Compensated Linear Vector Dipole Components Research Articles

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.

Bayesian regional moment tensor from ocean bottom seismograms recorded in the Lesser Antilles: implications for regional stress field

SUMMARY Seismic activity in the Lesser Antilles (LA) is characterized by strong regional variability along the arc reflecting the complex subduction setting and history. Although routine seismicity monitoring can rely on an increasing number of island stations, the island-arc setting means that high-resolution monitoring and detailed studies of fault structures require a network of ocean bottom seismometers (OBS). As part of the 2016–2017 Volatile recycling at the Lesser Antilles arc (VoiLA) project, we deployed 34 OBS stations in the forearc and backarc. During the deployment time, 381 events were recorded within the subduction zone. In this paper, we perform full-waveform regional moment tensor (RMT) inversions, to gain insight into the stress distribution along the arc and at depth. We developed a novel inversion approach, AmΦB—‘Amphibious Bayesian’, taking into account uncertainties associated with OBS deployments. Particularly, the orientation of horizontal components (alignment uncertainty) and the high noise level on them due to ocean microseisms are accounted for using AmΦB. The inversion is conducted using a direct, uniform importance sampling of the fault parameters within a multidimensional tree structure: the uniXtree-sampling algorithm. We show that the alignment of the horizontal OBS components, particularly in high noise level marine environments, influences the obtained source mechanism when using standard least-squares (L2) RMT inversion schemes, resulting in systematic errors in the recovered focal mechanisms including high artificial compensated linear vector dipole (CLVD) contributions. Our Bayesian formulation in AmΦB reduces these CLVD components by nearly 60 per cent and the aberration of the focal geometry as measured by the Kagan angle by around 40 per cent relative to a standard L2 inversion. Subsequently, we use AmΦB-RMT to obtain 45 (Mw > 3.8) regional MT solutions, out of which 39 are new to any existing database. Combining our new results with existing solutions, we subsequently analyse a total of 151 solutions in a focal mechanism classification (FMC) diagram and map them to the regional tectonic setting. We also use our newly compiled RMT database to perform stress tensor inversions along the LA subduction zone. On the plate interface, we observe the typical compressional stress regime of a subduction zone and find evidence for upper-plate strike slip and normal fault behaviour in the north that becomes a near arc-perpendicular extensional stress regime towards the south. A dominant slab perpendicular extensional stress regime is found in the slab at 100–200 km beneath the central part of the arc. We interpret this stress condition to be a result of slab pull varying along the arc due to partial slab detachment along previously hypothesized lateral slab tear near Grenada, at the southern end of the LA arc, leading to reactivation of pre-existing structures around the subducted Proto-Caribbean ridge.

Seismic Sources in Stress‐Induced Anisotropic Media

Rocks in the upper mantle are extensively subjected to initial stress. The rock exhibits elastic anisotropy under the deviatoric stress, which affects the seismic response of underground structures. This paper aims to study the effect of stress-induced anisotropy on the seismic source. The seismic moment tensor generated by a shear faulting in a homogeneous isotropic medium with initial stress is derived by using the motion description in the intermediate configuration, the constitutive relation of third-order elasticity, and the boundary condition considering the effect of initial stress. Then the seismic moment tensor is decomposed to investigate seismic source characters quantitatively. Our results show that shear faulting in a stress-induced anisotropic medium can produce significant non-double-couple (non-DC) mechanisms, including compensated linear vector dipole (CLVD) and isotropic (ISO) components. ISO and CLVD components vary linearly with the initial shear stress on faults. In addition, stress-induced anisotropy causes the double-couple (DC) to deviate from the plane defined by the fault normal and slip direction. The initial stress not only affects the source intensity but also affects the propagation of seismic waves. The radiation patterns of longitudinal waves have non-uniform lobes, which shows the characteristic of anisotropy. Stress-induced anisotropic parameters are smaller than intrinsic anisotropy at high-stress levels and a nearly linear function of the increased initial stress. These results underscore the importance of considering stress-induced anisotropy in the inversion of focal mechanisms and provide a new perspective for monitoring underground stress.

