Robust Phase Association and Simultaneous Arrival Picking for Downhole Microseismic Data Using Constrained Dynamic Time Warping

Accurate phase association and arrival time picking are pivotal for reliable microseismic event location and source characterization. However, the complexity of downhole microseismic wavefields, arising from heterogeneous subsurface structures, variable propagation paths, and ambient noise, poses significant challenges to conventional automatic picking methods, even when the signal-to-noise ratio (SNR) is moderate to high. Specifically, P-wave coda energy can obscure S-wave onsets analysis, and shear wave splitting can generate ambiguous arrivals. In this study, we propose a novel multi-channel arrival picking framework based on Constrained Dynamic Time Warping (CDTW) for phase identification and simultaneous P- and S-wave arrival estimation. The DTW algorithm aligns microseismic signals that may be out of sync due to differences in timing or wave velocity by warping the time axis to minimize cumulative distance. Time delay constraints are imposed to ensure physically plausible alignments and improve computational efficiency. Furthermore, we introduce a Multivariate CDTW approach to jointly process the three-component (3C) data, leveraging inter-component and inter-receiver arrival consistency across the entire downhole array. The method is validated against the Short-Term Average/Long-Term Average (STA/LTA) and waveform cross-correlation techniques using field data from a shale gas hydraulic fracturing. Results demonstrate that the proposed algorithm significantly enhances arrival time accuracy and inter-receiver consistency, particularly in scenarios involving P-wave coda interference and shear wave splitting.