TY - JOUR A1 - Vasyura-Bathke, Hannes A1 - Dettmer, Jan A1 - Dutta, Rishabh A1 - Mai, Paul Martin A1 - Jónsson, Sigurjón T1 - Accounting for theory errors with empirical Bayesian noise models in nonlinear centroid moment tensor estimation JF - Geophysical journal international / the Royal Astronomical Society, the Deutsche Geophysikalische Gesellschaft and the European Geophysical Society N2 - Centroid moment tensor (CMT) parameters can be estimated from seismic waveforms. Since these data indirectly observe the deformation process, CMTs are inferred as solutions to inverse problems which are generally underdetermined and require significant assumptions, including assumptions about data noise. Broadly speaking, we consider noise to include both theory and measurement errors, where theory errors are due to assumptions in the inverse problem and measurement errors are caused by the measurement process. While data errors are routinely included in parameter estimation for full CMTs, less attention has been paid to theory errors related to velocity-model uncertainties and how these affect the resulting moment-tensor (MT) uncertainties. Therefore, rigorous uncertainty quantification for CMTs may require theory-error estimation which becomes a problem of specifying noise models. Various noise models have been proposed, and these rely on several assumptions. All approaches quantify theory errors by estimating the covariance matrix of data residuals. However, this estimation can be based on explicit modelling, empirical estimation and/or ignore or include covariances. We quantitatively compare several approaches by presenting parameter and uncertainty estimates in nonlinear full CMT estimation for several simulated data sets and regional field data of the M-1 4.4, 2015 June 13 Fox Creek, Canada, event. While our main focus is at regional distances, the tested approaches are general and implemented for arbitrary source model choice. These include known or unknown centroid locations, full MTs, deviatoric MTs and double-couple MTs. We demonstrate that velocity-model uncertainties can profoundly affect parameter estimation and that their inclusion leads to more realistic parameter uncertainty quantification. However, not all approaches perform equally well. Including theory errors by estimating non-stationary (non-Toeplitz) error covariance matrices via iterative schemes during Monte Carlo sampling performs best and is computationally most efficient. In general, including velocity-model uncertainties is most important in cases where velocity structure is poorly known. KW - Inverse theory KW - Probability distributions KW - Waveform inversion KW - Earthquake source observations KW - Seismic noise Y1 - 2021 U6 - https://doi.org/10.1093/gji/ggab034 SN - 0956-540X SN - 1365-246X VL - 225 IS - 2 SP - 1412 EP - 1431 PB - Oxford University Press CY - Oxford ER - TY - JOUR A1 - Hammer, Conny A1 - Ohrnberger, Matthias A1 - Faeh, Donat T1 - Classifying seismic waveforms from scratch: a case study in the alpine environment JF - Geophysical journal international N2 - Nowadays, an increasing amount of seismic data is collected by daily observatory routines. The basic step for successfully analyzing those data is the correct detection of various event types. However, the visually scanning process is a time-consuming task. Applying standard techniques for detection like the STA/LTAtrigger still requires the manual control for classification. Here, we present a useful alternative. The incoming data stream is scanned automatically for events of interest. A stochastic classifier, called hidden Markov model, is learned for each class of interest enabling the recognition of highly variable waveforms. In contrast to other automatic techniques as neural networks or support vector machines the algorithm allows to start the classification from scratch as soon as interesting events are identified. Neither the tedious process of collecting training samples nor a time-consuming configuration of the classifier is required. An approach originally introduced for the volcanic task force action allows to learn classifier properties from a single waveform example and some hours of background recording. Besides a reduction of required workload this also enables to detect very rare events. Especially the latter feature provides a milestone point for the use of seismic devices in alpine warning systems. Furthermore, the system offers the opportunity to flag new signal classes that have not been defined before. We demonstrate the application of the classification system using a data set from the Swiss Seismological Survey achieving very high recognition rates. In detail we document all refinements of the classifier providing a step-by-step guide for the fast set up of a well-working classification system. KW - Time series analysis KW - Neural networks, fuzzy logic KW - Seismic monitoring and test-ban treaty verification KW - Early warning KW - Probability distributions Y1 - 2013 U6 - https://doi.org/10.1093/gji/ggs036 SN - 0956-540X SN - 1365-246X VL - 192 IS - 1 SP - 425 EP - 439 PB - Oxford Univ. Press CY - Oxford ER -