Moment Tensor Source Research Articles

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 reconstruction of micro-seismic events via topological derivative approach

Micro-seismic events, naturally occurring within geological formations and quasi-brittle engineered systems, provide a powerful window into the evolving processes of material degradation and failure. Accurate characterization of these events is critical for a comprehensive understanding of the underpinning fracturing mechanisms and potential implications. In this work, we present an algorithm for the spatial reconstruction and characterization of micro-seismic events in a three-dimensional bounded elastic body (with known geometry and nominal material properties) via combined source location and moment tensor inversion. Assuming availability of the full-waveform “acoustic emission” traces whose spectral content can be exposed via Fourier transform, the inverse solution is based on (i) a time-harmonic (forward) elastodynamic model and (ii) the concept of topological derivative as a framework for robust event reconstruction. On exploiting an equivalence between the elastic wavefield generated by the creation of a new micro-surface and that stemming from a suitable set of dipoles and double-couples (whose strengths are synthesized via the seismic moment tensor), we formulate the inverse problem as that for the real (in-phase) and imaginary (out-of-phase) components of the moment tensor at trial grid locations. In this way the optimal solution is obtained via a combinatorial search over a prescribed grid, inherently allowing for successive refinements of event reconstruction over the region(s) of interest. The analysis is illustrated by numerical experiments highlighting the key features of the inversion scheme including the reconstruction of multiple (i.e. contemporaneous) events, localization of the “off-grid” micro-seismic events, and the ability to handle noisy data. The results in particular highlight the utility of multi-frequency event reconstruction toward reducing the demand on the number of sensing locations.

Improved numerical solution of anisotropic poroelastic wave equation in microseismicity: Graphic process unit acceleration and moment tensor implementation

AbstractThe accuracy and computational efficiency of full waveform forward modelling in poroelastic media are crucial for microseismic monitoring. It enables intuitive, precise and efficient simulation of subsurface responses, thereby improving the reliability of moment tensor inversion and seismic source mechanism interpretation. Additionally, it reflects the role of fluid effects in waveform evolution. In this paper, based on the Biot mechanism, we derived the first‐order velocity–stress equation of poroelastic media and discretized the model using a rotated staggered grid. The rotated staggered grid can well adapt to anisotropic media with high contrast parameters. We provide the finite difference formula based on graphic process unit–acceleration and moment tensor and also provide the graphic process unit workflow for forward modelling of anisotropic poroelastic media. First, two models with different grid sizes were run based on single graphic process unit, 1‐thread Central Processing Unit (CPU) and 16‐thread CPU. The results show that the speedup factors are approximately 14.3 and 3.7, respectively, compared with the running time of 1‐thread CPU and 16‐thread CPU. Then, we compare and evaluate the response of three basic source mechanisms (isotropic expansion, double couple and compensated linear vector dipole) in the model. The comparison of analytical and numerical results verifies the effectiveness of the method. Furthermore, wavefield snapshots of two typical anisotropic media (vertical transversely isotropic and horizontal transversely isotropic) are analysed to correspond to different moment tensor sources. The results showed that the source mechanism does not change the isotropic and anisotropic plane and the wave travel time, but it does change the polarization amplitude of the velocity component. The attenuation of slow qP‐wave increases along with the increase of the value of viscosity. The effect of permeability on wavefield appears with the opposite effect of viscosity. Finally, the seismic waveform differences between multi‐layer elastic media and poroelastic media are compared and analysed. The results showed that the seismic wavefield and waveform of poroelastic media are more complex, the propagation speed of seismic waves is faster, but the attenuation of seismic waves is stronger.

