The USGS earthquake catalog indicates that a few earthquakes with >30 km focal depths occurred in the North-South Seismic Belt of China. Whether these focal depths are reliable or not is an important issue for the studies on the seismogenic mechanism, lithosphere strength and tectonic implications. The focal depths of five M4 similar to 5 earthquakes in the North-South Seismic Belt are carefully studied with broadband three-component waveforms from local and regional stations. With the traveltime difference between first P and sPL depth phase, the qualitative relations between the focal depth and the short-period Rayleigh wave (Rg wave), the amplitude ratio of Rg/P, and the focal mechanism inversion by Cut and Paste (CAP) methods, the focal depths of five M4 similar to 5 earthquakes in the North-South Seismic Belt are accurately determined. Synthetic seismic waveforms are calculated by frequency-wavenumber (FK) method. In the CAP method, three-component waveforms from local and regional stations with good azimuthal distributions are used to invert for the focal mechanisms and focal depth. The Pnl and surface wave are separately fitted to avoid the effects of the lateral variations of the crustal structure. The grid search scheme is used in the CAP method to find the best-fit focal depth and focal mechanisms. For the Rg wave, when the earthquakes have shallow focal depth (e.g. <10 km) and the stations is beyond 5 times epicentral distances, the Rg wave becomes strong in the radial or vertical components of the seismic waveforms. Together with the amplitude ratio of Rg/P, the Rg wave can be used to quantitatively determine the focal depth. The focal depths of the M4.7 earthquake in Huining, Ningxia (10 similar to 11 km), the M4.8 earthquake in Fumin, Yunnan (11 similar to 12 km) and the M4.7 earthquake in Huidong, Sichuan (8 similar to 9 km), are all within 8 similar to 12 km. The differences in focal depth from the sPL depth phase and the CAP method are about 2 similar to 3 km, which should be accurate enough to confirm that the earthquakes occurred in the upper or mid-lower crust. In contrast, the focal depths of all three earthquakes are greater than 30 km (31, 33 and 46 km depth) in the USGS earthquake catalog, which mistakenly means the three earthquakes all occurred in the mid-lower crust rather than upper crust. For the M4.6 and M4.9 earthquake in Longchang, Sichuan, the focal depth from sPL depth phase is about 1 similar to 2 km, which is shallower than the focal depth of 4 km from the CAP method. The independent result from amplitude ratio of Rg/P is 2 km, which is close to the results from the sPL depth phase. Since there is 2 similar to 3 km difference in the focal depth between results from the sPL depth phase, Rg/P and the CAP method, we inferred that the regional 1-D velocity model used in the synthetic waveform calculation in the CAP method could induce the bias on the focal depth due to the thick low-velocity sediments and/or strong lateral variations in the upper crustal structure. In contrast, the sPL depth phase method is not strongly affected by the bias of the velocity model. Therefore, for the extremely shallow earthquakes, the sPL depth phase and the amplitude ratio of Rg/P methods should be used to identify the focal depth rather than the CAP method only. In final, the focal depths of the M4.6 and M4.9 earthquake in Longchang, Sichuan should be 1 2 km, which belong to the extremely shallow earthquakes. There is still large bias in the USGS earthquake catalog compared to the focal depth of 10 km for the two earthquakes. It's meaningful to determine the focal depth with seismic waveforms at only one or two local stations for the regions with sparse seismic stations. With the sPL depth phase, the Rg wave, and the CAP methods, the focal depths of 5 M4 similar to 5 earthquakes in the North-South Seismic Belt are accurately determined. The focal depths of three earthquakes are within 8 similar to 12 km, and the focal depth of the other two earthquakes are 1 similar to 2 km, which indicates quite large discrepancies with the focal depths of the USGS earthquake catalog. Therefore, at least in the North-South Seismic Belt of China, the M4 similar to 5 earthquakes with deeper focal depths (e.g.,>30 km) in the USGS earthquake catalog need be further studied to identify their accuracy.
