Crustal Shear-Wave Velocity Models Retrieved ... - GeoScienceWorld

Bulletin of the Seismological Society of America, Vol. 103, No. 4, pp. 2266–2276, August 2013, doi: 10.1785/0120120187

Crustal Shear-Wave Velocity Models Retrieved from Rayleigh-Wave Dispersion Data in Northeastern North America by Dariush Motazedian, Shutian Ma, and Stephen Crane On 23 June 2010, a moderate earthquake with M w 5.2 occurred near the town of Val-des-Bois, Quebec, Canada, ∼60 km northeast of Ottawa, Ontario. The earthquake generated excellent crustal Rayleigh-wave records. We divided the 54 seismic stations that recorded clear Rayleigh-wave trains into 14 groups by station azimuth. In each group, we measured the Rayleigh-wave dispersion data station by station and formed one dispersion data file for the inversion. In this way, we obtained 14 crustal velocity models around the epicenter. We compared all 14 models and found that there are low-velocity layers in the top 10 km on the north side of the Ottawa–Bonnechere graben. Based on model similarity, we formed one model for the north side by averaging the north-side models and another model for the south side by averaging the south-side models. The separation of the north-side and south-side models appears to follow the Ottawa–Bonnechere graben. In the top 10 km, the velocities in the south model are obviously slower than those in the north model.

Abstract

Introduction On 23 June 2010, a moderate earthquake with Mw 5.2 occurred ∼60 km north-northeast of Ottawa, Ontario, Canada, near the town of Val-des-Bois, Quebec. The mainshock had a large impact on the population in northeastern North America. It was felt over an area of approximately three million square kilometers, throughout the Canadian provinces of Quebec and Ontario and in the United States from Maine to Illinois to Kentucky. It produced the strongest shaking on record in the Ottawa and Montreal regions. The mainshock also caused damage to buildings and bridges. It has, therefore, been studied for seismic engineering purposes (e.g., Atkinson and Assatourians, 2010) and for the basic features of the earthquake sequence and the related seismicity (e.g., Ma and Motazedian, 2012). This earthquake was very well recorded by many seismic stations. 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 Incorporated Research Institutions for Seismology (IRIS), by azimuth. It was found that, on the north side of the epicenter (Fig. 1), which is on the north side of the Ottawa–Bonnechere graben (OBG), starting from station ATKO and moving clockwise to station EMMW, the shorter-period Rayleigh waves arrived earlier than the longer-period Rayleigh waves (Fig. 2a). This reverse dispersion phenomenon shows that there are possibly low-velocity layers in the crust through which the Rayleigh waves travel. On the south side, however,

this was not the case (Fig. 2b). The dispersion differences show that the crustal structures on both sides of the epicenter are different, seemingly separated by the failed Iapetan rift arm known as the OBG (Forsyth, 1981; Adams and Basham, 1991; Ma and Eaton, 2007). This feature, simplified to a thick dashed line (of which the extension line runs approximately through the middle of stations ATKO and EYMN; Fig. 1), splits the north-side and south-side models. 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). We observed the Rayleigh-wave reverse dispersion phenomenon and were motivated to use these Rayleigh-wave dispersion data to estimate crustal structures in northeastern North America. We first analyzed the Rayleigh waves in some seismograms and found that the dominant periods were about 6–25 s. Figure 3 shows the Rayleigh-wave seismograms and their power spectra. The dominant frequencies were from about 0.04 to 0.15 Hz. The corresponding periods were from about 6 to 25 s. If we assume that the penetration depths of these waves were ∼40% of their wavelength (e.g., Lowrie, 2007) and the average speed of Rayleigh waves in the crust was ∼3:3 km=s, these waves traveled mainly through the crust (3:3 × 25 × 0:4 ∼ 33 km). This implies that the Rayleighwave dispersion data from the Val-des-Bois mainshock can provide good information for studying crustal structures. Taking advantage of many high-quality Rayleigh-wave records generated by the 23 June 2010 Val-des-Bois mainshock,

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Crustal Shear-Wave Velocity Models Retrieved from Rayleigh-Wave Dispersion Data

