Double-couple Research Articles

Discriminating a Nuclear Blast from A Natural Seismic Event Using A Full Moment-Tensor Inversion Method

Identification of seismic signals if they are generated by tectonic or volcanic origin or underground nuclear tests is of primary importance for impacts on environmental issues. The recent blast on September 3, 2017 has been in question due to its potential destruction on the global environment. Here, we applied a method of full moment-tensor inversions to analyse broadband waveforms generated by such an explosion. The signals were recorded by a network of 4 regional seismic stations (MAJO, INCN, MDJ, BJT), situated between 360 and 1,100 km away from the explosion epicenter. The results showed that a variance reduction of 72.6%, providing high confidence for all values obtained from the method used: a seismic moment of Mo = 6.25 · 1024 dyne cm, corresponding to a moment magnitude of Mw = 5.8, with a dominant volumetric component (ISO) of 50% relatively compared to a 6.8% double-couple (DC) part and a 43.2% compensated linear vector dipole (CLVD) part, and a centroid-depth of 1.0 km. The relative dominance of the ISO seismic component over the other two components, along with the shallow source extracted from the cross-correlation and source mechanism analysis, suggests that the September 3, 2017 explosion was induced by a suspected nuclear test.

Estimation of seismic source parameters in 3D elastic media using the reciprocity theorem

We have developed a novel method based upon reciprocity principles to simultaneously estimate the location of a seismic event and its source mechanism in 3D heterogeneous media. The method finds double-couple (DC) and non-DC mechanisms of microearthquakes arising from localized induced and natural seismicity. Because the method uses an exhaustive search of the 3D elastic media, it is globally convergent. It does not suffer from local minima realization observed with local optimization methods, including Newton, Gauss-Newton, or gradient-descent algorithms. The computational efficiency of our scheme is derived from the reciprocity principle, in which the number of 3D model realizations corresponds to the number of measurement receivers. The 3D forward modeling is carried out in the damped Fourier domain with a 3D finite-difference frequency-domain fourth- and second-order code developed to simulate elastic waves generated by seismic sources defined by forces and second-order moment density tensors. We evaluate the results of testing this new methodology on synthetic data for the Raft River geothermal field, Idaho, as well as determine its applicability in designing optimal borehole monitoring arrays in a fracking experiment at the Homestake Mine, South Dakota. We also find that the method proposed here can retrieve the moment tensors of the space distributed source with data arising from spatially restricted arrays with limited aperture. The effects of uncertainties on the source parameter estimation are also examined with respect to data noise and model uncertainty.

Complex seismic sources in volcanic environments: Radiation modelling and moment tensor inversions

Long period (LP) signals are special seismic events observed at volcanoes, which comprise both a high frequency onset due to brittle failure and a more energetic low frequency part due to resonance in a fluid-filled conduit. They are critical for volcano monitoring since they can be used as a volcanic forecasting tool. Classic seismology assumes planar faults for seismic sources; however, there is increasing evidence that suggests different fault shapes such as dyke faults and ring faults. We consider in this study narrow dykes and conduits rather than large calderas, hence, we model these complex sources by superposing vertical single double couple (DC) sources arranged along narrow fault structures with inner upward movement. We calculate seismic radiation patterns and synthetic seismograms for a rupture along a dyke, three different partial ring ruptures and a full-ring rupture. Results show that planar faults are the most effective at radiating energy. The more the source geometry deviates from a planar fault the smaller become the amplitudes and therefore the Moment Magnitudes. For example, the amplitudes decrease to 2.4% of the planar radiation for a full-ring rupture and to 0.7% for a dyke rupture. The waveforms produced by partial ring ruptures are in accordance to what is expected in the far field, representing the derivative of the source displacement and emulating radiation of a DC with different azimuths; however, the dyke and full-ring sources produce waveforms that appear to represent the second derivative of the source displacement and negative first onset polarisations. Moment Tensor Inversions support similarities between DC ruptures and partial ring ruptures; however, they show ambiguous solutions for the other sources. This point source assumption can lead to misinterpretations of slip history on the fault and a consistent underestimation of magnitudes which has direct implications for magma ascent estimations derived from seismic amplitudes.

