Scalar Moment Research Articles

SPECTRAL and SOURCE PARAMETERS of NORTH CAUCASUS EARTHQUAKES in 2020

The spectral parameters of the sources of 38 earthquakes in the North Caucasus were determined from the displacement spectra of S-waves for the period 2020. The calculations used events with an energy classes KR=9.3–12.9 and waveforms from stations with epicentral distances 50–250 km. The values of local magnitudes ML were calculated using a new calibration curve. The calculation of source spectra was carried out in the SEISAN program based on the frequency-dependent quality factor Q(f). The following values were obtained: 0 – spectral density, f0 – corner frequency, M0 – scalar seismic moment, Mw – moment magnitude,  – stress drop, and RMS for each of the parameters. For 30 earthquakes with KR=9.0–12.9 focal mechanisms were calculated, which are represented by reverse faults (including reverse faults with strike-slip components – 73 %), normal faults – 20 % and strike-slip – 7 %, which corresponds to deformation processes in the collision zone of the Arabian and Eurasian plates.

Database of Earthquake Focal Mechanisms for the East Arctic Region

In this paper, we present a description of a database of earthquake focal mechanisms, which is compiled from the data of international seismological agencies and literature sources for the East Arctic region. It consists of 595 focal mechanism solutions for 273 seismic events with M = 2.1–7.6, which occurred in 1927–2022. Information about the source depth, the scalar seismic moment, and the moment magnitude are also presented there for many events. In addition to the focal parameters, their quality assessments are available, which facilitates a comparison of different solutions in many cases. For user convenience, the database has a graphical interface that permits searching by various attributes (coordinates, time, magnitude, and depth). In terms of volume of the collected information, our database significantly exceeds all the analogues available at the present time. It can be used to perform a seismotectonic analysis, to estimate the stress–strain state of the lithosphere, and to assess seismic hazard for the entire East Arctic region or its separate areas. Implementation of the compiled database for comparison of different solutions of earthquake focal mechanisms and their seismotectonic analysis is illustrated in the paper on the example of seismic events occurred in the Olenek Bay of the Laptev Sea and adjacent territories. We suggest adding new information to the database every five years in future.

Metastable doubly charged Rydberg trimers

We examine an effectively one-electron system with three positive nuclei composed of a Rb*87 Rydberg atom interacting with a pair of Rb+87 ions and predict the existence of metastable vibrationally bound states of Rb32+87. These molecules are long-range trimers whose stability rests on the presence of core-shell electrons and favorable scaling of the Rydberg atom's quadrupole moment with the principal quantum number n. Unlike recently observed ion-Rydberg dimers, whose binding is due to internal flipping of the Rydberg atom's dipole moment, the binding of Rb32+87 arises from the interaction of the ions with the Rydberg atom's quadrupole moment. The stability of these trimers is highly sensitive to n. For n≤35, we estimate that the lifetime of the bound states should be limited by intercore tunneling of the Rydberg electron, which creates an instability in the system. However, we predict that the rate of this process decreases significantly with n, such that already for n=38 it is comparable in magnitude to the rate of spontaneous emission of the Rydberg state. The decreasing depth of the binding potential at larger n will further lead to an increase in the tunneling rate of the vibrational states from the molecular binding potential to dissociative regions of the adiabatic potential energy surface. Nonetheless, at n=38, this mechanism is only relevant for the highest-excited vibrational states in the binding potential. Published by the American Physical Society 2024

Numerical Tests to Evaluate the Effect of Constraining the Spectral Shape of Reference Events on Source Parameter Scaling

ABSTRACT Extracting source parameters from recorded spectra requires correction for attenuation effects. In consideration of the trade-off between source and propagation effects, various strategies have been proposed to constrain the inverse problem with a priori assumptions. The objective of this study is to assess the impact of constraining the source spectra of reference earthquakes in an attempt to remove a common unknown term from the spectral decomposition results. We perform numerical analyses to simulate the outcomes of the decomposition by generating source spectra for different stress drop versus seismic moment scaling, considering a large population of earthquakes with moment magnitudes between 1.8 and 6.5. Following the strategy of constraining the corner frequency of reference events, we evaluate the error of the retrieved source parameters when the applied constraint shows different levels of discrepancy with respect to the assumption used to generate the synthetics. The numerical tests show that an assumption that differs from the correct one can introduce a magnitude-dependent bias that could alter the scaling of the corner frequency with earthquake size. Furthermore, the source spectral shape for large events is also influenced by the constraints applied to the reference earthquakes. As a consequence, inferences about the self-similarity of the rupture process across the scales, or the selection of the most appropriate source model based on the goodness of the spectral fit, may be strongly biased by the constraint imposed on the reference earthquakes.

