## 4 Application
### MS Location Results  
MS-GSWI location results of the eight blasting events are shown in Table 1. The table demonstrates that the maximum location error of the waveform inversion-based location method is 25.0 m and the average error is 15.0 m. There are some uniform velocity model-based location results on the eight blasting events [56; 57; 58; 59], and their average location error is larger than 39.5 m. Particularly, [PERSON] et al. [56] show that location error of the blasting event three in their paper is very large when using automatically picked data. [PERSON] et al. [57] found that the average location error reaches 47.4 m for their selected three events. [PERSON] et al. [59] developed a new location method called VFOM to reduce the influence of large picking error, but still obtained an average error larger than 39.5 m. The average error obtained by [PERSON] et al. [6] using 3D ray tracing-based location method is reduced to 26.2 m, which confirms the importance of velocity model accuracy to a mine MS location. Furthermore, [PERSON] et al. [7] utilized a 3D Gaussian beam-based reverse-time migration location method, which has an average location error of only 17.0 m.  
Figure 7: MS-GSWI location results of the blasting event 3. The rest of the explanation is the same as Figure 6.  
The research [56, 57, 58, 59] used homogeneous velocity models and straight ray paths to locate an event, while [PERSON] et al. [6] used a 3D ray tracing-based shooting method. For the shooting method, we discretized the 3D space onto a grid with 10 m spacing, then an initial ray set with a 1\({}^{\circ}\) interval from the source was adopted for the first time search of ray tracing, which followed [PERSON]'s law between grids, and the two closest rays to the sensor were selected, then we narrowed the ray path region by the bisection method until the distance between the ray path and the sensor was smaller than 0.1 m, which was set as the ray path from the source to the sensor. Furthermore, there are some other ray tracing methods and codes/software packages, such as [PERSON] and [PERSON] [60] published a 1D velocity model-based location method-HYP071 (software package is available through [[http://pubs.usgs.gov/of/1999/off-99-0023/](http://pubs.usgs.gov/of/1999/off-99-0023/)]([http://pubs.usgs.gov/of/1999/off-99-0023/](http://pubs.usgs.gov/of/1999/off-99-0023/))), and its updated vision that considers different phase arrival time is also available (HYPOSAT, [[ftp://ftp.norsar.no/pub/outgoing/johannes/hyposat/](ftp://ftp.norsar.no/pub/outgoing/johannes/hyposat/)]([ftp://ftp.norsar.no/pub/outgoing/johannes/hyposat/](ftp://ftp.norsar.no/pub/outgoing/johannes/hyposat/))); [PERSON] and [PERSON] [61] developed a multi-stage fast marching method (FMM) for 3D travel time calculation (FMTOMO, [[http://rses.anu.edu.au/~nick/fmtomo.html](http://rses.anu.edu.au/~nick/fmtomo.html)]([http://rses.anu.edu.au/~nick/fmtomo.html](http://rses.anu.edu.au/~nick/fmtomo.html))), and it can be used for source location and tomography; another widely used ray tracing location method is the double difference approach proposed by [PERSON] and [PERSON] [62] (hypoDD, [[http://geophysics.eas.gatech.edu/people/cvu/teaching/hypoDD/hypoDD.html#part1_2](http://geophysics.eas.gatech.edu/people/cvu/teaching/hypoDD/hypoDD.html#part1_2)]([http://geophysics.eas.gatech.edu/people/cvu/teaching/hypoDD/hypoDD.html#part1_2](http://geophysics.eas.gatech.edu/people/cvu/teaching/hypoDD/hypoDD.html#part1_2))), they assumed that the propagation paths of wavefields generated by two adjacent seismic events are similar, which effectively reduces the influences of structural anomalies due to the similar ray path from receiver to adjacent earthquakes. The location results in this study are similar to those obtained by the 3D Gaussian beam-based method, proving that the location method considering finite-frequency effects of wave propagation is significantly superior to the geometric ray tracing-based location. According to [PERSON] et al.