Using Wavelet Covariance Models for Simultaneous Picking of OverlappingP‐ andS‐Wave Arrival Times in Noisy Single‐Component Data

Abstract

We present a method for automatically identifying overlapping elastice‐waveelastice‐wave phase arrivals in single‐component data. The algorithm applies to traditional near‐source seismic, microseismicity and picoseismicity monitoring, and acoustic emission monitoring; we use acoustic emissions examples as a worst‐case demonstration. These signals have low signal‐to‐noise and, because of small geometric dimensions, overlapping P ‐ and S ‐wave arrivals. Our method uses the statistics of temporal covariance across many wavelet scales. We use a nonnormalized rectilinity function of the scale covariance. The workflow begins by denoising signals and making a rough first‐arrival estimate. We then perform a continuous Daubechies wavelet transform over tens to hundreds of scales on the signal and find a moving covariance across transform scales. The nonnormalized rectilinity is calculated for each of the covariance matrices, and we sharpen changes in the rectilinity values with a maximization filter. We then estimate phase arrival times using thresholds of the filtered rectilinity. Overall, we have a high success rate for both P ‐ and S ‐wave arrivals. Remaining challenges include estimation of arrival times of long duration, cigar‐shape events, and culling complex high‐magnitude electrical noise. By using higher‐order Daubechies wavelet transforms, the scale covariance metric reflects variations in higher‐moment statistics (skewness and kurtosis) and changes in short‐term versus long‐term means, as well as the covariance across timescales of the signal. For single‐component data, it is necessary to preserve both amplitude and correlation information of the signal; this necessitates using the nonnormalized rectilinity function.