High-resolution source imaging and moment tensor estimation of acoustic emissions during brittle creep of basalt undergoing carbonation

SUMMARY As the high-frequency analogue to field-scale earthquakes, acoustic emissions (AEs) provide a valuable complement to study rock deformation mechanisms. During the load-stepping creep experiments with CO2-saturated water injection into a basaltic sample from Carbfix site in Iceland, 8791 AE events are detected by at least one of the seven piezoelectric sensors. Here, we apply a cross-correlation-based source imaging method, called geometric-mean reverse-time migration (GmRTM) to locate those AE events. Besides the attractive picking-free feature shared with other waveform-based methods (e.g. time-reversal imaging), GmRTM is advantageous in generating high-resolution source images with reduced imaging artefacts, especially for experiments with relatively sparse receivers. In general, the imaged AE locations are found to be scattered across the sample, suggesting a complicated fracture network rather than a well-defined major shear fracture plane, in agreement with X-ray computed tomography imaging results after retrieval of samples from the deformation apparatus. Clustering the events in space and time using the nearest-neighbour approach revealed a group of ‘repeaters’, which are spatially co-located over an elongated period of time and likely indicate crack, or shear band growth. Furthermore, we select 2196 AE events with high signal-to-noise-ratio (SNR) and conduct moment tensor estimation using the adjoint (backpropagated) strain tensor fields at the locations of AE sources. The resulting AE locations and focal mechanisms support our previously assertion that creep of basalt at the experimental conditions is accommodated dominantly by distributed microcracking.

Near Real-Time Detection and Moment Tensor Inversion of the 11 May 2022, Dharchula Earthquake

On 11 May 2022, an earthquake of Mw 5.2 occurred in the Dharchula region of Uttarakhand Himalayas, India. The Uttarakhand State Earthquake Early Warning System (UEEWS) detected and transmitted the warning within 11.61 s from the origin time, taking only 4.26 s for processing, location, and magnitude estimation and warning dissemination. The complete analysis was performed using three seconds of waveforms. Using the initial earthquake parameters provided by the UEEWS, moment tensor inversion was performed using the broadband seismometers network installed in northern India. The moment tensor (MT) inversion was performed for the event using both the body waves and the surface waves. The first motion polarity was used along with waveform data to enhance the solution’s stability. This paper discusses the importance of real-time event detection and efforts towards real-time MT source inversion of earthquakes in the Uttarakhand Himalayas. Relocation of two past earthquakes near Dharchula is also undertaken in this study. The outcome of this study provides insights into mitigating seismic hazards, understanding earthquake source mechanisms, and enhancing knowledge of local fault structures.

Microseismic wavefield modelling in anisotropic elastic media using integral equation method

AbstractIn this paper, we present a frequency‐domain volume integral method to model the microseismic wavefield in heterogeneous anisotropic‐elastic media. The elastic wave equation is written as an integral equation of the Lippmann–Schwinger type, and the seismic source is represented as a general moment tensor. The actual medium is split into a background medium and a scattered medium. The background part of the displacement field is computed analytically, but the scattered part requires a numerical solution. The existing matrix‐based implementation of the integral equation is computationally inefficient to model the wavefield in three‐dimensional earth. An integral equation for the particle displacement is, hence, formulated in a matrix‐free manner through the application of the Fourier transform. The biconjugate gradient stabilized method is used to iteratively obtain the solution of this equation. The integral equation method is naturally target oriented, and it is not necessary to fully discretize the model. This is very helpful in the microseismic wavefield computation at receivers in the borehole in many cases; say, for example, we want to focus only on the fluid injection zone in the reservoir–overburden system and not on the whole subsurface region. Additionally, the integral equation system matrix has a low condition number. This provides us flexibility in the selection of the grid size, especially at low frequencies for given wave velocities. Considering all these factors, we apply the numerical scheme to three different models in order of increasing geological complexity. We obtain the elastic displacement fields corresponding to the different types of moment tensor sources, which prove the utility of this method in microseismic. The generated synthetic data are intended to be used in inversion for the microseismic source and model parameters.

