**8. Summary and discussion**

162 Earthquake Research and Analysis – Seismology, Seismotectonic and Earthquake Geology

Fig. 20. Synthetic waveforms generated with the new crustal models listed in Table 2 at distance 2.20º and depth 12 km. Trace 125 was generated with Model 1 in Table 2; trace 225 with Model 2; trace 325 Model 3; trace 425 Model 4; trace 525 Model 5; trace 625 Model 6. Trace 001, 005, 010, 020, 030, 040 and 050 were generated with Model 1, but the thickness of the first layer was changed in steps to 0.01, 0.05, 0.1, 0.2, 0.3 0.4, and 0.5 km, successively.

There are distance windows in which regional depth phases are developed. Phase *sPg* is developed well within 100 km, *sPmP* is developed well within about 200 to 300 km, and *sPn* is developed at more than 300 km. Figs. 3, 4, and 5 show these distance windows. Because time differences *sPg*–*Pg*, *sPmP*–*PmP,* and *sPn*–*Pn* are not sensitive to station distance, we can align all records generated by an earthquake by station distance to identify these regional

1. Retrieve the catalogue from the official website of GSC (Geological Survey of Canada);

5. Based on the station distances in the pick file, arrange/display the waveform records; 6. In the above distance windows, align the records first and then search the regional

**7. Outline of the procedure to identify the regional depth phases** 

2. Select an earthquake to determine its focal depth using RDPM;

4. Retrieve all the available waveform records from the same website;

depth phases.

The procedure has the following steps:

3. Retrieve the pick file for the earthquake;

depth phase and its reference phase pairs.

There are many small earthquakes in eastern North America. These earthquakes do not have measurable teleseismic depth phases, and generally do not have close (<40 km) waveform records. No focal depths can be reliably estimated with either teleseismic depth phases or close seismic signals for most of these earthquakes, but the depths are crucial information for many topics, both theoretical and applied.

On regional waveform records, one or more phases are well developed between the first arrivals (*Pg* or *Pn*) and the *S*-wave train, and one or two of them are regional depth phases. Within about 100 km, the *sPg* phase is well developed on some records of earthquakes as small as *m*N 1.5. In the distance window from about 200 to 300 km, the *sPmP* phase is well developed on some records of earthquakes as small as *m*N 2.0. Beyond 300 km, the *sPn* phase is developed on some records of moderate and sub-moderate earthquakes. All these regional depth phases can be used to estimate focal depth.

When we generate synthetic depth phases, we use a default crustal model and default focal mechanism, and even a default station azimuth and default instrument response. In this way, we can conveniently generate synthetics for any small earthquake, and use the synthetic depth phases to estimate focal depth for that earthquake, if the arrival time difference between one observed depth phase and its reference phase is available.

We compared our modeled focal depths with those that were reliably obtained by other methods and found that the consistency in the comparisons is good.

The errors in our modeled focal depths are caused mainly by the crustal model used. The relative errors due to crustal model are estimated as within 15% when the error in the crustal velocity model is 10%, or when the thicknesses of layers in the crustal model have some errors, or the crustal medium differs from the assumed Poisson medium.

We have analyzed the regional depth phases for many earthquakes (Ma and Atkinson, 2006; Kim *et al*., 2006; Dineva *et al*., 2007; Ma and Eaton, 2007; Atkinson *et al*., 2008). For this chapter we selected some special cases to show that our modeling method is simple, reliable, and suitable for all regions where regional depth phases are developed.
