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We present an approach for rapidly estimating full moment tensors of earthquakes and their parameter uncertainties based on short time windows of recorded seismic waveform data by considering deep learning of Bayesian Neural Networks (BNNs). The individual neural networks are trained on synthetic seismic waveform data and corresponding known earthquake moment-tensor parameters. A monitoring volume has been predefined to form a three-dimensional grid of locations and to train a BNN for each grid point. Variational inference on several of these networks allows us to consider several sources of error and how they affect the estimated full moment-tensor parameters and their uncertainties. In particular, we demonstrate how estimated parameter distributions are affected by uncertainties in the earthquake centroid location in space and time as well as in the assumed Earth structure model. We apply our approach as a proof of concept on seismic waveform recordings of aftershocks of the Ridgecrest 2019 earthquake with moment magnitudes ranging from Mw 2.7 to Mw 5.5. Overall, good agreement has been achieved between inferred parameter ensembles and independently estimated parameters using classical methods. Our developed approach is fast and robust, and therefore, suitable for down-stream analyses that need rapid estimates of the source mechanism for a large number of earthquakes.
Earthquake localization is both a necessity within the field of seismology, and a prerequisite for further analysis such as source studies and hazard assessment. Traditional localization methods often rely on manually picked phases. We present an alternative approach using deep learning that once trained can predict hypocenter locations efficiently. In seismology, neural networks have typically been trained with either single-station records or based on features that have been extracted previously from the waveforms. We use three-component full-waveform records of multiple stations directly. This means no information is lost during preprocessing and preparation of the data does not require expert knowledge. The first convolutional layer of our deep convolutional neural network (CNN) becomes sensitive to features that characterize the waveforms it is trained on. We show that this layer can therefore additionally be used as an event detector. As a test case, we trained our CNN using more than 2000 earthquake swarm events from West Bohemia, recorded by nine local three-component stations. The CNN successfully located 908 validation events with standard deviations of 56.4 m in east-west, 123.8 m in north-south, and 136.3 m in vertical direction compared to a double-difference relocated reference catalog. The detector is sensitive to events with magnitudes down to M-L = -0.8 with 3.5% false positive detections.
On 7 January 2020, an M-w 6.4 earthquake occurred in the northeastern Caribbean, a few kilometers offshore of the island of Puerto Rico. It was the mainshock of a complex seismic sequence, characterized by a large number of energetic earthquakes illuminating an east-west elongated area along the southwestern coast of Puerto Rico. Deformation fields constrained by Interferometric Synthetic Aperture Radar and Global Navigation Satellite System data indicate that the coseismic movements affected only the western part of the island. To assess the mainshock's source fault parameters, we combined the geodetically derived coseismic deformation with teleseismic waveforms using Bayesian inference. The results indicate a roughly east-west oriented fault, dipping northward and accommodating similar to 1.4 m of transtensional motion. Besides, the determined location and orientation parameters suggest an offshore continuation of the recently mapped North Boqueron Bay-Punta Montalva fault in southwest Puerto Rico. This highlights the existence of unmapped faults with moderate-to-large earthquake potential within the Puerto Rico region.
Caldera unrest can lead to major volcanic eruptions. Analysis of subtle subsidence or inflation at calderas helps understanding of their subsurface volcanic processes and related hazards. Several subsiding calderas have shown similar patterns of ground deformation composed of broad subsidence affecting the entire volcanic edifice and stronger localized subsidence focused inside the caldera. Physical models of internal deformation sources used to explain these observations typically consist of two magma reservoirs at different depths in an elastic half-space. However, such models ignore important subsurface structures, such as ring faults, that may influence the deformation pattern. Here we use both analog subsidence experiments and boundary element modeling to study the three-dimensional geometry and kinematics of caldera subsidence processes, evolving from an initial downsag to a later collapse stage. We propose that broad subsidence is mainly caused by volume decrease within a single magma reservoir, whereas buried ring-fault activity localizes the deformation within the caldera. Omitting ring faulting in physical models of subsiding calderas and using multiple point/sill-like sources instead can result in erroneous estimates of magma reservoir depths and volume changes. (C) 2019 Elsevier B.V. All rights reserved.