Improvements and Heterogeneities of the Global Centroid Moment Tensor Catalog

Abstract Earthquake catalogs are heterogeneous, especially those developed over long time spans. Changes in seismological monitoring, which provides the records on which these catalogs are based, are common. Typically, instruments and networks become more sensitive over time, allowing for the detection and characterization of smaller earthquakes. In pursuit of improvement, new methods for routine data analysis are occasionally introduced, modifying the procedures for catalog compilation. The resulting heterogeneities may not be evident to users, but they should be unveiled and considered in any application of the catalog, especially in statistical seismology, which analyzes large earthquake data sets. The Global Centroid Moment Tensor catalog is considered the most homogeneous database of global seismicity. However, a detailed analysis of its heterogeneities has been lacking. This work reviews changes in the catalog’s development from 1976 to 2023 and reveals how these have caused improvements and heterogeneities in the resulting data. Several periods are distinguished, separated by milestones in the methods employed for moment tensor inversion and catalog compilation, as well as by the advent of global broadband monitoring in 2004. These changes are shown to have caused variations in the catalog’s completeness and in the determinations of centroid depths, scalar seismic moments, and moment tensors. The magnitude of completeness is measured here in detail, both temporally and spatially. It has decreased over the years and shows spatial variations within each period, correlated to regional differences in network monitoring and compilation biases. Moment tensor determinations have been significantly different since 2004, resulting in a different frequency distribution of rake angles and a different dependence of the double-couple component as a function of rake. This work is expected to benefit all future uses of the catalog, enabling better characterization of seismicity properties and improved building and testing of models for earthquake occurrence.

Seismic moment of local earthquakes in the central part of the Baikal rift by the coda envelope inversion

The article presents an estimation of scalar seismic moment by the coda envelope inversion of local earthquakes recordings in the central part of the Baikal rift zone. In addition to the earthquake source parameters, the method allows us to simultaneously estimate seismic energy loss and site amplification factors for frequency bands from 0.53 to 34 Hz. Because of the compromise between spectral source energy and site responses, we estimated amplification factors for used stations relative to the "UlanUde" (UUDB) reference site located in crystalline rock. In order to estimate intrinsic and scattering attenuation we used events recorded at three broadband seismic stations and epicentral distances between 40 and 120 km. The result suggests that intrinsic absorption is dominant over scattering attenuation in the central part of the Baikal rift zone for most frequency bands, but the seismic albedo B0, expressing the contribution of scattering to the total attenuation, showed variations from 0.23 to 0.6 for frequencies below 1 Hz, with mean B0 value 0.33. Attenuation and siteamplification factors were used to estimate the seismic moment and moment magnitudes Mw of local earthquakes. The resultant moment magnitudes exhibit a good agreement with routinely reported local magnitude (ML) estimates for the study area. The coda inversion estimates of seismic moment provide stable, unbiased moment magnitudes for events that are too small to be seen at teleseismic distances.

Source faulting properties of the 2021 M S 6.4 Yangbi, China, earthquake sequence

The 2021 Yangbi earthquake sequence occurred on the southwestern margin of the Chuandian block in China, which is a typical foreshock-mainshock-aftershock sequence. We investigate source properties of this earthquake sequence with seismic and geodetic data. Focal mechanisms of M ≥ 2.0 events in this earthquake sequence are determined using P wave first-motion polarity plus S/P amplitude ratio data from local short-period and broadband seismic stations. The determined focal mechanisms together with spatial distribution of the earthquake sequence indicate the overall northwest-southeast-trending seismogenic faults with dominant strike-slip motions. We conduct kinematic finite-fault inversion with strong-motion, local broadband seismic, and coseismic InSAR plus GNSS displacement data, finding that the mainshock ruptured a major asperity unilaterally with a rupture length and duration being approximately 15 km and 6.5 s, respectively. The released scalar seismic moment is 1.7 × 1018 Nm, corresponding to a moment magnitude M W 6.1. Besides, stress field inversion results manifest that source area is characterized by a strike-slip stress regime and the local stress field has changed before and after the mainshock. We suggest that rupture initiation, propagation, and arrest of the 2021 Yangbi earthquake sequence may be regulated by the immanent strength and stress heterogeneities of the seismogenic fault.

