Journal of Seismology

, Volume 17, Issue 2, pp 683–705 | Cite as

Shear wave velocity models retrieved using Rg wave dispersion data in shallow crust in some regions of southern Ontario, Canada

Original Article

Abstract

Many crucial tasks in seismology, such as locating seismic events and estimating focal mechanisms, need crustal velocity models. The velocity models of shallow structures are particularly important in the simulation of ground motions. In southern Ontario, Canada, many small shallow earthquakes occur, generating high-frequency Rayleigh (Rg) waves that are sensitive to shallow structures. In this research, the dispersion of Rg waves was used to obtain shear-wave velocities in the top few kilometers of the crust in the Georgian Bay, Sudbury, and Thunder Bay areas of southern Ontario. Several shallow velocity models were obtained based on the dispersion of recorded Rg waves. The Rg waves generated by an mN 3.0 natural earthquake on the northern shore of Georgian Bay were used to obtain velocity models for the area of an earthquake swarm in 2007. The Rg waves generated by a mining induced event in the Sudbury area in 2005 were used to retrieve velocity models between Georgian Bay and the Ottawa River. The Rg waves generated by the largest event in a natural earthquake swarm near Thunder Bay in 2008 were used to obtain a velocity model in that swarm area. The basic feature of all the investigated models is that there is a top low-velocity layer with a thickness of about 0.5 km. The seismic velocities changed mainly within the top 2 km, where small earthquakes often occur.

Keywords

Shear wave velocity models Rg wave dispersion Southern Ontario 

1 Introduction

In Canada, roughly one third of the population lives in the province of Ontario, with most people residing in southern Ontario. The Georgian Bay region is located within southern Ontario. Although the population of this region is not as crowded as that of the greater Toronto area, some critical facilities are located in the Georgian Bay region, such as the Bruce Energy nuclear power plant. Studies and prevention of the geological hazards, such as seismic hazards, in southern Ontario have, therefore, become increasingly important, and geological information is an absolute necessity. Seismic wave velocity, especially at shallow depths, is one of the basic parameters in the seismic studies of the region.

The accuracy of earthquake hypocenters plays a significant role in the study of tectonic processes and earthquake recurrence. It is also important in relating seismicity to geologic structures, which provide the background for hazard studies related to critical facilities, such as nuclear plants.

Reliable focal mechanism solutions can be used to study tectonic movement and are crucial information in earthquake source environment research. There is a challenge in that unreliable focal mechanism solutions are easily obtained for small earthquakes, if a waveform modeling method is used to retrieve the focal mechanism but the velocity model is not good. Some of the motivations for using Rayleigh (Rg) wave dispersion data to establish reasonable velocity models in the Go Home Lake (GHL) region, on the northern shore of Georgian Bay, are the determination of reliable hypocentral and focal mechanism solutions and further study of the GHL swarm and the surrounding seismicity.

Short period, fundamental mode Rg waves generated by small earthquakes or mining events have been recorded in both southern and northern Ontario. The group velocity dispersion of these Rg waves was sensitive to the details of the velocity structure in the upper few kilometers of the crust (Ma and Motazedian 2011). This feature has been successfully used to set up regional velocity models (e.g., Kafka and Reiter 1987; Chourak et al. 2003).

As an example, the bottom trace in Fig. 1 is the seismogram recorded at the SADO seismic station generated by an mN 3.0 event in 2010 in the same location as the 2007 GHL swarm. Figure 1 also displays four synthetic seismograms generated for the same station and the earthquake epicenter using four different velocity models, as given in Table 1. All other parameters that were needed to generate the synthetics were identical. The computer program used to generate the synthetics was developed by Randall (1994), using the reflectivity method of Kennett (1983). A thrust type focal mechanism (Ma 2010) was used to generate the synthetic seismograms.
Fig. 1

Synthetic seismograms generated using different velocity models and the recorded seismogram generated by a small earthquake in the GHL swarm location (Table 2, the third event). Trace 1 was generated using a one layer on top of a half space velocity model, trace 2 using a velocity model used in the RDPM package (Ma 2010), trace 3 using a velocity model used to study the GHL swarm (Ma and Eaton 2009), and trace 4 using a velocity model obtained by Rg wave dispersion analysis at SADO station (Table 4, second panel). The bottom trace is the observed record. All the synthetic seismograms were generated using a focal depth of 1.8 km

Table 1

Velocity models used for generating synthetic seismograms

No

One layer + half space

Ma (2010) model

Ma and Eaton (2009) model

Rg model at SADO

Δh

Vp

Vs

ρ

Δh

Vp

Vs

ρ

Δh

Vp

Vs

ρ

Δh

Vp

Vs

ρ

1

36

6.20

3.57

2.75

8

6.25

3.61

2.53

1

5.69

3.28

2.30

0.5

5.37

3.10

2.17

2

0

8.20

4.73

3.31

9

6.50

3.75

2.63

8

6.25

3.61

2.53

0.3

5.73

3.31

2.31

3

    

7

6.60

3.81

2.67

9

6.50

3.75

2.63

0.3

5.73

3.31

2.31

4

    

6

6.70

3.87

2.71

7

6.60

3.81

2.67

0.3

5.73

3.31

2.31

5

    

5

7.10

4.10

2.87

6

6.70

3.87

2.71

0.3

5.80

3.35

2.34

6

    

0

8.00

4.62

3.23

5

7.10

4.10

2.87

0.3

5.87

3.39

2.37

7

        

0

8.00

4.62

3.23

0.6

5.93

3.42

2.40

8

            

0.6

6.03

3.48

2.44

9

            

1.3

6.12

3.53

2.47

10

            

1.3

6.12

3.53

2.47

11

            

2.53

6.14

3.55

2.48

12

            

5.3

6.25

3.61

2.53

13

            

9.0

6.50

3.75

2.63

14

            

7.0

6.60

3.81

2.67

15

            

6.0

6.70

3.87

2.71

16

            

5.0

7.10

4.10

2.87

             

0.0

8.00

4.62

3.23

From left to right, the first panel is a one layer on the top of a half space velocity model (Geological Survey of Canada model, used for locating events in eastern Canada); the second panel is the model used by Ma (2010); the third panel is the model used by Ma and Eaton (2009; called the GHL model); the fourth panel is the model obtained in Section 4 (the deeper part was taken from Ma 2010); Δh is the layer thickness (in kilometers), Vp is the P wave velocity (in kilometers per second), Vs is the S wave velocity (in kilometers per second), and ρ is the density (in grams per cubic centimeter). A layer thickness of 0 means that layer is a half space

Trace 1 was generated using a velocity model of one layer on top of a half space (the first panel in Table 1). Trace 2 was created with a velocity model that is used as the default velocity model in the regional depth phase modeling (RDPM) computer program package (Ma 2010; the second panel in Table 1). Trace 3 was generated with a velocity model that was used to study the GHL earthquake swarm (Ma and Eaton 2009; the third panel in Table 1). Trace 4 was the result of the velocity model obtained by Rg wave dispersion inversion at the SADO seismic station (see Section 4).

It can be seen in Fig. 1 that the arrival times of the Rg phase were different along the different traces. If the velocity model used to generate trace 1 was used to locate events in the GHL region, the error in the epicenter may have been larger. However, if the velocity model used to generate trace 4 was used to locate events, the epicentral error may have been small. It becomes obvious that a reasonable velocity model is important and can easily be justified.

