**2.3 Synthetics generated with different focal mechanisms**

To generate synthetics we need a focal mechanism. Generally, no focal mechanism solutions are available for small earthquakes. To solve this problem, we used a default focal mechanism for all earthquakes to generate synthetics to measure focal depths. Because focal mechanisms do not determine the arrival times of seismic phases, we used a default focal mechanism to generate synthetic phases for their arrival times. Because we do not use waveform shapes to estimate focal depth, we do not have to use a strike–slip focal mechanism to generate synthetics for earthquakes with strike–slip focal mechanisms.

### **3. Demonstration for the assumed** *sPmP* **and** *PmP* **phases**

In eastern North America many *P* portions of waveform records are similar to trace CRLO/EHZ in Fig. 9. On this trace, the first weak phase is *Pn*. We assumed that the second phase is *PmP* and the third phase (the largest) is *sPmP*. To demonstrate that the assumptions are correct, we prepared Fig. 9 using explosive and earthquake source models. On trace EXPL/140, no strong assumed depth phase appears at the position corresponding to that on trace CRLO/140 which was generated with the same depth and crustal model. The reason is that an explosive source does not directly generate *S*-waves. According to the definition of *sPmP*, the phase should arrive at a station progressively later as the focal depth increase because the total path length becomes longer. The third phase on traces CRLO/130, 135, 140, 145, and 150 arrives progressively later as the depth increases. This feature and the absence of the strong phase on EXPL/140 indicate that the "assumed *sPmP*" is *sPmP*.

Fig. 9. Synthetic waveforms generated with an earthquake source model (Fig. 2, bottom-left) (traces CRLO/130 to 150), an explosive source model (traces EXPL/140 to 150), and the *P*  portion recorded at station CRLO generated by a small earthquake (1995/09/12, *m*N 3.7, west Quebec; trace CRLO/EHZ). CRLO/130 was generated with depth 13 km at distance 2.10º and azimuth 283°. EXPL/140 was generated with depths 14.0 km. Trace CRLO/EHZ is the *P* portion generated by the small earthquake. The modeled focal depth for this earthquake is 14.5 km.

To demonstrate that the phase has experienced reflection from the Moho, we prepared Fig. 10 by using different crustal models and depths. In group 2 (2/130, 2/140, 2/150), a weak *sPmP* appears. This might be because the interface at depth 8 km is above the sources. When we put the sources at the same depths in a half space, the weak *sPmP* disappears. In groups 3 (3/130, 3/140, 3/150), 4 (4/130, 4/140, 4/150), 5 (5/130, 5/140, 5/150), and 6 (6/130, 6/140, 6/150), the assumed *PmP* and *sPmP* appear and are clear. The time differences *sPmP*–*PmP* are almost the same on traces 3/130, 4/130, 5/130, and 6/130, etc. "*PmP*" and "*sPmP*" from different interfaces can pile up at similar positions. Fig. 10 demonstrates that the assumed depth phase *sPmP* experienced reflection at the Moho, because its shapes, for example, on traces 3/150, 4/150, 5/150, and 6/150, are different.

In eastern North America many *P* portions of waveform records are similar to trace CRLO/EHZ in Fig. 9. On this trace, the first weak phase is *Pn*. We assumed that the second phase is *PmP* and the third phase (the largest) is *sPmP*. To demonstrate that the assumptions are correct, we prepared Fig. 9 using explosive and earthquake source models. On trace EXPL/140, no strong assumed depth phase appears at the position corresponding to that on trace CRLO/140 which was generated with the same depth and crustal model. The reason is that an explosive source does not directly generate *S*-waves. According to the definition of *sPmP*, the phase should arrive at a station progressively later as the focal depth increase because the total path length becomes longer. The third phase on traces CRLO/130, 135, 140, 145, and 150 arrives progressively later as the depth increases. This feature and the absence

Fig. 9. Synthetic waveforms generated with an earthquake source model (Fig. 2, bottom-left) (traces CRLO/130 to 150), an explosive source model (traces EXPL/140 to 150), and the *P*  portion recorded at station CRLO generated by a small earthquake (1995/09/12, *m*N 3.7, west Quebec; trace CRLO/EHZ). CRLO/130 was generated with depth 13 km at distance 2.10º and azimuth 283°. EXPL/140 was generated with depths 14.0 km. Trace CRLO/EHZ is