Faults and Non‐Double‐Couple Components for Induced Earthquakes

AbstractFocal mechanisms of induced earthquakes reflect anthropogenic contributions to preexisting geological features and fault slippages. In this paper, we examine fault‐related (double‐couple (DC)) and possibly fluid‐related (non‐double‐couple (non‐DC)) mechanisms of induced earthquakes (M2–6) at regional scales. We systematically compare well‐resolved focal mechanisms of 33 events in the Western Canada Sedimentary Basin, among which 12 were induced by hydraulic fracturing and one by secondary recovery. Most of the seismicity is dominated by strike‐slip/thrust faulting regimes, whereas limited (but consistent) non‐DC components are obtained from injection‐induced seismicity in central Alberta. We interpret the persistent compensated‐linear‐vector‐dipole components (M2.1–3.8) as reflecting fracture growth and/or noncoplanar faults slippages during hydraulic‐fracturing stimulations. We further expand the moment tensor decomposition analysis to four representative classes of induced seismicity globally and find that the overall contribution of non‐DC components is comparable between induced and tectonic earthquakes.

Teleseismic body wave inversion

Body wave inversion methodology is developed to determine the earthquake source parameters in teleseismic distances. The generalized inversion technique, based on the singular value decomposition method, is applied to determine the deviatone moment tensor which is decomposed in two parts. The first one is related to the pure Double Couple (DC) and the second one to the compensated linear vector dipoles (CLVD). The best solution of the overdetermined problem is obtained by minimizing the misfit between observed and synthetic seismograms. The proposed methodology is applied for the four strongest earthquakes that occurred recently in Greece (2001-2006)

Evidence of a Large Triggered Event in the Nepal Himalaya Following the Gorkha Earthquake: Implications Toward Enhanced Seismic Hazard

A DC (double couple) constrained multiple point-source moment-tensor inversion is performed on the band-passed (0.008–0.10 Hz) displacement data of the 25 April (Mw 7.8) 2015 Nepal mainshock, from 17 broadband stations in India. Our results reveal that the 25 April event (strike = 324°, dip = 14°, rake = 88°) ruptured the north-dipping main Himalayan thrust (MHT) at 16 km depth. We modeled the Coulomb failure stress changes (ΔCFS) produced by the slip on the fault plane of the 25 April Nepal mainshock. A strong correlation with occurrences of aftershocks and regions of increased positive ΔCFS is obtained below the aftershock zone of the 2015 Nepal mainshock. We notice that predicted ΔCFS at 16 km depth show a positive Coulomb stress of 0.06 MPa at the location of the 12 May 2015 event. These small modeled stress changes can lead to trigger events if the crust is already near to failure, but these small stresses can also advance the occurrence of future earthquakes. The main finding of our ΔCFS modeling implies that the 25 April event increased the Coulomb stress changes by 0.06 MPa at 16 km depth below the site of the 12 May event, and thus, this event can be termed as triggered. We propose that the seismic hazard in the Himalaya is not only caused by the mainshock slip on the MHT; rather, the occurrence of large triggered event on the MHT can also enhance our understanding of the seismic hazard in the Nepal Himalaya.

Determination of source parameters of the 2017 Mount Agung volcanic earthquake from moment-tensor inversion method using local broadband seismic waveforms

Monitoring of volcanoes has been an important issue for many purposes, particularly hazard mitigation. With regard to this, the aims of the present work are to estimate and analyse source parameters of a volcanic earthquake driven by recent magmatic events of Mount Agung in Bali island that occurred on September 28, 2017. The broadband seismogram data consisting of 3 local component waveforms were recorded by the IA network of 5 seismic stations: SRBI, DNP, BYJI, JAGI, and TWSI (managed by BMKG). These land-based observatories covered a full 4-quadrant region surrounding the epicenter. The methods used in the present study were seismic moment-tensor inversions, where the data were all analyzed to extract the parameters, namely moment magnitude, type of a volcanic earthquake indicated by percentages of seismic components: compensated linear vector dipole (CLVD), isotropic (ISO), double-couple (DC), and source depth. The results are given in the forms of variance reduction of 65%, a magnitude of MW 3.6, a CLVD of 40%, an ISO of 33%, a DC of 27% and a centroid-depth of 9.7 km. These suggest that the unusual earthquake was dominated by a vertical CLVD component, implying the dominance of uplift motion of magmatic fluid flow inside the volcano.

