To obtain station data with a high signal-to-noise ratio (S/N) and avoid dominant location deviation caused by over-dense local network (such as USArray in the United States), a series of specific measures are adopted to preprocess the data:

a) According to the time and centroid location of the teleseismic event reported by GCMT, we select the waveform data of all available stations using a time window within 30 min before and after, separately, the original time and within the epicenter range from 30° to 90°. Then the mean value, linear trend, and instrument response are removed from the waveform data. After that, a 0.25–5.00 Hz band-pass filtering is carried out.

The technique used for preliminary hypocenter location of TeleHypo is modified from S-SNAP published by Tan et al. (2019). S-SNAP can automatically detect seismic events from continuous waveforms and determine the original time, magnitude, and spatial location of earthquakes. In the locating process, S-SNAP first scans the continuous waveform using the SSA method (Kao and Shan, 2004) to obtain the possible onset time and location of the event; Then, waveform segments containing the direct waves are intercepted and used to automatically pick up the first arrival time of P and S through the kurtosis function (Baillard et al., 2014). These first arrival times are used to improve the location accuracy of the original time and spatial location of the earthquake via the MAXI method (Font et al., 2004). Finally, the results obtained by MAXI are used as a preliminary solution.

It must be pointed out that there are two reasons for using S-SNAP in this paper. Firstly, we need to use S-SNAP to relocate the epicenter based on GCMT. Secondly, this will provide a teleseismic relocation algorithm to more researchers, facilitating their own location works and improving the convenience of scientific research.

It should also be pointed out that for earthquakes of large magnitudes, the centroid and hypocenter may not necessarily be at the same spatial location (see Figure 1). TeleHypo uses S-SNAP to determine the hypocenter (i.e., the starting point of the source rupture), which may not be approximated by the centroid provided by GCMT. In addition, for the station data with an epicenter distance range of 30°–90°, S-SNAP locates the epicenter mainly through the plane wave information of each station. Therefore, we believe that the epicenter location of S-SNAP is robust, which also indicates that when the station is far away from the hypocenter of the earthquake, the accuracy of depth obtained by S-SNAP is often poor because the ray path of direct phase is insensitive to source depth. To overcome this defect, we conjunct the DSA method of Yuan et al. (2020) to improve the hypocenter depth location for teleseismic events.

Depth-phase templates are calculated by transforming the direct phase obtained in the first step (Section 2.1) into frequency domain, applying phase shift to the direct phase spectra, and transforming back into the time domain (as shown in Figure 2). With these templates, we carry out matching filter (Shelly et al., 2007) to find out all possible depth phases in the Z/R/T waveforms. Then the arrival time difference between each possible depth phase and direct wave is calculated and treated as observed data. These observed data will be compared with the theoretical ones, which is calculated by using the widely used TauP program (Krischer et al., 2015) with a series of given hypothetical source depths.

For each presumed source depth, we count the number of matches and calculate the differential time residuals between the arrival times of the predicted depth phases and the observed with respect to the direct phase. This process is repeated for a range of assumed source depths at an increment of 1 km. Then, the same process is repeated for all available stations. After all stations are scanned for possible depth phases, we sum the total number of phase matches for each assumed focal depth and calculate the corresponding differential arrival time residual. Focal depths with the number of matches exceeding ≥ 90 % of the largest number of matches are taken as preliminary candidates. Among them, the hypothetical depth with the smallest total of travel time difference among these candidates is selected as the high-precision hypocenter depth solution. Finally, the theoretical depth phases (i.e., pP, sP, and sS) calculated by Taup corresponding to this depth solution are used to calibrate the observed depth-phase candidates that meet the matching conditions.

The Mw 6.3 Chile earthquake occurred on 4 March 2010 at 22:39:29, at 22.360°N and 68.690°W, with a centroid depth of 118.7 km (the red star in Figure 3A).

There are 966 stations (the gray, blue, and green triangles in Figure 3A) within the range of 30°–90° epicentral distance, and the 60 min width time window beginning 30 min before and ending 30 min after the earthquake original time provided by the GCMT. The waveform data of these stations were processed using the first step of TeleHypo. We kept the wavefield information within the frequency band of 0.25–5.0 Hz (Figure 3B). Next, the theoretical travel times of direct waves (P and S) were calculated according to the GCMT centroid and the position of each station (red circle in Figure 3B). The ratio of the largest absolute amplitudes of the waveforms (the purple and green windows in Figure 3B) is defined as the signal-to-noise ratio (S/N). To avoid systematic biases caused by nonuniform distribution of station-density, we divided stations into 36 regions at an azimuth interval of 10°, and selected only the top 5 high S/N stations from each region. We finally selected 56 high S/N stations (the green triangle in Figure 3A) for the following precise hypocenter location.

