Scalar Moment Research Articles

Uncertainties in Seismic Moment Tensors Inferred from Differences between Global Catalogs

AbstractCatalogs of moment tensors form the foundation for a wide variety of seismological studies. However, assessing uncertainties in the moment tensors and the quantities derived from them is difficult. To gain insight, we compare 5000 moment tensors in the U.S. Geological Survey (USGS) and the Global Centroid Moment Tensor (Global CMT) Project catalogs for November 2015–December 2020 and use the differences to illustrate the uncertainties. The differences are typically an order of magnitude larger than the reported errors, suggesting that the errors substantially underestimate the uncertainty. The catalogs are generally consistent, with intriguing differences. Global CMT generally reports larger scalar moments than USGS, with the difference decreasing with magnitude. This difference is larger than and of the opposite sign from what is expected due to the different definitions of the scalar moment. Instead, the differences are intrinsic to the tensors, presumably in part due to different phases used in the inversions. The differences in double-couple components of source mechanisms and the fault angles derived from them decrease with magnitude. Non-double-couple (NDC) components decrease somewhat with magnitude. These components are moderately correlated between catalogs, with correlations stronger for larger earthquakes. Hence, small earthquakes often show large NDC components, but many have large uncertainties and are likely to be artifacts of the inversion. Conversely, larger earthquakes are less likely to have large NDC components, but these components are typically robust between catalogs. If so, these can indicate either true deviation from a double couple or source complexity. The differences between catalogs in scalar moment, source geometry, or NDC fraction of individual earthquakes are essentially uncorrelated, suggesting that the differences reflect the inversion rather than the source process. Despite the differences in moment tensors, the location and depth of the centroids are consistent between catalogs. Our results apply to earthquakes after 2012, before which many moment tensors were common to both catalogs.

Evolution of Solar Wind Turbulence from 0.1 to 1 au during the First Parker Solar Probe–Solar Orbiter Radial Alignment

Abstract The first radial alignment between Parker Solar Probe and Solar Orbiter spacecraft is used to investigate the evolution of solar wind turbulence in the inner heliosphere. Assuming ballistic propagation, two 1.5 hr intervals are tentatively identified as providing measurements of the same plasma parcels traveling from 0.1 to 1 au. Using magnetic field measurements from both spacecraft, the properties of turbulence in the two intervals are assessed. Magnetic spectral density, flatness, and high-order moment scaling laws are calculated. The Hilbert–Huang transform is additionally used to mitigate short sample and poor stationarity effects. Results show that the plasma evolves from a highly Alfvénic, less-developed turbulence state near the Sun, to fully developed and intermittent turbulence at 1 au. These observations provide strong evidence for the radial evolution of solar wind turbulence.

Micromechanisms of coal fracture: Insights from quantitative AE technique

Three-dimensional location and characterization of microcracks in controlled fracture tests of hard coal beams were experimentally conducted through the quantitative acoustic emission (AE) technique. The recorded AE events were physically interpreted as displacement discontinuities (DD), i.e. microcracks, involving only opening/closing and shear-sliding mechanisms to describe the fracture modes directly anticipated within a mechanically loaded material. Based on the AE sensor calibration using a scalar sensitivity parameter and the first motion of P-wave, the moment tensor components were determined through minimizing the errors between the measured and calculated displacements at each sensor location, subjected to a restriction from this “crack-only” source model. Source characterization results were presented in a statistical form, which showed mixed mode mechanisms of microcracks with approximately equal contribution of shear and tensile displacements locally due to the considerably tortuous crack path in the microstructural level of coal material. However, the microcrack volume decomposition under the global coordinate system indicated a mode-I opening micromechanisms dominantly, which was compatible with the expected mechanism from the three-point bending test. Additionally, the orientations of microcrack planes were more or less vertical, with an average angle of 20.4° from the global fracture plane. And around 79.6% of the AE sources with an angle, made by the displacement vectors with horizontal direction, less than 30°. AE magnitudes followed the Gutenberg-Richter relation with a b-value of around 1.3 during coal fracture. Owing to the physical basis of energy dissipation and the linear relationship with scalar moment, the so-called “crack volume” |b|ΔA was used as an index of the absolute AE energy. Energy dissipation region moved forward together with the crack propagation, and most of the energy was dissipated above the crack tip by separating the crack face.