When the velocity model of the RDPM was used to generate synthetic seismograms, the dispersion of the generated Rg waves was not similar to that of the observed seismograms. The Rg phase along trace 2 was not dispersive, while the Rg phase along the bottom trace in Fig. 1 was normally dispersed (the first half period is longer than the second half). In order to generate a similar dispersion of the synthetic Rg waves, it was necessary to modify the velocity model used by Ma (2010), by laying a low-velocity layer with a thickness of 1 km on the top of the crust (Ma and Eaton 2009).

Based on previous studies (e.g., White et al. 2000), a low-velocity layer on the top few kilometers of the crust in the Georgian Bay region indeed exists. To obtain better crustal structure information, the above crust model with the low-velocity top layer formed manually needed to be further quantified; therefore, we have retrieved some regional velocity models using Rg dispersion data. Table 2 provides four small earthquakes (first one was mining induced event) that have occurred in southern Ontario, Canada. The seismograms generated by these events were used to measure the Rg wave dispersion.
Table 2

Source parameters for the events used in this article

No.

Date

Time

Latitude

Longitude

Depth

mN

Region

1

13 March 2005

17:08:14

46.54

−80.98

1.0

3.6

Sudbury (mining induced event)

2

19 October 2008

04:05:07

48.33

−89.48

0.8

2.3

Thunder Bay west (natural event)

3

22 October 2010

09:06:22

44.98

−79.96

1.8

3.0

Georgian Bay north (natural event)

4

24 December 2011

17:22:39

45.51

−79.56

1.5

2.8

Georgian Bay north (natural event)

The focal depth for no. 1 was assigned by the Geological Survey of Canada (GSC); the focal depth for no. 2 was retrieved using the Rg/Sg spectral ratio method (Ma and Motazedian 2011); the focal depths for nos. 3 and 4 were retrieved using the RDPM method (Ma 2010). Other parameters were provided by the GSC

3D structures are present in the studied regions, but the effects on the waveforms are not very strong, so we used a 1D approximation to set up crustal models. We introduce these models retrieved using Rg wave dispersion data in a 1D structure.

The region we studied is a part of North America. The results we obtained may be representative of other areas and may be a model that can be adapted for other similar studies in other continents.

2 Geological background in the Georgian Bay northern region

Figure 2 shows some general information on the surface geological structure (Jamieson et al. 2007). In the figure, the star symbol in the Go Home region shows the approximate location of the GHL swarm. On the north side of the swarm, the pink-colored areas are transported polycyclic rocks. The yellow-colored areas are post-1,500-Ma monocyclic rocks and include reworked material from adjacent units. The light pink-colored areas are parautochthonous polycylic rocks. The green areas are composite arc belt boundary zones, including some reworked Laurentian material.
Fig. 2

Geology map of the northeast Georgian Bay region (after Jamieson et al. 2007). For a summary of the geological and structural features, abbreviations, and references, see Table 2 of Jamieson et al. (2007). The star in the Go Home domain approximately shows the location of the 2007 GHL earthquake swarm

The nature of the faults at different depths may be different. Based on the focal mechanism solution of the 2005 Georgian Bay mN 4.3 earthquake (focal depth ~12 km), the fault is a thrust type (Dineva et al. 2007), whereas the focal mechanism solution of the 2007 GHL swarm (focal depth ~1.5 km) indicates that the fault may be of the strike-slip type (Ma and Eaton 2009). The surface geology and available focal mechanism solutions show that the geological background in the Georgian Bay region is complex. Detailed geological units and structure summary can be found in Jamieson et al. (2007).

3 Group velocity measurement and Rg dispersion data inversion methods

The methods used in this article have already been published. However, for readers’ convenience, 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, converted the velocity type into displacement records. The records were then filtered with a frequency band-pass filter at 0.17 to 1.7 s, which is within the instrument’s response range (0.05~50 s). After the displacement records were obtained and the records containing clear Rg waves in the period range of interest were selected, the group velocities were measured using a technique called multiple filter technique (MFT; Dziewonski et al. 1969) in a computer program (CP) package developed by Herrmann and Ammon (2002, version 3.3). When the Rg dispersion data were available, the inversion procedure developed by Corchete et al. (2007) and the procedure in the CP package were used in the inversion. Inversion issues are not discussed as they are not within the scope of this research.

3.1 MFT method

The MFT is a filtering technique used to retrieve a group velocity dispersion curve from a pre-processed waveform record. In the technique, the time corresponding to the maximum of the envelope of the filtering seismic record, given by Eq. (1), is the group arrival time for the 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 travel time (arrival time − origin time).
$$ {h_n}\left( {{\omega_n},t,r} \right)=\int\limits_{{-\propto}}^{\propto } {\left| {F(\omega )} \right|} {e^{{-\alpha {{{\left( {\frac{{\omega -{\omega_n}}}{{{\omega_n}}}} \right)}}^2}}}}\cos \left[ {k\left( \omega \right)r-\omega t} \right]d\omega $$
(1)
where F(ω) is the Fourier transformation of the record being analyzed, t is the time, r is the epicentral distance, and \( {e^{{-\alpha {{{\left( {\frac{{\omega -{\omega_n}}}{{{\omega_n}}}} \right)}}^2}}}} \) is a Gaussian window function, in which α is a constant and ωn is a center frequency.
The envelope of the filtering Rg wave record can be computed using the equation proposed by (Båth 1974):
$$ {g_n}(t)=\sqrt{{h_n^2\left( {{\omega_n},t} \right)+\overline{h}_n^2\left( {{\omega_n},t} \right)}} $$
(2)
where \( \overline{h}\left( {{\omega_n},t} \right) \) is the Hilbert transform of \( {h_n}\left( {{\omega_n},t} \right). \) For more details, see the paper by Dziewonski et al. (1969) and the CP package menu by Herrmann and Ammon (2002).

3.2 Inversion procedure

Once an Rg wave group velocity curve is measured at a specific seismic station, the curve is used to estimate the shear-wave velocities along a path through which the Rg waves propagate. We first set up an initial crustal model between an earthquake and a seismic station where the Rg waves generated by the earthquake were recorded. We then revise the model based on the fitness between the observed Rg group velocities and the synthetic Rg group velocities generated using the crustal model. The revised model that can generate the best fitness is our solution. The paragraphs below outline the inversion procedure.

We assume that δU(ωk) is the Rg group velocity difference between the observed and synthetic group velocities at frequency, (ωk), that the crustal model has N horizontal layers on the top of a half space and that, in the nth layer, the shear-wave velocity is βn (n is the index for the layer). The difference at frequency ωk (k = 1, … , M) can then be approximated using the following equation:
$$ \delta U\left( {{\omega_k}} \right)=\frac{{\partial U\left( {{\omega_k}} \right)}}{{\partial {\beta_1}}}\delta {\beta_1}+\frac{{\partial U\left( {{\omega_k}} \right)}}{{\partial {\beta_2}}}\delta {\beta_2}+\ldots +\frac{{\partial U\left( {{\omega_k}} \right)}}{{\partial {\beta_N}}}\delta {\beta_N} $$
(3)
where the partial derivatives, \( \frac{{\partial U\left( {{\omega_k}} \right)}}{{\partial {\beta_n}}} \) (n = 1, 2, … , N), can be calculated using the equation proposed by Rodi et al. (1975):
$$ \frac{{\partial U\left( {{\omega_k}} \right)}}{{\partial {\beta_n}}}=\frac{{U\left( {{\omega_k}} \right)}}{{C\left( {{\omega_k}} \right)}}\left( {2-\frac{{U\left( {{\omega_k}} \right)}}{{C\left( {{\omega_k}} \right)}}} \right)\frac{{\partial C\left( {{\omega_k}} \right)}}{{\partial {\beta_n}}}+{\omega_k}\frac{{{U^2}\left( {{\omega_k}} \right)}}{{{C^2}\left( {{\omega_k}} \right)}}\frac{\partial }{{\partial \omega }}\left( {\frac{{\partial C\left( \omega \right)}}{{\partial {\beta_n}}}} \right) $$
(4)
where C(ωk) is the phase velocity.