Seismic Moment Tensor Inversion of an Induced Microseismic Event, Offshore Norway: An Insight into the Possible Cause of Wellbore Liner Failure during a Drilling Operation

Abstract A microseismic event with Mw∼0.8 was recorded at the Grane oilfield, offshore Norway, in June 2015. This event is believed to be associated with a failure of the wellbore liner in well 25/11-G-8 A. The failure mechanism has been difficult to explain from drilling parameters and operational logs alone. In this study, we analyzed the detected microseismic event to shed light on the possible cause of this event. We inverted for the seismic moment tensor, analyzed the S/P amplitude ratio and radiation pattern of seismic waves, and then correlated the microseismic data with the drilling reports. The inverted seismic moment indicates a shear-tensile (dislocation) event with a strong positive isotropic component (67% of total energy) accompanied by a positive compensated linear vector dipole (CLVD) and a reverse double-couple (DC) component. Drilling logs show a strong correlation between high pump pressure and the occurrence of several microseismic events during the drilling of the well. The strongest microseismic event (Mw∼0.8) occurred during peak pump pressure of 277 bar. The application of high pump pressure was associated with an attempt to release the liner hanger running tool (RT) in the well, which had been obstructed. Improper setting of the liner hanger could have caused the forces from the RT release to be transferred to the liner and might have resulted in ripping and parting of the pipe. The possible direct impact of the ripped liner with the formation or the likely sudden hydraulic pressure exposure to the formation caused by the liner ripping may explain the estimated isotropic component in the moment tensor inversion in the well. This impact can promote slip along the pre-existing fractures (the DC component). The presence of gas in the formation or the funneled fluid to the formation caused by the liner ripping may explain the CLVD component.

The 2014–2015 complex collapse of the Bárðarbunga caldera, Iceland, revealed by seismic moment tensors

Between August 2014 and February 2015, a caldera collapse process in Bárðarbunga volcano accompanied a fissure eruption at the Holuhraun lava field after magma had propagated laterally 45 km from the Bárðarbunga magma chamber to the lava field. The Icelandic Meteorological Office (IMO) reported around 30,000 earthquakes at the caldera, including more than 70 earthquakes with moment magnitude MW ≥ 5.0. We built a moment tensor catalog of around 230 seismic events at the caldera with MW between 3.7 and 5.5 using a waveform inversion method. We identified five event families based on focal mechanisms, double couple (DC) and compensated linear vector dipole (CLVD) components, epicentral distribution relative to the caldera center, and time of occurrence. The main characteristics of these families are (1) DC to CLVD normal faulting events with steep (50°–70°) to near-vertical (>70°) dip angles on the northern side of the caldera; (2) DC to CLVD normal events with predominant steep (50°–70°) dip angles on the southern side of the caldera; (3) intra-caldera oblique strike-slip events; and (4) thrust events at the eastern side of the caldera with a horizontal tension axis compensated linear vector dipole (T-CLVD) component. Each family provided new insights about the Bárðarbunga collapse mechanism such as (1) a systematic increase in the CLVD component with magnitude, corroborating that the curvature in the ring fault is the likely cause for the vertical CLVD moment tensors observed for the largest events; (2) seismic evidence of near-vertical dip angles in agreement with the vertical faults observed in many calderas worldwide, and numerical and analog models of caldera collapse structures; (3) intra-caldera oblique and strike-slip events on the western side of the caldera occurred by asymmetric collapse; (4) thrust horizontal T-CLVD events observed at the last stage of the eruption, possibly related to a viscoelastic response.