Comparison between rupture parameters of intermediate and deep earthquakes at the Peru–Brazil–Bolivia border and northern Chile

We determined the main parameters of the source rupture process of intermediate- and deep-depth earthquakes occurring in the Peru–Brazil–Bolivia border region and northern Chile. The parameters of depth, fault-plane orientation, scalar seismic moment, slip distribution, and radiated seismic energy are obtained from seismograms. We selected 15 intermediate-depth earthquakes (100 km < h < 300 km) and 10 very deep earthquakes (h > 500 km) with magnitudes MW ≥ 6.0. For most events, the slip distribution over the rupture plane shows a single asperity, and the source time function presents a simple pulse. There are differences between intermediate-depth and deep earthquakes. The rupture areas, maximum slip and source time function (STF) duration are larger for intermediate-depth events than for deep events. Additionally, the STF’s show a sharper increase for deep earthquakes. The scaled radiated seismic energy shows larger values for deep depth events. The stress regime pattern derived from the obtained focal mechanism agrees with the geometry of the subduction of the Nazca plate. At intermediate depths, in the northern area up to 12°S, the stress pattern corresponds to a horizontal extension, while in the southern area, the tension axes dip at an angle of 30°. At deep depths, the stress regime corresponds to vertical compression in the north and dips of approximately 45° in the south.

Yield estimation of North Korean underground nuclear tests using Lg-wave source spectra

In seismic nuclear monitoring, attenuation models are important prerequisites for reliably estimating the explosive yield in an uncalibrated region without the occurrence of standard events. The seismic moment obtained by fitting source spectra is related to the source energy. This approach is appropriate for estimating yield, as the attenuation effects on the propagation path can be accurately considered. In this study, we collected 2022 vertical component waveforms in and around the Korean Peninsula from May 2010 to May 2022 to construct a high-resolution broadband Lg-wave attenuation model and inverted the Lg-wave source excitation spectra of the nuclear explosion simultaneously with attenuation correction. We obtained the scalar seismic moments by fitting the theoretical source spectra based on the Brune (J. Geophys. Res., 1970, 75, 4997–5009) model. Under the given emplacement conditions and burial depths, the seismic moments can be used to estimate yields of the North Korean nuclear tests, which are 4.6, 8.5, 19.9, 20.9, 24.7, and 337.4 kt for six nuclear explosions that occurred between 2006 and 2017. Our results are consistent with those obtained from previous teleseismic observations.

Joint Inversion of Regional Waveform, First-Motion Polarity, and Synthetic Aperture Radar Surface Displacement for the Fourth and Sixth North Korean Declared Nuclear Explosions

ABSTRACT This study analyzed the Democratic People’s Republic of Korea’s (DPRK) fourth (DPRK4, 6 January 2016 Mw 4.49) and sixth (DPRK6, 7 September 2017 Mw 5.2) declared nuclear tests, employing a joint seismic and Interferometric Synthetic Aperture Radar (InSAR) inversion to improve understanding of these events and enhance moment tensor (MT) inversion capabilities. The recent efforts have focused on employing seismic waveform and InSAR geodetic deformation data separately to analyze these and the previous nuclear tests (e.g., Chiang et al., 2018; Myers et al., 2018; Wang et al., 2018). Building upon our previous work (Chi-Durán et al., 2021), we performed a joint regional waveform, first-motion (FM) polarity, and surface displacement inversion, which demonstrated improved source-type discrimination, a revised MT solution with reduced scalar moment uncertainty, and an independently constrained location. In this article, we build on the previous results for DPRK6 by including an analysis using a four-layered velocity model with free-surface topography to compute the near-source static deformation Green’s functions. The model consists of a 50 m basalt layer (VP=2.07 km/s, VS=1.2 km/s), a 250 m stratified volcanic deposit layer (VP=1.73 km/s, VS=1.0 km/s), a 700 m weathered granodiorite layer (VP=2.5 km/s, VS=1.3 km/s), and a granodiorite half-space (VP=5.35 km/s, VS=3.09 km/s). The half-space shares the velocity of the regional MDJ2 velocity model (Ford et al., 2010), which has proven effective for waveform inversion in the region. This model considers the range of reported values for various lithologies and weathering effects. Our findings show that using the layered velocity model enhances the recovery of source location and depth for both the explosions by improving fits and reducing uncertainties. The joint inversion also improves source-type discrimination and better constrains the scalar seismic moment necessary for downstream yield estimation.