Confirmation and Characterization of the Rupture Model of the 2017 Ms 7.0 Jiuzhaigou, China, Earthquake

AbstractOn 8 August 2017, an Ms 7.0 earthquake struck the Jiuzhaigou town, Sichuan Province, China, rupturing an unmapped fault, which is adjacent to the Maqu seismic gap in the Min Shan uplift zone in the easternmost part of the Bayan Har block. Having summarized the previous studies on the source of this earthquake, we confirmed the rupture model by jointly inverting the teleseismic P-wave and SH-wave data, Interferometric Synthetic Aperture Radar line-of-sight displacement data, and the near-field seismic and strong-motion data, a most complete dataset until now. The confirmation showed that a scalar seismic moment of 6.6×1018 N·m was released (corresponding to a moment magnitude of Mw 6.5), and 95% of the release occurred in the first 10 s. The slip area was composed of two asperities, with a horizontal extension of ∼20 km and a depth range of ∼2–15 km. A bilateral extending occurred at shallow depths, but the rupturing upward from deep depth dominated in the early time. The rupture process was found generally featuring the slip-pulse mode, which was related to the weak prestress condition. The aftershocks almost took place in gaps of the mainshock slip because of the coulomb stress change. Combining the aftershock relocations, aftershock focal mechanism solutions, and our confirmed rupture model, we suggest that the seismogenic fault was a northward extension of the mapped Huya fault. The occurrence of this earthquake made the Maqu seismic gap at a higher level of seismic risk, in addition to the moderate to high strain accumulation on the easternmost tip of the Kunlun fault system and the weak lower crust below.

Moment method for the Boltzmann equation of reactive quaternary gaseous mixture

We are interested in solving the Boltzmann equation of chemically reacting rarefied gas flows using the Grad’s-14 moment method. We first propose a novel mathematical model that describes the collision dynamics of chemically reacting hard spheres. Using the collision model, we present an algorithm to compute the moments of the Boltzmann collision operator. Our algorithm is general in the sense that it can be used to compute arbitrary order moments of the collision operator and not just the moments included in the Grad’s-14 moment system. For a first-order chemical kinetics, we derive reaction rates for a chemical reaction outside of equilibrium thereby, extending the Arrhenius law that is valid only in equilibrium. We show that the derived reaction rates (i) are consistent in the sense that at equilibrium, we recover the Arrhenius law and (ii) have an explicit dependence on the scalar fourteenth moment, highlighting the importance of considering a fourteen moment system rather than a thirteen one. Through numerical experiments we study the relaxation of the Grad’s-14 moment system to the equilibrium state.

Complexities of underground mining seismic sources.

This paper presents a numerical investigation on the influence of the mining environment on seismic sources, with a focus on pillar failure mechanisms in tabular mining. We investigate the influence of the mining stope (underground excavation or void) on seismic inversions for the scalar moment, corner frequency, source radius, stress drop and moment tensor using synthetic events created within elastodynamic numerical modelling software, WAVE3D. The main objective is to determine whether the source parameters calculated from the recorded waveforms are due to a combination of the stope source and the pillar sources, rather than being related only to crushing of the pillar or shearing in the pillar footwall. The main finding is that the presence of stopes, and types of pillars, have a significant impact on the seismic moment and other source parameters. This is important since the moment is viewed as a robust parameter on which seismic magnitude is often based; however, this study indicates that moments calculated for pillar failure in a tabular stoping environments are less representative of the shearing or crushing source than originally thought. This article is part of the theme issue 'Fracture dynamics of solid materials: from particles to the globe'.