The Mechanism of Microearthquakes Related to a Gas Storage Using Differently Constrained Source Models: A Case Study of the Háje Location, Czech Republic

The resolution of a source mechanism is investigated in terms of three differently constrained source models: the moment tensor, the shear-tensile crack source model, and the double couple source model. The moment tensor (MT) is an unconstrained description of a general dipole source; the shear-tensile crack (STC) represents a slip along a fault with an off-plane component and the double couple (DC) corresponds to a simple shear slip along a fault. The inversion of body wave amplitudes is applied on microseismic events located in the vicinity of underground gas storage Haje (Czech Republic) where volume changes in the source can be expected. The orientation of the simple shear fracture component is resolved almost always well, independently of the source model used. On the other hand, the non-shear components differ largely among the source models considered, from both the model definition and robustness of the inversion. A comparison of the inversion results for the three alternative source models permits an assessment of the reliability of the non-shear components retrieved. Application of the STC model to all events appears to be the most appropriate. The analysis confirms a shear slip for three events and a tensile fracturing for other three events.

Focal mechanisms and size distribution of earthquakes beneath the Krafla central volcano, NE Iceland

AbstractSeismicity was monitored beneath the Krafla central volcano, NE Iceland, between 2009 and 2012 during a period of volcanic quiescence, when most earthquakes occurred within the shallow geothermal field. The highest concentration of earthquakes is located close to the rock‐melt transition zone as the Iceland Deep Drilling Project‐1 (IDDP‐1) wellbore suggests and decays quickly at greater depths. We recorded multiple swarms of microearthquakes, which coincide often with periods of changes in geothermal field operations, and found that about one third of the total number of earthquakes are repeating events. The event size distribution, evaluated within the central caldera, indicates average crustal values with b = 0.79 ± 0.04. No significant spatial b value contrasts are resolved within the geothermal field nor in the vicinity of the drilled melt. Besides the seismicity analysis, focal mechanisms are calculated for 342 events. Most of these short‐period events have source radiation patterns consistent with double‐couple (DC) mechanisms. A few events are attributed to non‐shear‐faulting mechanisms with geothermal fluids likely playing an important role in their source processes. Diverse faulting styles are inferred from DC events, but normal faulting prevails in the central caldera. The best fitting compressional and tensional axes of DC mechanisms are interpreted in terms of the principal stress or deformation rate orientations across the plate boundary rift. Maximum compressive stress directions are near‐vertically aligned in different study volumes, as expected in an extensional tectonic setting. Beneath the natural geothermal fields, the least compressive stress axis is found to align with the regional spreading direction. In the main geothermal field both horizontal stresses appear to have similar magnitudes causing a diversity of focal mechanisms.

Probabilistic waveform inversion for 22 earthquake moment tensors in Hungary: new constraints on the tectonic stress pattern inside the Pannonian basin

We have successfully estimated the full moment tensors of 22 local earthquakes with local magnitude ranging from 1.2 to 4.8 that occurred in the Hungarian part of the Pannonian basin between 1995 and 2014. We used a probabilistic waveform inversion procedure that takes into account the effects of the random noise contained in the seismograms, the uncertainty of the hypocentre determined from arrival times and the inaccurate knowledge of the velocity structure, while estimating the error affecting the derived focal parameters. The applied probabilistic approach maps the posterior probability density functions (PPDFs) for both the hypocentral coordinates and the moment tensor components. The final estimates are given by the maximum likelihood points of the PPDFs, while solution uncertainties are presented by histogram plots. The estimated uncertainties in the moment tensor components are plotted on the focal sphere in such a way, that the significance of the double couple (DC), the compensated linear vector dipole (CLVD) and the isotropic (ISO) parts of the source can be assessed. We have shown that the applied waveform inversion method is equally suitable to recover the source mechanism for low-magnitude events using short-period local waveforms as well as for moderate-size earthquakes using long-period seismograms. The non-DC components of the retrieved focal mechanisms are statistically insignificant for all the analysed earthquakes. The negligible amount of the ISO component implies the tectonic nature of the investigated events. The moment tensor solutions reported by other agencies for five of the ML > 4 earthquakes studied in this paper are very similar to those calculated by the applied waveform inversion algorithm. We have found only strike-slip and thrust faulting events, giving further support to the hypothesis that the Pannonian basin is currently experiencing a compressional regime of deformation. The orientations of the obtained focal mechanisms are in good agreement with the main stress pattern published for the Pannonian region. The azimuth of the subhorizontal P principal axis varies from about NNE-SSW in SW Hungary through NE-SW well inside the basin to around E-W in the NE part of the country. Most of the analysed earthquakes occurred on faults or subfaults differently oriented than the main fault system.