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.
Surface displacement at volcanic edifices is related to subsurface processes associated with magma movements, fluid transfers within the volcano edifice and gravity-driven deformation processes. Understanding of associated ground displacements is of importance for assessment of volcanic hazards. For example, volcanic unrest is often preceded by surface uplift, caused by magma intrusion and followed by subsidence, after the withdrawal of magma. Continuous monitoring of the surface displacement at volcanoes therefore might allow the forecasting of upcoming eruptions to some extent. In geophysics, the measured surface displacements allow the parameters of possible deformation sources to be estimated through analytical or numerical modeling. This is one way to improve the understanding of subsurface processes acting at volcanoes. Although the monitoring of volcanoes has significantly improved in the last decades (in terms of technical advancements and number of monitored volcanoes), the forecasting of volcanic eruptions remains puzzling. In this work I contribute towards the understanding of the subsurface processes at volcanoes and thus to the improvement of volcano eruption forecasting. I have investigated the displacement field of Llaima volcano in Chile and of Tendürek volcano in East Turkey by using synthetic aperture radar interferometry (InSAR). Through modeling of the deformation sources with the extracted displacement data, it was possible to gain insights into potential subsurface processes occurring at these two volcanoes that had been barely studied before. The two volcanoes, although of very different origin, composition and geometry, both show a complexity of interacting deformation sources. At Llaima volcano, the InSAR technique was difficult to apply, due to the large decorrelation of the radar signal between the acquisition of images. I developed a model-based unwrapping scheme, which allows the production of reliable displacement maps at the volcano that I used for deformation source modeling. The modeling results show significant differences in pre- and post-eruptive magmatic deformation source parameters. Therefore, I conjecture that two magma chambers exist below Llaima volcano: a post-eruptive deep one and a shallow one possibly due to the pre-eruptive ascent of magma. Similar reservoir depths at Llaima have been confirmed by independent petrologic studies. These reservoirs are interpreted to be temporally coupled. At Tendürek volcano I have found long-term subsidence of the volcanic edifice, which can be described by a large, magmatic, sill-like source that is subject to cooling contraction. The displacement data in conjunction with high-resolution optical images, however, reveal arcuate fractures at the eastern and western flank of the volcano. These are most likely the surface expressions of concentric ring-faults around the volcanic edifice that show low magnitudes of slip over a long time. This might be an alternative mechanism for the development of large caldera structures, which are so far assumed to be generated during large catastrophic collapse events. To investigate the potential subsurface geometry and relation of the two proposed interacting sources at Tendürek, a sill-like magmatic source and ring-faults, I have performed a more sophisticated numerical modeling approach. The optimum source geometries show, that the size of the sill-like source was overestimated in the simple models and that it is difficult to determine the dip angle of the ring-faults with surface displacement data only. However, considering physical and geological criteria a combination of outward-dipping reverse faults in the west and inward-dipping normal faults in the east seem to be the most likely. Consequently, the underground structure at the Tendürek volcano consists of a small, sill-like, contracting, magmatic source below the western summit crater that causes a trapdoor-like faulting along the ring-faults around the volcanic edifice. Therefore, the magmatic source and the ring-faults are also interpreted to be temporally coupled. In addition, a method for data reduction has been improved. The modeling of subsurface deformation sources requires only a relatively small number of well distributed InSAR observations at the earth’s surface. Satellite radar images, however, consist of several millions of these observations. Therefore, the large amount of data needs to be reduced by several orders of magnitude for source modeling, to save computation time and increase model flexibility. I have introduced a model-based subsampling approach in particular for heterogeneously-distributed observations. It allows a fast calculation of the data error variance-covariance matrix, also supports the modeling of time dependent displacement data and is, therefore, an alternative to existing methods.