Comparison of force and moment tensor estimations of subevents during the 2022 Hunga–Tonga submarine volcanic eruption

SUMMARYThe 2022 January 15 Hunga–Tonga submarine volcanic eruption was unprecedented in the modern era for its size, in terms of its plume height and atmospheric waves, including sound. Global seismic stations recorded maximal radiated energy during 30 min of the plume-forming phase of the eruption (04:00 to 04:30 UTC), with the largest subevents occurring over a 5-min interval starting at 04:15:17 UTC. Here, we consider two simple point-source models—force and moment tensor—and separately consider the single main subevent and the sequence of four subevents. Estimation of source models for the first subevent in the sequence is achieved with a complete search of model parameter space to find the global minimum of a waveform misfit function (body or surface waves). We performed 25 runs to explore the impact of depth, source model (force or moment tensor), wave type (body or surface), and component (vertical, radial, and transverse) on the waveform fits and estimated best-fitting source. Visualization of the misfit function reveals complex trade-offs among model parameters, highlighting the importance of characterizing uncertainties and parameter trade-offs. The four-subevent source model has up to 28 model parameters and requires an efficient search algorithm to find the best-fitting source. For this, we use the covariance matrix adaptation evolution strategy implemented on a high-performance computing cluster. The 10 four-subevent runs for each source model return sequences of subvertical downward forces and explosive-like moment tensors for each subevent. Our results show that these two simple source models provide comparable fits to regional and global seismic waveforms and that the source types for each subevent—either force direction or moment tensor source type on the eigenvalue lune—are similar enough to each other to consider that the subevents originate from the same process. Our estimation of the source mechanisms, sizes, and relative timing should benefit a physical interpretation of the eruption sequence.

Strain-based forward modeling and inversion of seismic moment tensors using distributed acoustic sensing (DAS) observations

This study used a waveform inversion of distributed acoustic sensing (DAS) data, acquired in two horizontal monitoring wells, to estimate the moment tensor (MT) of two induced microearthquakes. An analytical forward model was developed to simulate far-field tangential strain generated by an MT source in a homogeneous and anisotropic medium, averaged over the gauge length along a fiber of arbitrary orientation. To prepare the data for inversion, secondary scattered waves were removed from the field observations, using f-k filtering and time-windowing. The modeled and observed primary arrivals were aligned using a cut-and-paste approach. The MT parameters were inverted via a least-squares approach, and their uncertainties were determined through bootstrap analysis. Using simulated data with additive noise derived from the field data and the same fiber configuration as the monitoring wells, the inversion method adequately resolved the MT. Despite the assumption of Gaussian noise, which underlies the least-squares inversion approach, the method was robust in the presence of heavy-tailed noise observed in field data. When the inversion was applied to field data, independent inversion results using P-waves, S-waves, and both waves together yielded results that were consistent between the two events and for different wave types. The agreement of the inversion results for two events resulting from the same stress field illustrated the reliability of the method. The uncertainties of the MT parameters were small enough to make the inversion method useful for geophysical interpretation. The variance reduction obtained from the data predicted for the most probable MT was satisfying, even though the polarity of the P-waves was not always correctly reproduced.

Propagation of a vector wavelet through von Kármán-type random elastic media: Monte Carlo simulation by using the spectrum division method

