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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.
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.
The design of an array configuration is an important task in array seismology during experiment planning. Often the array response function (ARF), which depends on the relative position of array stations and frequency content of the incoming signals, is used as the array design criterion. In practice, additional constraints and parameters have to be taken into account, for example, land ownership, site-specific noise levels or characteristics of the seismic sources under investigation. In this study, a flexible array design framework is introduced that implements a customizable scenario modelling and optimization scheme by making use of synthetic seismograms. Using synthetic seismograms to evaluate array performance makes it possible to consider additional constraints. We suggest to use synthetic array beamforming as an array design criterion instead of the ARF. The objective function of the optimization scheme is defined according to the monitoring goals, and may consist of a number of subfunctions. The array design framework is exemplified by designing a seven-station small-scale array to monitor earthquake swarm activity in Northwest Bohemia/Vogtland in central Europe. Two subfunctions are introduced to verify the accuracy of horizontal slowness estimation; one to suppress aliasing effects due to possible secondary lobes of synthetic array beamforming calculated in horizontal slowness space and the other to reduce the event’s mislocation caused by miscalculation of the horizontal slowness vector. Subsequently, a weighting technique is applied to combine the subfunctions into one single scalar objective function to use in the optimization process.
Understanding and constraining the source of geodetic deformation in volcanic areas is an important component of hazard assessment. Here, we analyse deformation and seismicity for one year before the March 2021 Fagradalsfjall eruption in Iceland. We generate a high-resolution catalogue of 39,500 earthquakes using optical cable recordings and develop a poroelastic model to describe three pre-eruptional uplift and subsidence cycles at the Svartsengi geothermal field, 8 km west of the eruption site. We find the observed deformation is best explained by cyclic intrusions into a permeable aquifer by a fluid injected at 4 km depth below the geothermal field, with a total volume of 0.11 ± 0.05 km3 and a density of 850 ± 350 kg m–3. We therefore suggest that ingression of magmatic CO2 can explain the geodetic, gravity and seismic data, although some contribution of magma cannot be excluded.
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.
The occurrence of deep low-frequency (DLF) microearthquakes beneath volcanoes is commonly attributed to mass transport in the volcanic plumbing system and used to infer feeding channels from and into magma reservoirs. The key question is how magmas migrate from depth to the shallow crust and whether magma reservoirs are currently being recharged. For the first time since the improvement of the local seismic networks in the East Eifel region (Rhineland-Palatinate, Germany), we detect and locate recurrent DLF earthquakes in the lower crust and upper mantle beneath the Laacher See Volcano (LSV), using a joint data set of permanent sensors and a temporary deployment. So far, eight DLF earthquake sequences were observed in four distinct clusters between 10 and 40 km depth. These clusters of weak events (M-L< 2) align along an approximately 80. southeast dipping line south of the LSV. Moment tensor solutions of these events have large shear components, and the irregular dispersion and long coda of body waves indicate interaction processes between shear cracks and fluids. We find a rotation of P-axes orientation for shallow tectonic earthquakes compared to DLF events, indicating that the stress field in the depth interval of DLF events might favour a vertical migration of magma or magmatic fluids. The caldera of the LSV was formed by the last major eruption of the East Eifel Volcanic Field only 12.9 kyr ago, fed by a shallow magma chamber at 5-8 km depth and erupting a total magma volume of 6.7 km(3). The observed DLF earthquake activity and continuous volcanic gas emissions around the LSV indicate an active magmatic system, possibly connected with an upper mantle melt zone.
