, China. Their advice has dramatically improved this article. We also express our sincere thanks to R. Herrmann for providing us with valuable instructions for using his programs.

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Department of Earth Sciences Carleton University 1125 Colonel By Drive Ottawa, Ontario K1S 5B6, Canada [email protected] Manuscript received 14 October 2013; Published Online 3 June 2014