SUMMARY For the study of the random velocity fluctuation of the solid Earth medium, it is useful to measure the collapse of a seismic wavelet with increasing travel distance and the excitation of coda waves. Radiative transfer theory (RTT) is a powerful tool for synthesizing the propagation of a seismic wavelet in random media statistically characterized by the power spectral density function (PSDF) of the fractional velocity fluctuation. The Born scattering coefficient is a key building block of RTT. As the centre wavenumber of a wavelet increases, the phase shift across the correlation length increases and the Born approximation leads to an extremely large forward scattering exceeding the applicable range of the perturbation method. In such a case, the Eikonal approximation is able to explain the envelope broadening with increasing travel distance; however, it can not explain the coda excitation. To overcome the difficulty, we have proposed a hybrid Monte Carlo (MC) simulation for scalar waves. In the case of von Kármán-type random media, when the centre wavenumber is higher than the corner wavenumber, taking the centre wavenumber as a reference, we divide the PSDF into two spectral components. Applying the Born and Eikonal approximations to the high- and low-wavenumber spectral components, we statistically evaluate the wide-angle scattering and the narrow-angle ray bending, respectively. The proposed MC simulation serially using two kinds of scattering processes successfully synthesizes the time trace of the wave energy density from the onset to the late coda. The travel-distance fluctuation derived from the one-way propagation of the Eikonal approximation is also important. This paper extends this method for the propagation of a vector wavelet in random elastic media. We suppose that random fractional fluctuations of the P- and S-wave velocities and the mass density are linearly proportional to each other, which maintains the linear polarization of an Swave throughout the scattering process. Using the hybrid MC simulation with the spectrum division, we synthesize three-component energy density time traces for the anisotropic radiation from a moment tensor source, from which we derive three-component root mean square (RMS) velocity amplitude time traces at different azimuths. In parallel, we synthesize the propagation of a vector wavelet in many realized random elastic media by the finite-difference simulation, then we calculate three-component RMS velocity amplitude time traces. Using them as a benchmark, we confirm the validity of the proposed MC simulation for specific cases.

Semi-analytical solution for the elastic wave propagation due to a dislocation source in a transversely isotropic half-space

SUMMARY In this paper, the 3-D theoretical seismogram at the free surface of an elastic half-space with ‘vertical transverse isotropy (VTI)’ and an ‘elliptic anisotropy‘ is synthesized via semi-analytical formulation. To this end, the time-domain solution is obtained via the Hankel and Laplace integral transforms and the Cagniard contour integration scheme. The formulations include complete Green's functions expressed in compact and elegant formulations in terms of some elementary line integrals over the finite interval (0, π/2), due to the general point force and point double-couple source of arbitrary orientation, varying with time as Heaviside step function. This solution is further implemented to model seismic waves generated from moment tensor source with a ramp-type slip function. The solution clearly delineates compressional P waves, shear SV waves and SH waves, diffracted SPwaves and surface Rayleigh waves, with two critical distances in which the mode conversion happens. The first marks the conversion of the total reflection of SV wave into the diffracted SPwave travelling on the free surface with the velocity of compressional wave. The second, however, marks a location where the order of arrival times of SP and SH waves is reversed. The interesting phenomenon of shear wave splitting by the apparent time lag between the arrivals of SV and SHwaves is further demonstrated. Studied also is the effect of non-double-couple (non-DC) components of the moment tensor of the shear fault. Particularly, it is shown that non-DC components may lead to large amplitude of the P wave in the presence of anisotropy, resulting in the changed polarity of P wave at the onset of the motion. It is found that for the elliptic anisotropy, and for oblique-thrust faults, the isotropic moment (ISO) is always negative if the elastic constants satisfy C11 > C33 and C44 > C66, whereas it is always positive if C11 < C33 and C44 < C66 (for oblique-reverse faults, the situation is reversed). It is shown that for some sedimentary rocks, the decomposition of moment tensor in the general VTI and in its elliptic approximation are close to each other, and that the moment tensor decomposition in VTI media is very sensitive to the elastic coefficients, such that a small change in the elastic constants may lead to a remarkable change in the moment tensor decomposition. Particularly, the effect of elastic constant C13 is shown to be significant. While the time-domain solution obtained in this paper can be also degenerated to the solution in the corresponding isotropic half-space, the Mathematica code of the solution provided can be served as benchmark to other numerical solutions, applicable for the computation of the theoretical seismogram in the involved media.