C(ωk), U(ωk), and \( \frac{{\partial C\left( {{\omega_k}} \right)}}{{\partial {\beta_n}}} \) can be obtained using standard Thomson–Haskell matrix calculations, and \( \frac{\partial }{{\partial \omega }}\left( {\frac{{\partial C\left( \omega \right)}}{{\partial {\beta_n}}}} \right) \) can be obtained by numerically differentiating \( \frac{{\partial C\left( {{\omega_k}} \right)}}{{\partial {\beta_n}}} \) (Rodi et al. 1975).

If we let m = (δβ1, δβ2, … ,δβN), d = (δU (ω1) , δU (ω2), … , δU (ωM)), and Gk,n = \( \frac{{\partial U\left( {{\omega_k}} \right)}}{{\partial {\beta_n}}} \) (k = 1, 2, … , M; n = 1, 2, … , N), we can obtain a linear equation:
$$ d=Gm $$
(5)

After solving this equation, we can obtain a set of corrections to the shear-wave velocities in the N layers (δβ1, δβ2, … ,δβN) and assign the shear-wave velocity in the nth layer, βn_new = βn + δβn, to generate a new model. If this new model cannot be used to generate a satisfactory synthetic group velocity dispersion curve, the above steps are repeated.

4 Velocity models retrieved in the GHL swarm area

A small earthquake swarm occurred near a small lake, called Go Home Lake, near Georgian Bay in 2007. The swarm was studied by Ma and Eaton (2009). A top low-velocity layer was found to be necessary for generating Rg phase with dispersion, and a crustal model was formed by laying a low-velocity layer manually on the top of a previously used crustal model (Ma 2010). Therefore, a more reasonable velocity model is required to further study the swarm and the seismicity in that region. Figure 3 shows the location of the 2007 GHL swarm (indicated by the star labeled 07-swarm) and the locations of other events. In this section, we present the velocity models in this swarm area retrieved using a small but stronger earthquake that occurred in October 2010 (no. 3 in Table 2 and the circle labeled 10-1022 in Fig. 3; the same location with the 2007 swarm) in the swarm source area.
Fig. 3

The distributions of seismic stations (triangles), Rg wave travel paths (dashed lines), and some epicenters (circles) in the region between Georgian Bay and the Ottawa River. The two diamonds show the locations of the cities of Toronto and Ottawa

4.1 Setup of an initial velocity model

The velocity model used by Ma and Eaton (2009) to study the GHL swarm (given in the third panel in Table 1) was too simple for further study of the seismicity of the area. Thus, we used it as a starting point, and the dispersion data measured from the Rg wave trains generated by one of the five largest events in the swarm and the inversion procedure by Corchete et al. (2007) were utilized to obtain several velocity models. We then took the average of these models as one model, which was employed as an initial model for further inversion.

4.2 Velocity models retrieved using Rg wave dispersion generated by an mN 3.0 event

The small but stronger October, 22, 2010 mN 3.0 earthquake (10-1022) in the GHL swarm location was also very shallow. The preliminary focal depth solution retrieved using the RDPM method (Ma 2010) was about 1.8 km. Figure 4 shows the clear Rg waves generated by the 2010 event at four seismic stations (SADO, BUKO, CLWO, and KLBO). This figure indicates that these Rg waves were normally dispersive; hence, the velocities on the whole should increase with depth. In this section, we use these Rg wave dispersion data to estimate the shear-wave velocity models in the swarm region.
Fig. 4

Rg wave records at BUKO, CLWO, KLBO, and SADO stations generated by the October 22, 2010 event

First, we filtered the vertical component records at the four stations using a frequency band-pass filter (0.6 to 6 Hz, equivalent to a period range of 0.17 to 1.7 s). We then measured the Rg wave dispersion data to obtain the group velocity using the MFT (Dziewonski et al. 1969). The group velocity segments used in the inversion are listed in Table 3.
Table 3

The measured Rg group velocities (in kilometers per second) at SADO, BUKO, CLWO, and KLBO stations used for the inversion. These data were the dispersion data from the records in Fig. 4

Period (s)

Group velocity SADO

Group velocity BUKO

Group velocity CLWO

Group velocity KLBO

1.7

3.13825

2.92800

2.94537

3.12662

1.6

3.10113

2.93512

2.94509

3.09923

1.5

3.06820

2.93685

2.93418

3.07791

1.4

3.04355

2.93326

2.91375

3.06369

1.3

3.02381

2.92605

2.88857

3.04587

1.2

3.00960

2.91503

2.85433

3.02658

1.1

2.99294

2.90672

2.82135

3.00443

1.0

2.97610

2.90112

2.79437

2.99660

0.95

2.96915

2.89872

2.78495

2.99910

0.90

2.96315

2.89708

2.78109

2.99819

0.85

2.95709

2.89527

2.78232

2.99205

0.80

2.94987

2.89255

2.78032

2.98066

0.75

2.94017

2.88747

2.77155

2.96314

0.70

2.92690

2.87728

2.75589

2.94249

0.65

2.91078

2.86154

2.73379

2.92508

0.60

2.89162

2.83742

 

2.91299

0.55

2.87321

2.80630

 

2.90506

0.50

2.85924

2.78359

 

2.89777

0.48

2.85446

2.77841

 

2.89111

0.46

2.85088

2.77438

 

2.87722

0.44

2.84653

2.77170

 

2.85920

0.42

2.84085

2.77149

 

2.84541

0.40

2.83542

2.77281

 

2.83734

0.38

 

2.77577

 

2.83277

0.36

   

2.83275

0.34

   

2.83064

0.32

   

2.82339

To select the measured Rg dispersion data for a record, we used the station distance and the dominant Rg group travel time to calculate an Rg group velocity. We then employed the MFT to obtain all available dispersion data along the record, and we selected a group from the measured dispersion data. The velocities in the group were in the order of the Rg group velocity manually estimated from the travel time of the observed Rg group along the record and the station distance.

The output from the MFT program includes the group velocities that come from weak signals. If we use these velocity measurements in our inversion, the solutions are not necessarily good. Therefore, we select the data segments corresponding to strong signals.