Figure 1. The distribution of the selected seismic stations at which Rayleigh waves were clearly recorded. These stations were divided into 14 groups. In each group, stations had similar azimuths, see Figure 10a,b for the station names in each group. The grouping starts at station ATKO, moving clockwise to station EYMN. The map is separated approximately into north (stations in each group are connected by thin dashed lines), south (by solid lines), and east sides (by thick dashed lines) of the OBG, which is indicated by the thick dashed lines in the middle. The stations on the north side start at station ATKO, moving clockwise to station BATG, and on the east side from stations BATG to WVL; all other stations belong to the south side. The closest station to the epicenter (white circle) was VLDQ (∼310 km), and the farthest was FRB (∼2035 km). The diamonds with letters D, S, O, M, Q, T, B, and N show the locations of the towns of Dryden and Sudbury and the cities of Ottawa, Montreal, Quebec City, Toronto, Boston, and New York, respectively. we estimated shear-wave velocity models using those crustal Rayleigh-wave dispersion data and focused our efforts on shear-wave velocity models in the crust. In the following sections, we briefly review the concepts of normal and reverse dispersion. We demonstrate a specific procedure to obtain a shear-wave velocity model at one north-side station and one south-side station. We divide the stations in Figure 1 into 14 groups by azimuth and obtain 14 crustal models. We then divide the groups into north and south sides of the epicenter and provide one average crustal model for each side, which can be used for practical applications, such as locating seismic events. We estimated the reliability of our velocity models, discussed the related issues, and summarized our study using Rayleigh-wave dispersion data.

Group Velocity Measurement and Rayleigh-Wave Dispersion Data Inversion Methods In this section we briefly discuss the methods used to process waveform records and retrieve the shear-wave velocity models. The digital waveform records were velocity type with instrument responses. First, we removed the instrument responses with SAC2000 software and, at the same time,

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converted the velocity records into displacement records. The records were then filtered with a band pass of 1–30 s. 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 a technique called MFT (multiple filter technique, Dziewonski et al., 1969) in a computer program package developed by Herrmann and Ammon (2002, version 3.3), hereafter referred to as the HA package. When we obtained the group velocity measurements, we used the inversion program surf96 in the HA package to retrieve the crustal shear-wave velocity models. The MFT is a filtering technique developed by Dziewonski et al. (1969). The method is used to retrieve a group velocity dispersion curve from a preprocessed waveform record (instrument response removed). In the technique, the time when the envelope of the filtering seismic record reaches the maximum is the group time for a center frequency, ωn , which is selected as the center of the Gaussian filter. The group velocity is obtained through the division of the epicentral distance by the group time. Once a Rayleigh-wave group velocity curve is measured at a specific seismic station, the curve is used to retrieve the average shear-wave velocities along a path between the source and the station at which the Rayleigh waves are recorded. We first set up an initial crustal model between an earthquake and a seismic station where the Rayleigh waves generated by the earthquake are recorded. We then revise the model based on the fit between the observed Rayleigh group velocities and the synthetic Rayleigh group velocities generated using the crustal model. A revised model that can generate the best fit is our solution. The methods using Rayleigh-wave dispersion data to retrieve shear-wave velocity models have been extensively studied and used (e.g., Kafka and Reiter, 1987; Badal et al., 1990, 1992). Ma et al. (2013) outlined the theoretical background for retrieving shear-wave velocity models using Rayleigh-wave dispersive data.

Concept Review of Normal and Reverse RayleighWave Dispersion The Rayleigh-wave dispersive phenomenon refers to waves with different frequencies having different arrival times at a seismic station when they travel through the Earth. When the waves with longer periods arrive first, the dispersion is considered to be normal, and when the waves with shorter periods arrive first, the dispersion is considered to be reverse. The dispersive phenomenon, normal or reverse, is related to the structures of the Earth through which the waves travel. The use of normal Rayleigh-wave dispersion to retrieve Earth structures has a long history (e.g., McEvilly, 1964), and many works have used normal dispersion data. In contrast, only a few studies have utilized reverse Rayleigh-wave dispersion (e.g., Duret et al., 2010). In this article, we use

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D. Motazedian, S. Ma, and S. Crane

Figure 2. (a) The vertical components of the Rayleigh-wave displacement records at 31 of the 54 seismic stations. These records are arranged by group. In each group, they are arranged by station distance. The first four records belong to group 1, the second four to group 2, etc. The symbol at the left side of each trace is the station name. Also shown are the stations on the north and east sides of the OBG (G1–G9). (b) Shown are the 23 records at the stations on the south side of the OBG (G10–G14). Most of the Rayleigh waves in this figure are not reversely dispersed.

