Time-Delay Estimation of Microseismic DAS Data Using Band-Limited Phase-Only Correlation

Time-delay estimation is a critical step in many geophysical applications. Conventional approaches are mainly based on the cross correlation of waveforms in time domain but show strong distortions with multiple oscillations and side lobes. We propose a band-limited phase-only correlation (POC) algorithm for time-delay estimation. The algorithm involves the following key steps: 1) transforming 1-D waveform into 2-D time–frequency spectra using S-transform; 2) calculating the band-limited POC function of the transformed spectra; and 3) measuring time delays by analyzing POC coefficient. We demonstrate the effectiveness of the proposed algorithm using synthetic and real microseismic fiber-optic distributed acoustic sensing (DAS) datasets. Results show that POC can effectively and accurately estimate the time delays of waveforms. Compared with the performance of the conventional cross correlation method in time domain, the proposed method has three main advantages: 1) better identification of event and noise waveforms; 2) lower uncertainty of narrow correlation peaks; and 3) weaker distortions with small oscillations and side lobes.