Automatic Slowness Vector Measurements of Seismic Arrivals with Uncertainty Estimates using Bootstrap Sampling, Array Methods and Unsupervised Learning

Horizontal slowness vector measurements using array techniques have been used to analyse many Earth phenomena from lower mantle heterogeneity to meteorological event location. While providing observations essential for studying much of the Earth, slowness vector analysis is limited by the necessary and subjective visual inspection of observations. Furthermore, the interpretation of the observations is also limited as uncertainties of slowness vector measurements are usually not analysed. To address these limitations, we present a method to automatically identify seismic arrivals and measure their slowness vector properties with un- certainty bounds. We do this by bootstrap sampling waveforms, and use linear beamforming to measure the coherent power at a range of slowness vectors. For each sample, we take the top N peaks from each power distribution as the slowness vectors of possible arrivals. The slowness vectors of all bootstrap samples are gathered and the clustering algorithm DBSCAN (Density-Based Spatial Clustering of Applications with Noise) is used to identify arrivals as clusters of slowness vectors. The mean of each cluster gives the slowness vector measurement for that arrival and the distribution of slowness vectors in each cluster gives the uncertainty estimate. We tuned the parameters of DBSCAN using a dataset of 2489 SKS and SKKS observations at a range of frequency bands from 0.1 Hz to 1 Hz. Each observation was labelled with the number of arrivals (either 0, 1 or 2) by visual inspection. This dataset is used to compare the prediction from the detection algorithm in the tuning. The parameters chosen can correctly identify >90% of observations with 1 arrival, >65% of observations with 2 arrivals and >85% of the observations with 0 arrivals in the example dataset. We then present examples at higher frequencies (0.5 to 2.0 Hz) than the example dataset, identifying PKP precursors, and lower frequency by identifying multipathing in surface waves (0.04 to 0.06 Hz). This method allows for much larger datasets to be analysed without visual inspection of data. Phenomena such as multipathing, reflections or scattering can be identified automatically in body or surface waves and their properties analysed with uncertainties. Code is publicly available at https://github.com/eejwa/Array_Seis_Circl.