Seismological data versus rheological modelling: Comparisons across the Aegean Region for improving the seismic hazard assessment

Compared analyses of the seismicity cutoff depth and the corresponding BDT (brittle-ductile transition) depth obtained from rheological modelling have been performed for numerous test sites all over the Aegean Region. The major goal of this research is to determine whether the rheological transition could be effectively correlated to the seismological one, so that both information can independently contribute in determining the seismogenic layer thickness and hence in constraining the maximum width of active faults affecting a region. As concerns the seismological data, only relocated events have been considered for the purpose of this paper, included either in seismic sequences associated with a mainshock, or in datasets of background seismicity. In the same areas, we carried out rheological modelling for reconstructing the local strength envelope, focusing our attention on the BDT depth. The systematic comparison at the investigated sites indicates that 90% of the relocated seismicity always occurs within the corresponding rheological transition. Moreover, for the datasets also providing magnitudes, 99% of the total seismic scalar moment is always released above the BDT depth. Such results are verified for different tectonic regimes and geological settings, both extensional, transcurrent and compressional. The achieved results confirm that the BDT depth based on accurate strength envelopes could be considered a reliable indicator for the thickness of the seismogenic layer, thus contributing to constrain the maximum widths for active faults affecting those regions. Based on these constraints, we also applied some empirical relationships to estimate the possible maximum magnitude for seismogenic sources in correspondence of the tested sites, thus potentially improving our seismic hazard assessment analyses for these areas.

Comparing turbulence in a Kelvin–Helmholtz instability region across the terrestrial magnetopause

ABSTRACTThe properties of turbulence observed within the plasma originating from the magnetosheath and the magnetospheric boundary layer, which have been entrained within vortices driven by the Kelvin–Helmholtz Instability (KHI), are compared. The goal of such a study is to determine similarities and differences between the two different regions. In particular, we study spectra, intermittency and the third-order moment scaling, as well as the distribution of a local energy transfer rate proxy. The analysis is performed using the Magnetospheric Multiscale data from a single satellite that crosses longitudinally the KHI. Two sets of regions, one set containing predominantly magnetosheath plasma and the other containing predominantly magnetospheric plasma, are analysed separately, thus allowing us to explore turbulence properties in two portions of very different plasma samples. Results show that the dynamics in the two regions is different, with the boundary layer plasma presenting a shallower spectra and larger energy transfer rate, indicating an early stage of turbulence. In both regions, the effect of the KHI is evidenced.

The source parameters of earthquakes of Bishkek geodynamic proving ground (Northern Tien Shan)

Based on the method of polarity of signs of P-waves, the focal mechanisms of 1674 earthquakes with M ≥ 1.6, which occurred on the territory of the Bishkek geodynamic proving ground (BGPG) from 1994 to 2020, were determined. Some characteristics of the complete catalogue are presented. Quantitative distributions by the type of mechanisms and diagrams of azimuths of the main stress axes are constructed. A variety of focal mechanism of earthquake is observed, most of them are reverse fault, oblique reverse fault, and horizontal strike-slip fault. The compression axis for most of the events has a north-northwest direction and a sub-horizontal position. For 183, dynamic parameters (DP, source parameters) were obtained: spectral density Ω0, corner frequency f0, scalar seismic moment M0, source radius (Brune radius) r, and stress drop Δσ. The correlations between DP and energy characteristic (magnitude) and scalar seismic moment are investigated. The smallest correlation coefficient was obtained for stress drop.

STRONG SEISMIC EVENTS on the SOUTH-WESTERN FLANK of the BAIKAL RIFT in 2014: November 1, 2014, Кp=13.6, Mw=4.6, I0=7–8 URIK EARTHQUAKE and December 5, 2014, Кp=13.9, Mw=4.9, I0=7–8 HOVSGOL EARTHQUAKE

We consider two earthquakes occurred at the south-western flank of the Baikal rift zone (BRZ): Urik, November 1, 2014 (Mwreg=4.6) and Hovsgol, December 5, 2014 (Mwreg=4.9). First of them is localized within the area of the Main Sayan fault, the second one is located at the north of the Hovsgol Lake. Seismic moment tensors (focal mechanisms, scalar seismic moments, moment magnitudes and hypocentral depths) of the study seismic events were calculated based on surface wave amplitude spectra. Earthquake hypocenters were found to be situated in the middle crust (h=14–21 km). Both events occurred under the strike-slip stress-strain field. The strike-slip was combined with a normal fault component in the source of the Urik earthquake and with a thrust fault component in the source of the Hovsgol earthquake. In both cases, shaking intensity in the nearest settlements (=42–124 km) was less than 4–5. Analysis of historical seismicity, seismological data on the Urik and Hovsgol earthquakes and the tectonic position of their sources demonstrates that the considered events are typical for the south-western flank of the BRZ and confirms the existence of the transition zone from rift structures at the central parts of the BRZ to regional compression structures in Northern Mongolia.

