@article{VasyuraBathkeDettmerDuttaetal.2021, author = {Vasyura-Bathke, Hannes and Dettmer, Jan and Dutta, Rishabh and Mai, Paul Martin and J{\´o}nsson, Sigurj{\´o}n}, title = {Accounting for theory errors with empirical Bayesian noise models in nonlinear centroid moment tensor estimation}, series = {Geophysical journal international / the Royal Astronomical Society, the Deutsche Geophysikalische Gesellschaft and the European Geophysical Society}, volume = {225}, journal = {Geophysical journal international / the Royal Astronomical Society, the Deutsche Geophysikalische Gesellschaft and the European Geophysical Society}, number = {2}, publisher = {Oxford University Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggab034}, pages = {1412 -- 1431}, year = {2021}, abstract = {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.}, language = {en} } @article{NooshiriBeanDahmetal.2021, author = {Nooshiri, Nima and Bean, Christopher J. and Dahm, Torsten and Grigoli, Francesco and Kristjansdottir, Sigriour and Obermann, Anne and Wiemer, Stefan}, title = {A multibranch, multitarget neural network for rapid point-source inversion in a microseismic environment}, series = {Geophysical journal international}, volume = {229}, journal = {Geophysical journal international}, number = {2}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggab511}, pages = {999 -- 1016}, year = {2021}, abstract = {Despite advanced seismological techniques, automatic source characterization for microseismic earthquakes remains difficult and challenging since current inversion and modelling of high-frequency signals are complex and time consuming. For real-time applications such as induced seismicity monitoring, the application of standard methods is often not fast enough for true complete real-time information on seismic sources. In this paper, we present an alternative approach based on recent advances in deep learning for rapid source-parameter estimation of microseismic earthquakes. The seismic inversion is represented in compact form by two convolutional neural networks, with individual feature extraction, and a fully connected neural network, for feature aggregation, to simultaneously obtain full moment tensor and spatial location of microseismic sources. Specifically, a multibranch neural network algorithm is trained to encapsulate the information about the relationship between seismic waveforms and underlying point-source mechanisms and locations. The learning-based model allows rapid inversion (within a fraction of second) once input data are available. A key advantage of the algorithm is that it can be trained using synthetic seismic data only, so it is directly applicable to scenarios where there are insufficient real data for training. Moreover, we find that the method is robust with respect to perturbations such as observational noise and data incompleteness (missing stations). We apply the new approach on synthesized and example recorded small magnitude (M <= 1.6) earthquakes at the Hellisheioi geothermal field in the Hengill area, Iceland. For the examined events, the model achieves excellent performance and shows very good agreement with the inverted solutions determined through standard methodology. In this study, we seek to demonstrate that this approach is viable for microseismicity real-time estimation of source parameters and can be integrated into advanced decision-support tools for controlling induced seismicity.}, language = {en} } @article{DahmHeimannMetzetal.2021, author = {Dahm, Torsten and Heimann, Sebastian and Metz, Malte and Isken, Marius Paul}, title = {A self-similar dynamic rupture model based on the simplified wave-rupture analogy}, series = {Geophysical journal international / the Royal Astronomical Society, the Deutsche Geophysikalische Gesellschaft and the European Geophysical Society}, volume = {225}, journal = {Geophysical journal international / the Royal Astronomical Society, the Deutsche Geophysikalische Gesellschaft and the European Geophysical Society}, number = {3}, publisher = {Oxford Univ. Press}, address = {Oxford}, issn = {0956-540X}, doi = {10.1093/gji/ggab045}, pages = {1586 -- 1604}, year = {2021}, abstract = {The investigation of stresses, faults, structure and seismic hazards requires a good understanding and mapping of earthquake rupture and slip. Constraining the finite source of earthquakes from seismic and geodetic waveforms is challenging because the directional effects of the rupture itself are small and dynamic numerical solutions often include a large number of free parameters. The computational effort is large and therefore difficult to use in an exploratory forward modelling or inversion approach. Here, we use a simplified self-similar fracture model with only a few parameters, where the propagation of the fracture front is decoupled from the calculation of the slip. The approximative method is flexible and computationally efficient. We discuss the strengths and limitations of the model with real-case examples of well-studied earthquakes. These include the M-w 8.3 2015 Illapel, Chile, megathrust earthquake at the plate interface of a subduction zone and examples of continental intraplate strike-slip earthquakes like the M-w 7.1 2016 Kumamoto, Japan, multisegment variable slip event or the M-w 7.5 2018 Palu, Indonesia, supershear earthquake. Despite the simplicity of the model, a large number of observational features ranging from different rupture-front isochrones and slip distributions to directional waveform effects or high slip patches are easy to model. The temporal evolution of slip rate and rise time are derived from the incremental growth of the rupture and the stress drop without imposing other constraints. The new model is fast and implemented in the open-source Python seismology toolbox Pyrocko, ready to study the physics of rupture and to be used in finite source inversions.}, language = {en} }