Improved Wigner distribution function for interference imaging location of microseismic events

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Accurate and rapid event location is crucial for microseismic monitoring in hydraulic fracturing. We present an improved Wigner distribution function (WDF) to enhance the accuracy and efficiency of the interferometric imaging location method. Unlike traditional approaches, our strategy processes cross-correlation stacked images directly in the spatial domain and employs WDF for focusing, thus eliminating the need for complex waveform polarity correction and significantly simplifying the computation process. During the imaging process, an adaptive weighting function is designed to effectively suppress energy artifacts and optimize the energy focusing of the source location. Additionally, to enhance spatial resolution, we develop an adaptive window function based on Gaussian distribution, which adjusts the window's standard deviation to flexibly meet different imaging requirements. Synthetic data test results demonstrate that the proposed method achieves a smaller absolute location error compared to the traveltime inversion (TTI), single correlation stacking (SCS), and cross-correlation phase weighting (CCPW) approaches. Moreover, the average processing time of the developed method is only 0.86 s, which is 15.69% faster than TTI and 68.52% faster than the CCPW method. Test results using real data further confirm that the developed method achieves location errors that are 81.12%, 78.73%, and 50.53% better than the average location errors of the SCS, CCPW, and TTI methods, respectively.