Using wavelet covariance models for simultaneous picking of overlapping P- and S-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.