TeleHypo uses the centroid position of GCMT as a reference to search for hypocenter location. The search range for the hypocenter location is 22.36 ± 1°N and 68.69 ± 1°W, with a latitude and longitude interval of 0.1°. The depth scanning range is within the centroid depth ± 50 km, with a depth interval of 1 km. We extracted waveform segments from each station using a sliding window of 50 s with a step size of 1 s. The sum (called E) of squares of the waveform amplitudes within the sliding time window is calculated as a function of scanning time step (Figure 4A). Then, we searched for the P- and S-wave arrival times for possible events with E exceeding threshold of 1 (the red line in Figure 4A). Using the MAXI method (Font et al., 2004), the earthquake origin time of 4 March 2010, 22:39:26 and hypocenter location of 22.060°N, 68.465°W were located (the white circle in the upper right panel of Figure 4B). Finally, depth phases were matched with the templates at each assumed depth for each station below the hypocenter location. The scanning depth at 111 km with the highest number of successful matches is token as the hypocenter depth (the vertical dashed line in Figure 4C), along with the corresponding matched depth phases (Figure 4D).

Comparing the solution obtained by TeleHypo (22.060°N, 68.465°W, 111 km, see the white circle in Figure 4B) with that of ISC-EHB (22.261°N, 68.400°W, 103.4 km, see the green circle in Figure 4B), we found that the two methods differ by about 0.201°N, 0.065°W in the epicenter location and 7.6 km in the source depth. The good agreement between the TeleHypo and ISC-EHB in this application example demonstrates the practicality of our method.

To further test the practicality of TeleHypo for global teleseismic events, we applied TeleHypo to 54 moderate-to-strong teleseismic events occurring in different seismogenic regions of the world (the open circles in Figure 5A). The source parameters of these earthquakes were obtained from the GCMT earthquake catalog, with magnitudes ranging from Mw 5.5 to 7.5, and centroid depths ranging from 20 to 200 km.

We used TeleHypo with the same parameters as the previous example of the Chile earthquake to locate the hypocenters of these teleseismic events. The location results obtained by TeleHypo are compared with those of the ISC-EHB (see details in Supplementary Table S1 in the appendix). It is showed that the differences of the original time (Figure 5B), epicenter distance (Figure 5C), and hypocenter depth (Figure 5D) between the two methods were 1.4 ± 2.0 s, 0.2 ± 0.1°, and 1.6 ± 6.9 km, respectively. The depth distributions obtained by ISC-EHB (The blue dotted line in Figure 6) and TeleHypo (The orange dotted line in Figure 6) has good agreement. These high precision results demonstrate that TeleHypo has good applicability to teleseismic events occurring in different regions of the world.

To test the influence of the number of stations used on the location accuracy of TeleHypo, we conducted experiments on the Chile earthquake case in Section 3.1 by using 1, 3, and 5 stations with high S/N, separately, selected from each azimuthal area. We also conducted similar experiments on 54 global earthquakes in Section 3.2. The difference of origin time, epicentral location, and hypocenter depth between TeleHypo and ISC-EHB catalog were calculated. The statistical results showed that when we use only one station from each azimuthal area, the difference in origin time, epicentral location, and hypocenter depth are 1.1 ± 1.6 s, 0.2 ± 0.1°, and 5.8 ± 24.8 km, respectively (the right column of Figure 7). When three stations from each azimuthal area are used, the differences are 1.6 ± 1.6 s, 0.3 ± 0.1°, and 4.7 ± 9.0 km, respectively (the middle column of Figure 7). When the number of stations in each azimuthal sector reached 5, the differences are 1.5 ± 1.7 s, 0.2 ± 0.1°, and 2.0 ± 6.6 km, respectively (the left column of Figure 7). It indicates that using number of 5 stations with high S/N selected from each azimuthal area is suitable for TeleHypo.