Seismic radiation analyses in anisotropic media based on general dislocation source model

AbstractAnisotropy affects the focal mechanism and makes it complicated. A shear motion generates a pure double-couple (DC) source in isotropic media. While in anisotropic media, it will produce non-DC components, which contain isotropic (ISO) and compensated linear vector dipole (CLVD) components. Besides, coupled with the diversity of fault motion, the source may become extremely complicated. In this paper, the seismic moment tensor is obtained based on the dislocation model, and then a variety of analyses are performed with the moment tensor, including moment tensor decomposition, radiation pattern, radiated energy ratio and seismic propagation characteristics. Since the anisotropy of the medium also influences seismic wave propagation, a hypothesis is made that the source region is minimal and anisotropic, but the propagation path is isotropic. The research gives some interesting conclusions. It is found that the anisotropy mainly affects the focal mechanism under low slope angle while high slope angle has little effect on the polarity. In terms of the moment tensor decomposition, if only one of ISO or CLVD exists, it can be asserted that the source region is anisotropic because ISO components are accompanied by CLVD components in isotropy media. As for the DC component, the results indicate it is one of the most important factors for determining the ratio of radiant energy. This paper presents some valuable findings of the focal mechanism of the general dislocation source under anisotropy, which helps to recognise the source characteristics of the earthquake and build solid foundations for the subsequent inversion of the focal mechanism.

Effects of Secondary Sources of Underground Nuclear Explosions on the mb : Ms Criterion and Implications for Discrimination of the DPRK’s Nuclear Tests

ABSTRACTThe mb : Ms (mb vs. Ms) relationship is an important criterion for screening explosions from earthquakes and has been widely adopted in seismological monitoring by the Comprehensive Nuclear-Test-Ban Treaty Organization. In general, the earthquakes have larger Ms than the underground explosions with equivalent mb. However, it has been reported that this recognition criterion failed to identify some explosions at the North Korea nuclear test site. In this study, we investigate the potential effects of secondary source components, including the compensated linear vector dipole (CLVD) and double-couple (DC) sources, on mb and Ms magnitude measurements and the physical mechanism of the mb : Ms recognition criterion by calculating synthetic seismograms. The results show an apparent critical body-wave magnitude of 5 when using the mb : Ms method to discriminate North Korean underground nuclear explosions. The Ms measurements decrease as the CLVD components increase, whereas the effects from the DC source can be neglected. Small events, such as the first five North Korean nuclear tests, generate weak CLVD components, leading to the failure of mb : Ms-based discrimination, whereas the last event, with a larger magnitude, caused extensive damage and hence can be successfully discriminated. In addition, the large difference between the source spectrum of explosions and those of earthquakes might be another important factor in the successful mb : Ms-based discrimination of the sixth North Korean nuclear test.

Generalized orthonormal moment tensor decomposition and its source-type diagram

Moment tensor decomposition is a method for deriving the isotropic (ISO), double-couple (DC), and compensated linear vector dipole (CLVD) components from a seismic moment tensor. Currently, there are two families of methods, namely, standard moment tensor decomposition and Euclidean moment tensor decomposition. Although both methods can usually provide workable solutions, there are some minor inconsistencies between the two methods: an equality inconsistency that occurs in standard moment tensor decomposition and the pure CLVD unity and flip basis inconsistency encountered in Euclidean moment tensor decomposition. Moreover, there is a sign problem when disentangling the CLVD component from a DC-dominated case. To address these minor inconsistencies, we propose a new moment tensor decomposition method inspired by both previous methods. The new method can not only avoid all these minor inconsistencies but also withstand deviations in ISO- or CLVD-dominated cases when using source-type diagrams.

Non-Double-Couple Components of the Moment Tensor in a Transversely Isotropic Medium

ABSTRACTThe non-double-couple (non-DC) components of the moment tensor provide insight into the earthquake processes and anisotropy of the near-source region. We investigate the behavior of the isotropic (ISO) and compensated linear vector dipole (CLVD) components of the moment tensor for shear faulting in a transversely ISO medium with an arbitrarily oriented symmetry axis. Analytic formulas for ISO and CLVD depend on the orientation of the fault relative to the anisotropy symmetry axis as well as three anisotropic parameters, which describe deviations of the medium from isotropy. Numerical experiments are presented for the preliminary reference Earth model. Both ISO and CLVD components are zero when the axis of symmetry is within the fault plane or the auxiliary plane. For any orientation in which the ISO component is zero, the CLVD component is also zero, but the opposite is not always true (e.g., for strong anisotropy). The relative signs of the non-DC components of neighboring earthquakes may help distinguish source processes from source-region anisotropy. We prove that an inversion of ISO and CLVD components of a set of earthquakes with different focal mechanisms can uniquely determine the orientation and strength of anisotropy. This study highlights the importance of the ISO component for constraining deep slab anisotropy and demonstrates that it cannot be neglected.