To demonstrate that the phase has experienced reflection from the Moho, we prepared Fig. 10 by using different crustal models and depths. In group 2 (2/130, 2/140, 2/150), a weak *sPmP* appears. This might be because the interface at depth 8 km is above the sources. When we put the sources at the same depths in a half space, the weak *sPmP* disappears. In groups 3 (3/130, 3/140, 3/150), 4 (4/130, 4/140, 4/150), 5 (5/130, 5/140, 5/150), and 6 (6/130, 6/140, 6/150), the assumed *PmP* and *sPmP* appear and are clear. The time differences *sPmP*–*PmP* are almost the same on traces 3/130, 4/130, 5/130, and 6/130, etc. "*PmP*" and "*sPmP*" from different interfaces can pile up at similar positions. Fig. 10 demonstrates that the assumed depth phase *sPmP* experienced reflection at the Moho, because its shapes, for example, on traces 3/150, 4/150, 5/150, and 6/150, are different.

the *P* portion generated by the small earthquake. The modeled focal depth for this

earthquake is 14.5 km.

**3. Demonstration for the assumed** *sPmP* **and** *PmP* **phases** 

of the strong phase on EXPL/140 indicate that the "assumed *sPmP*" is *sPmP*.

The waveform contents of the *sPmP* on trace 6/150, for example, contain contributions from all interfaces beneath the source.

From the definition of *PmP* we know that as focal depth increases, *PmP* should arrive earlier, because the total travel path becomes shorter. Generally, we use the phase recorded in the distance window of about 200 to 300 km. At these distances, the feature that *PmP* arrives earlier as focal depth increases is not easy to examine without *Pg* as the reference phase. So we traced the assumed *PmP* to close distances where *Pg* exists. Fig. 11 is the synthetic waveforms generated with an explosive source model. Trace 210 in Fig. 11 is similar to trace EXPL/140 in Fig. 9, which was generated with depth 14 km at distance 2.10°. Let us trace the assumed *PmP* in Fig. 11 from trace 080 to trace 150 where both *Pg* and the assumed *PmP* exist. At such a close distance, the first phase is *Pg*. We then generated synthetics at fixed distance 0.8° with depths of 1.0 to 35.0 km (Moho depth). Fig. 12 shows that the two phases become closer as depth increases, and they merge at the Moho. This test shows that the assumed *PmP* is *PmP*. Based on these tests, the assumed phases *PmP* and *sPmP* on trace CRLO/EHZ are *PmP* and *sPmP*, because these two phases have the same features as those on traces CRLO/130 to CRLO/150.

Fig. 10. Synthetic waveforms generated with the five crustal models listed in Table 1 at distance 2.10° and with depths 13, 14, and 15 km. Trace Group 2 (2/130, 2/140, 2/150) was generated with a two-layer crustal model (Model 5 in Table 1); Group 3 with a three-layer crustal model (Model 4 in Table 1); Group 4 with a four-layer crustal model (Model 3 in Table 1); Group 5 with a five-layer crustal model (Model 2 in Table 1); Group 6 with a sixlayer crustal model (Model 1 in Table 1).

Fig. 11. Synthetic waveforms generated with depth 13 km, an explosive source model, and crustal model 1 in Table 1, at distances of 0.5° to 3.0°. Trace 210 was generated at 2.10°. The *Pg* phase disappears at about 1.5° (trace 150). The *PmP* phase is clear from 1.7° to 2.8° (traces 170 to 280).

Fig. 12. Synthetic waveforms generated at distance 0.8° with depths of 1.0 to 34.9 km, an explosive source model, and crustal model 1 in Table 1. Trace 130 in this figure is the same as trace 080 in Fig. 11. Because the total path length becomes shorter with focal depth, the *PmP* phase arrives progressively earlier with depth.

Fig. 11. Synthetic waveforms generated with depth 13 km, an explosive source model, and crustal model 1 in Table 1, at distances of 0.5° to 3.0°. Trace 210 was generated at 2.10°. The *Pg* phase disappears at about 1.5° (trace 150). The *PmP* phase is clear from 1.7° to 2.8° (traces

Fig. 12. Synthetic waveforms generated at distance 0.8° with depths of 1.0 to 34.9 km, an explosive source model, and crustal model 1 in Table 1. Trace 130 in this figure is the same as trace 080 in Fig. 11. Because the total path length becomes shorter with focal depth, the

*PmP* phase arrives progressively earlier with depth.

170 to 280).