After we obtained the group velocities, we performed the inversion using the procedure in the CP package (Herrmann and Ammon 2002). Table 4 shows the initial velocity model and the velocity models retrieved using the dispersion data at BUKO, CLWO, KLBO, and SADO stations. Figure 5 plots all the models given in Table 4. At CLWO and KLBO stations, the Rg waves travel partially across an area covered by water; thus, the velocity models retrieved at these two stations may not be as good as those retrieved from BUKO and SADO stations.
Table 4

The initial velocity model and the new velocity models

No

Initial velocity model

New model (SADO)

New model (BUKO)

New model (CLWO)

New model (KLBO)

Average model

Δh

Vp

Vs

ρ

 

Vp

Vs

ρ

 

Vp

Vs

ρ

 

Vp

Vs

ρ

 

Vp

Vs

ρ

 

Vp

Vs

ρ

1

0.5

5.34

3.08

2.16

 

5.46

3.15

2.59

 

5.31

3.06

2.56

 

5.19

2.99

2.54

 

5.48

3.16

2.60

 

5.36

3.09

2.57

2

0.3

5.84

3.37

2.36

 

5.90

3.40

2.68

 

5.67

3.27

2.63

 

5.59

3.23

2.62

 

5.94

3.43

2.69

 

5.78

3.33

2.66

3

0.3

5.86

3.39

2.37

 

5.92

3.43

2.68

 

5.69

3.28

2.64

 

5.56

3.22

2.61

 

5.92

3.43

2.68

 

5.77

3.34

2.65

4

0.3

5.88

3.40

2.38

 

5.98

3.46

2.70

 

5.70

3.30

2.64

 

5.66

3.28

2.63

 

5.95

3.44

2.69

 

5.82

3.37

2.66

5

0.3

5.91

3.41

2.39

 

6.08

3.50

2.72

 

5.71

3.30

2.64

 

5.85

3.38

2.67

 

6.05

3.49

2.71

 

5.92

3.42

2.69

6

0.3

5.93

3.42

2.39

 

6.21

3.58

2.76

 

5.74

3.31

2.65

 

6.01

3.46

2.70

 

6.16

3.55

2.75

 

6.03

3.48

2.71

7

0.6

5.95

3.43

2.40

 

6.35

3.66

2.80

 

5.79

3.34

2.66

 

6.09

3.51

2.73

 

6.27

3.61

2.78

 

6.12

3.53

2.74

8

0.6

5.99

3.46

2.42

 

6.45

3.73

2.83

 

5.88

3.40

2.68

 

6.06

3.50

2.72

 

6.33

3.66

2.80

 

6.18

3.57

2.76

9

1.3

6.03

3.48

2.44

 

6.45

3.73

2.83

 

5.96

3.44

2.69

 

6.01

3.47

2.70

 

6.33

3.65

2.80

 

6.19

3.57

2.76

From left to right, the first panel is the initial model for the inversion. The second panel is the model retrieved using the Rg dispersion curve at SADO station, the third panel is the model at BUKO station, the fourth panel is the model at CLWO station, and the fifth panel is the model at KLBO. The last panel is the average model of four stations (SADO, BUKO, CLWO, KLBO), listed here for use in Section 5

Fig. 5

Velocity models retrieved at BUKO, CLWO, KLBO, and SADO stations. For each panel, the solid lines show the new model, the dash-dot lines show the GHL model (Ma and Eaton 2009), and the dashed lines show the initial model

4.3 Reasonability of the new retrieved velocity models

A comparison of the similarities between the dispersion curves obtained from the observed and synthetic seismograms is a way to determine if the new models are reasonable. Figure 6 compares the group velocities of the observed and synthetic Rg waves generated at SADO station using different velocity models. It is clear that there was better agreement between the group velocities of the observed seismograms and those generated using the new velocity model retrieved at SADO station (the two bottom panels in Fig. 6). The greater consistency implies that the new velocity model is better than the other two models (initial and previous).
Fig. 6

Dispersion curve comparisons at SADO station. The upper-left panel was obtained using the MFT for the synthetic displacement seismogram generated with the initial crustal model (Table 4, first panel); the bottom-left panel was obtained using the observed record at SADO station (Fig. 4, bottom trace); the upper-right panel was created from the synthetic seismogram generated with the GHL model (Table 1, third panel); the bottom-right panel was generated using the new crustal model (Table 4, second panel). By visual inspection, we see the curves in the two bottom panels are similar

5 Relocating the five largest events in the GHL swarm using different velocity models

When an earthquake is located, with either a conventional locating method or the hypoDD technique (Waldhauser and Ellsworth 2000), a velocity model is necessary for operating the locating programs. If the velocity model is good, the errors in the epicenter are small.

In this section, we compare the locations for the five largest events in the GHL swarm obtained using the revised hypoDD technique (Ma and Eaton 2011) with a previously used velocity model (Ma and Eaton 2009) and the average model in Table 4. The first panel in Table 5 lists the epicenters and the corresponding errors obtained using the velocity model (Ma and Eaton 2009), and the second panel lists the epicenters and the corresponding errors obtained using the new velocity model.
Table 5

Source parameters for the five largest events in the GHL swarm obtained using the revised hypoDD package (Ma and Eaton 2011) and different velocity models

No.

Date

Time

Latitude (deg)

Longitude (deg)

Depth (km)

err/ew (m)

err/ns (m)

err/h (m)

mN

 

1

2006–1209

02:51:21.210

44.9898

−79.8620

1.5

39.9

39.9

57

2.2

GHL crustal model

2

2007–0220

23:09:18.760

44.9878

−79.8654

1.3

39.9

40.0

57

2.0

3

2007–0301

22:20:22.920

44.9894

−79.8615

1.5

40.0

39.9

57

2.2

4

2007–0315

19:42:34.380

44.9887

−79.8681

1.3

42.9

41.4

60

2.3

5

2007–0329

17:35:22.360

44.9873

−79.8671

1.3

41.8

43.8

61

2.0

1

2006–1209

02:51:21.210

44.9899

−79.8620

1.5

37.2

36.9

52

2.2

Rg crustal model (average)

2

2007–0220

23:09:18.760

44.9878

−79.8654

1.3

37.0

36.6

52

2.0

3

2007–0301

22:20:22.920

44.9895

−79.8615

1.5

37.3

37.0

53

2.2

4

2007–0315

19:42:34.360

44.9884

−79.8683

1.3

43.5

42.4

61

2.3

5

2007–0329

17:35:22.360

44.9875

−79.8669

1.3

39.2

40.6

56

2.0

The GHL velocity model (Table 1, the third panel) is used in the first (upper) panel, and a new velocity model (Rg model, the right panel in Table 4) is used in the second (bottom) panel. err/ew is the error in the east–west direction, err/ns is the error in the north–south direction, and err/h is the error in the horizontal direction. On the whole, the numbers (bold) in the err/h column in the second panel are smaller

On the whole, the errors for the solutions obtained using the new velocity model were smaller. The err/h values (bold numbers) in the bottom panel in Table 5 are smaller than those in the upper panel. For the five events in the upper panel, the average horizontal error was 58.4, and in the bottom panel, the average was 54.8, a reduction of 6 %. This indicates that the epicenter locations for these five events were improved when the new velocity model was used.

As the errors in the epicenters are also related to other factors (e.g., the accuracy of the measured P and S phase arrival times) and the hypoDD method is not sensitive to crustal models, the above test only partially shows the improvement to the crustal models. It would be better to use a conventional locating program package for this test; unfortunately, we do not operate any such programs.