Seismic Detection of a Magma Reservoir beneath Turtle Island of Taiwan by S-Wave Shadows and Reflections

Although surface geology, eruption information and clustering seismicity all suggest Turtle Island (Kueishantao) of northern Taiwan is an active volcano, there was no direct evidence to conclude that magma reservoirs exist beneath it. Even less evidence is available to determine their spatial configuration. If the magma reservoirs are filled by liquids and melt, S-waves are totally reflected and leave behind a shadow, like when passing through the Earth’s outer core. We detect both these S-wave shadows and strong reflections from the surface using earthquakes at different depths and azimuths. These observations identify a km-scale molten-filled volume located beneath Turtle Island. The magmatic nature of the reservoir is supported by the onset of non-double-couple earthquakes with strong CLVD (Compensated Linear Vector Dipole) and ISO (Isotropic) components, which show a tensor crack compatible with some volume changes within the reservoir. Combining these results with two independent 3-D velocity models and aeromagnetic anomalies recorded in Taiwan, a partially-molten ~19% low-velocity volume is estimated in the mid-crust (13–23 km), with spatial uncertainties of ~3 km. The elongated direction approximately follows the strike of the Okinawa trough, indicating that the source of the magma reservoir might be a back-arc opening.

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.

Resolution of non-double-couple components in the seismic moment tensor using regional networks—I: a synthetic case study

We perform a detailed synthetic study on the resolution of non-double-couple (non-DC) components in the seismic moment tensors from short-period data observed at regional networks designed typically for monitoring aftershock sequences of large earthquakes. In addition, we test two different inversion approaches—a linear full moment tensor inversion and a non-linear moment tensor inversion constrained to a shear-tensile source model. The inversions are applied to synthetic first-motion P- and S-wave amplitudes, which mimic seismic observations of aftershocks of the 1999 Mw = 7.4 Izmit earthquake in northwestern Turkey adopting a shear-tensile source model. To analyse the resolution capability for the obtained non-DC components inverted, we contaminate synthetic amplitudes with random noise and incorporate realistic uncertainties in the velocity model as well as in the hypocentre locations. We find that the constrained moment tensor inversion yields significantly smaller errors in the non-DC components than the full moment tensor inversion. In particular, the errors in the compensated linear vector dipole (CLVD) component are reduced if the constrained inversion is applied. Furthermore, we show that including the S-wave amplitudes in addition to P-wave amplitudes into the inversion helps to obtain reliable non-DC components. For the studied station configurations, the resolution remains limited due to the lack of stations with epicentral distances less than 15 km. Assuming realistic noise in waveform data and uncertainties in the velocity model, the errors in the non-DC components are as high as ±15 per cent for the isotropic and CLVD components, respectively, thus being non-negligible in most applications. However, the orientation of P- and T-axes is well determined even when errors in the modelling procedure are high.

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.

Non-double-couple mechanisms of microearthquakes induced during the 2000 injection experiment at the KTB site, Germany: A result of tensile faulting or anisotropy of a rock?