GPU-acceleration 3D rotated-staggered-grid solutions to microseismic anisotropic wave equation with moment tensor implementation

To improve the accuracy of microseismic inversion, seismic anisotropy and moment tensor source should be carefully considered in the forward modelling stage. In this study, 3D microseismic anisotropy wave forward modelling with a moment tensor source was proposed. The modelling was carried out based on a rotated-staggered-grid (RSG) scheme. In contrast to staggered-grids, the RSG scheme defines the velocity components and densities at the same grid, as do the stress components and elastic parameters. Therefore, the elastic moduli do not need to be interpolated. In addition, the detailed formulation and implementation of moment-tensor source loaded on the RSG was presented by equating the source to the stress increments. Meanwhile, the RSG-based 3D wave equation forward modelling was performed in parallel using compute unified device architecture (CUDA) programming on a graphics processing unit (GPU) to improve its efficiency. Numerical simulations including homogeneous and anisotropic models were carried out using the method proposed in this paper, and compared with other methods to prove the reliability of this method. Furthermore, the high efficiency of the proposed approach was evaluated. The results show that the computational efficiency of proposed method can be improved by about two orders of magnitude compared with traditional central processing unit (CPU) computing methods. It could not only help the analysis of microseismic full wavefield records, but also provide support for passive source inversion, including location and focal mechanism inversion, and velocities inversion.

Full-Waveform Inversion of Fiber-Optic VSP Data From Deviated Wells

Distributed acoustic sensing (DAS) technology permits measuring the strain or strain rate along a fiber deployed in a well due to seismic wave propagation. In vertical seismic profiling (VSP) acquisitions where seismic waves are excited at the surface and measured by subsurface receivers in the well, the DAS serves as a fast alternative to a conventional geophone array. Like conventional multicomponent VSP velocity measurements, DAS VSP data contain information about the subsurface properties that are encoded in seismic events and attributes such as compressional and shear direct arrivals, reflections, converted modes, multiples, and amplitude and phase variations. These seismic data can be used to obtain elastic properties of the formation and characterize the reservoir. Full-waveform inversion (FWI) extracts the elastic properties of the formation from the seismic wavefield by minimizing the misfit between real measurements and synthetically modeled wavefields. The synthetically generated wavefields are obtained by solving partial differential equations that accurately model the physical phenomena of the real waveforms. For conventional geophone sensors, FWI is formulated for the particle velocity field. In this paper, we present a formulation of the modeling and inversion specifically for DAS measurements as an averaged strain along the fiber. The algorithm does not require converting the data to velocities. The gradient of the misfit function, by adjoint formulation, is a cross correlation in time of the forward-propagated wavefield and backward-propagated residuals injected from the receivers. For conventional sensors, the residuals are injected as force terms, but for DAS data, the residuals are averaged in space first and then injected as moment tensor sources with radiation patterns determined by the well deviation. For multi-offset in-plane and out-of-plane VSP acquisitions, a two-dimensional (2D) algorithm has been developed that inverts for a 2D distribution of elastic medium properties and includes three-dimensional (3D) well deviation effects. This paper will present the results of applying the inversion to real multi-offset, highly out-of-plane VSP fiber data acquired in a deviated well. Simulations confirm that the well trajectory has a considerable impact on the data amplitude and must be included in the modeling and inversion to reproduce amplitude variations. The inverted compressional and shear velocities agree well with the reference model based on sonic data. Another real data example is a multi-offset walk-above acquisition where a targeted domain is located below a deviated portion of the well. The inversion matches reflections and produces an image in the target area.

Ultra and Very Long Period Seismic Signatures of Unsteady Eruptions Predicted From Conduit Flow Models