6 Error estimate using an artificial crustal structure

Many factors contribute to the errors in the retrieved velocity models. The major factors may be the noise level in the observed waveform records and the error in the epicentral distance to the seismic station at which the Rg waves were used to retrieve the velocity models. In this section, we try to estimate the error in the retrieved velocity model generated by the error in the epicenter.

As the real crustal structures at the GHL region are unknown, we assumed a velocity model (the first panel in Table 6) to be a real structure and the synthetic seismogram generated using the model at a distance of 62.2 km (0.56°—the distance between BUKO station and the 2007 GHL swarm) to be real observations. We then measured the Rg group velocities from the synthetic seismogram at a distance of 60 km (i.e., an epicenter error of 2.2 km) using the MFT program. The first panel of Fig. 7 shows these measured group velocities.
Table 6

The errors in the retrieved velocity model generated by the error in the epicenter

No

Assumed structure

Retrieved model

Absolute error

Relative error

Δh

Vp

Vs

ρ

Vp

Vs

ρ

ΔVp

ΔVs

Δρ

ΔVs/Vs (%)

1

0.5

5.36

3.09

2.57

5.19

3.00

2.54

−0.165

−0.095

−0.033

−3.1

2

0.3

5.89

3.40

2.68

5.69

3.28

2.64

−0.201

−0.116

−0.040

−3.4

3

0.3

5.94

3.43

2.69

5.69

3.28

2.64

−0.251

−0.146

−0.050

−4.2

4

0.3

5.97

3.45

2.70

5.71

3.29

2.64

−0.269

−0.155

−0.054

−4.5

5

0.3

6.05

3.49

2.71

5.78

3.34

2.66

−0.261

−0.151

−0.057

−4.3

6

0.3

6.15

3.55

2.74

5.91

3.41

2.68

−0.240

−0.139

−0.063

−3.9

7

0.6

6.26

3.61

2.78

6.05

3.49

2.71

−0.212

−0.123

−0.063

−3.4

8

0.6

6.32

3.65

2.79

6.14

3.54

2.74

−0.182

−0.105

−0.054

−2.9

9

1.3

6.32

3.65

2.80

6.16

3.56

2.75

−0.156

−0.090

−0.046

−2.5

10

1.3

6.28

3.63

2.78

6.14

3.54

2.74

−0.141

−0.081

−0.042

−2.2

11

2.3

6.27

3.62

2.78

6.15

3.55

2.74

−0.123

−0.071

−0.037

−2.0

12

5.3

6.37

3.68

2.81

6.26

3.62

2.78

−0.105

−0.061

−0.031

−1.7

The first panel is the assumed crustal structure (also the initial model), the second panel is the retrieved model, the third panel is the absolute error (the difference between the retrieved model and the assumed structure), and the fourth panel is the relative error (absolute error/a parameter value of the assumed structure). ΔVp, ΔVs, and Δρ are the absolute error

Fig. 7

The upper panel, the observed group velocities measured from the seismogram generated using the assumed crustal structure at a distance 60 km; the bottom panel, the assumed crustal structure and retrieved velocity model

We then used the measured group velocities and the assumed real structure as the initial model for the inversion. Table 6 lists the retrieved velocity model (the second panel), the differences between the retrieved velocity model and the assumed crustal structure (the absolute errors), and the relative errors.

The second panel of Fig. 7 shows the differences between the assumed structure and the retrieved velocity model. From Table 6, we find that when the epicentral distance had a relative error of 3.5 % (2.2/62.2), the relative errors in the retrieved velocity model were on a similar order, e.g., 3.1 % (0.095/3.09).

7 Velocity models in the region between Georgian Bay and the Ottawa River and in the Thunder Bay area

In the above sections, we retrieved velocity models using the Rg wave dispersion data in the GHL swarm area, estimated the reasonability of the retrieved new models, proved the new models were better by relocating the five largest events in the GHL swarm, and estimated the possible error in the new model caused by the error in the epicentral distance. In this section, we present the results from three other events that occurred on the northern shore of Georgian Bay and in the Sudbury and Thunder Bay areas. To save page space, we only present the major results.

7.1 Velocity models for the northern shore of Georgian Bay

On December 24, 2011, an earthquake with mN 2.8 (Table 2, fourth event) occurred on the northern shore of Georgian Bay. The circle indicated with 11-1224 in Fig. 3 shows the location. This earthquake generated clear Rg and Love (Lg) phases at local distances. Figure 8 displays the three-component records at BUKO and KLBO stations. Both the Rg and Lg phases were normally dispersive (i.e., the Rg waves with longer periods traveled faster than those with shorter periods). The vertical Rg records at these two stations were used to retrieve the velocity models along the two paths between BUKO station and the epicenter and between KLBO station and the epicenter. Table 7 lists the two retrieved velocity models in shallow crust, as well as the initial velocity model used in the inversion.
Fig. 8

Three-component records at BUKO station (~15 km) and KLBO station (~54 km) generated by the December 24, 2011, event. Both Rg and Lg phases were normally dispersed. The Rg wave train along trace BUKO/HHZ was simple, while the Rg wave train along KLBO/HHZ was complex

Table 7

Velocity models

Initial model

Model at KLBO

Model at BUKO

Model at KLBO

Model at KLBO

Δh (km)

Vp (km/s)

Vs (km/s)

ρ (g/cm3)

Δh (km)

Vp (km/s)

Vs (km/s)

ρ (g/cm3)

Δh (km)

Vp (km/s)

Vs (km/s)

ρ (g/cm3)

Δh (km)

Vp (km/s)

Vs (km/s)

ρ (g/cm3)

Δh (km)

Vp (km/s)

Vs (km/s)

ρ (g/cm3)

0.3

5.17

2.98

2.09

0.3

5.41

3.13

2.58

0.3

5.10

2.94

2.52

0.3

5.25

3.03

2.38

0.3

5.41

3.13

2.58

0.3

5.17

2.98

2.09

0.3

5.67

3.27

2.63

0.3

5.69

3.29

2.64

0.3

5.67

3.27

2.63

0.3

5.67

3.27

2.63

0.3

5.49

3.17

2.22

0.3

6.07

3.51

2.72

0.3

5.80

3.35

2.66

0.3

6.07

3.51

2.72

0.3

6.07

3.51

2.72

0.3

5.68

3.28

2.30

0.3

6.00

3.47

2.70

0.3

5.97

3.45

2.69

0.3

6.00

3.47

2.70

0.3

6.00

3.47

2.70

0.3

5.74

3.31

2.32

0.3

5.75

3.32

2.65

0.3

6.00

3.46

2.70

0.3

5.75

3.32

2.65

0.6

6.08

3.51

2.72

0.3

6.23

3.60

2.52

0.3

6.08

3.51

2.72

0.3

6.38

3.69

2.82

0.3

6.08

3.51

2.72

1.0

6.10

3.52

2.73

1.0

6.25

3.61

2.53

1.0

6.10

3.52

2.73

1.0

6.28

3.63

2.78

1.0

6.10

3.52

2.73

1.0

6.27

3.62

2.78

1.0

6.25

3.61

2.53

1.0

6.27

3.62

2.78

1.0

6.26

3.62

2.78

1.0

6.27

3.62

2.78

2.0

6.31

3.65

2.79

2.0

6.25

3.61

2.53

2.0

6.31

3.65

2.79

2.0

6.26

3.62

2.78

2.0

6.31

3.65

2.79

2.0

6.27

3.62

2.78

2.0

6.25

3.61

2.53

2.0

6.27

3.62

2.78

2.0

6.26

3.61

2.78

2.0

6.27

3.62

2.78

    