Seismic Magnitude Estimation Using Low-Frequency Strain Amplitudes Recorded by DAS Arrays at Far-Field Distances

ABSTRACT Downhole distributed acoustic sensing (DAS) data are now routinely acquired on fiber-optic cables deployed in wells for seismic imaging and microseismic monitoring. We develop a semiempirical workflow for estimating scalar seismic moment and moment magnitude of earthquakes using strain data recorded by downhole DAS arrays. At far-field distances, the time integral of axial strain is proportional to the displacement scaled by apparent slowness. Therefore, seismic moment can be directly estimated from the amplitude of the low-frequency plateau of the strain spectra divided by frequency, similar to the methodology commonly employed for far-field displacement spectra. The effect of polarization on strain amplitudes for different types of body waves is accounted for. Benefitting from the large spatial coverage provided by DAS arrays, moment estimates from multiple channels are averaged and an average radiation coefficient is assumed over the focal sphere. We validate the methods using data of microseismic events simultaneously recorded by a surface geophone array and by DAS on fiber deployed in two horizontal wells during a hydraulic fracturing experiment. For 106 microseismic events in the magnitude range ∼ −0.65 to ∼ +0.55, we find the DAS-derived magnitudes to be consistent with the magnitudes derived from the geophone array using traditional methods, with ∼95% of the magnitude estimates differing by less than ∼0.26 units. The workflow can be potentially extended to DAS arrays in vertical wells and to S waves recorded on dark fiber DAS arrays at the surface. This methodology does not require any calibration beyond knowledge of local seismic properties, and the use of the lowest possible frequencies reduces the influence of subsurface heterogeneities and the finite spatiotemporal extent of earthquake ruptures. The capacity to estimate robust seismic magnitudes from downhole DAS arrays allows improved evaluation and management of fracture growth and more effective mitigation of induced seismicity.

Graph convolutional multi-mesh autoencoder for steady transonic aircraft aerodynamics

Calculating aerodynamic loads around an aircraft using computational fluid dynamics is a user’s and computer-intensive task. An attractive alternative is to leverage neural networks (NNs) bypassing the need of solving the governing fluid equations at all flight conditions of interest. NNs have the ability to infer highly nonlinear predictions if a reference dataset is available. This work presents a geometric deep learning based multi-mesh autoencoder framework for steady-state transonic aerodynamics. The framework builds on graph NNs which are designed for irregular and unstructured spatial discretisations, embedded in a multi-resolution algorithm for dimensionality reduction. The test case is for the NASA common research model wing/body aircraft configuration. Thorough studies are presented discussing the model predictions in terms of vector fields, pressure and shear-stress coefficients, and scalar fields, total force and moment coefficients, for a range of nonlinear conditions involving shock waves and flow separation. We note that the cost of the model prediction is minimal having used an existing database.

Background earthquakes and aftershock sequences of the strongest intraplate earthquakes in Central Asia

Within the analyzed observation period (1971–2021), the values of the total magnitude of the scalar seismic moment obtained from the aftershocks of the strongest earthquakes (Мw ≥ 7.6) Asia (φ=20–50 N, λ=60–105° E), are weakly correlated with the total magnitude of the scalar seismic moment of background seismicity in the region of the main earthquake. A high level of seismic activity is manifested in the zones of large active faults and is reflected in the total magnitude of the scalar seismic moment of aftershock sequences. The types of movements in the foci of the main events do not affect the degree of aftershock activity (the total values of the scalar seismic moment) and occur at different background levels. Over the past 50 years, the magnitude of the strongest earthquakes has increased compared to the previous fifty-year period.

The MW5.5 earthquake on August 6, 2023, in Pingyuan, Shandong, China: A rupture on a buried fault