MUYAKAN-II EARTHQUAKE on MAY 23, 2014 with КР=14.3, Mw=5.5, I0=7–8 (Northern Baikal region)

We consider the May 23, 2014 Muyakan earthquake (Mw=5.5) occurred in the Muyakan Range at the north-east of the Baikal rift zone near the eastern tunnel portal of the Baikal-Amur Mainline. This event was followed by numerous aftershocks (КР=5.6–9.9) which number exceeded 2000 by the end of the year. Spatio-temporal analysis of the Muyakan seismic sequence shows that its epicentral field consists of two isolated clusters: eastern and western ones. All the main events including the foreshocks, main shock and the strongest aftershocks (Mw=4.4; 4.5) occurred in the eastern cluster while only small seismic events (КР<10.0) were recorded in the western one. Seismic moment tensor was calculated for the Muyakan earthquake from surface wave amplitude spectra. As a result, we obtained information about the rift type focal mechanism, scalar seismic moment (M0=1.9•1017 Nm), moment magnitude (Mw=5.5) and hypocentral depth (h=24 km). From regional data, hypocentral depths of the main shock and the major number of the following earthquakes (80 %) were distributed in the depth range h=3–11 km. Maximum intensity of the main shock (4–5 according to MSK-64) was felt in Severomuysk urban village (=29 km). The obtained results could be used for seismic hazard assessment of the crucial part of the Baikal-Amur Mainline.

BAIKAL and TRANSBAIKALIA

We considered the character of the seismic process in the Baikal and Transbaikalia region in 2014. 8782 earthquakes with КР≥5.6 were recorded within the study territory during that year, 94 % of them were located in the Baikal rift zone. 26 seismic events were felt in the cities, towns and local settlements with the intensity not exceeding 5. The strongest of them (Mw=5.5) occurred in the Baikal-Muya region of the Baikal rift zone and was followed by a large earthquake sequence. Focal mechanisms were determines for 46 shocks from the data on P-wave first motion polarities, seismic moment tensor (focal mechanism, scalar seismic moment (M0), moment magnitude (Mw) and hypocentral depth (h)) was calculated for 11 events from the data on amplitude surface wave spectra. It has been found that normal fault movements are realized in the sources of 59 % of the earthquakes with the obtained focal mechanisms. In general, high level of seismic activity is a characteristic feature of the considered territory in 2014.

Single-molecule tracking measurement of PDMS layer during curing process

The curing process of poly(dimethylsiloxane) (PDMS) was microscopically investigated by the single-molecule tracking method based on the diffusion motion of fluorescent dye molecules adding to the PDMS layer stored at a temperature of 308K. The PDMS layer was completely cured at 900 min after adding a curing agent. We compared the time- and ensemble-averaged mean square displacements (MSDs) of the tracked molecules at 90, 510, and 900 min after adding the curing agent into the PDMS layer. The discrepancies were observed between the time- and ensemble-averaged MSDs, indicating weak ergodicity breaking. The spatially averaged diffusion coefficient exhibited a two-step decrease: first step was rapid decrease suggesting the extent of crosslinking, and second step was slow one suggesting the increase of crosslink density. The single-molecule trajectory scale analysis revealed the heterogeneous distribution of the diffusion coefficient. By calculating the heat map from the slope of moment scaling spectrum (MSS) of each single-molecule trajectory, cluster structures were recognized. The spatial correlation of the slope of MSS decreased with the time elapsed. These results suggested the existence of the heterogeneous structure in the PDMS layer during the curing process.

The March 29, 2019 Earthquake in the Western Part of the Tunka Rift Basin System: Source Parameters and Macroseismic Effects

The paper considers one of the perceptible earthquakes that occurred on March 29, 2019, in the western part of the Tunka rift basin system. The epicenter of this seismic event was localized within the Hoytogol basin. The earthquake source parameters were as follows: hypocentral depth (h = 36–37 km), scalar seismic moment (M0 = 1.6 × 1016 N m), moment magnitude (Mw = 4.8), and focal mechanism—were determined using joint inversion of surface wave amplitude spectra and polarities of P-wave first arrivals. The focal mechanism demonstrates the predominance of combined thrust and strike-slip movements, indicating uplifting tectonic movements in the Hoytogol basin. The shaking from the earthquake was felt within a vast area, with an intensity of up to I = III at epicentral distances up to 490 km. Macroseismic data were obtained using different methods, including an interactive questionnaire hosted on the website of the Baikal Branch of GS RAS. Analysis of the macroseismic data made it possible to formulate the goal of refining the regional macroseismic field equation.

