**4. Comparison of RDPM focal depths with those from other methods**

In eastern Canada and the New York State region, some moderate and strong earthquakes have reliable focal depth solutions. For the same earthquakes we compared focal depth solutions obtained by RDPM with those obtained by other methods. We found that the consistency is good.

#### **4.1** *sPn* **modeling for the** *M***W 5.0 2002/04/20 Au Sable Forks, New York earthquake**

We analyzed the waveform records for this earthquake and found many *sPn* records. We modeled the *sPn* and *Pn* phases recorded at a POLARIS station, Canada (Fig. 13). From *sPn* and *Pn* paths in a one-layered crustal model of Poisson medium, the following equation calculates focal depth using the time difference *sPn*–*Pn*:

$$t\text{tf(h;sPn} - Pn) = \frac{h}{V\_{p1}} \left[ \sqrt{3 - k^2} + \sqrt{1 - k^2} \right];\tag{1}$$

where *kV V p p* 1 2 / ; *V*p1 and *V*p2 are *P*-wave velocities in and beneath the crust, respectively; *h* is the focal depth; and *t* is the differential time. The differential time is independent of station distance and crustal thickness. Even if we have only one pair of reliable *sPn* and *Pn* observations, we can obtain a focal depth solution with a small error without considering the earthquake location error. The time difference *sPn*–*Pn* on trace ACTO/HHZ is 4.06 sec. When we take *Vp*1 = 6.25 km/sec and *Vp*2 = 8.0 km/sec, the focal depth from equation (1) is 11.7 km; this depth is close to the focal depth (about 11.5 km) determined by RDPM.

Fig. 13. Phase *sPn* modeling for 2002/04/20 Au Sable Forks, New York, *M*W 5.0 earthquake. Trace ACTO/100 was generated with depth 10 km at station ACTO (517 km). Trace ACTO/HHZ is the earthquake observation; it matches a trace somewhere between ACTO/110 and ACTO/115. We can take 11 km or 11.5 km as the modeled focal depth. The time difference *sPn*–*Pn* on trace ACTO/HHZ is 4.06 sec. Using this number in equation (1) gives a focal depth of 11.7 km.

To compare the RDPM depth, we analyzed the teleseismic depth phase *sP* and its reference phase *P* at YKA (Yellowknife Array, Canada). Fig. 14 shows some of the records. The time difference *sP*–*P* is 4.85 sec. The following equation calculates focal depth from differential time:

$$t(h, a; \mathbf{s}; \mathbf{P} - P) = \frac{h}{V\_p \sqrt{1 - \frac{1}{3} \sin^2 a}} \left(\sqrt{3} + 1 - \frac{4}{3} \sin^2 a\right);\tag{2}$$

where *V*P is the *P*-wave velocity in a one-layered crustal model of Poisson medium, *α* is the *P*-wave take-off angle, *t* is the differential time, and *h* is the focal depth. If we take *V*P = 6.25 km/sec and *α* = 29.68° the focal depth from equation (2) is 12 km.

Fig. 14. Teleseismic depth phases records of 2002/04/20 Au Sable Forks, New York, *M*W 5.0 earthquake at YKA (Yellowknife Array, Canada). Based on the time difference *sP*–*P* (4.85 sec), the focal depth from equation (2) is about 12 km.

#### **4.2** *sPg* **modeling for the** *m***N 4.3 1993/11/16 Montreal south earthquake and its aftershocks**

Many *sPg* (and *sPmP*) records are available in eastern Canada and New York region. As an example we selected the records from station MNT (37 km from a main shock and its

Fig. 15. *sPg* and *Pg* modeling for earthquakes No. 15, 16, 17, and 20 in Table 2 of Ma, 2010. Traces labeled 15, 16, 17, and 20 are *P* portions recorded at station MNT (37 km). Traces 153, 159, 160, and 163 are synthetics generated with depths 15.3, 15.9, 16.0, and 16.3 km at station MNT. The subtle differential times *sPg*–*Pg* show that these earthquakes occurred on a fault that ruptured about 1 km at depth about 15 km.

where *V*P is the *P*-wave velocity in a one-layered crustal model of Poisson medium, *α* is the *P*-wave take-off angle, *t* is the differential time, and *h* is the focal depth. If we take *V*P = 6.25

Fig. 14. Teleseismic depth phases records of 2002/04/20 Au Sable Forks, New York, *M*W 5.0 earthquake at YKA (Yellowknife Array, Canada). Based on the time difference *sP*–*P* (4.85

Many *sPg* (and *sPmP*) records are available in eastern Canada and New York region. As an example we selected the records from station MNT (37 km from a main shock and its

Fig. 15. *sPg* and *Pg* modeling for earthquakes No. 15, 16, 17, and 20 in Table 2 of Ma, 2010. Traces labeled 15, 16, 17, and 20 are *P* portions recorded at station MNT (37 km). Traces 153, 159, 160, and 163 are synthetics generated with depths 15.3, 15.9, 16.0, and 16.3 km at station MNT. The subtle differential times *sPg*–*Pg* show that these earthquakes occurred on a fault

**4.2** *sPg* **modeling for the** *m***N 4.3 1993/11/16 Montreal south earthquake and its** 

3 *<sup>p</sup>*

*V*

*<sup>h</sup> t h sP P*

km/sec and *α* = 29.68° the focal depth from equation (2) is 12 km.

sec), the focal depth from equation (2) is about 12 km.

that ruptured about 1 km at depth about 15 km.

**aftershocks** 

2 <sup>4</sup> (, ; ) 3 1 sin ;

<sup>1</sup> <sup>3</sup> 1 sin

2

(2)

aftershocks; No. 15, 16, 17, and 20 in Table 2 of Ma, 2010). Fig. 15 shows that the main shock is the deepest and the last aftershock is the shallowest, and the depth difference between, for example, No. 15 and 16, is about 0.3 km.

#### **4.3** *sPmP* **modeling for the** *M***L 5.1 1983/10/07 New York region earthquake and its aftershock (No. 5 in Table 2 of Ma 2010)**

We selected the records from station SBQ (244 km) as an example. In Fig. 16, trace SBQ/SHZ 10:18:12.0 is the record of the main shock at station SBQ, and trace SBQ/SHZ 10:39:06.0 is the record of its aftershock. From the time differences *sPmP*–*PmP* on the synthetics SBQ/079 and SBQ/085, we found that the aftershock is shallower than the main shock by about 0.5 km. The modeled focal depth for the main shock is 8.5 km. The focal depth obtained by the Geological Survey of Canada is 10.0 km. From the first record we see the *Pn* phase clearly, but from the second record we cannot. This means that the *Pn* phase disappeared or was too weak to be measured.

Fig. 16. *sPmP* and *PmP* modeling for earthquake No. 5 in Table 2 of Ma, 2010 and one of its aftershocks (1983/10/07 10:39:39.0, *M*L3.5). The top trace is the record of the earthquake at station SBQ; the second trace is the record of the aftershock. Traces SBQ/079 and SBQ/085 are synthetic waveforms generated with depths 7.98 and 8.5 km at station SBQ. The subtle differential times *sPmP*–*PmP* show that the two earthquakes occurred at different depths. On the second trace the *Pn* phase is not measurable.