normal and reverse Rayleigh-wave dispersion data to retrieve crustal structures. To give readers a clear concept of normal and reverse dispersions, we generated synthetic seismograms using two types of crustal models to demonstrate the two types of dispersion. Figure 4 shows the normal and reverse Rayleigh-wave dispersions. The upper-left panel is the crustal model retrieved in the Thunder Bay region of Ontario, Canada, using Rg wave dispersion data (Ma et al., 2013). The upper-right panel shows that the synthetic seismogram was normally dispersed. The upper-middle panel shows that the group velocities were faster when the periods were longer. The bottomleft panel was a synthetic model. The bottom-right panel shows that the synthetic Rayleigh waves with shorter periods arrived first. The bottom-middle panel shows that the measured group velocities were slower when the periods were longer. Figure 3. Rayleigh-wave records at (a) north-side station ULM and (c) south-side station BLA. (b) Power spectra for station ULM. (d) Power spectra for station BLA. The dominant frequencies are from about 0.04 to 0.15 Hz. The corresponding periods are from about 6 to 25 s. These waves travel mainly through the crust. Scales on vertical axes were omitted for clarity.

Operational Procedure to Obtain Shear-Wave Velocity Models We selected 27 waveform records from those provided by the GSC and 27 records from those retrieved from the


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Figure 4. Comparison between normal and reverse dispersion. The upper-left panel is the crustal model in which the velocities increase with depth. The upper-right panel is the synthetic seismogram, generated using the crustal model at the left. Along the synthetic trace, the Rayleigh waves with longer periods arrive first. The upper-middle panel shows the measured normal dispersion data (small squares). The bottom-left panel is the crustal model in which there are some lower velocity layers. The bottom-right panel is the synthetic seismogram, generated using the model at the left. Along the synthetic, the Rayleigh waves with shorter periods arrive first. The bottom-middle panel shows the reverse dispersion measurements (small squares). IRIS database. The 54 corresponding stations are presented in Figure 1. The stations were separated into 14 groups by station azimuth. Figure 2a shows the seismograms in the first nine groups, and Figure 2b shows the seismograms in the remaining five groups. In each group, the stations had similar azimuths, and the seismograms were arranged by the source–station distances, indicated by, for example, G1. We used the do_mft program in the HA package to measure group velocities from a selected record that has a relatively clear Rayleigh-wave train. As an example, the curve formed by the small squares in Figure 5 shows the measured group velocities from the record at station ULM.

Using the group velocity values and the inversion program surf96 in the HA package, we obtained a shear-wave velocity model for the path between station ULM and the epicenter. Figure 6a shows the retrieved shear-wave velocity model and the initial model (a previously used model; Mereu et al., 1986; Ma, 2010). The thick layers in the initial model were divided into thin layers 2 or 1 km thick 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 6b shows the observed group velocities (small triangles) and the predicted group velocity curve (solid line). The

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Figure 5. Demonstration of the group velocity measurements using the program do_mft in the HA package. The curve formed by the small squares shows the measured group velocities at station ULM (station distance ∼1590 km). In the figure, the period range is 1–30 s. The waves showed reverse dispersion below period 20 s and normal dispersion above 20 s. consistency between periods of 10 and 20 s was better than those in periods below 10 and above 20 s. The consistency at periods below ∼10 s was not very good. This shows that modeling at shorter periods is more difficult than that at longer periods because the Rayleigh waves with short periods sample the shallow part of the crust, and the heterogeneity in the shallow part is stronger than that in the deeper part.


Station ULM belongs to a group on the north side of the OBG. The dispersion along trace ULM in Figure 2a is reverse, whereas seismograms in Figure 2b do not show this feature. In contrast, some seismograms show that the Rayleigh waves had normal dispersion. For example, trace BLA shows the Rayleigh waves were normally dispersed. With the same procedure used to process the record at station ULM, we processed the seismogram at station BLA. Figure 7 shows the measured group velocities. The waves in the period range of 5–12 s had normal dispersion; those in the period range of 12–16 s had reverse dispersion; and those above 16 s had normal dispersion. Figure 8a shows that in the shallow part the velocities in the retrieved model were obviously slower than those in the initial model. Figure 8b shows that the consistency between the observed and predicted group velocities in the period range of 6 to 21 s was good. To examine if the retrieved velocity model was reasonable in the time domain, we first generated synthetic seismograms using the new crustal and initial models and then compared the similarities between the synthetic and observed seismograms. Figure 9 shows the comparison. We see reverse dispersion in the Rayleigh waves along the top trace, whereas the Rayleigh waves along the bottom trace were normally dispersed. The similarity between the shapes of the Rayleigh waves along the top and observed traces was better than those along the observed and bottom traces. This implies that the retrieved model is better than the initial model. The computer program we often use to generate synthetic seismograms was developed by Randall (1994) using the reflectivity method of Kennett (1983). To cover the peak period (∼7 s, Fig. 3b) of the record at station ULM, we used