On August 6, 2023, a magnitude MW5.5 earthquake struck Pingyuan County, Dezhou City, Shandong Province, China. This event was significant as no large earthquakes had been recorded in the region for over a century, and no active fault had been previously identified. This study collects 1309 P-wave arrival times and 866 S-wave arrival times from 74 seismic stations less than 200 km to the epicenter to constrain the spatial distribution of the mainshock and its 125 early aftershocks by the double difference earthquake relocation method, and selects 864 P-waveforms from 288 stations located within 800 km of the epicenter to constrain the focal mechanism solution of the mainshock through centroid moment tensor inversion. The relocation and the inversion indicate, the Pingyuan MW5.5 earthquake was caused by a rupture on a buried fault, likely an extensive segment of the Gaotang fault. This buried fault exhibited a dip of approximately 75° to the northwest, with a strike of 222°, similar to the Gaotang fault. The rupture initiated at the depth of 18.6 km and propagated upward and northeastward. However, the ground surface was not broken. The total duration of the rupture was ∼6.0 s, releasing the scalar moment of 2.5895 × 1017 N·m, equivalent to MW5.54. The moment rate reached the maximum only 1.4 seconds after the rupture initiation, and the 90% scalar moment was released in the first 4.6 s. In the first 1.4 seconds of the rupture process, the rupture velocity was estimated to be 2.6 km/s, slower than the local S-wave velocity. As the rupture neared its end, the rupture velocity decreased significantly. This study provides valuable insights into the seismic characteristics of the Pingyuan MW5.5 earthquake, shedding light on the previously unidentified buried fault responsible for the seismic activity in the region. Understanding the behavior of such faults is crucial for assessing seismic hazards and enhancing earthquake preparedness in the future.

Сейсмотектонические деформации и сброшенные напряжения землетрясений Центрального Тянь-Шаня

Based on the seismic moment tensor (SMT) data of 270 earthquakes in the Central Tien Shan, which occurred from 1978 to 2021 and include 63 events from the Global Centroid Moment Tensor catalog and 207 events from the works of Aleksander D. Kostyuk and Naylya A. Sycheva, the focal parameters (seismotectonic deformations (STD), kinematic and dynamic parameters, source radius, and stress drop) were calculated. The STD calculation was based on the approaches proposed in the studies of Yuriy V. Riznichenko and Sergei L. Yunga. The area under consideration is characterized by such deformation modes as thrust, transpression, underpression, and oblique. The distribution of the Lode–Nadai coefficient was calculated and plotted. A significant part of the study area is characterized by simple compression deformation, dominated by simple compression and simple shear. To calculate the stress drop , the values of the scalar seismic moment M0, which are determined in the SMT calculation, and the source radii r, which are calculated on the basis of theoretical and experimental models of the dependence of the source radius on the moment magnitude, were used. The radii r and stress drops  were calculated for two models of earthquake sources: the Brune model and the Madariaga–Kaneko–Shearer model. A catalog of dynamic parameters was compiled. The comparison of the kinematic and dynamic parameters of earthquakes was carried out, and the relationship of the dropped stresses with the type of movement in the source, as well as with the Lode–Nadai coefficient, was established. The results obtained in the study can be useful for specialists in other fields of knowledge – geodesy, geology, and geophysics.

Parallel optimization approaches for scattering source term and angle merging in MOC high-order anisotropic computation on GPUs

The introduction of high-order anisotropic scattering and thousand-group calculations significantly increases the computational workload of the MOC method, posing difficulties for practical parallel computation on GPUs. In this paper, a GPU-based MOC algorithm is optimized, focusing on the performance optimization of the kernel function that merges high-order anisotropic angular flux density into scalar flux density moments, as well as the optimization of the scattering source term calculation method in thousand-group calculations. Two parallel algorithms based on azimuthal and polar angles are proposed for high-order anisotropic scattering. For the thousand-group calculation, a data structure is designed according to the physical characteristics of the anisotropic scattering matrix, and then two optimization algorithms are proposed from the perspectives of memory access and parallelism. Based on the KAIST-3A reference problem, the parallel expansion of the polar angle in the merging calculation is more advantageous. Based on the KAIST-3A reference problem, the parallel expansion of the polar angle in the merging calculation is found to be more advantageous. Based on a self-designed fast reactor fuel lattice, it is concluded that the parallelism-oriented calculation method for the thousand-group anisotropic scattering source term is more efficient. Finally, the Roofline model is used to analyze the advantages of the algorithm.