Earthquake source arrays
(2020)
A collection of earthquake sources recorded at a single station, under specific conditions, are considered as a source array (SA), that is interpreted as if earthquake sources originate at the station location and are recorded at the source location. Then, array processing methods, that is array beamforming, are applicable to analyse the recorded signals. A possible application is to use source array multiple event techniques to locate and characterize near-source scatterers and structural interfaces. In this work the aim is to facilitate the use of earthquake source arrays by presenting an automatic search algorithm to configure the source array elements. We developed a procedure to search for an optimal source array element distribution given an earthquake catalogue including accurate origin time and hypocentre locations. The objective function of the optimization process can be flexibly defined for each application to ensure the prerequisites (criteria) of making a source array. We formulated four quantitative criteria as subfunctions and used the weighted sum technique to combine them in one single scalar function. The criteria are: (1) to control the accuracy of the slowness vector estimation using the time domain beamforming method, (2) to measure the waveform coherency of the array elements, (3) to select events with lower location error and (4) to select traces with high energy of specific phases, that is, sp- or ps-phases. The proposed procedure is verified using synthetic data as well as real examples for the Vogtland region in Northwest Bohemia. We discussed the possible application of the optimized source arrays to identify the location of scatterers in the velocity model by presenting a synthetic test and an example using real waveforms.
With the present study, we introduce a fast and robust method to calculate the source displacement spectra of small earthquakes on a local to regional scale. The work is based on the publicly available Qopen method of full envelope inversion, which is further tuned for the given purpose. Important source parameters-seismic moment, moment magnitude, corner frequency, and high-frequency fall off-are determined from the source spectra by fitting a simple earthquake source model. The method is demonstrated by means of a data set comprising the 2018 West Bohemia earthquake swarm. We report moment magnitudes, corner frequencies, and centroid moment tensors inverted from short-period body waves with the Grond package for all earthquakes with a local magnitude larger than 1.8. Moment magnitudes calculated by envelope inversion show a very good agreement to moment magnitudes resulting from the probabilisitc moment tensor inversion. Furthermore, source displacement spectra from envelope inversion show a good agreement with spectra obtained by multiple taper analysis of the direct onsets of body waves but are not affected by the large scatter of the second. The seismic moments obtained with the envelope inversion scale with corner frequencies according to M-0 proportional to f(c)(-4.7). Earthquakes of the present data set result in a smaller stress drop for smaller magnitudes. Self-similarity of earthquake rupture is not observed. In addition, we report frequency-dependent site amplification at the used stations.
Full-waveform-based characterization of acoustic emission activity in a mine-scale experiment
(2020)
Understanding fracturing processes and the hydromechanical relation to induced seismicity is a key question for enhanced geothermal systems (EGS). Commonly massive fluid injection, predominately causing hydroshearing, are used in large-scale EGS but also hydraulic fracturing approaches were discussed. To evaluate the applicability of hydraulic fracturing techniques in EGS, six in situ, multistage hydraulic fracturing experiments with three different injection schemes were performed under controlled conditions in crystalline rock at the Aspo Hard Rock Laboratory (Sweden). During the experiments the near-field ground motion was continuously recorded by 11 piezoelectric borehole sensors with a sampling rate of 1 MHz. The sensor network covered a volume of 30x30x30 m around a horizontal, 28-m-long injection borehole at a depth of 410 m. To extract and characterize massive, induced, high-frequency acoustic emission (AE) activity from continuous recordings, a semi-automated workflow was developed relying on full waveform based detection, classification and location procedures. The approach extended the AE catalogue from 196 triggered events in previous studies to more than 19600 located AEs. The enhanced catalogue, for the first time, allows a detailed analysis of induced seismicity during single hydraulic fracturing experiments, including the individual fracturing stages and the comparison between injection schemes. Beside the detailed study of the spatio-temporal patterns, event clusters and the growth of seismic clouds, we estimate relative magnitudes and b-values of AEs for conventional, cyclic progressive and dynamic pulse injection schemes, the latter two being fatigue hydraulic fracturing techniques. While the conventional fracturing leads to AE patterns clustered in planar regions, indicating the generation of a single main fracture plane, the cyclic progressive injection scheme results in a more diffuse, cloud-like AE distribution, indicating the activation of a more complex fracture network. For a given amount of hydraulic energy (pressure multiplied by injected volume) pumped into the system, the cyclic progressive scheme is characterized by a lower rate of seismicity, lower maximum magnitudes and significantly larger b-values, implying an increased number of small events relative to the large ones. To our knowledge, this is the first direct comparison of high resolution seismicity in a mine-scale experiment induced by different hydraulic fracturing schemes.