Moment Tensor Components Research Articles

Wave-Equation Moment Tensor Inversion of Microseismic Events Using Multi-Well DAS Recording

The directional nature of Distributed Acoustic Sensing (DAS) measurements can limit their usefulness for moment tensor estimation, which is traditionally inverted using multi-component sensors. However, we show that moment tensor inversion using DAS data acquired in a dual-well microseismic monitoring scenario can yield reliable estimations of all moment tensor components. Our approach is based on the adaptation of a linear waveform inversion method, utilizing 3-D anisotropic viscoelastic Green's functions, to DAS data. We estimate the moment tensors of 20 microseismic events recorded at the Hydraulic Fracturing Test Site II (HFTS2) site after relocation and velocity model updates. We observe a very good match between field and synthetic data generated using the inverted moment tensors. Accurate event locations and reasonable velocity models are important for successful moment tensor inversion. Resolution analysis of each moment tensor component, taking into account the influence of the array and the noise-dependent uncertainty, shows that the unidirectional recording of DAS is not a limiting factor for this acquisition geometry. Noise unevenly influences the uncertainty of the different moment tensor components, but most of them remain resolvable for most events even with low signal-to-noise ratio. We show that the horizontal parts of the array contribute mostly to Mxx, Myy, and Mxy, whereas the vertical parts are important for Mzz, Myz, and Mxz. The inversion and resolution analysis methodology is scale-independent and can be used to study the moment tensor resolution of alternative acquisition geometries in microseismic monitoring configurations or seismological studies.

Source analysis of low frequency seismicity at Mt. Vesuvius by a hybrid moment tensor inversion

Seismicity at Mt. Vesuvius has been relatively weak in the last decades. While the occurrence of shallow volcano-tectonic (VT) events at Mt. Vesuvius is well known, the occurrence of deeper low frequency events (LF) was only recently recognized. Previous source studies only targeted VT events, which were found to have quite heterogeneous focal mechanisms. In this paper, we perform for the first time the source inversion of LF seismicity at Mt. Vesuvius, analysing 27 LF events recorded from 2012 to 2021 with the aim to investigate their source processes. Given the challenges of analysing weak LF earthquakes, we implement a specific moment tensor (MT) inversion approach that combines the fit of displacement seismograms in the time domain and amplitude spectra in the frequency domain. The inversion is simultaneously performed for the source depth and moment tensor components in the 2–7 and 2–5 Hz frequency band, assuming either a full or deviatoric MT representation. Source parameter uncertainties are estimated by using a Bayesian bootstrapping scheme. Our results confirm a larger depth of LF events compared to VTs and show a strong heterogeneity of the LF seismic sources, which present various rupture types, different orientations and heterogeneous, whilst poorly resolved, non-double-couple components. The MT variability is qualitatively confirmed by significant differences among the recorded waveforms. The heterogeneity of both VT and LF source processes is attributed to complex source processes in a highly fractured seismogenic volume submitted to a heterogeneous stress field.

Full-waveform automatic location of small seismic events in an underground mine using synthetic strain Greens tensors

A reliable method to locate microseismic evets is an important objective for routine mine seismic monitoring. We developed an algorithm that can automatically and reliably locate an event from a single uniaxial trace. Signals created by microseismic events are recorded as seismograms that consist of direct P- and S-waves as well as the waves reflected off the underground excavations. We take advantage of the extra complexity these reflections introduce as they make the signal more unique. In our investigation we cross-correlated unaltered synthetic seismograms against trial waveforms created from a linear combination of appropriate waveforms from a library of numerically calculated strain Green's tensors. We use a single uniaxial synthetic seismogram to invert for the source location, six moment tensor components, and frequency. The resulting cost functions are constructed as maximal correlations at each node in the mine grid through the true source x-planes. This function is maximized by differential evolution to simultaneously yield the source parameters. Sensitivity tests such as shifting the mine plans and altering the background velocities of the media are investigated to test the robustness of the method. We contaminate the data with 40% white noise to test the resolution against simulated real recorded seismograms. The method is demonstrated using synthetic data calculated with a realistic underground 3D velocity model.