Geological, Geophysical and Macroseismic Data on the September 28, 2019, Mw= 5.1 Earthquake That Occurred at the Northeast of the Baikal Rift

This paper considers the September 28, 2019 earthquake that occurred on the northeastern flank of the Baikal Rift Zone (BRZ), called the Lenger earthquake after its location. The seismic moment tensor and hypocentral depth of the event are calculated from data on surface wave amplitude spectra with additional information on P-wave first-arrival polarities recorded at regional stations. The hypocentral depth is 11–12 km, the moment magnitude Mw = 5.1, and the scalar seismic moment M0 = 5 × 1016 N m. The earthquake source is formed under the influence of horizontal submeridional extension and subhorizontal NE–SW compression. The latter approximately coincides with the azimuth of the fast S-wave velocity in the upper mantle obtained from SKS-splitting and surface wave tomography data. The Lenger earthquake was felt at epicentral distances of more than 600 km. Comparison of its macroseismic effects with effects of other strong seismic events in the study area demonstrates that the regional macroseismic field equation should be actualized for the territory of the northeastern flank of the BRZ. Analysis of the obtained data, along with the available information on the stress-strain field of the crust of this area indicates that the geodynamical pattern of the conjunction zone of the northeastern flank of the BRZ and the Olekma–Stanovoi orogenic system influences the low-active Transbaikalia block. However, due to low tectonic activity, the tectonic stress accumulation period sufficient for the occurrence of relatively strong seismic events is larger than in regions with high-level tectonic activity.

The Seismic Moment and Seismic Efficiency of Small Impacts on Mars

AbstractSince landing in late 2018, the InSight lander has been recording seismic signals on the surface of Mars. Despite nominal prelanding estimates of one to three meteorite impacts detected per Earth year, none have yet been identified seismically. To inform revised detectability estimates, we simulated numerically a suite of small impacts onto Martian regolith and characterized their seismic source properties. For the impactor size and velocity range most relevant for InSight, crater diameters are 1–30 m. We found that in this range scalar seismic moment is 106–1010 Nm and increases almost linearly with impact momentum. The ratio of horizontal to vertical seismic moment tensor components is ∼1, implying an almost isotropic P wave source, for vertical impacts. Seismic efficiencies are ∼10−6, dependent on the target crushing strength and impact velocity. Our predictions of relatively low seismic efficiency and seismic moment suggest that meteorite impact detectability on Mars is lower than previously assumed. Detection chances are best for impacts forming craters of diameter >10 m.

Impact of 3-D Earth structure on W-phase CMT parameters

SUMMARYWe investigate the impact of unmodelled 3-D structural heterogeneity on inverted W-phase source parameters. We generate a large data set of synthetic seismograms accounting for the Earths 3-D structure for 250 earthquakes globally distributed. The W-phase algorithm is then used to invert for earthquake CMT parameters, assuming a spherical Earth model. The impact of lateral heterogeneity is assessed by comparing inverted source parameters with those used to compute the 3-D synthetics. Results show that the 3-D structure mainly affects centroid location while the effect on the other source parameters remains small. Centroid mislocations present clear geographical patterns. In particular, W-phase solutions for earthquakes in South America are on average biased 17 km to the east of the actual centroid locations. This effect is significantly reduced using an azimuthally well balanced distribution of seismological stations. Source parameters are generally more impacted by mantle heterogeneity while the scalar moment of shallow earthquakes seems to be mainly impacted by the crustal structure. Shallow earthquakes present a variability of Mrθ and Mrϕ moment tensor elements, resulting both from the small amplitude and a larger uncertainty of the associated Green’s functions.