Moment tensors of microearthquakes induced during the 2000 injection experiment at the KTB deep drilling borehole at a depth level of 5.4 km are studied. A family of 37 most reliable moment tensors contains significant non-double-couple (non-DC) components. The DC is on average 60% and the non-DC is 40%. Fault plane solutions computed from the DC part show preferred strike-slip mechanisms with small normal or reverse components. A predominant azimuth of P and T axes is in the range of N320°–340°E and of N230°–250°E, respectively. The non-DC components contain both the isotropic (ISO) and compensated linear vector dipole (CLVD) components. The mean value of ISO is 1.5%, the mean value of CLVD is − 5.7%. The predominantly negative CLVD components are inconsistent with the concept of the non-DC mechanisms as a result of tensile faulting due to fluid injection into the rock. The main origin of the non-DC components is probably anisotropy in the focal area. The other origins are errors produced by mismodelling of the medium when calculating the Green functions, and numerical errors produced by noise and limitations of input data. Adopting four alternative models of anisotropy obtained by other seismic measurements at the KTB, we have employed the non-DC components for estimating an optimum orientation of anisotropy in the focal area. The optimum orientation of the symmetry plane of anisotropy is nearly vertical with a strike of N335°–340°E. This strike coincides well with the strike of 330° typical for many major lithological units and faults and with the orientation of the transversely isotropic model inferred by other authors. After removing the anisotropy effects from the moment tensors by calculating the source tensors, the distribution of ISO is significantly narrowed. This indicates predominantly shear, but not tensile faulting.

Focal mechanisms in anisotropic media

Focal mechanisms of seismic sources in anisotropic media are more complicated than in isotropic media. Planar shear faulting produces pure double-couple (DC) mechanism in isotropy, but generally non-double-couple (non-DC) mechanism in anisotropy. The non-DC mechanism can comprise both the isotropic (ISO) and compensated linear vector dipole (CLVD) components. The amount of the ISO and CLVD components depends on strength and symmetry of anisotropy and on the orientation of faulting. Shear faulting in anisotropy generates a pure DC mechanism, provided that faulting is situated in symmetry planes of orthorhombic or of higher anisotropy symmetries. The fault plane solution, i.e. the orientation of the fault normal and the slip direction, can be retrieved from the seismic moment tensor and from elastic parameters describing anisotropy at the source. Numerical modelling shows that shear faulting in anisotropic rocks present in the Earth crust, the Earth mantle or in the subduction zones can produce mostly mechanisms with the CLVD up to 30 per cent and with the ISO up to 15 per cent. The fault plane solutions calculated under the assumption of isotropy typically deviate from the true solutions by an angle of 5° to 10°.

Analysis of broad-band regional waveforms of the 1996 September 29 earthquake at Bárdarbunga volcano, central Iceland: investigation of the magma injection hypothesis

SUMMARY Large earthquakes near active volcanoes, that exhibit non-double-couple source properties are usually interpreted as the result of either magma intrusion or geometrical complexity along the fault plane. Such an earthquake occurred in 1996 September 29 at Bardarbunga volcano in central Iceland, to be followed 2 days later by a major volcanic eruption at the area between Bardarbunga and the nearby Grimsvotn volcano. Both of these active volcanic centres lie underneath the Vatnajokull glacier, a permanent ice cap that covers a large area of central Iceland. This event was recorded by a temporary network (HOTSPOT) that consisted of 30 broad-band three-component seismometers covering most of Iceland. The waveforms of this event at all stations show an emergent, low-amplitude, high-frequency onset that is superposed on a longer-period signal. The corresponding amplitude spectra show a low-frequency content (<1 Hz) and prominent peaks around the corner frequency (∼0.25 Hz) and higher frequencies. These regional waveforms were inverted in order to obtain the best-fitting deviatoric and full moment tensor using a linear, time-domain inversion method. The results for the deviatoric moment tensor indicate a large (∼60 per cent) compensated linear vector dipole (CLVD) component, a hypocentral depth of 3.5 km, a moment magnitude of 5.4 and a best double-couple solution showing thrust motion in good agreement with the previously published Harvard CMT solution. The results for the full moment tensor on the other hand, indicate an implosive isotropic component of 8.5 per cent, a reduced CLVD component of 47.2 per cent and a best double-couple solution showing normal faulting. However, a statistical F-test revealed that the full moment tensor does not fit the data significantly better than the deviatoric at a confidence level of not more than 76 per cent. All of these results were found not to change substantially when a different source time function was used or when the data were weighted according to their distance from the source. The data are consistent with an earthquake of this magnitude, caused by the failure of an asperity and the formation of a tensile crack due to increasing fluid pressure. The dimensions of the crack may have been 10 × 3k m 2 and 0.5 m thickness and the volume of the injected fluid was found to be 15 × 10 6 m 3 . The calculated viscosity for the fluid (0.04 Pa s) points to the possibility of water being injected rather than magma, that is also supported by the short source duration of the earthquake (∼5 s). Taking into account the water saturation of the upper crust in Vatnajokull due to the presence of the glacier, this event may have been caused by increased pressure of water that was heated by magma injected through a dyke below the asperity.