Figure 6. (a) Comparison between the retrieved crustal shear-wave velocity model (solid line) and the initial model (dashed line) in the inversion at station ULM. (b) Comparison between the observed group velocity values (small triangles; the errors were plotted in Fig. 12a) and the predicted group velocity values (solid curve) generated using the new model at (a). The period range used in the inversion is 6–22 s.


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the individual dispersion data files into one file for the inversion. Once the dispersion file was formed for a group, we used the file to perform the inversion using the same procedure as in the Operational Procedure to Obtain Shear-Wave Velocity Models section. The initial model was also the same as the one used in the same section. In this way, we obtained 14 crustal velocity models. We plotted the 14 models in Figure 9a,b and listed them in Table 1. The primary wave (P-wave) velocity value and the density corresponding to the secondary wave (S-wave) velocity 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): ρ 1:6612V P − 0:4721V 2P 0:0671V 3P − 0:0043V 4P 0:000106V 5P : Figure 7. Demonstration of the group velocity measurements. The curve formed by the small squares shows the measured group velocities at station BLA (station distance ∼1047 km). The period range is 1–30 s. The waves in the period range of 5–12 s have normal dispersion; those in the period range of 12–16 s have reverse dispersion; and those above 16 s have normal dispersion. the period range 1 ∼ 10 s to generate synthetic seismograms in Figure 9.

Shear-Wave Velocity Models at 14 Azimuthal Directions For each group, we measured the group velocities from each seismogram, using the program do_mft, and copied

(1)

After looking over the model curves in Figure 9a,b, we found that: 1. The velocities in models 1–7 (on the north side of the OBG) were close to those in the initial model in the shallow part, and there were low-velocity layers at depths between about 5 and 8 km. 2. In the shallow part, the velocities in models 10–14 (on the south side) were slower than those in the initial model, with no low-velocity layers at depths between about 5–8 km. Model 8 was simple: no low-velocity layers appeared in the shallow part. This model was retrieved using the seismograms at stations BATG and SJNN. The Rayleigh waves

Figure 8. (a) Comparison between the retrieved crustal shear-wave velocity model (solid line) and the initial model (dashed line) at station BLA. (b) Comparison between the observed group velocity values (small triangles; the errors were plotted in Fig. 12c) and the predicted group velocity values (solid curve) generated using the new model in (a). The period range used in the inversion is 6–22 s.

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Figure 9. Comparison between the synthetic and observed Rayleigh waves at station ULM (station distance ∼1590 km, Az ∼ 295°). Trace ULM/New is generated using the new crustal model retrieved at station ULM. Trace ULM/BHZ is the observed vertical component displacement at ULM. Trace ULM/INIT is generated using the initial model. “L” along the three traces shows the longer half periods, which show reverse or normal dispersion. Except for the crustal models, all other parameters used to generate the synthetics are identical.

Average Crustal Models on the North and South Sides of the OBG

along the two traces at the bottom of Figure 2a were also simple. It is hard to see whether the Rayleigh waves along trace BATG were reversely or normally dispersed, and the Rayleigh waves along trace SJNN were only very slightly reversely dispersed. As the velocity values in the shallow part were similar to those in the south models, we moved model 8 into the south group (Fig. 10b). Model 9 was retrieved using the seismograms at stations GBN, HAL, EMMW, and WVL. The Rayleigh waves along these four traces at the bottom of Figure 2a were noticeably reversely dispersed; therefore, the crustal structure through which the Rayleigh waves propagated had the same features as the north groups. The velocity layers in the shallow part, however, had values similar to those in the south groups. We also moved this group into the south groups (Fig. 10b).

