**2. Synthetic regional depth phases** *sPg***,** *sPmP,* **and** *sPn*

To generate synthetics we need a crustal model, earthquake location, focal mechanism, and focal depth. To generate synthetics for smaller earthquakes, the source time function is not important. We use a triangle as the source time function. Because the focal mechanism does not determine the arrival times of the seismic phases—the crustal structures determine the arrival times—the crustal model is a key factor in generating synthetic regional depth phases. Western Quebec is one of the more active seismic zones in eastern North America and the crustal structures are relatively well known. Mereu *et al*. (1986) "conducted a major long-range seismic refraction and wide-angle reflection experiment across the Grenville province of Canadian Shield," and obtained some crustal models. After studying these crustal models and modifying them slightly, we obtained one crustal model and put it in our program package as the default crustal model (Fig. 2; model 1 in Table 1). Because the focal mechanisms in western Quebec are predominantly thrust type (e.g., Adams *et al*., 1989; Bent and Perry, 1999; Ma and Eaton, 2007), we used a thrust type focal mechanism as the default (Fig. 2, bottom left).

Because regional depth phases are easier to discern on displacement records than on velocity records, we used displacement records in the RDPM. All the synthetic and observed waveforms in this chapter are the vertical component.

Fig. 2. The default crustal model and default focal mechanism (left; right focal mechanism is for comparison) in the RDPM method. Except if specified, all synthetic waveforms were generated with the default crustal model and default focal mechanism.


Table 1. The crustal models. Model 1 is the default in the RDPM program package. Crustal models 2, 3, 4, and 5 were formed by deleting the last layer successively from model 1. *h* = layer thickness (km); *Vp* = velocity of the *P*-wave (km/sec); *Vs* = velocity of the *S*-wave (km/sec); *ρ* = crustal density (g/cm3).

#### **2.1 Synthetics generated at different distances with a fixed focal depth**

To observe features of the regional depth phases that are displayed when the distance changes, we generated synthetic waveforms at distances ranging from 0.3º to 4.8° and plotted them (Figs. 3, 4, and 5). Fig. 3 shows that the *sPg* phase is well developed at distances ranging from 0.7º to 0.9º (trace 070 to 090). The distance range within which *sPg* is well

Fig. 3. Synthetic waveforms generated with depth 12 km, azimuth 236º, at distances 0.3º to 2.0º (also used to generate Figs. 4, 5, 6, 7, and 8). Trace number = distance in degrees 100. Trace 030 was generated at distance 0.3º. Traces are aligned on the first phase. On trace 070 phases *Pg* and *sPg* and on trace 140 phases *PmP* and *sPmP* are labeled.

Model 3 (4 layers)

8 6.25 3.61 2.53 9 6.50 3.75 2.63 7 6.60 3.81 2.67 0 6.70 3.87 2.71

Table 1. The crustal models. Model 1 is the default in the RDPM program package. Crustal models 2, 3, 4, and 5 were formed by deleting the last layer successively from model 1. *h* = layer thickness (km); *Vp* = velocity of the *P*-wave (km/sec); *Vs* = velocity of the *S*-wave

To observe features of the regional depth phases that are displayed when the distance changes, we generated synthetic waveforms at distances ranging from 0.3º to 4.8° and plotted them (Figs. 3, 4, and 5). Fig. 3 shows that the *sPg* phase is well developed at distances ranging from 0.7º to 0.9º (trace 070 to 090). The distance range within which *sPg* is well

Fig. 3. Synthetic waveforms generated with depth 12 km, azimuth 236º, at distances 0.3º to 2.0º (also used to generate Figs. 4, 5, 6, 7, and 8). Trace number = distance in degrees 100. Trace 030 was generated at distance 0.3º. Traces are aligned on the first phase. On trace 070

phases *Pg* and *sPg* and on trace 140 phases *PmP* and *sPmP* are labeled.

**2.1 Synthetics generated at different distances with a fixed focal depth** 

Model 4 (3 layers)

8 6.25 3.61 2.53 9 6.50 3.75 2.63 0 6.60 3.81 2.67

Model 5 (2 layers)

8 6.25 3.61 2.53 0 6.50 3.75 2.63

Model 1 (6 layers) h Vp Vs ρ

8 6.25 3.61 2.53 9 6.50 3.75 2.63 7 6.60 3.81 2.67 6 6.70 3.87 2.71 5 7.10 4.10 2.87 0 8.00 4.62 3.23

Model 2 (5 layers)

8 6.25 3.61 2.53 9 6.50 3.75 2.63 7 6.60 3.81 2.67 6 6.70 3.87 2.71 0 7.10 4.10 2.87

(km/sec); *ρ* = crustal density (g/cm3).

developed changes with focal depth: the range shifts farther as the focal depth increases. The time difference *sPg*–*Pg* changes very slightly with distance. For the distance range of about 1.0º to 1.7º (trace 100 to 170), *Pg*, *PmP*, *sPg,* and *sPmP* co-exist. Fig. 4 shows that *Pg* disappears at 1.6º (or *Pg* and *PmP* merge there; trace 160); *sPg* disappears at 1.9º (trace 190). For the distance window of about 1.8º to 2.8º (trace 180 to 280), the waveforms are quite simple. The first phase is *Pn* (generally weak); the second phase is *PmP* and the third phase is *sPmP*. Fig. 5 shows that *sPn* stands out at about 3.0º (trace 300). The time difference *sPn*– *Pn* is independent of distance. For distances larger than 2.9º (trace 290), waveforms become complex. At about 4.1º (trace 410) there is another distance window in which waveforms are relatively simple.