Low-Frequency Properties of Intermediate-Focus Earthquakes

Intermediate-focus earthquakes are known to show features such as non-double-couple focal mechanisms that indicate source complexities. To characterize these features, we have systematically studied the low-frequency radiation from 108 intermediate-focus earthquakes recorded by high-performance seismic networks from 1989–1997 whose total moment was > 3 × 10 18 N m. We determined frequency-dependent focal mechanisms and source phase and amplitude spectra for each earthquake, estimating the uncertainties for all parameters. Frequency-dependent focal mechanisms were obtained from vertical-component, free-oscillation data in 1-mHz bands over the range of 1–11 mHz. Source amplitude and phase-delay spectra were determined to 20 mHz from a combination of free-oscillation and surface-wave data. The population of intermediate-focus earthquakes in our catalog is not equally divided between compressional and tensional stress-release mechanisms; instead, 59% are down-dip tensional, 25% are down-dip compressional, and 16% are neither. We have assessed the statistical significance of any non-double-couple component of the source for every earthquake in the catalog. We represent a deviatoric focal mechanism by its principle axes and a scalar ξ that ranges from –1, for a compensated linear vector dipole (CLVD) with a compressional axis of symmetry through 0 for a double couple, to +1, for a CLVD with a tensional axis of symmetry. ξ varies from –0.91 to +0.64 in this dataset. Fifty-six of the 108 events have a significant CLVD component (ξ ≠ 0) at the 95% confidence level; 15 events have an unusually large CLVD component of the focal mechanism (|ξ| ≥ 0.4). We do not observe a correlation between the CLVD component and seismic moment or depth. T -type CLVD mechanisms correlate weakly with slab stress state, but no correlation was similarly found for P -type CLVD events. Seven earthquakes in the catalog are slow or compound, and three show strong frequency dependence of the moment tensor.

Body wave inversion of the 1970 and 1963 South American large deep‐focus earthquakes

A comprehensive set of teleseismic waveforms from two South American deep‐focus earthquakes of the predigital era, the 1970 Colombia (Mw = 8.1) and 1963 Peru‐Bolivia (Mw = 7.7) events, are inverted for source mechanism, seismic moment, rupture history, and centroid depth. The P and SH wave inversion of the Colombia event confirms previous work, indicating that rupture occurred on a plane that dips steeply west. Rupture direction paralleled the trend of the Wadati‐Benioff zone. We decompose the source into subevents, based on a source time function which shows two major moment release pulses separated by ∼20 s. The first subevent is located near the initiation point at a depth of ∼630 km. The main moment release was located ∼70 km to the southeast and ∼20 km shallower. Rupture subsequently propagated farther southeast. The source time function has an initial subevent accounting for ∼30% of the moment release of the entire event, whereas the long‐period centroid moment tensor (CMT) analysis [Russakoff et al., 1997] has the initial subevent yielding ∼50%. The high‐angle nodal plane rotated ∼15° clockwise during the rupture, explaining the large compensated linear vector dipole (CLVD) component inferred from CMT solutions. Individual subevents have large CLVD and compressive isotropic components. A full moment tensor inversion of the Colombia and 1994 Bolivia events suggests that the initial subevents might contain a large non‐double‐couple (NDC) component. For the 1963 Peru‐Bolivia event, using P waves, rupture propagated NNW for a distance of ∼70 km, parallel to the high‐angle nodal plane and the trend of the Wadati‐Benioff zone. The focal mechanism changed dramatically after the second subevent, causing a very large NDC component. Both events, together with the 1994 Bolivia earthquake, have a precursor separated in space and time from the main rupture and show rupture velocities varying between 3 and 4 km/s between subevents, with &lt;2.0 km/s on average for the entire event. Low seismic efficiencies and rupture velocities support a highly dissipative, temperature‐dependent rupture mechanism for large deep‐focus South American earthquakes, compared with events in cold subducting slabs.