Although ring faults are present at many ancient, deeply eroded volcanoes, they have been detected at only very few modern volcanic centers. At the so far little studied Tendurek volcano in eastern Turkey, we generated an ascending and a descending InSAR time series of its surface displacement field for the period from 2003 to 2010. We detected a large (similar to 105km(2)) region that underwent subsidence at the rate of similar to 1cm/yr during this period. Source modeling results show that the observed signal fits best to simulations of a near-horizontal contracting sill located at around 4.5km below the volcano summit. Intriguingly, the residual displacement velocity field contains a steep gradient that systematically follows a system of arcuate fractures visible on the volcano’s midflanks. RapidEye satellite optical images show that this fracture system has deflected Holocene lava flows, thus indicating its presence for at least several millennia. We interpret the arcuate fracture system as the surface expression of an inherited ring fault that has been slowly reactivated during the detected recent subsidence. These results show that volcano ring faults may not only slip rapidly during eruptive or intrusive phases, but also slowly during dormant phases.
The computation of such synthetic GFs is computationally and operationally demanding. As a consequence, the onthe-fly recalculation of synthetic GFs in each iteration of an optimisation is time-consuming and impractical. Therefore, the pre-calculation and efficient storage of synthetic GFs on a dense grid of source to receiver combinations enables the efficient lookup and utilisation of GFs in time-critical scenarios. We present a Python-based framework and toolkit - Pyrocko-GF - that enables the pre-calculation of synthetic GF stores, which are independent of their numerical calculation method and GF transfer function. The framework aids in the creation of such GF stores by interfacing a suite of established numerical forward modelling codes in seismology (computational back ends). So far, interfaces to back ends for layered Earth model cases have been provided; however, the architecture of Pyrocko-GF is designed to cover back ends for other geometries (e.g. full 3-D heterogeneous media) and other physical quantities (e.g. gravity, pressure, tilt). Therefore, Pyrocko-GF defines an extensible GF storage format suitable for a wide range of GF types, especially handling elasticity and wave propagation problems. The framework assists with visualisations, quality control, and the exchange of GF stores, which is supported through an online platform that provides many pre-calculated GF stores for local, regional, and global studies. The Pyrocko-GF toolkit comes with a well-documented application programming interface (API) for the Python programming language to efficiently facilitate forward modelling of geophysical processes, e.g. synthetic waveforms or static displacements for a wide range of source models.
Data recorded by distributed acoustic sensing (DAS) along an optical fibre sample the spatial and temporal properties of seismic wavefields at high spatial density. Often leading to massive amount of data when collected for seismic monitoring along many kilometre long cables. The spatially coherent signals from weak seismic arrivals within the data are often obscured by incoherent noise. We present a flexible and computationally efficient filtering technique, which makes use of the dense spatial and temporal sampling of the data and that can handle the large amount of data. The presented adaptive frequency-wavenumber filter suppresses the incoherent seismic noise while amplifying the coherent wavefield. We analyse the response of the filter in time and spectral domain, and we demonstrate its performance on a noisy data set that was recorded in a vertical borehole observatory showing active and passive seismic phase arrivals. Lastly, we present a performant open-source software implementation enabling real-time filtering of large DAS data sets.
Large earthquakes are usually modeled with simple planar fault surfaces or a combination of several planar fault segments. However, in general, earthquakes occur on faults that are non-planar and exhibit significant geometrical variations in both the along-strike and down-dip directions at all spatial scales. Mapping of surface fault ruptures and high-resolution geodetic observations are increasingly revealing complex fault geometries near the surface and accurate locations of aftershocks often indicate geometrical complexities at depth. With better geodetic data and observations of fault ruptures, more details of complex fault geometries can be estimated resulting in more realistic fault models of large earthquakes. To address this topic, we here parametrize non-planar fault geometries with a set of polynomial parameters that allow for both along-strike and down-dip variations in the fault geometry. Our methodology uses Bayesian inference to estimate the non-planar fault parameters from geodetic data, yielding an ensemble of plausible models that characterize the uncertainties of the non-planar fault geometry and the fault slip. The method is demonstrated using synthetic tests considering slip spatially distributed on a single continuous finite non-planar fault surface with varying dip and strike angles both in the down-dip and along-strike directions. The results show that fault-slip estimations can be biased when a simple planar fault geometry is assumed in presence of significant non-planar geometrical variations. Our method can help to model earthquake fault sources in a more realistic way and may be extended to include multiple non-planar fault segments or other geometrical fault complexities.