It should be pointed out that the selection of stations for TeleHypo is centered around the epicenter of CGMT. The coverage is divided into 36 regions at intervals of 10° in azimuth. A maximum of 5 high S/N stations are selected from each region. Since the number of high S/N stations in some azimuthal areas can be less than 5, the total number of high S/N stations in all azimuth areas is usually less than 180, which also means that the number of depth phases with high quality will be less than 180. Section 4.4 below presents the statistical results of the number of high S/N stations and depth phases available for each of the five shallow earthquakes (see Figure 10). It indicates that TeleHypo does not necessarily need to use 180 depth phases to obtain accurate source depths.

TeleHypo needs to use velocity model to calculate the travel times of direct waves and depth phases during location. To test the influence of different velocity models on the location of TeleHypo, we selected the IASP91 (Kennett and Engdahl, 1991) (see their Table 2) and AK135 (Kennett et al., 1995) (see their Table 3) velocity models for testing. The P-wave velocities of these two velocity models are almost the same. However, there are slight differences in their S-wave velocities, especially in the velocities above mantle where the S-wave velocity difference can reach 0.1 km/s. This difference can affect the travel time of S-waves and their associated free surface reflection phases (such as sP and sS), resulting in source location differences using these two velocity models.

We used the IASP91 velocity model to reconducted the locating experiments in Section 3.2. Other experimental parameters are the same as Section 3.2. When IASP91 is used, the differences between TeleHypo and ISC-EHB in origin time, epicentral location, and hypocenter depth are 1.8 ± 2.1 s, 0.2 ± 0.1°, and 0.8 ± 7.6 km, respectively (the left column of Figure 8). When AK135 is used, those differences are 1.4 ± 2.0 s, 0.2 ± 0.1°, and 1.6 ± 6.9 km, respectively (the right column of Figure 8). It suggests that IASP91 is more suitable for TeleHypo to locate the hypocenter depth.

In addition to providing hypocenter parameters, TeleHypo can also provide the arrival times and be used to extract waveform of direct waves and depth phases (as shown in Figure 9), which is useful for building database for direct waves and depth phases of global earthquakes. The direct waves (P and S) and depth phases (pP, sP, and sS) for all teleseismic events in this paper were automatically picked by TeleHypo. There were, in total, 1245 P, 1245 S, 566 pP, 453 sP, and 456 sS phases. Since artificial intelligence nowadays still depends on good training data, TeleHypo can be used to provide a large number of training dataset and labels for artificial intelligence in teleseismic phase identification.

Among the 55 teleseismic events used in this paper (see the Supplementary Table S1 in the appendix), there are 5 shallow earthquakes with focal depths less than 30 km. The number of high S/N stations for these five events is 54, 73, 38, 67, and 25, separately. From each of these stations, TeleHypo successfully identified 32 (59.3 % ), 25 (34.2 % ), 13 (34.2 % ), 28 (41.8 % ), and 8 (32.0 % ) pP/sP phases, and 35 (64.8 % ), 20 (27.4 % ), 9 (23.7 % ), 18 (26.9 % ), and 7 (28.0 % ) sS seismic phases, respectively. Statistics show that TeleHypo has an average successful identification rate of 40.3 % for pP/sP and 34.2 % for sS. The depth solutions of TeleHypo (The orange histograms in Figure 10) for these 5 shallow earthquakes are consistent with that of ISC-EHB (The blue histograms in Figure 10), with an average depth difference of 2.32 km. This suggests that it is possible to use TeleHypo to locate shallow earthquakes occurring within the crust (e.g., source depth < 30 km) if the direct waves and depth phases can be separately identified.

To investigate the depth phase identification of TeleHypo for shallow events, we analyzed the depth phase matching process of the event of 2017-03-27T10:50:23.37Z in Figure 10. The Z-component record of station N4.P46A of the event (Figure 10B) shows obvious direct P-waves (The orange waveform in Figure 10B). We obtained the pP phase through template matching (The red dot and dashed line in Figure 10B). As the source depth of this event was only 18 km, the pP phase followed closely behind the direct P-wave. The direct S-wave (The orange waveform in Figure 10C) and sS phase (The red dot and dashed line in Figure 10C) in the T-component record also exhibit similar characteristics. This means that shallow earthquakes with a focal depth of 18 km are approaching the depth location limit of TeleHypo. If the source is too shallow, there may be interference between the direct waves and depth phases, leading to waveform distortion and potentially causing TeleHypo to fail. In addition, when the direct wave or depth phase is not obvious, TeleHypo may also fail due to the inability to match the correct phase.