For practical purposes, such as locating seismic events using conventional methods, simplified crustal models are useful. Based on the features displayed by the models on the north and south sides of the OBG, we merged models 1–7 into the north model and models 8–14 into the south model. Figure 11a shows that the model for the south side had obviously slower velocity layers than those in the north model in the shallow part (< 8 km). There were low-velocity layers at depths of about 5–8 km in the north model. Below 8 km, the north and south models were similar. Figure 11b shows that the average model was slower than the initial

Table 1 Shear-Wave Velocity Models in 14 Groups Group Indexes H

1

2

3

4

5

6

7

8

9

10

11

12

13

14

North

South

2 4 6 8 10 12 14 16 17 19 21 23 24 26 28 30 33 36 40 0

3.60 3.60 3.58 3.54 3.65 3.65 3.66 3.68 3.70 3.77 3.79 3.79 3.78 3.83 3.82 3.81 4.03 4.03 4.42 4.42

3.61 3.59 3.53 3.44 3.52 3.51 3.54 3.60 3.64 3.74 3.76 3.72 3.65 3.63 3.53 3.44 3.60 3.59 4.06 4.23

3.56 3.56 3.54 3.49 3.59 3.56 3.56 3.57 3.59 3.67 3.69 3.69 3.67 3.70 3.66 3.61 3.80 3.78 4.20 4.29

3.57 3.56 3.53 3.46 3.55 3.53 3.53 3.56 3.59 3.67 3.69 3.68 3.64 3.65 3.58 3.51 3.68 3.66 4.08 4.21

3.59 3.58 3.54 3.48 3.57 3.55 3.57 3.61 3.65 3.74 3.76 3.74 3.68 3.68 3.59 3.51 3.68 3.66 4.11 4.25

3.53 3.53 3.49 3.44 3.54 3.54 3.56 3.60 3.63 3.71 3.72 3.69 3.64 3.63 3.55 3.48 3.66 3.65 4.10 4.24

3.59 3.58 3.55 3.49 3.58 3.56 3.57 3.60 3.63 3.72 3.74 3.73 3.68 3.68 3.60 3.53 3.70 3.68 4.12 4.26

3.36 3.37 3.37 3.37 3.53 3.54 3.57 3.59 3.60 3.68 3.68 3.66 3.63 3.66 3.63 3.60 3.82 3.83 4.27 4.36

3.45 3.45 3.44 3.41 3.53 3.52 3.53 3.56 3.58 3.67 3.69 3.69 3.66 3.69 3.64 3.59 3.78 3.77 4.19 4.29

3.40 3.43 3.48 3.50 3.62 3.59 3.58 3.59 3.62 3.70 3.72 3.72 3.67 3.67 3.59 3.50 3.65 3.61 4.02 4.15

3.40 3.40 3.40 3.39 3.54 3.57 3.60 3.63 3.65 3.73 3.72 3.69 3.63 3.63 3.56 3.49 3.68 3.67 4.11 4.24

3.40 3.43 3.47 3.48 3.60 3.58 3.57 3.58 3.60 3.68 3.70 3.69 3.64 3.64 3.57 3.49 3.65 3.62 4.06 4.20

3.39 3.40 3.43 3.45 3.59 3.59 3.60 3.61 3.62 3.69 3.70 3.69 3.66 3.69 3.65 3.62 3.82 3.82 4.25 4.33

3.37 3.37 3.37 3.37 3.52 3.54 3.58 3.61 3.64 3.72 3.72 3.69 3.63 3.62 3.53 3.44 3.60 3.58 4.01 4.15

3.58 3.57 3.54 3.48 3.57 3.56 3.57 3.60 3.63 3.72 3.74 3.72 3.68 3.69 3.62 3.56 3.74 3.72 4.16 4.27

3.40 3.41 3.42 3.42 3.56 3.56 3.58 3.60 3.62 3.70 3.70 3.69 3.65 3.66 3.60 3.53 3.71 3.70 4.13 4.25

The numbers in the leftmost column are the depths of the layers (km). Numbers 1 through 14 across the top are the 14 group indexes. The column of numbers below each index are the shear-wave velocities (km=s) in the retrieved crustal models. See Figures 10a,b and 1 for the group distribution. The depth value of 0 indicates that layer is a half-space. The columns North and South were prepared for Figure 11.