A Systematic Analysis of Seismic Moment Tensor at The Geysers Geothermal Field, California

The Geysers geothermal field is one of the most seismically active regions in northern California. Most of the events occur at shallow depths and are related to stress and hydrological perturbations due to energy production operations. To better understand the relationships between seismicity and operations, better source mechanism information is needed. Seismic moment tensors offer insight into the nature of equivalent forces causing the seismicity. Fifty-three M>3 events located at The Geysers geothermal field were selected from the University of California Berkeley Moment Tensor Catalog for analysis of seismic moment tensor solutions and associated uncertainties. Deviatoric and full moment tensor solutions were computed, and statistical tests were employed to assess solution stability, resolution, and significance. In this study, we examine several source models including double-couple (DC), pure isotropic (ISO; volumetric change), and volume-compensated linear vector dipole (CLVD) sources, as well as compound sources such as DC+CLVD, DC+ISO, and shear–tensile sources. In general, we find from a systematic approach toward characterizing uncertainties in moment tensor solutions that The Geysers earthquakes, as a population, deviate significantly from northern California seismicity in terms of apparent volumetric source terms and complexity.

Analysis of post-blasting source mechanisms of mining-induced seismic events in Rudna copper mine, Poland

Abstract The exploitation of georesources by underground mining can be responsible for seismic activity in areas considered aseismic. Since strong seismic events are connected with rockburst hazard, it is a continuous requirement to reduce seismic risk. One of the most effective methods to do so is blasting in potentially hazardous mining panels. In this way, small to moderate tremors are provoked and stress accumulation is substantially reduced. In this paper we present an analysis of post-blasting events using Full Moment Tensor (MT) inversion at the Rudna mine, Poland, underground seismic network. In addition, we describe the problems we faced when analyzing seismic signals. Our studies show that focal mechanisms for events that occurred after blasts exhibit common features in the MT solution. The strong isotropic and small Double Couple (DC) component of the MT, indicate that these events were provoked by detonations. On the other hand, post-blasting MT is considerably different than the MT obtained for strong mining events. We believe that seismological analysis of provoked and unprovoked events can be a very useful tool in confirming the effectiveness of blasting in seismic hazard reduction in mining areas.

Non-double-couple mechanism of moderate earthquakes occurred in Lower Siang region of Arunachal Himalaya: Evidence of factors affecting non-DC

Moment Tensor solutions of 104 earthquakes which were observed at local distances in Lower Siang region of Arunachal Himalaya have been estimated using ISOLA code. The magnitude range of analyzed earthquakes lies between 1.8 (Mw) and 5.3 (Mw). Out of 104 earthquakes, only 32 events are having good data. The signal noise ratio of these 32 events is greater than 6 with magnitude greater than 2.5. All possible sources of non-DC such as, noise present in the data, depth of the source, low azimuthal coverage of the event and non-DC as a part of real earthquake source process are examined. The study reveals that non-DC is highly dependent on the source depth as comparatively shallow events shows high CLVD%. The CLVD is also highly affected by the noise present in the data. Another factor is the magnitude of the event. The high magnitude event shows quite high DC%. So the source mechanisms of high magnitude events are double couple (DC).

Moment tensor decompositions revisited

The decomposition of moment tensors into isotropic (ISO), double-couple (DC) and compensated linear vector dipole (CLVD) components is a tool for classifying and physically interpreting seismic sources. Since an increasing quantity and quality of seismic data allow inverting for accurate moment tensors and interpreting details of the source process, an efficient and physically reasonable decomposition of moment and source tensors is necessary. In this paper, the most common moment tensor decompositions are revisited, new equivalent formulas of the decompositions are derived, suitable norms of the moment tensors are discussed and the properties of commonly used source-type plots are analysed. The Hudson skewed diamond plot is introduced in a much simpler way than originally proposed. It is shown that not only the Hudson plot but also the diamond CLVD–ISO plot and the Riedesel–Jordan plot conserve the uniform distribution probability of moment eigenvalues if the appropriate norm of moment tensors is applied. When analysing moment tensor uncertainties, no source-type plot is clearly preferable. Since the errors in the eigenvectors and eigenvalues of the moment tensors cannot be easily separated, the moment tensor uncertainties project into the source-type plots in a complicated way. As a consequence, the moment tensors with the same uncertainties project into clusters of a different size. In case of an anisotropic focal area, the complexity of moment tensors of earthquakes prevents their direct interpretation, and the decomposition of moment tensors must be substituted by that of the source tensors.