The model in the first panel is the initial model, the model in the second panel was obtained at KLBO station, the model in the third panel was obtained at BUKO station, the model in the fourth panel was formed by making the top velocity layer in the second panel lower, and the model in the fifth panel was formed by removing the fifth layer in the second panel and the thickness of fifth layer was changed to 0.6 km. These last two models are listed for Section 8.3

The Rg wave segment along the BUKO/HHZ trace was simple. The first half period was longer than the second, showing that the Rg wave was normally dispersed. Accordingly, the crustal structure that the Rg wave passed through should produce Rg waves that are faster with depth. The velocity model in the first panel in Fig. 9 shows this case. On the other hand, the Rg wave segment along the KLBO/HHZ trace was complex; therefore, the crustal structure through which the wave train traveled is also complex. The velocity model in second panel in Fig. 9 shows this situation.
Fig. 9

Comparisons between velocity models (solid lines) obtained using the dispersion data calculated from the waveform records in Fig. 8 and the model (dash-dot lines) previously used (Ma and Eaton 2009), as well as the initial model (dashed lines). The upper panel shows the velocity model that was obtained using the Rg wave dispersion data at BUKO station, and the bottom panel shows the velocity model that was obtained at KLBO

7.2 Velocity models between Georgian Bay and the Ottawa River

In the region between Georgian Bay and the Ottawa River, there are some Portable Observatories for Lithospheric Analysis and Research Investigating Seismicity (POLARIS) seismic stations (Fig. 3). These stations often have high-quality waveform records, and reasonable velocity models can be obtained for that region using the Rg dispersion data from these POLARIS stations.

We searched the Rg wave records and found an event (earthquake or mining event) that occurred on March 13, 2005 (05-0313) in the Sudbury region (Table 2, first event), which had clear Rg wave records. Figure 10 shows records from nine stations in the study area. Using the Rg dispersion data calculated from these nine records and the initial model given in the first panel in Table 4, we retrieved nine velocity models corresponding to the nine paths. As some paths had similar azimuths, we merged the nine models into five models, as listed in Table 8. The common feature of these models was that the low-velocity layers were within about the top 2 km. Except for the model shown by in the bottom panel in Fig. 11, the other four models were similar.
Fig. 10

Waveform records generated by the event that occurred on March 13, 2005, in the Sudbury region. From top to bottom, the records are arranged by station distances—the closest one (RSPO) was about 107 km, and the farthest (PLVO) was about 346 km

Table 8

Velocity models obtained using the dispersion data calculated from the waveform records in Fig. 10

Average at ALGO and PEMO

Average at RSPO and PLVO

Average at BUKO, BANO, and DELO

LINO

KLBO

Δh (km)

Vp (km/s)

Vs (km/s)

ρ (g/cm3)

Δh (km)

Vp (km/s)

Vs (km/s)

ρ (g/cm3)

Δh (km)

Vp (km/s)

Vs (km/s)

ρ (g/cm3)

Δh (km)

Vp (km/s)

Vs (km/s)

ρ (g/cm3)

Δh (km)

Vp (km/s)

Vs (km/s)

ρ (g/cm3)

0.5

5.21

3.01

2.54

0.5

5.29

3.05

2.56

0.5

5.42

3.13

2.58

0.5

5.48

3.16

2.60

0.5

5.21

3.01

2.54

0.3

5.74

3.31

2.65

0.3

5.75

3.32

2.65

0.3

5.89

3.40

2.68

0.3

5.94

3.43

2.69

0.3

5.96

3.44

2.69

0.3

5.81

3.36

2.66

0.3

5.84

3.38

2.67

0.3

5.92

3.43

2.68

0.3

5.93

3.43

2.69

0.3

6.04

3.50

2.71

0.3

5.87

3.39

2.67

0.3

6.00

3.47

2.70

0.3

6.01

3.47

2.70

0.3

5.98

3.46

2.70

0.6

5.98

3.45

2.70

0.3

5.93

3.42

2.69

0.3

6.13

3.54

2.74

0.3

6.11

3.53

2.73

0.3

6.06

3.50

2.72

0.3

6.08

3.50

2.72

0.3

5.97

3.44

2.69

0.3

6.15

3.55

2.74

0.3

6.17

3.56

2.75

0.3

6.13

3.54

2.74

0.6

6.22

3.59

2.77

0.6

6.01

3.46

2.70

0.6

6.10

3.52

2.73

1.2

6.18

3.57

2.75

0.6

6.17

3.56

2.75

0.6

6.31

3.64

2.79

1.9

6.05

3.49

2.72

0.6

6.12

3.53

2.74

1.3

6.22

3.59

2.77

0.6

6.18

3.57

2.75

1.3

6.28

3.62

2.78

1.3

6.03

3.48

2.71

1.3

6.27

3.62

2.78

1.3

6.35

3.67

2.80

1.3

6.17

3.56

2.75

1.3

6.24

3.61

2.77

2.3

6.01

3.47

2.70

3.6

6.46

3.73

2.84

2.3

6.41

3.70

2.82

1.3

6.21

3.59

2.76

2.3

6.20

3.58

2.76

0.0

6.22

3.59

2.77

0.0

6.33

3.66

2.80

0.0

6.34

3.66

2.80

2.3

6.22

3.59

2.77

0.0

6.28

3.63

2.78

            

0.0

6.29

3.64

2.79

    

The first panel shows the average of the models obtained at ALGO and PEMO stations. The models in the second and third panels are also averages. The last two panels show the models from LINO and KLBO stations, respectively. Some adjacent layers that have very close parameter values were merged

Fig. 11

Comparisons between velocity models (solid lines) obtained using the dispersion data calculated from the waveform records in Fig. 10 and the model (dash-dot lines) previously used (Ma and Eaton 2009), as well as the initial model (dashed lines). The first (top) panel shows the average of the models obtained at ALGO and PEMO stations. The models (solid lines) in the second and third panels are also averages. The fourth and fifth panels show the models from LINO and KLBO stations, respectively

The closest epicenter distance (at RSPO station) in Fig. 3 was about 107 km; thus, the five velocity models were approximations along the paths between the epicenter of the 05-0313 event and the stations. In other words, if we cut a segment from a path and estimate a velocity model for that segment, the model for this segment may be biased and different from the model for the whole path.