Earthquake source inversion by integrated fiber-optic sensing

We present an earthquake source inversion using a single time series produced by integrated fiber-optic sensing in a phase noise cancellation (PNC) system used for frequency metrology. Operating on a 123 km long fiber between Bern and Basel (Switzerland), the PNC system recorded the Mw3.9 Mulhouse earthquake that occurred on 10 September 2022 around 10 km north-west of the northern fiber end. A generalised least-squares inversion in the 4 - 13 s period band constrains the components of a double-couple moment tensor with an uncertainty that corresponds to around 0.2 moment magnitude units, nearly independent of prior information. Uncertainties for hypocenter location and original time are more variable, ranging between 4 - 20 km and 0.1 - 1 s, respectively, depending on whether injected prior information is realistic or almost absent. This work is a proof of concept that quantifies the resolvability of earthquake source properties under specific conditions using a single-channel stand-alone integrated (non-distributed) fiber-optic measurement. It thereby constitutes a step towards the integration of long-range phase-transmission fiber-optic sensors into existing seismic networks in order to fill significant seismic data gaps, especially in the oceans.

Which Global Moment Tensor Catalog Provides the Most Precise Non-Double-Couple Components?

Abstract The availability of digital seismic waveform data enabled compilation of seismic moment tensor catalogs that provide information about earthquake source processes beyond what could be derived from earlier methods that assume double-couple sources representing slip on planar faults. This additional versatility involves additional complexity. Moment tensors are determined by inversions minimizing the misfit between observed and synthetic waveforms, and depend on the specifics of the data inverted, the inversion algorithm, and the Earth structure assumed. Hence, substantial uncertainties arise in moment tensors and quantities derived from them, which can be assessed by comparing moment tensors from multiple global and regional catalogs using different data and inversion procedures. While the double-couple (DC) components of moment tensors are generally determined with greater certainty, non-double-couple (NDC) components for the same earthquake sometimes differ significantly between catalogs. This observation raises questions about the reliability of their determination and hence their geological significance. Using the correlation between NDC components in different catalogs, we quantify the reliability of NDC components in moment tensor catalogs through the determination of the effects of unmodeled and inaccurately modeled effects contained in them. We determine that the NDC components in the Global Centroid Moment Tensor catalog are, on average, more precise than in other catalogs, and thus studies on NDC components should be based on this catalog. Furthermore, their uncertainties are largely unrelated to uncertainties in the DC components. Therefore, the reliability of fault angles derived from a moment tensor is largely independent from the reliability of its NDC components.

Simultaneous waveform inversion of seismic-while-drilling data for P-wave velocity, density, and source parameters

Full-waveform inversion (FWI), as an optimization-based approach to estimating subsurface models, is limited by incomplete acquisition and illumination of the subsurface. The incorporation of additional data from new and independent raypaths should be expected to result in significant increase in the accuracy of FWI models. In principle, seismic-while-drilling (SWD) technology can supply these additional raypaths; however, it introduces a new suite of unknowns, namely precise source locations (i.e., drilling path), source signature, and radiation characteristics. A new FWI algorithm is formulated in which the source radiation patterns and positions join the velocity and density values of the grid cells as unknowns to be determined. Several numerical inversion experiments are then conducted with different source settings using a synthetic model. The SWD sources are supplemented by explosive sources and multicomponent receivers at the surface, simulating a conventional surface acquisition geometry. The subsurface model and SWD source properties are recovered and analyzed. The analysis is suggestive that SWD involvement can enhance the accuracy of FWI models, with varying degrees of enhancement depending on factors such as trajectory inclination, source density, and drill path extension. The impact of SWD-FWI over standard FWI is reduced when low-frequency data are missing, but improvements over the models constructed with no subsurface sources remain. This formulation permits general source information, such as position and moment tensor components, to be independently obtained. This inversion scheme may lead to a range of potential applications for which medium properties and source information are required.