AbstractExplosive volcanic eruptions radiate seismic waves as a consequence of pressure and shear traction changes within the conduit/chamber system. Kinematic source inversions utilize these waves to determine equivalent seismic force and moment tensor sources, but relation to eruptive processes is often ambiguous and nonunique. In this work, we provide an alternative, forward modeling approach to calculate moment tensor and force equivalents of a model of eruptive conduit flow and chamber depressurization. We explain the equivalence of two seismic force descriptions, the first in terms of traction changes on conduit/chamber walls, and the second in terms of changes in magma momentum, weight, and momentum transfer to the atmosphere. Eruption onset is marked by a downward seismic force, associated with loss of restraining shear tractions from fragmentation. This is followed by a much larger upward seismic force from upward drag of ascending magma and reduction of magma weight remaining in the conduit/chamber system. The static force is upward, arising from weight reduction. We calculate synthetic seismograms to examine the expression of eruptive processes at different receiver distances. Filtering these synthetics to the frequency band typically resolved by broadband seismometers produces waveforms similar to very long period seismic events observed in strombolian and vulcanian eruptions. However, filtering heavily distorts waveforms, accentuating processes in early, unsteady parts of eruptions and eliminating information about longer (ultra long period time scale depressurization and weight changes that dominate unfiltered seismograms. Our workflow can be utilized to directly and quantitatively connect eruption models with seismic observations.

A machine-learning-based method of detecting and picking the first P-wave arrivals of acoustic emission events in laboratory experiments

SUMMARY Detecting and picking the first P-wave arrivals of seismic events in seismograms is fundamental in observational seismology. Recently, several machine-learning-based algorithms have been developed to incorporate human expertise for picking P-wave arrival times automatically. One shortcoming of these models is that they pick arrival times at individual seismic stations separately, which need to be sorted and associated to identify the seismic event. Also, most of them rely on existence of P-wave arrivals in the seismograms to be picked. Here, we developed a machine-learning-based seismic event detection and P-wave arrival time picking method called MultiNet and applied it to acoustic emission (AE) waveform data recorded in laboratory experiments. The MultiNet uses 2-D waveform images from multichannel AE recordings as the input to a convolutional neural network (CNN) to detect whether there is an AE event in an image and, if so, uses a fully convolutional neural network (FCN) to pick the P-wave arrival time at each channel in the image. We tested the MultiNet using 550 known AE events recorded during syn-deformational phase transformation from olivine to spinel in Mg2GeO4 (an analogue to Mg2SiO4) in a high-pressure experiment. Waveform data of 50 events were used to train the neural networks and the rest of data were used to validate the method. At the optimal image length and detection threshold, the CNN was able to detect all 500 known events plus 48 more events missed previously. Overall, 98.7 per cent of P-wave arrival times picked by the FCN were within 0.5 $\mu$s from the manually picked times. The average picking errors at different channels range from 0.01 ± 0.05 to −0.06 ± 0.22 $\mu$s. Our method greatly reduces the amount of human labour in picking P-wave arrival times for event location and source moment tensor inversion. It can be easily adapted to process continuous waveform data of a seismic network for earthquake detection and location in real time.

An efficient diffraction stacking interferometric imaging location method for microseismic events

Migration-based location methods automatically obtain microseismic event locations without manual picking and often are used in microseismic monitoring during hydraulic fracturing. They use waveform stacking over all receivers to enhance the ability to detect weak events. However, these methods may fail to effectively increase the signal-to-noise ratio (S/N) of the stacked trace and may not obtain an accurate source location if polarity reversals occur in seismic records. To overcome this problem, traditional approaches rely on polarity correction by characteristic function or polarity determination by source moment-tensor inversion and focal mechanism search. To ensure location accuracy and efficiency, we have developed the diffraction stacking interferometric imaging (DSII) method for locating microseismic events. We first obtain the approximately symmetrical pattern responding to the source moment tensor by using diffraction stacking (DS) and then apply interferometric imaging to focus the pattern onto its center and extract the source location. The DSII method overcomes the inaccurate location problem under polarity reversal caused by source mechanisms, and it also benefits from the high efficiency and noise suppression of the DS. Moreover, the symmetrical pattern in the DS source image also can be used as a means of quality control for field data. We use synthetic and field data to demonstrate the location ability of this method. Our results indicate that the DSII can efficiently reduce the effects of strong noise on event detection and location. We can achieve a quasi-symmetrical pattern on the DS image and obtain a focused interferometric image when the velocity has systematic errors. Compared with the DS, the DSII method also has a better performance on sparse-receiver networks. Finally, the DSII method is applied to field data acquired using a surface array during hydraulic fracturing.