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Figure 10. (a) The retrieved crustal velocity models at seven azimuthal directions (the thin lines show the initial models, which are identical for all groups). For each panel, the station names are in the upper-right corner, and the group index and azimuth are in the bottom-left corner (e.g., 1-293 indicates group 1 at azimuth 293°, the average of the azimuths of stations of PNPO, ATKO, EPLO, and ULM). These seven groups are on the north side of the OBG. (b) The retrieved crustal velocity models at the other seven azimuthal directions. Groups 8 and 9 are on the east side of the OBG, and groups 10–14 are on the south side of the OBG. The velocities in the shallow part are noticeably slower than those in groups 1 through 7. model and that the velocity in the crustal model used by the GSC was faster than those in the average model in the depth shallower than ∼10 km and slower than those in the average model in the depth deeper than ∼15 km.

Reliability Estimates to our Velocity Models Figure 2a shows that those Rayleigh waves recorded at the north-side stations had reverse dispersion, whereas Figure 2b shows that those recorded at the south-side stations did not have similar features. Some Rayleigh waves were normally dispersed, such as those at station BLA. As the crustal models were retrieved from these Rayleigh-wave dispersion data, the models carry the features that are related to the features of the Rayleigh waves. The errors in the

measurements of the dispersion data may generate those differences between the models on the north and the south sides, however. To prove that these key differences were not artificial, we performed the following test using Rayleigh-wave records at north-side station ULM and south-side station BLA (Fig. 1). At each station, we formed two sets of dispersion data by adding or subtracting the measurement errors (which are output from the program do_mft ) to or from the observed dispersion data sets at stations ULM and BLA, respectively. We then made three inversions at each station. Figure 12 shows the retrieved crustal velocity models, as well as the formed dispersion curves. From Figure 12, we see that the low-velocity zone exists at about 5–8 km in the

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Figure 11.

Comparison between shear-wave velocity models. (a) The average models on the north and south sides (thick line shows the average of models 1–7 in Figure 10a; the thin line shows the average of models 8–14 in Figure 10b). The values of the two velocity models were listed in Table 1. (b) The thick line shows the average of the north and south models in (a); the thin line shows the initial model used in the inversion; and the dashed line shows the model used by the GSC for locating seismic events in eastern Canada.

Figure 12.

Comparison between crustal velocity models retrieved from the observed dispersion data sets and the data sets formed by adding or subtracting the measurement errors to or from the observed data sets at station ULM and BLA, respectively. (a) The thick lines show the V S and V P models retrieved from the observed dispersion data, and the thin lines on the left and right sides of the thick lines show the V S and V P models retrieved from the two formed dispersion data sets. (b) The thick line is the observed dispersion curve in the period range of 6–22 s, and the two thin lines are the dispersion curves formed by adding or subtracting the errors to or from the observed curve at station ULM. (c, d) Explanations are the same as for (a) and (b) but for station BLA. The fine lines in (a) and (c) show the initial model, which is identical in the two panels.

Crustal Shear-Wave Velocity Models Retrieved from Rayleigh-Wave Dispersion Data model retrieved at station ULM, and the velocities on the top layers retrieved at station BLA were slower than those at ULM. These differences between the velocity models can be seen directly from the differences between the dispersion curves in Figure 12b,d. For most Rayleigh-wave records, the longest period used to measure group velocities was about 22 or 23 s. The corresponding penetration depth was ∼30 km. Therefore, the low-velocity layers between about 25 and 30 km may not be very reliable. From Figures 4 and 6, we see, for periods above 17 s, wide ridges used to measure group velocities. The errors in the measured group velocities may have been large. Therefore, the model parameters below 22 km may have had larger errors. This analysis also shows that the lowvelocity layers between about 25 and 30 km may not be reliable. To confirm or deny the solutions between about 25 and 30 km, another way needs to be found. Moschetti et al. (2007) found that, using the PREM model, the radial sensitivity kernels for Rayleigh waves are sensitive at depths of ∼10 km for period 8 s, about 10 ∼ 20 km for period 16 s, and about 20 ∼ 35 km for period 24 s. The longest period we used was around 22 or 23 s. Therefore, our solutions at depths from about 5 to 25 km may be reliable. From Figures 5 and 7, we also see that, for periods below 17 s, the ridges were narrow. Accordingly, the model parameters above 22 km should be reliable. In other words, the difference between models on the north and south sides should be reliable, and the low-velocity layers at about 5–10 km in the northside models may be reliable.