Seismic moment tensor inversion with theory errors from 2-D Earth structure: implications for the 2009–2017 DPRK nuclear blasts

SUMMARY Determining the seismic moment tensor (MT) from the observed waveforms with available Earth's structure models is known as seismic waveform MT inversion. It remains challenging for small to moderate-size earthquakes at regional scales. First, because shallow isotropic (ISO) and compensated linear vector dipole (CLVD) components of MT radiate similar long-period waveforms at regional distances, an intrinsic ISO-CVLD ambiguity impedes resolving seismic sources at shallow depths within the Earth's crust. Secondly, regional scales usually bear 3-D structures; thus, inaccurate Earth's structure models can cause unreliable MT solutions but are rarely considered a theory error in the MT inversion. So far, only the error of the 1-D earth model (1-D structural error), apart from data errors, has been explicitly modelled in the source studies because of relatively inexpensive computation. Here, we utilize a hierarchical Bayesian MT inversion to address the above problems. Our approach takes advantage of affine-invariant ensemble samplers to explore the ISO-CLVD trade-off space thoroughly and effectively. Station-specific time-shifts are also searched for as free parameters to treat the structural errors along specific source–station paths (2-D structural errors). Synthetic experiments demonstrate the method's advantage in resolving the dominating ISO components. The explosive events conducted by the Democratic People's Republic of Korea (DPRK) are well-studied, and we use them to demonstrate highly similar source mechanisms, including dominating ISO and significant CLVD components. The recovered station-specific time-shifts from the blasts present a consistent pattern, which provides a better understanding of the azimuthal variation of Earth's 2-D structures surrounding the events’ location.

Study on the semi-circular bend method for characterizing the mixed mode I/II fracture toughness of sandstone: A micro-perspective

Manufacturing and precracking specimens for semi-circular bend (SCB) tests are simple processes and do not require complicated loading devices. They have been used to conduct mode I, mode II and mixed mode I/II fracture tests on brittle materials. However, characterizing mode I and mode II fractures from a microcosmic and quantitative perspective has never been thoroughly evaluated. In this paper, high-resolution digital image correlation (DIC) and moment tensor inversion are first used to quantitatively measure micron-level displacement and analyse microfailure types. The DIC results indicate that SCB specimens with a notch inclination angle exhibit both opening displacement and sliding displacement, resulting in a mixed mode I/II fracture. A quantitative analysis of three typical classification methods based on moment tensor inversion suggests that SCB specimens with mixed loads are mainly tensile mechanisms. Some tensile sources are not pure tensile cracks, and shear components also play an important role. It is also observed that the moment tensor components, nature of sources and Hudson k value are associated with the notch inclination angle, which sheds new light on the mechanism of mixed mode I/II fractures.

Constraint on the focal mechanism of the 2011 Tohoku earthquake from the radial modes

Different from other normal modes of the Earth's free oscillation that depend on all the six components (Mrr, Mtt, Mpp, Mrt, Mrp, and Mtp) of the centroid moment tensor, the amplitudes of the radial modes depend on the Mrr component (e.g., scalar moment (M0), dip (δ), and slip (λ)) and hypocenter depth of the focal mechanism, and hence can be easily used to constrain these parameters of the focal mechanism. In this study, we use the superconducting gravimeter (SG) records after the 2011 Tohoku earthquake to analyze the radial modes 0S0 and 1S0. Based on the solutions of the focal mechanism provided by the GCMT and USGS, we can obtain the theoretical amplitudes of these two radial modes. Comparing the theoretical amplitudes with the observation amplitudes, it is found that there are obvious differences between the former and the latter, which means that the GCMT and USGS focal mechanisms cannot well represent the real focal mechanism of the 2011 event. Taking the GCMT solution as a reference and changing the depth and the three parameters of the Mrr moment, the scalar moment (M0) and the dip (δ) have significant influences, but the effects of the slip (λ) and the depth are minor. After comparisons, we provide a new constraint (M0 = 5.8 ± 0.09 × 1022 N·m, δ = 10.1 ± 0.08°, λ = 88°, and depth = 20 km) for the focal mechanism of the 2011 event. In addition, we further determine the center frequency (1.631567 ± 2.6e-6 mHz) and quality factor (2046.4± 50.1) of the 1S0 mode.