Subduction Interface Earthquake Rise-Time Scaling Relations

ABSTRACT The slip duration in a fault plane, also known as the rise time (Tr), is determined in finite-fault rupture models (FFRMs) through the analysis of seismic source inversions using strong ground-motion (SGM) records and teleseismic data. For subduction interface earthquakes (megathrust), models exist that provide estimates for Tr values. The finite-source rupture model database and National Earthquake Information Center databases include FFRMs that allow for the extension of source-scaling relations. Currently, Tr versus seismic moment (M0) scaling relations specifically derived for large megathrust earthquakes in the near-source region are scarce. The relationship between stress drop and M0 is not straightforward; therefore, the logarithmic distribution of stress drop among earthquakes of different magnitudes (Mw) appears to be constant or self-similar. This self-similarity refers to a symmetry of the time-dependent fields, which remain unchanged under certain scale transformations in space and time characterized by similarity exponents and a function of the scaled variable, called the scaling function. In this study, Tr scaling has been conducted using 45 FFRMs derived from large megathrust earthquakes (Mw≥7.3) obtained from the previously mentioned databases. The scaling relation derived from the FFRMs based on SGM records closely approximates log(Tr)=const+1/3log(M0), which agrees with the self-similarity assumption for earthquake ruptures. On the other hand, the scaling relation obtained from the teleseismic dataset exhibits a smaller slope, indicating that the teleseismic data may overestimate source time characteristics compared with SGM data from seismic stations located close to the source.

EARTHQUAKE of APRIL 24, 2018 with KR=10.5, Мw3.9 and I0=5 in the ANAPA-NOVOROSSIYSK ZONE

The article presents instrumental and macroseismic data on the earthquake of April 24, 2018 with Мw=3.9, which occurred at the Black Sea coast near the Abrau Peninsula. The earthquake was felt in 15 settlements at distances up to 52 km from the epicenter with an intensity of 3 to 5 points. The earthquake occurred in the Black Sea zone of occurrence of earthquakes. The scalar seismic moment М0 and the spectral moment magnitude Mw=3.9 were calculated based on the spectra of seven regional stations. The focal mechanism was constructed based on the signs of the first movement in the P-wave at 68 stations. It is established that a thrust has occurred in the source along a northwest-trending plane dipping to the northeast, which is consistent with the orientation and dip of the fault planes of tectonic structures in the area of the source. The macroseismic manifestations of the April 24, 2018 earthquake made it possible to choose the most acceptable depth value and calculate the intensity at the epicenter (h=10 km, I0=5)

SPECTRAL and SOURCE PARAMETERS of NORTH CAUCASUS EARTHQUAKES in 2018–2019

The dynamic parameters of the sources of 44 earthquakes in the North Caucasus were determined from the amplitude spectra of S-waves for the period 2018–2019 with an energy class according to T.G. Rautian scale KR=9.1–14.1. Earthquake records from regional digital seismic stations of the North Caucasus network, with epicentral distances of no more than 300 km were used for the calculation. The source spectra were calculated based on the frequency-dependent quality factor Q(f) for earthquakes in the North Caucasus western zone – Q(f)=90f 1.02 – and eastern zone – Q(f)=97f 0.89 . The SEISAN program was used for the spectral analysis of 31 earthquakes. The following values were obtained: 0 – spectral density, f0 – corner frequency, M0 – scalar seismic moment, Mw – moment magnitude, L – length of the rupture at the source of an earthquake, or r – radius of the circular area,  – stress drop. Relationships between lgM0 and KR and Mw and KR are obtained.

Improved Observations of Deep Earthquake Ruptures Using Machine Learning

AbstractElevated seismic noise for moderate‐size earthquakes recorded at teleseismic distances has limited our ability to see their complexity. We develop a machine‐learning‐based algorithm to separate noise and earthquake signals that overlap in frequency. The multi‐task encoder‐decoder model is built around a kernel pre‐trained on local (e.g., short distances) earthquake data (Yin et al., 2022, https://doi.org/10.1093/gji/ggac290) and is modified by continued learning with high‐quality teleseismic data. We denoise teleseismic P waves of deep Mw5.0+ earthquakes and use the clean P waves to estimate source characteristics with reduced uncertainties of these understudied earthquakes. We find a scaling of moment and duration to be M0 ≃ τ4, and a resulting strong scaling of stress drop and radiated energy with magnitude ( and ). The median radiation efficiency is 5%, a low value compared to crustal earthquakes. Overall, we show that deep earthquakes have weak rupture directivity and few subevents, suggesting a simple model of a circular crack with radial rupture propagation is appropriate. When accounting for their respective scaling with earthquake size, we find no systematic depth variations of duration, stress drop, or radiated energy within the 100–700 km depth range. Our study supports the findings of Poli and Prieto (2016, https://doi.org/10.1002/2016jb013521) with a doubled amount of earthquakes investigated and with earthquakes of lower magnitudes.