Discussion In northeast North America, the crustal thicknesses are in the range of about 35–45 km. When we measured the group velocities, we set 1 s and 30 s as the two limits and took the group velocity values in a period range of about 5–22 or 23 s for the inversion, that is to say, we confined our inversion results mainly to within the crust. After carefully observing the velocity curves in Figure 10a, we see that the low-velocity layers existed at about 5–8 km and about 25–30 km on panels 1–7. In Figure 2a, all the Rayleigh waves were reversely dispersed. The low-velocity layers may relate to the reverse dispersion. Panels 10–14 in Figure 10b show that the velocities at top layers were obviously slower than the values in the initial model, whereas the velocities at top layers in Figure 10a were close to the values in the initial model. This difference directly shows that the geological structures on the north and south sides are different and separated approximately by the OBG. 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) and know that a small error does not necessarily mean that the model is realistic. At the moment, we do not have ways to estimate absolute errors in the inversion results. Our tests show that

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the degree of the similarity between the synthetic Rayleighwave train (Fig. 9) generated using the new model and the observed Rayleigh-wave train was higher than that between the synthetic Rayleigh-wave train generated using the initial model and the observed Rayleigh-wave train. This implies that the new models from the crustal Rayleigh-wave dispersion data are closer to the real velocity structure than the initial model that was used in our previous research (e.g., Ma, 2010). The observed group velocities were calculated based on the station distance and travel time. Therefore, the error in the epicenter could generate an error in the observed group velocities, and this error would propagate to the retrieved shear-wave velocity solutions. The 23 June 2010 Val-desBois earthquake had records from nearby stations, the closest source–station distance was ∼20 km. The absolute error in the epicenter was at most 2 km. The relative error in the observed group velocities caused by the error in the epicenter was in the same order as that in the epicenter (Ma et al., 2013). Thus, if the source–station distance is 500 km, the relative error would be 2=500 0:004. The source–station distances we used were about 500–2000 km; thus, the errors in the retrieved velocity models caused by the error in the epicenter were negligible. Vlahovic et al. (1998) retrieved P- and S-wave velocity models for the Eastern Tennessee Seismic Zone (ETSZ, ∼36° N, 84° W). We compared our solutions in panels 11-200 and 12-239 (the two panels are approximately in the ETSZ direction) in Figure 10b and found that our solutions had some similarities with theirs in the shallow part (their fig. 4 and table 1). These similarities support our crustal models in that direction. On the south and northwest sides of the epicenter (Fig. 1), there were low-velocity layers in the top couple of kilometers (e.g., Saikia et al., 1990; Ma et al., 2013). We ignored these low-velocity layers in our current work, as the shortest period we used in this article was ∼5 s. Rayleigh waves with a period of 5 s are not sensitive to the crustal structures in the top couple of kilometers. To retrieve velocity structures in the top few kilometers, the appropriate periods of Rayleigh waves are around 1 s.

Summary The 23 June 2010 M w 5.2 Val-des-Bois earthquake generated excellent crustal Rayleigh-wave records. We retrieved the crustal velocity models around the epicenter (Fig. 1). At the stations on the north side of the OBG, the Rayleigh waves were reversely dispersed; therefore, there were some low-velocity layers in the retrieved crustal models. In the top 8 km on the south side, the velocities in the models increased with depth. The average velocities were obviously slower on the south side than those on the north side in the top 8 km (Fig. 11a). The major results provided in the section, Shear-Wave Velocity Models at 14 Azimuthal Directions, were obtained

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using the dispersion data in the period range of about 5–22 s, in which the Rayleigh waves propagated mainly through the crust. Tests showed that, if the period range of 5–30 s was used, the solutions could have changed. The basic features were kept, however: on the north side, there were lowvelocity layers at depths of about 5–8 km, and there were no low-velocity layers in the models on the south side in the same depth range.

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 10 August 2011) and Incorporated Research Institutions for Seismology (IRIS) at http://www.iris.edu/hq/ (last accessed 10 August 2011).

Acknowledgments The authors gratefully acknowledge the financial support of the Natural Sciences and Engineering Research Council of Canada under the Strategic Research Networks and Discovery Grant programs. We are grateful for Associate Editor Haijiang Zhang and reviewers Shahram Pezeshk at the University of Memphis, and Fiona Darbyshire at the Université du Québec à Montréal for their constructive comments and significant suggestions, which dramatically improved this article.

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Department of Earth Sciences Carleton University 1125 Colonel By Drive Ottawa, Ontario K1S 5B6, Canada [email protected]

Manuscript received 31 May 2012