When are Non-Double-Couple Components of Seismic Moment Tensors Reliable?

There has been considerable discussion as to how to assess when non-double-couple (NDC) components of seismic moment tensors represent real source processes. We explore this question by comparing moment tensors (MTs) of earthquakes in three global catalogs, which use different inversion procedures. Their NDC components are only weakly correlated between catalogs, suggesting that they are largely artifacts of the inversion. A monotonic decrease in the NDC components' standard deviation with magnitude indicates increased reliability of the NDC components for larger earthquakes. The standard deviation begins to decrease for large NDC components exceeding 60%, suggesting that they represent real source processes. Randomly generated NDC components with the same mean and standard deviation as in the MT catalogs only reproduce some of this decrease. Thus NDC components of large earthquakes and NDC components that exceed 60% are likely to represent real source processes.

Optimum sensor configuration of surface arrays for retrieving accurate source mechanisms of microseismic events

Hydraulic fracturing and induced networks are significant for effective production of oil and gas from unconventional resources. The knowledge of fracturing source mechanisms is helpful for optimizing hydraulic fracturing treatments to maximize production. For source monitoring, the moment tensor inversion is commonly used and the source mechanisms are interpreted by the radiation patterns of microseismic waves. The accuracy of source interpretation is significantly influenced by sensor configurations, which still need further researches. In this study, the mechanism of sensor arrangements to suppress noise effect is analyzed and clarified mathematically, then an optimization method of searching for proper sensor configurations is proposed. For superior sensor configurations, errors caused by noise can be allocated evenly to the 6 moment tensor components and the source interpretation based on the moment tensor decomposition is till accurate, but errors can not be completely eliminated by optimizing sensor configurations. Generally, high-precision inversion results can be calculated by the sensor configuration that one sensor is at the center and the others are around at the same angular intervals. Compared with tradition sensor configurations, this new one can achieve similar inversion accuracy by less than a third of the sensors. Sensor numbers are not the more the better and dependent on the sizes of the regions of sensor arrangement. The conclusions arrived in this study are helpful for evaluating and designing sensor configurations for hydraulic fracturing monitoring.

Moment Tensor Solutions for Earthquakes in the Southern Korean Peninsula Using Three-Dimensional Seismic Waveform Simulations

Precise estimates of earthquake source properties are crucial for understanding earthquake processes and assessing seismic hazards. Seismic waveforms can be affected not only by individual event properties, but from the Earth’s interior heterogeneity. Therefore, for accurate constraints on earthquake source parameters, the effects of three-dimensional (3D) velocity heterogeneity on seismic wave propagation need evaluation. In this study, regional moment tensor solutions for earthquakes around the southern Korean Peninsula were constrained based on the spectral-element moment tensor inversion method using a recently developed high-resolution regional 3D velocity model with accurate high-frequency waveform simulations. Located at the eastern margin of the Eurasian plate, the Korean Peninsula consists of complex geological units surrounded by thick sedimentary basins in oceanic areas. It exhibits large lateral variations in crustal thickness (> 10 km) and seismic velocity (>10% dlnVs) at its margins in the 3D model. Seismic waveforms were analyzed from regional earthquakes with local magnitudes > 3.4 that occurred within and around the peninsula recorded by local broadband arrays. Moment tensor components were inverted together with event locations using the numerically calculated Fréchet derivatives of each parameter at periods ≥ 6 s. The newly determined solutions were compared with the results calculated from the one-dimensional (1D) regional velocity model, revealing a significant increase in a double-couple component of > 20% for earthquakes off of the coastal margins. Further, compared to initial solutions, ≤ 5 km change in depth was observed for earthquakes near the continental margin and sedimentary basins. The combination of a detailed 3D crustal model and accurate waveform simulations led to an improved fit between data and synthetic seismograms. Accordingly, the present results provide the first confirmation of the effectiveness of using 3D velocity structures for accurately constraining earthquake source parameters and the resulting seismic wave propagation in this region. We suggest that accurate 3D wave simulations, together with improved source mechanisms, can contribute a reliable assessment of seismic hazards in regions with complex continental margin structures and sedimentary basins from offshore earthquakes whose seismic waveforms can be largely affected by 3D velocity structures.