Connection between the cross correlation and the Green's function: strain and rotation of surface waves

SUMMARY Recent developments of distributed acoustic sensing (DAS) techniques and rotational seismometers enable us to record strain and rotational seismograms. This prompts us to adapt the methods used for traditional translational seismograms to strain and rotational seismograms. Recently, we extended the formulation of the spatial autocorrelation (SPAC) method to strain, rotation and tilt records. According to seismic interferometry for translation seismograms, cross correlations have clear connections to Green's functions under the isotropy and equipartition of noise wavefields. In this study, we clarify similar connections for strain and rotation seismograms. Because we extend the formulation in the frequency domain, we actually study the connection between the cross-spectral matrix of strain and rotation at two receivers and the Green's tensor. First, we provide a proof under a general framework by simply extending the proof for translation to that for strain and rotation. The proof shows the following results: (1) The cross-spectral matrix of (i, j)-component strains at two receivers is found to be proportional to the strain Green's tensor at one receiver for the sum of (i, j)- and (j, i)-components of the moment tensor source at the other receiver. (2) The cross-spectral matrix of (i, j)-component rotations at two receivers is found to be proportional to the rotation Green's tensor at one receiver for the difference of (i, j)- and (j, i)-components of the moment tensor source at the other receiver. Necessary assumptions for the proof are the isotropy and equipartition of the wavefield. We then check this proof with specific calculations for surface waves observed on the free surface. The proof is confirmed for the isotropic incidence of random-phase surface waves with a specific ratio between Rayleigh and Love wave energies. Seismic interferometry for strain and rotation was already studied. However, the connection of cross correlations to the Green's function for strain and rotation seismograms is discovered by this study for the first time. A specific proof for body waves that is assured by the general proof will be our next study.

Insight into the 2017–2019 Lurestan arc seismic sequence (Zagros, Iran); complex earthquake interaction in the basement and sediments

SUMMARY Despite its high-seismogenic potential, the details of the seismogenic processes of Zagros Simply Folded Belt (SFB) remains debated. Three large earthquakes (Mw 7.3, 5.9 and 6.3) struck in the Lurestan arc of the Zagros SFB in 2017 and 2018. The sequence was recorded by seismic stations at regional, and teleseismic distances. Coseismic surface displacements, measured by Sentinel-1A/B satellites, provide additional data and a unique opportunity to study these earthquakes in detail. Here, we complement previous studies of the coseismic slip distribution of the 12 November 2017 Mw 7.3 Ezgeleh earthquake by a detailed analysis of its aftershocks, and we analysed the rupture process of the two interrelated earthquakes (25 August 2018 Mw 5.9 Tazehabad and the 25 November 2018 Mw 6.3 Sarpol-e Zahab earthquakes). We model the surface displacements obtained from Interferometric Synthetic Aperture Radar (InSAR) measurements and seismic records. We conduct non-linear probabilistic optimizations based on joint InSAR and seismic data to obtain finite-fault rupture of these earthquakes. The Lurestan arc earthquakes were followed by a sustained aftershock activity, with 133 aftershocks exceeding Mn 4.0 until 30 December 2019. We rely on the permanent seismic networks of Iran and Iraq to relocate ∼700 Mn 3 + events and estimate moment tensor solutions for 85 aftershocks down to Mw 4.0. The 2017 Ezgeleh earthquake has been considered to activate a low-angle (∼17°) dextral-thrust fault at the depth of 10–20 km. However, most of its aftershocks have shallow centroid depths (8–12 km). The joint interpretation of finite source models, moment tensor and hypocentral location indicate that the 2018 Tazehabad and Sarpol-e Zahab earthquakes ruptured different strike-slip structures, providing evidence for the activation of the sinistral and dextral strike-slip faults, respectively. The deformation in the Lurestan arc is seismically accommodated by a complex fault system involving both thrust and strike-slip faults. Knowledge about the deformation characteristics is important for the understanding of crustal shortening, faulting and hazard and risk assessment in this region.