Tectonic Process and Non Double Couple Component of CMT Solution on Focal Mechanism: Pacific Plate did not subduct before East Japan Super Earthquake

Tectonic Process and Non Double Couple Component of CMT Solution on Focal Mechanism: Pacific Plate did not subduct before East Japan Super Earthquake

Disputable Non-Double-Couple Mechanisms of Several Strong Earthquakes: Second-Degree Moment Approach

The earthquake source mechanism (description of the geometry of the source and its strength in terms of forces equivalent to rupturing of the rock mass) is routinely modeled as a moment tensor (MT) describing the earthquake focus as a point. However, sometimes this approximation is not satisfied, and seismic radiation keeps the directivity due to the finite extent of the source. Inversion into the MT then may yield a biased mechanism. Synthetic study in the Adamova and Silený (2010) demonstrated the appearance of spurious non‐double‐couple components in the mechanism even for a pure double‐couple (DC) source. Their method was designed to reduce the spurious source components by using the second‐degree moments to evaluate their contribution into the records and subtract it from the data. Here we applied the procedure to five moderate to large regional events with large nonshear components. They are mostly located on large tectonic faults where predominantly pure shear slip is expected. We studied one event on the prominent North Anatolian fault, three events in the Pacific area, and one event in Bolivia. In most cases, the non‐DC components essentially were reduced, and the geometry of the mechanism remained largely unchanged. This confirms the hypothesis that part of the non‐DC components in regional MT solutions may be spurious due to the neglect of the source finiteness in the routine procedure of the MT retrieval. In addition, the geometrical and kinematical characteristics of the foci provided by the second‐degree moments (the source ellipsoid and rupture velocity vector) are mostly consistent with the fault geometry, aftershock distribution, and estimates of rupture speed from available previous studies.

Double-couple earthquake source: symmetry and rotation

We consider statistical analysis of double couple (DC) earthquake focal mechanism orientation. The symmetry of DC changes with its geometrical properties, and the number of 3-D rotations one DC source can be transformed into another depends on its symmetry. Four rotations exist in a general case of DC with the nodal-plane ambiguity, two transformations if the fault plane is known, and one rotation if the sides of the fault plane are known. The symmetry of rotated objects is extensively analyzed in statistical material texture studies, and we apply their results to analyzing DC orientation. We consider theoretical probability distributions which can be used to approximate observational patterns of focal mechanisms. Uniform random rotation distributions for various DC sources are discussed, as well as two non-uniform distributions: the rotational Cauchy and von Mises-Fisher. We discuss how parameters of these rotations can be estimated by a statistical analysis of earthquake source properties in global seismicity. We also show how earthquake focal mechanism orientations can be displayed on the Rodrigues vector space.

Source mechanisms of the 2000 earthquake swarm in the West Bohemia/Vogtland region (Central Europe)