How well constrained are well‐constrained T, B, and P axes in moment tensor catalogs?

The T, B and P axes of earthquake moment tensors (MT) are often used to evaluate regional stress directions and other tectonic parameters; we here undertake three comparisons to assess the uncertainty in the orientations of these axes. These are (1) a direct comparison of common MT in the Harvard, U.S. Geological Survey, or Earthquake Research Institute (ERI) catalogs; (2) a comparison of MT slip vectors and plate motion vectors in several tectonically straightforward regions; and (3) an analysis of the axial variability in the Harvard and ERI catalogs implied by the reported uncertainties in individual MT components. All three comparisons indicate that there is considerable variability within the catalog concerning the axial orientation of MT, but all suggest that axis orientations of the majority of Harvard MT have uncertainties of 15° or less. For compensated linear vector dipole (CLVD) components among the three catalogs, the correlation is very low. For the Harvard catalog, three statistics are especially useful for selecting better constrained MT; these are (1) the relative error Erel, which is the ratio of the scalar moments of the reported error tensor and of the MT itself; (2)ƒCLVD, a measure of the strength of the CLVD component; and (3) nfree, the number of MT elements not fixed at zero in the inversion. For selecting better constrained MT, the appropriate statistical cutoffs chosen depend on the problem of interest, the data available, arid personal preference. However, for analysis of shallow earthquakes we have used Erel ≤ 0.15, ƒCLVD ≤ 0.20, and nfree = 6. While this eliminates 53% of the catalog, our calculations suggest that nearly all the remaining events have T, B, and P axes with azimuth and inclination angle uncertainties of 5°–10° or less.

The effect of focal depth error on moment tensor inversion

In the determination of focal mechanism and rupture process of earthquake sources by using moment tensor inversion technique, it is difficult to guarantee the focal depth used in calculating the Green’s functions (theoretical focal depth) is exactly equal to the real focal depth. The difference between the theoretical and real focal depths, i. e., the focal depth error, will affect the moment tensor inversion to some extent. Using synthetic seismograms, the effect of the focal depth error on moment tensor inversion for three basic types of faults is discussed systematically. For the normal and thrust fault, the focal depth error mainly affects the explosive (EP) component and the compensated linear vector dipole (CLVD) component. In the case that the theoretical focal depth is greater than the real focal depth, the focal depth error causes a false positive EP component and a false negative CLVD component for the normal fault. However, it produces a false negative EP component and a false positive CLVD component for the thrust fault. The absolute values of the false EP and CLVD components for both normal fault and thrust fault cases increase with increasing focal depth error. In the case that the theoretical focal depth is smaller than the real focal depth, the focal depth error causes a false negative EP component and a false positive CLVD component for the normal fault. However, it produces a false positive EP component and a false negative CLVD component for the thrust fault. Similarly, the absolute values of the false EP and CLVD components for both normal fault and thrust fault cases increase with increasing focal depth error. For a pure strike-slip fault the focal depth error mainly affects the shape of source the function, unlike for the normal and thrust faults. The source time functions have artificially extended tails when either the theoretical focal depth is greater or smaller than the real focal depth. The numerical experiments show that the focal depth error less than 20 km has no significant effect on the overall focal mechanism of the earthquake. In addition, the effect of the focal depth error on the inversion result is slighter in case that the theoretical focal depth is greater than the real focal depth than in the case that the theoretical focal depth is smaller than the real focal depth.