An explosive component in a December 2020 Milan earthquake suggests outgassing of deeply recycled carbon

Carbon dragged at sub-arc depths and sequestered in the asthenospheric upper mantle during cold subduction is potentially released after millions of years during the breakup of continental plates. However, it is unclear whether these deep-carbon reservoirs can be locally remobilized on shorter-term timescales. Here we reveal the fate of carbon released during cold subduction by analyzing an anomalously deep earthquake in December 2020 in the lithospheric mantle beneath Milan (Italy), above a deep-carbon reservoir previously imaged in the mantle wedge by geophysical methods. We show that the earthquake source moment tensor includes a major explosive component that we ascribe to carbon-rich melt/fluid migration along upper-mantle shear zones and rapid release of about 17,000 tons of carbon dioxide when ascending melts exit the carbonate stability field. Our results underline the importance of carbon-rich melts at active continental margins for emission budgets and suggest their potential episodic contributions to atmospheric carbon dioxide.

PS interferometric imaging condition for microseismic source elastic time-reversal imaging

SUMMARYThe time-reversal imaging method utilizes the wave equation to back-propagate recorded seismic data and a proper imaging condition to locate a passive seismic source. For an explosive source, the reconstructed wavefield is focused at the seismic source location and origin time. Although the elastic time-reversal wavefield for a moment tensor source may not exhibit a maximum at the true location at the origin time, it does exhibit a quasi-symmetrical spatial distribution around the source location that represents the radiation pattern of the moment tensor source. We propose the use of an interferometric imaging condition to solve the radiation pattern problem, which is combined with elastic PS cross-correlation imaging condition (referred to as the PS interferometric cross-correlation imaging condition) to locate a moment tensor source using elastic time-reversal imaging method. 2-D and 3-D numerical tests demonstrate that our proposed method can identify the moment tensor source location in complex velocity models with a high noise level. In tests of the sensitivity of the method to the accuracy of the velocity model, we find that the method can still get focused images under about 10–25 per cent random perturbations in P- and S-wave velocities, but only under about 5 per cent correlated perturbation of global P- and S-wave velocities with a potential bias in the location.

Comparison of Single-Well Microseismic Focal Mechanism Inversions with Different Source Models

ABSTRACT Through downhole monitoring, the focal mechanisms of microearthquakes can be quantitatively determined, thus providing valuable information for characterizing the fracturing process and the in situ stress status. The double-couple (DC) and moment tensor (MT) source models are commonly used to study microearthquakes. However, the DC model fails to include non-DC mechanisms, and MT inversion from single-well data is still challenging. One possible way to address this is using the shear–tensile general dislocation (GD) source model. We provide a detailed comparison of the DC, GD, and MT models, and introduce the differences in their modeling and inversion theories. These three models are described by four, five, and six parameters, and correspond to a single point, a straight line, and the entire space in the Hudson source-type plots, respectively. Both the DC and GD models yield nonlinear inversions, whereas the MT inversion is linear. Synthetic tests set up from a field single-well monitoring case are performed to study the resolvability of the DC, GD, and MT models in single-well focal mechanism inversions. The results indicate that the inversion error increases from DC→GD→MT for a single-well acquisition system, and the GD and DC inversions are both stable, whereas the MT inversion deviates from the inputs in cases with a perfectly vertical receiver array, 5% model velocity perturbations, 10 m horizontal source location errors, or 40% noise levels. We also find that the focal mechanism inversion mainly depends on the horizontal source–receiver azimuth coverage, and that the nonvertical well direction is helpful for constraining single-well inversions. According to our study, focal mechanism inversions based on the GD model can obtain reliable solutions from near-vertical single-well data, which will help improve non-DC earthquake studies.