An efficient method to propagate model uncertainty when inverting seismic data for time domain seismic moment tensors

SUMMARY We present a computationally efficient method to approximately propagate uncertainty when linearly inverting seismic data for point source, time variable moment tensor components. The method is based on the assumption that the data residual, given by the difference between the observed seismic data and the data predicated by a linear inversion, contains the effects of both data and model uncertainty. Our method uses a distribution of data residuals, added directly to the data, in a pseudo-Monte Carlo scheme. Using the assumption that the data residual is a stochastic process, we use the well-known Karhunen–Loève (KL) theorem to construct a distribution of data residuals, where the required basis functions are constructed using Fourier series. The Fourier series are scaled by a product of a random variable and the real-valued spectral amplitudes of the original data residual’s spectrum. Thus, the Fourier series and spectral amplitudes are eigenfunction-eigenvalue pairs used in the KL-based construction of data residual distribution. Using tests with synthetic data, we show that our method compares closely with a Finite Difference Monte Carlo (FDMC) method that we presented previously. More importantly, the method presented here is computationally several orders of magnitude faster than our previous FDMC method, and requires no a priori assumptions of model and/or data uncertainty.

Waveform Energy Focusing Tomography With Passive Seismic Sources

By taking advantage of the information carried by the entire seismic wavefield, Full Waveform Inversion (FWI) is able to yield higher resolution subsurface velocity models than seismic traveltime tomography. However, FWI heavily relies on the knowledge of source information and good initial models, and could be easily trapped into local minima caused by cycle skipping issue because of its high nonlinearity. To mitigate these issues in FWI, we propose a novel method called Waveform Energy Focusing Tomography (WEFT) for passive seismic sources. Unlike conventional FWI, WEFT back-propagates the seismic records directly instead of the data residuals, and updates the velocity models by maximizing the stacking energy for all the moment tensor components from back-propagated wavefields around the sources. Therefore, except for source locations and origin times, WEFT does not require other source attributes in advance for the inversion. Since WEFT does not aim at fitting synthetic and observed waveforms, it has lower nonlinearity and is less prone to the cycle skipping issue compared to FWI. For the proof of concept, we have validated WEFT using several 2D synthetic tests to show it is less affected by inaccurate source locations and data noise. These advantages render WEFT more applicable for tomography using passive seismic sources when the source information is generally not accurately known. Although the inverted model from WEFT is inevitably influenced by the source distribution as well as its radiation patterns, and its resolution is likely lower than that of FWI, it can act as an intermediate step between traveltime tomography and FWI by providing a more reliable and accurate velocity model for the latter.

Moment tensor catalogue of earthquakes in West Bohemia from 2008 to 2018

Abstract. We present a unique catalogue of full moment tensors (MTs) of earthquakes with ML between 0.5 and 4.4 that occurred in West Bohemia, Czech Republic, in the period from 2008 to 2018 (Vavryčuk et al., 2022a, b). The MTs were calculated from vertical components of P-wave amplitudes. The MT inversion was based on principal component analysis applied to optimally filtered velocity records of local seismic stations deployed in the West Bohemia area. The minimum number of inverted stations is 15, and the rms between theoretical and observed amplitudes is lower than 0.5. The catalogue is exceptional in several aspects: (1) it represents an extraordinary, extensive dataset of more than 5100 MTs; (2) it covers a long period of seismicity in the studied area, during which several prominent earthquake swarms took place; (3) the locations and retrieved MTs of earthquakes are of a high accuracy. Additionally, we provide three-component records at the West Bohemia (WEBNET) seismic stations, the velocity model in the region, and the technical specification of the stations. The dataset is ideal for being utilized by a large community of researchers for various seismological purposes, e.g. for studies of (1) the migration of foci and the spatiotemporal evolution of seismicity, (2) redistribution of stress during periods of intense seismicity, (3) the interaction of faults, (4) the Coulomb stress along the faults and local stress anomalies connected to fault irregularities, (5) diffusivity of fluids along the activated faults, or (6) the time-dependent seismic risk due to the migration of seismicity in the region. In addition, the dataset is optimum for developing and testing new inversions for MTs and for tectonic stress. Since most of the earthquakes are non-shear, the dataset can contribute to studies of non-double-couple components of MTs and their relation to shear–tensile fracturing and/or seismic anisotropy in the focal zone.

