Signal arrival-time estimation plays a critical role in a variety of downstream seismic analyses, including location estimation and source characterization. Any arrival-time errors propagate through subsequent data-processing results. In this article, we detail a general framework for refining estimated seismic signal arrival times along with full estimation of their associated uncertainty. Using the standard short-term average/long-term average threshold algorithm to identify a search window, we demonstrate how to refine the pick estimate through two different approaches. In both cases, new waveform realizations are generated through bootstrap algorithms to produce full a posteriori estimates of uncertainty of onset arrival time of the seismic signal. The onset arrival uncertainty estimates provide additional data-derived information from the signal and have the potential to influence seismic analysis along several fronts.
In this paper, we assert the importance of uncertainty quantification for machine learning and sketch an initial research agenda. We define uncertainty in the context of machine learning, identify its sources, and motivate the importance and impact of its quantification. We then illustrate these issues with an image analysis example. The paper concludes by identifying several specific research issues and by discussing the potential long-term implications of uncertainty quantification for data analytics in general.