7.3 Velocity model in the 2008 Thunder Bay earthquake swarm area

In October and November 2008, an earthquake swarm occurred near the city of Thunder Bay, Ontario (Fig. 12). There was not a good local seismic network coverage to determine the epicenter of this swarm; however, the swarm generated clear Rg waves.
Fig. 12

The locations of the 2008 Thunder Bay earthquake swarm (circles), TBO station (triangle), and the city of Thunder Bay (diamond)

Figure 13 shows the Rg wave train generated by the largest event in the swarm, which was recorded at TBO station. We used the maximum power spectral ratio method to determine the focal depths for all 13 events in the swarm (Ma and Motazedian 2011). The average focal depth was about 1.5 km, meaning that this swarm was shallow and that the events generated clear Rg wave trains at high frequencies even though they were small. From Fig. 13, we can see that the dispersion was normal. This implies that the trend of the shear-wave velocity should be faster with increased depth.
Fig. 13

Vertical waveform record at TBO station (~36 km) generated by the largest event (October 19, 2008) in the 2008 Thunder Bay swarm

Good epicentral distances were required in the method that we used to estimate crustal structure. Unfortunately, since the station coverage was not good, the station distances were not accurate for this event. The epicentral distance at TBO station was about 36 km, calculated based on the epicenter provided by the Geological Survey of Canada (GSC). As GSC used a simple velocity model (Fig. 14, dash-dot vertical line; Table 1, the first panel) to locate events in eastern Canada, the low-velocity layers were not considered. With the same station distance, the differential time between the Sg and Pg phases would be shorter than when the low-velocity layers are considered.
Fig. 14

Comparisons between velocity models (solid lines) obtained using the dispersion data calculated from the waveform record in Fig. 13 and the model (dash-dot lines) used by the GSC, as well as the initial model (dashed lines)

Given a specific differential time between the Sg and Pg phases, the determined station distance is shorter when these two phases travel in low-velocity layers than in high-velocity layers. To correct the station distance, we first changed the distance to 32.37 km from 36 km, measured the group velocities at TBO station, and then performed the velocity inversion using the Rg wave dispersion data and the initial model in Table 7. Figure 14 shows the velocity model obtained at TBO station. This figure also clearly illustrates that there are low-velocity layers in the swarm region. The values of the model parameters are listed in Table 9.
Table 9

The velocity model parameters corresponding to Fig. 14

New model (TBO)

Δh (km)

Vp (km/s)

Vs (km/s)

ρ (g/cm3)

0.3

4.68

2.70

2.43

0.3

5.31

3.06

2.56

0.3

5.35

3.09

2.57

0.3

5.47

3.16

2.59

0.3

5.49

3.17

2.60

0.3

5.92

3.42

2.68

1.0

5.90

3.41

2.68

1.0

5.94

3.43

2.69

2.0

5.98

3.45

2.70

2.0

6.02

3.48

2.71

2.0

6.33

3.65

2.80

2.0

6.38

3.68

2.82

2.0

6.44

3.72

2.83

8 Further confirmation of low-velocity layers

In southern Ontario, low-velocity layers in the top few kilometers do indeed exist. We can confirm this phenomenon by analyzing the recorded Lg phase and by synthetic seismograms.

8.1 Analyzing the observed Lg phase

An Rg phase can be generated along the surface of a half space (Stein and Wysession 2003), while an Lg phase (here Lg refers to a Love wave traveling in granite) requires a velocity structure that varies with depth. An Lg wave cannot exist along the surface of a homogeneous elastic half space. If we see an Lg phase along a waveform record, a velocity layer must exist along the path through which the Lg phase propagates, i.e., we can use the existence of an Lg wave to confirm if a low-velocity layer exists in the region of interest.

The simplest geometry in which an Lg wave can be generated is a material layer with thickness h, in which the shear-wave velocity is β1, underlain by a half space of material with a higher shear-wave velocity, β2, The dispersion relation can be expressed as a function of any two of the three related parameters: apparent velocity, cx; circular frequency, ω; and horizontal wave number, kx, i.e., ω = cxkx.
$$ \tan \left[ {\left( {{{{\omega h}} \left/ {{{c_x}}} \right.}} \right){{{\left( {{{{c_x^2}} \left/ {{\beta_1^2-1}} \right.}} \right)}}^{1/2 }}} \right]=\frac{{{\mu_2}{{{\left( {{{{1-c_x^2}} \left/ {{\beta_2^2}} \right.}} \right)}}^{1/2 }}}}{{{\mu_1}{{{\left( {{{{c_x^2}} \left/ {{\beta_1^2-1}} \right.}} \right)}}^{1/2 }}}} $$
(6)
where μ1 and μ2 are the shear modulus in the layer and the half space, respectively.

The tangent function is defined for real values; therefore, the square roots must be real. If we take β2 = 3.43 km/s (Table 4, the third layer in the third panel), we can make the apparent velocity be bounded by β1 < cx < β2.

As mentioned in Section 4.2, we have retrieved crustal models at four seismic stations in the GHL region. We tested the models using Eq. (6). As the four models are similar, we only tested one of them.

Figure 15 shows the three-component seismograms generated by the GHL October 2010 mN 3.0 earthquake recorded at SADO station. We found the Lg phase indeed exists, meaning that a top low-velocity layer in the GHL region must exist. From Fig. 15, the observed apparent velocity (cx) was 3.34 km/s. From Fig. 16, the observed dominant circular frequency (ω) was 7.36 rad/s. In the following paragraphs, we try to estimate the layer thickness.
Fig. 15

Three-component seismograms recorded at SADO station generated by the GHL October 2010, mN 3.0 event. The upper trace is the tangential component, and the middle and bottom traces are the radial and vertical components, respectively. The amplitudes are scaled by the maximum along each trace. The station distance is ~62 km, and the apparent velocity of Lg phase is 3.34 km/s

Fig. 16

The Lg segment and the corresponding power spectra. The dominant frequency of Lg phase is 1.17 Hz (7.36 rad/s)

To be able to use Eq. (6), we may simplify the crustal model in the second panel of Table 4. We take the velocity β1 = 3.15 km/s in the top layer, treat the other layers as a half space, and take the velocity of β2 = 3.43 km/s (in the third layer) in the half space. With the relations, \( {\mu_1}={\rho_1}\beta_1^2 \) and \( {\mu_2}={\rho_2}\beta_2^2, \) Eq. (6) becomes:
$$ \tan \left( {\frac{{\omega h}}{3.34}\times {{{\left( {{{{{3.34^2}}} \left/ {{{3.15^2}-1}} \right.}} \right)}}^{{{1 \left/ {2} \right.}}}}} \right)=\frac{{{3.43^2}\times 2.68\times {{{\left( {{{{1-{3.34^2}}} \left/ {{{3.43^2}}} \right.}} \right)}}^{{{1 \left/ {2} \right.}}}}}}{{{3.15^2}\times 2.59\times {{{\left( {{{{{3.34^2}}} \left/ {{{3.15^2}-1}} \right.}} \right)}}^{{{1 \left/ {2} \right.}}}}}} $$
(7)
The h value that satisfies Eq. (7) is the solution. We obtained a solution 0.86 km for h.

As the issue of the velocity models is complex, the discrepancy between the results obtained using different methods are unavoidable. The above procedure has been used to confirm the existence of a top low-velocity layer, and the crustal model used in this test was further simplified. Therefore, the h value may be used as a reference showing the existence of the top low-velocity layer.

8.2 Synthetic seismograms to confirm top low-velocity layers

In this section, we further confirm the existence of low-velocity layers on the top of the crust in the GHL region, by presenting synthetic seismograms for three components generated using two types of crustal models—one with low-velocity layers and the other without.