Inferring In Situ Hydraulic Pressure From Induced Seismicity Observations: An Application to the Cooper Basin (Australia) Geothermal Reservoir

AbstractAn approach is proposed for estimating in situ reservoir pressure changes based on induced earthquakes with overlapping slip patches. The approach is independent of absolute (tectonic) stresses and can also be applied in a scenario where the (unknown) tectonic stresses are strongly heterogeneous. Based on Coulomb friction, the approach makes use of the fact that stress‐strength conditions are in equilibrium at the time of seismic activation. Coseismic stress changes inferred from seismogram recordings provide the stress‐state relative to the failure stress immediately after seismic activation. If the same fracture patch is seismically activated again, relative changes of fluid pressure, that is, the fluid pressure change at which stress‐strength conditions reach equilibrium again, can be inferred from the stress‐deficit when accounting for stress re‐load from neighboring patches. The performance of the technique is demonstrated using a data set of 20,736 earthquakes induced during a hydraulic injection experiment in a geothermal reservoir in the Cooper Basin, Australia. The spatial hypocenter distribution indicates that the seismicity mainly occurred on a single‐layer structure with slip direction controlled by the regional stress field as evidenced by fault mechanisms. Due to the high earthquake density, interearthquake stress interaction is pronounced. The spatial stress impact associated with each earthquake is simulated using a slider‐block type propagation pattern based on Okada's analytical solutions. Using the scalar seismic moment determined from S‐wave spectra, the spatio‐temporal evolution of hydraulic pressure changes is inferred on a reservoir scale. Results indicate that hydraulic flow is most pronounced into NW‐SE direction.

Stress drop assessment of the August 8, 2017, Jiuzhaigou earthquake sequence and its tectonic implications*

By using a broadband Lg attenuation model developed for the Tibetan Plateau, we isolate source terms by removing attenuation and site effects from the observed Lg-wave displacement spectra of the M7.0 earthquake that occurred on August 8, 2017, in Jiuzhaigou, China, and its aftershock sequence. Thus, the source parameters, including the scalar seismic moment, corner frequency and stress drop, of these events can be further estimated. The estimated stress drops vary from 47.1 kPa to 7149.6 kPa, with a median value of 59.4 kPa and most values falling between 50 kPa and 75 kPa. The estimated stress drops show significant spatial variations. Lower stress drops were mainly found close to the mainshock and on the seismogenic fault plane with large coseismic slip. In contrast, the highest stress drop was 7.1 MPa for the mainshock, and relatively large stress drops were also found for aftershocks away from the major seismogenic fault and at depths deeper than the zone with large coseismic slip. By using a statistical method, we found self-similarity among some of the aftershocks with a nearly constant stress drop. In contrast, the stress drop increased with the seismic moment for other aftershocks. The amount of stress released during earthquakes is a fundamental characteristic of the earthquake rupture process. As such, the stress drop represents a key parameter for improving our understanding of earthquake source physics.

On the Lamb problem: forced vibrations in a homogeneous and isotropic elastic half-space

The problem of vibrations generated in a homogeneous and isotropic elastic half-space by spatially concentrated forces, known in Seismology as (part of) the Lamb problem, is formulated here in terms of Helmholtz potentials of the elastic displacement. The method is based on time Fourier transforms, spatial Fourier transforms with respect to the coordinates parallel to the surface (in-plane Fourier transforms) and generalized wave equations, which include the surface values of the functions and their derivatives. This formulation provides a formal general solution to the problem of forced elastic vibrations in the homogeneous and isotropic half-space. Explicit results are given for forces derived from a gradient, localized at an inner point in the half-space, which correspond to a scalar seismic moment of the seismic sources. Similarly, explicit results are given for a surface force perpendicular to the surface and localized at a point on the surface. Both harmonic time dependence and time $$\delta $$ -pulses are considered (where $$\delta $$ stands for the Dirac delta function). It is shown that a $$\delta $$ -like time dependence of the forces generates transient perturbations which are vanishing in time, such that they cannot be viewed properly as vibrations. The particularities of the generation and the propagation of the seismic waves and the effects of the inclusion of the boundary conditions are discussed, as well as the role played by the eigenmodes of the homogeneous and isotropic elastic half-space. Similarly, the distinction is highlighted between the transient regime of wave propagation prior to the establishment of the elastic vibrations and the stationary-wave regime.