Rock Fracture Monitoring Based on High-Precision Microseismic Event Location Using 3D Multiscale Waveform Inversion

Figure 5

Fitting performance of the source-time function modeled by the fractional-order Gaussian function on typical windowed waveforms and their amplitude spectra. (a) Fitting performance of the fractional-order Gaussian source-time function on typical windowed MS signals. The black curve represents the windowed waveform of the first arrival phase; the blue dotted line indicates the Gaussian source-time function with an individual optimal fractional order through a two-parameter grid search for each recording sensor; the red dotted line represents the optimal fractional-order Gaussian source-time function under the condition of performing an overall grid search on all waveform records and keeping the value the same in the searching process. The number corresponds to the renumbering of sensors, which is arranged according to the first-arrival time of seismic phases. The variations of correlation coefficients for different traces are 0.81 to 0.91 (#1), 0.73-0.80 (#3), 0.84-0.87 (#6), and 0.94-0.95 (#11) for the optimal fractional-order Gaussian function fitting procedure through the overall grid search on all waveform records and the individual trace grid search, respectively; the difference between the two grid search strategies is not evident. (b) Normalized amplitude spectra of the corresponding colored waveforms in (a). The vertical dotted line represents the peak frequency, while the horizontal dotted line implies the range of a half-bandwidth. The intersection of the right side of the half-bandwidth line and the amplitude spectral curve corresponds to the highest cut-off frequency for numerical wavefield modeling.

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