The top three traces in Fig. 17 were generated using the crustal model in the second panel of Table 1. The thickness of the top layer is 8 km, which is a half space for the high-frequency Lg phase (period <2 s); therefore, the Lg phase in the layer was not generated. The second phase (indicated with S2 in the figure) is a reflected phase, possibly a depth phase. The Rg phase can be generated in the top layer, but not dispersed.
Fig. 17

Comparison between synthetic seismograms generated using crustal models with and without top low-velocity layers. The upper three traces were generated using the crustal model in the second panel of Table 1. The thickness of the top layer in the model is 8 km. For high frequencies (period <2 s), this thickness is a half space; therefore, the Lg phase cannot be generated. The second phase along the top trace indicated with S2 is a reflected phase. The middle three traces were generated using the crustal model in the second panel of Table 4. The model has a top low-velocity layer with a thickness of about 0.5 km. Along the tangential component TAN_New, the Lg phase was generated. Along the radial (RAD_New) and vertical (U_D_New) components, a normally dispersed Rg phase was generated. In the wave train, the waves with low frequencies arrive earlier than those with higher frequencies. The bottom three traces were generated by the third event in Table 2, recorded at SADO station. Along the tangential (SADO/BHt) component, the Lg phase was well developed. Along the radial (SADO/BHr) and vertical (SADO/BHZ) components, the normally dispersed Rg was also well developed

The middle 3 traces in Fig. 17 were generated using the crustal model in the second panel of Table 4. This time the Lg phase was generated along the tangential component, i.e., trace TAN_New. The Rg phases generated along the radial (RAD_New) and vertical (U_D_New) components were normally dispersed because velocity is faster with increased depth.

The bottom three traces of Fig. 17 were generated by the third event in Table 2 and recorded at SADO station. Along the tangential component of SADO/BHt, the Lg phase was normally dispersed. Along the radial (SADO/BHr) and vertical (SADO/BHZ) components, the Rg phases were obviously dispersed. The observed and synthetic seismograms show that, in the region we studied, the low-velocity layers at the top of the crust indeed exist.

The similarity of the Rg wave shapes between the observed and synthetic seismograms can also be used as a factor to judge the quality of the retrieved crustal models. The focal mechanism we used to generate synthetics is a thrust type, which dominates the Western Quebec Seismic Zone (e.g., Ma and Motazedian 2012). The Rg wave shapes along trace U_D_New and trace SADO/BHZ in Fig. 17 were very similar. This also shows that the retrieved crustal model does not have serious problems.

On the other hand, the Rg wave shapes along radial traces RAD_New and SADO/BHr, as well as along tangential traces TAN_New and SADO/BHt, were not similar (although the frequency contents seem similar). This implies that the focal mechanism used to generate synthetics is possibly not correct for the October 2010 event. Further studies for the focal mechanism may be performed in the future.

8.3 Synthetic seismograms to show a possible low-velocity layer

We have confirmed that top low-velocity layers exist in the Georgian Bay region by showing the recorded and synthetic Lg phases. These validations may not be able to show that the low-velocity layer at about 1.5 km obtained at KLBO station in Section 7.1 (Fig. 9) really exists. In order to show that the low-velocity layer may exist, we generated synthetic seismograms of the vertical component at KLBO station using three crustal models. Figure 18 shows these synthetics and the observed record at KLBO station. The synthetics were generated using focal depths of 0.9, 1.1, 1.3, and 1.5 km. The other used parameters were identical, except the crustal models.
Fig. 18

Synthetic seismograms generated using three crustal models in Table 7. The upper four traces (U_D_1 0.9, U_D_2 1.1, U_D_3 1.3, U_D_4 1.5; the number 0.9 shows the focal depth used to generate the trace) were generated using the model in the fourth panel of Table 7, the middle four traces (U_D_5 0.9, U_D_6 1.1, U_D_7 1.3, U_D_8 1.5) were generated using the model in the second panel of Table 7, and the bottom four traces (U_D_9 0.9, U_D_10 1.1, U_D_11 1.3, U_D_12 1.5) were generated using the model in the right panel of Table 7. Trace KLBO/HHZ is the observed record at KLBO station

In the Rg phase along the observed trace, the coda first attenuated sharply and then lasted for about 2 s with similar amplitudes. Trace U_D_7 1.3 was generated with the model in the second panel in Table 7. The coda along the trace also first attenuated sharply, but lasted for only about 1 s.

Trace U_D_11 1.3 was generated with the model (the low-velocity layer at about 1.5 km was removed) in the fifth panel of Table 7. The coda along this trace also lasted about 1 s, but the amplitudes attenuated gradually. This behavior was not similar to that of the observed Rg coda.

Trace U_D_3 1.3 was generated with the model (the low-velocity layer at the top was made lower manually) in the fourth panel in Table 7. The coda along this trace lasted approximately as long as that the observed coda did, and its amplitudes attenuated first sharply and then gradually.

The above analysis shows that the low-velocity layer at about 1.5 km in the model retrieved at KLBO station possibly exists, as the similarity of the synthetic Rg coda to that of the observed coda decreased when the low-velocity layer at about 1.5 km was removed (see the Rg wave trains along traces U_D_11 1.3 and KLBO/HHZ). On the other hand, the model retrieved at KLBO station still has room for improvement, as the similarity between the coda along trace U_D_3 1.3 and that along trace KLBO/HHB increased. The inversion has been performed several times, but no better solutions have been obtained.

9 Conclusions

The dispersion of high-frequency (>0.5 Hz) Rg waves is sensitive to shallow crustal structures. In southern Ontario, clear Rg phases at high frequencies have often been observed. We used the Rg dispersion data observed from the waveform records generated by the events that occurred in the 2007 GHL swarm area, in the Sudbury region in 2005, and in the 2008 Thunder Bay swarm to estimate the shallow crustal structures in the region between Georgian Bay and the Ottawa River and the western coast of Thunder Bay. The common feature of the retrieved crust models is that there is a top low-velocity layer with a thickness of around 0.5 km, and the seismic velocities change mainly within the top 2 km, in which small earthquakes often occur.

A high-frequency Lg phase was also observed from the waveform records generated by the events mentioned above. If we see an Lg phase along a waveform record, a low-velocity layer must exist along the path through which the Lg phase propagates, as this phase requires a low-velocity structure to be generated. The existence of the Lg wave is a confirmation of the low-velocity layers in the regions of interest.

Many factors can generate errors in the retrieved velocity model. If the data quality is high, the key factor in generating the error in the model is the error in the epicentral distance. Based on the test in Section 6, if the data quality is good, the relative error in the retrieved model is on a similar order as that of the epicentral distance.

Group velocities in a single-event single-station method are the ratios between the station distance and the travel time of Rg wave groups. The error in station distance can generate an error in the measured group velocities. The error in the measured Rg wave group arrival times can also generate an error in the group velocities. In our experience, the selection of a waveform segment that contains a clear Rg wave train and the proper selection of the value of the MFT filter parameter, α, can partially reduce the errors in the measured group velocities.

The shallow natural events in Table 2 seem to have occurred beneath the top low-velocity layer. This finding needs further study.

Notes

Acknowledgments

This research was supported by the Natural Sciences and Engineering Research Council of Canada under the Strategic Research Networks and Discovery Grant programs. We gratefully acknowledge the constructive comments and suggestions from the Editor-in-Chief, T. Dahm, and reviewers. The seismograms and earthquake catalogs used in this article were retrieved from the Natural Resources Canada official website. The waveform records were processed using SAC2000, redseed and geotool programs.

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Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  • Shutian Ma
    • 1
  • Dariush Motazedian
    • 1
  • Victor Corchete
    • 2
  1. 1.Department of Earth SciencesCarleton UniversityOttawaCanada
  2. 2.Department of Applied PhysicsUniversity of AlmeriaAlmeriaSpain

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