Fig. 4. Synthetic waveforms generated with depth 12 km, azimuth 236º, at distances 1.0° to 3.0°. Trace 100 was generated at distance 1.0°. Traces are aligned on *Pg* or *PmP*. The distance window in which waveforms are simple is from about 200 to 300 km (trace 180 to 280). The *Pn* phase is weak. Traces 100 to 200 correspond to the early parts of those traces with the same labels in Fig. 3, but with amplitude enlarged and timescale expanded.

Fig. 5. Synthetic waveforms generated with depth 12 km, azimuth 236º, at distances 2.0º to 4.8º. Top trace 200 was generated at distance 2.0°. Traces are aligned on *Pn*. The *sPn* phase stands out at 3.0º (trace 300), but is buried at closer distances. After 2.8º (trace 280) waveforms become complex. Around trace 410 (4.1°) waveforms are simple again.

#### **2.2 Synthetics generated with a range of focal depths at fixed distances**

To observe how regional depth phases change with focal depth, we generated synthetic *sPg*, *sPmP,* and *sPn* with a range of depths at fixed distances 0.9º, 2.1º, and 4.1º. Fig. 6 shows that the time difference *sPg*–*Pg* becomes progressively larger with focal depth. The position of *sPg* shifts by about half a cycle when the depth changes by 1 km. This means that the time difference *sPg*–*Pg* is very sensitive to focal depth. At distance 0.9°, *sPmP* is not well developed. Fig. 7 shows that the time difference *sPmP*–*PmP* becomes larger as depth increases. The position of *sPmP* also shifts by about half a cycle when focal depth changes by 1 km. The *Pn* phase is also a depth phase, but it is not as sensitive as *sPmP* to focal depth. For example, on trace 210, the time difference between *Pn* and *PmP* is about half that

Fig. 5. Synthetic waveforms generated with depth 12 km, azimuth 236º, at distances 2.0º to 4.8º. Top trace 200 was generated at distance 2.0°. Traces are aligned on *Pn*. The *sPn* phase

To observe how regional depth phases change with focal depth, we generated synthetic *sPg*, *sPmP,* and *sPn* with a range of depths at fixed distances 0.9º, 2.1º, and 4.1º. Fig. 6 shows that the time difference *sPg*–*Pg* becomes progressively larger with focal depth. The position of *sPg* shifts by about half a cycle when the depth changes by 1 km. This means that the time difference *sPg*–*Pg* is very sensitive to focal depth. At distance 0.9°, *sPmP* is not well developed. Fig. 7 shows that the time difference *sPmP*–*PmP* becomes larger as depth increases. The position of *sPmP* also shifts by about half a cycle when focal depth changes by 1 km. The *Pn* phase is also a depth phase, but it is not as sensitive as *sPmP* to focal depth. For example, on trace 210, the time difference between *Pn* and *PmP* is about half that

stands out at 3.0º (trace 300), but is buried at closer distances. After 2.8º (trace 280) waveforms become complex. Around trace 410 (4.1°) waveforms are simple again.

**2.2 Synthetics generated with a range of focal depths at fixed distances** 

between *sPmP* and *PmP*. The time difference *Pn*–*PmP* changes obviously with distance (Fig. 5). These features of *Pn* can be used to identify *sPmP* in its distance window (200 to 300 km). Fig. 8 shows how the time difference *sPn*–*Pn* changes with focal depth. Because the *sPn* phase is stronger than *Pn*, it is possible that some of the observed "*Pn*" phase beyond 300 km is *sPn*.

Fig. 6. Synthetic waveforms generated at distance 0.9º with depths from 1 to 33 km. Trace number = depth in km 10. Trace 010 was generated with depth 1 km at distance 0.9°.

Fig. 7. Synthetic waveforms generated at distance 2.1º with depths from 1 to 33 km. Trace 010 was generated with depth 1 km at distance 2.1º. On trace 070 phases *PmP* and *sPmP* are labeled. The *Pn* phase is weak, and is labeled on traces 120, 220, and 330.

Fig. 7. Synthetic waveforms generated at distance 2.1º with depths from 1 to 33 km. Trace 010 was generated with depth 1 km at distance 2.1º. On trace 070 phases *PmP* and *sPmP* are

labeled. The *Pn* phase is weak, and is labeled on traces 120, 220, and 330.


Fig. 8. Synthetic waveforms generated with depths of 1 to 33 km at distance 4.1°. Trace 010 was generated with depth 1 km at distance 4.1º. The *Pn* phase is weak; *sPn* is stronger than *Pn*. From trace 260 (26 km) *sPn* merges with other phases. Traces are aligned on the *Pn* phase.
