### Waveform Inversion-Based Location Methods  
Waveform inversion-based location methods constantly update synthetic waveforms by changing input source parameter models, and the source location is determined when the synthetic and observed waveforms have the best fitting. As early as 1982, [PERSON] [26] numerically modeled wavefield propagation in a two-dimensional (2D) uniform-velocity model using the FDM, and he inverted the source location and origin time of MS events. Then, [PERSON] and [PERSON] [27] inverted source location and magnitude based on a more efficient PSM and approximate linear iterative algorithm. [PERSON] et al. [28] developed a 1D velocity model and waveform fitting-based full moment tensor inversion and source location method, which has been applied to microseismic event location in the fields of mining engineering [29] and gas injection [30]. [PERSON] and [PERSON] [31] simultaneously obtained the source location, origin time and point source moment tensor in a 2D inhomogeneous velocity model by the utilizing waveform inversion method. In addition, [PERSON] and [PERSON] [32] and [PERSON] and [PERSON] [33] used waveform inversion to jointly inverse the microseismic event location and velocity model. [PERSON] and [PERSON] [34] put forward a source function independent waveform inversion to obtain a microseismic source location, origin time, and velocity model. [PERSON] et al. [8], [PERSON] et al. [35], and [PERSON] et al. [24; 25] performed joint inversion on point source moment tensor and location for natural earthquakes in regional scales under high-resolution 3D velocity models. Multi-parameter joint inversion greatly increases the search dimensions and the nonlinearity of the waveform inversion problem, and the multi-parameters are essentially highly coupled in the inversion process, which make the nonlinear waveform inversion difficult to converge. Therefore, more search times or iteration numbers are needed to find the global optimal location.  
Therefore, some studies have simplified the source parameter model into an inversion that only considers source locations (the simplification process and description are shown in Section 2.1), which improves inversion speed and reduces the nonlinearity of convergence. [PERSON] and [PERSON] [36] formulated an FWI scheme for determining hydraulic fracturing and mining microseismic event locations, and synthetic test on the 2-D SEG/EAGE overthrust model demonstrates its feasibility. [PERSON] et al. [37] derived a waveform inversion-based location method using the time-domain wave equation and cross-correlation travel time measurement between simulated and observed waveform as the misfit. They tested the proposed location algorithm through 2D and 2.5D (a 2D velocity model is adopted in the vertical plane determined by the source location and sensor location) field and regional velocity models. While [PERSON] et al. [38; 39] derived a waveform inversion-based location method that is independent from source-time characteristics, and they successfully applied the fast convergent truncated Newton method for microseismic source location based on 2D and 3D velocity models. Iteration-based optimization technique is often used in the above nonlinear waveform inversion-based location problem, which may be strongly affected by the initial model choice and cannot fully search the whole model space to obtain global convergence. In view of the above difficulties, we adopted the SEM for accurate wavefield modeling and global grid search idea from [PERSON] et al. [24] for global source location. The difference is that a multi-scale grid generation and search strategy depending on recording waveform frequency content (the fine grid wavefield only stored near the active mining zones) was used in this study, which greatly reduces the computational time and storage for global grid search.