An earthquake swarm of magnitudes up to ML = 3.2 occurred in the region of West Bohemia/Vogtland (border area between Czech Republic and Germany) in autumn 2000. This swarm consisted of nine episodic phases and lasted four months. We retrieved source mechanisms of 102 earthquakes with magnitudes between ML = 1.6 and 3.2 applying inversion of the peak amplitudes of direct P and SH waves, which were determined from ground motion seismograms. The investigated events cover the whole swarm activity in both time and space. We use data from permanent stations of seismic network WEBNET and from temporal stations, which were deployed in the epicentral area during the swarm; the number of stations varied from 7 to 18. The unconstrained moment tensor (MT) expression of the mechanism, which describes a general system of dipoles, i.e. both double-couple (DC) and non-DC sources, was applied. MTs of each earthquake were estimated by inversion of three different sets of data: P-wave amplitudes only, Pand SH-wave amplitudes, and P-wave amplitudes along with the SH-wave amplitudes from a priori selected four “base” WEBNET stations, the respective MT solutions are nearly identical for each event investigated. The resultant mechanisms of all events are dominantly DCs with only insignificant non-DC components mostly not exceeding 10 per cent. We checked reliability of the MTs in jack-knife trials eliminating some data; we simulated the mislocation of hypocentre or contaminated the Pand SH-wave amplitudes by accidental errors. These tests proved stable and well constrained MT solutions. The massive dominance of the DC in all investigated events implies that the 2000-swarm consisted of a large number of pure shears along a fault plane. The focal mechanisms indicate both oblique-normal and oblique-thrust faulting, however, the obliquenormal faulting prevails. The predominant strikes and dips of the oblique-normal events fit well the geometry of the main fault plane Nový Kostel (NK) and also match the strike, dip, and rake of the largest ML=4.6 earthquake of a strong swarm in 1985/86. On the contrary, the 2000-source mechanisms differ substantially from those of the 1997-swarm (which took place in two fault segments at the edge of the main NK fault plane) in both the faulting and the content of non-double-couple components. Further we found that the scalar seismic moment M0 is related to the local magnitude ML used by WEBNET as M0  10 which differs from the scaling law using moment magnitude Mw, i.e. M0  10 (Kanamori, 1977).

Combination of double couple and non-double couple events during the Van, Turkey, 2011 earthquake sequence

A combination of double couple (DC) and non-double couple (non-DC) earthquakes hit Eastern Turkey, in the vicinity of Lake Van, in October–November 2011. Teleseismic waveform inversion was used to find the best fitting double couple and deviatoric moment tensors on four large and medium sized events of this sequence. The aftershocks of the Mw=7.1, 2011/10/23:10:41 earthquake built a NE–SW aftershock zone where the Mw=5.7, 2011/10/25 aftershock was located. The Mw=6.0, 2011/10/23:20:45 event was located around the terminal section of the Mw=7.1 aftershock zone which might be triggered by this event (aftershocks of this event propagated from W to E to build a W–E aftershock zone where the Mw=5.7, 2011/11/09 event was located). For these events the calculated best fitting grid search parameters are not very different from GCMT results, but DC components, after deviatoric moment tensor inversion, represent much more difference with GCMT and grid search. The important feature of deviatoric moment tensor inversion is the existence of a notable compensated linear vector dipole (CLVD) component on the Mw=5.7, 2011/10/25:14:55 and Mw=5.7, 2011/11/09:19:23 aftershocks. According to the regional seismotectonics, these CLVD components could be related to crustal rheology and volcanic activities. Based on the results, the existence of a cylindrical aftershock distribution could be taken as an indication of induced seismic activity on complex-ring structures resulted from magma or water–magma injection. However, the existence of Karst like structures suggests that the CLVD components may be under the influence of high-pressure water or gas injection rather than magma.

Seismic Network Calibration for Retrieving Accurate Moment Tensors

We present a method for calibrating seismic networks in order to retrieve highly accurate seismic moment tensors. The method is based on a joint inversion of large datasets of earthquakes for moment tensors and for amplifications of the network stations, which encompass the instrumental amplifications of sensors and the gain factor of the acquisition system, as well as the local site effects neglected in modeling of Green’s functions. The method is capable of detecting the reverse polarity of sensors, incorrect orientation of sensors, or anomalous site effects caused by local geological conditions at individual stations. The robustness and accuracy of the method are tested on synthetic data with different noise levels, station configurations, and a variety of focal mechanisms. The numerical modeling confirms that the inversion code works well and yields robust results. The tests show that the moment tensors, calculated from data of properly calibrated seismic networks, are significantly more accurate. Finally, the method is applied to observations in West Bohemia, Czech Republic, in order to calibrate a network of 22 local seismic stations operated in this region and to calculate accurately the double‐couple (DC) and non‐double‐couple (non‐DC) components of moment tensors of 200 selected micro‐earthquakes. The results indicate that the method is efficient and can easily be used to calibrate other networks. For example, it can be used in inverting laboratory data, where the coupling effects between the sensor and a rock sample are difficult to quantify, or mining and borehole data, where the calibration and orientation of the sensors are frequently unknown. Moreover, the method can be applied to all studies, which deal with retrieving and interpreting highly accurate moment tensors and their DC and non‐DC components.