Combining translational and rotational seismic motions to invert local-scale seismic data for time-variable moment tensors: do rotational motions help for high-frequency seismic data produced by underground explosions?

SUMMARY We present an analysis of combining translational and rotational seismic data in an inversion for the time-variable source time functions corresponding to the components of the seismic moment tensor. We conduct a series of numerical experiments where the data are simulated by a combination of an underground explosion and a co-located double couple shear source and recorded on surface-mounted seismometers within 1–2 km of the source. The experiments are designed to mimic explosion seismology experiments, and thus the data are in the 1–10 Hz frequency range and contain very few surface waves. We use a Monte Carlo method to propagate Earth model uncertainty into the estimates of seismic source parameters. In our experiments, we find that the uncertainty of the estimated seismic source parameters increases when we add rotational seismic motions to the inversion when using a constant number of data channels. In this case, the increased degree of uncertainty in the final results is most likely due to the near-surface Earth model uncertainty that we introduce in our simulations. However, for a fixed number of seismic stations, adding rotational seismic motions to the inversion acts to decrease the uncertainty of the estimated seismic source parameters, most likely due to the increase in the number of data channels used in the inversion.

Consistency of Non-Double-Couple Components of Seismic Moment Tensors with Earthquake Magnitude and Mechanism

Abstract Earthquake moment tensors can be decomposed into double-couple components describing slip on planar faults and non-double-couple (NDC) components. NDC components can arise in three ways. Some appear to be intrinsic, indicating complex source processes differing from slip on a fault for earthquakes in specific geologic environments, notably volcanic areas. Others are additive, reflecting the combined effect of double-couple sources on multiple faults with different geometries. Alternatively, they may be artifactual, results of the inversion without geologic meaning. Combining moment tensors from three global and four regional catalogs for 2016–2020 provides a dataset of NDC components of 12,856 earthquakes with 2.9<Mw<8.2 in various geologic environments. The distributions of NDC components vary only slightly with magnitude, with a mean deviation from a double-couple source of around 20%. The consistency suggests that most NDC components do not reflect rupture on multiple faults, which is expected only for larger earthquakes. Similarly, there are only small differences in NDC components between earthquakes with different faulting mechanisms or in different geologic environments. These consistencies suggest that most NDC components are not intrinsic due to complex source processes that are often assumed to be most likely in volcanic and thus extensional areas. Hence, it appears that for most earthquakes, especially smaller ones, the NDC components are largely artifacts of the inversion.

Investigating the effects of random data errors on the waveform-based moment tensor inversion

SUMMARY The linear Gauss–Markov model for waveform-based moment tensor inversion often relies on the overdetermined least-squares method. It needs a proper stochastic model of the observables for accurate and precise estimates of the unknown parameters. Furthermore, estimating the level and distribution of random errors in the observed waveforms is challenging due to assessing the minimum-variance unbiased estimator (MVUE). Hence, according to the considerable effects of random data errors in assessing the uncertainty of the moment tensor components, this paper aims to describe an MVUE of the data covariance matrix and its application on uncertainty quantification of the moment tensor. The used mathematical prescription allows us to use the covariance matrix for the three-component noise records at every station and all possible cross-correlations among the recorded noise wavefield. To illustrate the proposed method’s performance, we conducted tests with synthetic data using configuration of the 2018 Mw 6.8 Zakynthos (Ionian Sea, Greece) earthquake. Both uncorrelated and correlated random noise traces were added to the synthetic waveform data in amounts between 5 and 20 per cent of the maximum amplitude. In order to test the efficiency of the method, we considered three different structures of covariance matrix: (i) diagonal matrix (contains a variance of individual measurements at seismic stations), (ii) block-diagonal matrix (considering cross-covariance among three components at each station), and (iii) full covariance matrix. Test results are presented by comparison of the moment tensor inversion outcomes with known noise levels of generated synthetic data and with synthetic focal mechanisms, the ability of the estimated full covariance matrix in illustrating the minimum variance of parameters (namely, minimum posterior uncertainties), unbiased of the parameters, and values of the cross-correlations between the components of each station and also among stations. Finally, we applied the method to the real waveforms of the Zakynthos earthquake having inferred focal mechanism of strike/dip/rake angles 13/40/171 (deg) with 33 per cent double couple (DC) and −61 per cent compensated linear vector dipole component (CLVD). The focal mechanism solution has strike/dip/rake angles 19/34/177 (deg) with 69 per cent DC and −23 per cent CLVD when using our estimated full covariance matrix.

