## 4 Application
### MS Location Examples  
Taking the blasting events 1 and 3 as the cases to illustrate 3D MS-GSWI location method, their location results are shown in Figures 6 and 7, respectively. Figures 6b-d and 7b-d also demonstrate that velocity parameter sensitivity kernels of cross-correlation travel time anomaly \(\Delta T_{i}(\mathbf{x}_{r})\) have broader and more reasonable illumination range compared with the simple infinite-frequency assumption-based geometric ray tracing methods (Figures 6b and 7b). The sensitivity kernels of cross-correlation travel time anomaly are closely related to the frequency content of the wavefield, and here only the distribution of sensitivity kernels calculated by the Gaussian source-time function with main frequency of 120 Hz  
Figure 5: Fitting performance of windowed observed waveforms and synthetic waveforms based on different source-time function estimation approaches and their corresponding amplitude spectra. **(a)** Waveform fitting illustration of synthetic waveforms generated by the data-driven singular value decomposition averaged fractional derivative (DD-SVD-FD) source-time wavelet (red curve) and frictional-order Gaussian source-time function (blue curve). The black curve represents the windowed observed waveforms. The normalized cross-correlation coefficient between DD-SVD-FD source-time function and windowed observed waveform is shown in red text, while the normalized cross-correlation coefficient between frictional-order Gaussian source-time function and windowed observed waveform is shown in blue text. The number corresponds to the renumbering of sensors, which is ranked from early to late according to the initial P phase arrival time. **(b)** Normalized amplitude spectra correspond to the colored waveforms shown in **(a)**. The vertical dotted line is the peak frequency and the shaded region shows the half-bandwidth frequency range. is displayed. If the frequency bands tend to infinite high frequency, the sensitivity kernels of travel time anomaly will shrink to a very narrow tube just like the geometric ray. The sensitivity kernels of travel time based on numerical waveform modeling can better reveal multi-path effects around strong low-velocity anomalies (Figures 6c,d and 7c) and evident wavefield interference influence (Figure 7d). In strongly heterogeneous media, the changes of sensitivity kernels of travel time corresponding to the changes of source location will also present very sophisticated characteristics. The whole velocity field perturbation in the Fresnel zone is weighted by amplitude of sensitivity kernels of travel time anomaly (the red to blue color scale shows the intensity value of positive and negative strength of the sensitive kernel), which finally affects waveforms at sensors and thus leads to complex frequency-dependent perturbation of arrival time and waveform interference. Both the SEM modeled waveforms based on MS-GSWI location result and premeasured true source location can fit the observed waveforms well, with an overall correlation coefficient about 0.8. It should be noted that an appropriate band-pass filtering has been conducted to the waveforms modeled for different sensors to better fit the corresponding observed waveforms. In addition, the total cross-correlation  
Figure 6: MS-GSWI location results of the blasting event 1. (**a**) Ray paths (black dotted curves) from the MS-GSWI location result to corresponding triggered sensors. The background is a 2D sliced plane of the 3D velocity model, the wavefronts modeled by the SEM are shown at a time interval of 0.04 s. It can be observed that each ray is orthogonal to numerical wave front, demonstrating the effectiveness of the SEM modeling. (**b**) Sensitivity kernels of cross-correlation travel time anomaly from the MS-GSWI location to triggered sensors, which is synthesized by the Gaussian source-time function with a main frequency of 120 Hz. The red to blue color scale shows the intensity value of positive and negative strength of sensitive kernel.