Modeling of earthquake source parameters on December 12, 2018 (08:49:56,16; 36,4478° N; 140,5788° E; H = 62,0 km; Mw = 4,3, Japan)

Modeling of earthquake source parameters, such as the orientation of the fault plane and the direction of the fault slip, is important for understanding the physics of earthquake source processes, determining the stress-strain state of the geological medium and seismic hazard estimation. For modeling source parameters of the earthquake on December 12, 2018 at 08:49:56,16 (UTC) in Japan (36,4478° N, 140,5788° E, Northern Ibaraki Pref region) at a depth of 62 km with a magnitude of Mw = 4.3, the waveforms inversion was used to determine seismic moment tensor and representation it through a focal mechanism. The earthquake source is considered as a point source of seismic waves which propagate in a medium represented by a set of horizontally homogeneous elastic layers. An algorithm for determining seismic tensor components based on the forward problem solved by the matrix method, and using the generalized inverse solution, selecting only direct waves is applied. The input data for determining seismic moment components are data of only direct P waves selected from the observed records at six seismic stations of the Japanese local network NIED F-net: TSK, YMZ, ASI, ONS, SBT, KSK. The seismic moment tensor components were determined through waveform inversion using the matrix method. The obtained results, presented through a focal mechanism, are compared to the results obtained by the National Research Institute of Earth Sciences and Resistance to Natural Disasters (NIED CMT solutions). As a result of focal mechanisms comparison, it is concluded that the proposed algorithm for determining seismic moment tensor components can be used if it is impossible to use another method, or requires some refinement for another method. This approach is especially relevant for regions with low seismicity and insufficient number of stations. In addition, this method reduces the effects of an inaccurate medium model, because direct waves are much less distorted than reflected and converted, and that increases the accuracy and reliability of the method.

Accelerating Bayesian microseismic event location with deep learning

Abstract. We present a series of new open-source deep-learning algorithms to accelerate Bayesian full-waveform point source inversion of microseismic events. Inferring the joint posterior probability distribution of moment tensor components and source location is key for rigorous uncertainty quantification. However, the inference process requires forward modelling of microseismic traces for each set of parameters explored by the sampling algorithm, which makes the inference very computationally intensive. In this paper we focus on accelerating this process by training deep-learning models to learn the mapping between source location and seismic traces for a given 3D heterogeneous velocity model and a fixed isotropic moment tensor for the sources. These trained emulators replace the expensive solution of the elastic wave equation in the inference process. We compare our results with a previous study that used emulators based on Gaussian processes to invert microseismic events. For fairness of comparison, we train our emulators on the same microseismic traces and using the same geophysical setting. We show that all of our models provide more accurate predictions, ∼ 100 times faster predictions than the method based on Gaussian processes, and a 𝒪(105) speed-up factor over a pseudo-spectral method for waveform generation. For example, a 2 s long synthetic trace can be generated in ∼ 10 ms on a common laptop processor, instead of ∼ 1 h using a pseudo-spectral method on a high-profile graphics processing unit card. We also show that our inference results are in excellent agreement with those obtained from traditional location methods based on travel time estimates. The speed, accuracy, and scalability of our open-source deep-learning models pave the way for extensions of these emulators to generic source mechanisms and application to joint Bayesian inversion of moment tensor components and source location using full waveforms.