Similar scaling laws for earthquakes and Cascadia slow-slip events

Low-frequency tremor-like episodes before the 2023 MW 7.8 Türkiye earthquake linked to cement quarrying

Recent advances in artificial intelligence have enhanced the detection and identification of transient low-amplitude signals across the entire frequency spectrum, shedding light on deformation processes preceding natural hazards. This study investigates low-frequency, low-amplitude signals preceding the 2023 MW 7.8 Kahramanmaraş earthquake in Türkiye. Using a deep neural network, we extract key features from the spectrograms of continuous seismic signals and employ unsupervised clustering to reveal distinct transient patterns. We identify an increased occurrence of low-frequency tremor-like signals during the six months preceding the mainshock. However, the location of these signals suggests that their origin is not tectonic, but rather related to anthropogenic activities at cement plants along the Narlı Fault, where the MW 7.8 mainshock nucleated. Such findings highlight the importance of understanding the origin of patterns detected by machine-learning methods and the large variety of seismic signals due to anthropogenic activities. Furthermore, the search for the origin of the tremor-like signals motivated an investigation into the local seismicity around the Narlı Fault. The resulting extended seismicity catalog suggests that seismicity in this area arises from a combination of tectonic and anthropogenic processes.

Parallel dynamics of slow slips and fluid-induced seismic swarms

Earthquake swarms may be driven by fluids, through hydraulic injections or natural fluid circulation, but also by slow and aseismic slip transients. Understanding the driving factors for these prolific sequences and how they can potentially develop into larger ruptures remains a challenge. A notable and almost ubiquitous feature of swarms is their hypocenters migration, which occurrence is closely related to the processes driving the observed seismicity, in a similar way as seismicity accompanies slow-slip events at subduction zones. Here, we analyze global data on migrating sequences, and identify scaling laws for migration velocity, moment and duration measured on natural and injection-induced swarms, foreshock sequences, and slow slip events. We highlight two different behaviors among these sequences: one linked to slow slips, with elevated migration velocities and moments, and the other related to fluid-induced processes, featuring lower velocities and moments. These results provide metrics for distinguishing between the drivers of earthquake swarms, fluid or slow-slip related, and prompt a reevaluation of scaling laws of fault slip transients, especially for swarms.

Global subduction slow slip events and associated earthquakes

Three decades of geodetic monitoring have established slow slip events (SSEs) as a common mode of fault slip, sometimes linked with earthquake swarms and in a few cases escalating to major seismic events. However, the connection between SSEs and earthquake hazard has been difficult to quantify and contextualize beyond regional studies. We aggregate a geodetic record of SSEs from subduction zones in the circum-Pacific region. In aggregate, earthquake rates increase up to threefold concurrent with and proximal to SSEs. The relative amplitude of this increase is correlated with the SSE size and, to a lesser extent, their depth and region. The subdued and coincident earthquake response to SSE stress transfer suggests a more limited role of static stress transfer and a very short relaxation timescale for the triggered seismicity. The observed range of behavior does not support a major connection between SSEs and earthquake hazard.

Using a physics-informed neural network and fault zone acoustic monitoring to predict lab earthquakes

Predicting failure in solids has broad applications including earthquake prediction which remains an unattainable goal. However, recent machine learning work shows that laboratory earthquakes can be predicted using micro-failure events and temporal evolution of fault zone elastic properties. Remarkably, these results come from purely data-driven models trained with large datasets. Such data are equivalent to centuries of fault motion rendering application to tectonic faulting unclear. In addition, the underlying physics of such predictions is poorly understood. Here, we address scalability using a novel Physics-Informed Neural Network (PINN). Our model encodes fault physics in the deep learning loss function using time-lapse ultrasonic data. PINN models outperform data-driven models and significantly improve transfer learning for small training datasets and conditions outside those used in training. Our work suggests that PINN offers a promising path for machine learning-based failure prediction and, ultimately for improving our understanding of earthquake physics and prediction.

Integrated rupture mechanics for slow slip events and earthquakes

Slow slip events occur worldwide and could trigger devastating earthquakes, yet it is still debated whether their moment-duration scaling is linear or cubic and a fundamental model unifying slow and fast earthquakes is still lacking. Here, we show that the rupture propagation of simulated slow and fast earthquakes can be predicted by a newly-developed three-dimensional theory of dynamic fracture mechanics accounting for finite rupture width, an essential ingredient missing in previous theories. The complete spectrum of rupture speeds is controlled by the ratio of fracture energy to energy release rate. Shear stress heterogeneity can produce a cubic scaling on a single fault while effective normal stress variability produces a linear scaling on a population of faults, which reconciles the debated scaling relations. This model provides a new framework to explain how slow slip might lead to earthquakes and opens new avenues for seismic hazard assessment integrating seismological, laboratory and theoretical developments.

Linking the scaling of tremor and slow slip near Parkfield, CA

There has been much debate about the fault zone processes that generate slow earthquakes, including tremor and slow slip. Indeed, we still debate whether tremor and slow slip are generated by the same process operating at different scales or by two distinct processes. Here we investigate tremor scaling near Parkfield, California; we examine how rupture duration scales with moment. We thoroughly search for and detect the low frequency earthquakes (LFEs) that constitute tremor and robustly estimate their durations. Our results show varying durations (0.1–0.6 s) and spectra for LFEs at the same location. These variations confirm a common assumption, that LFEs’ observed low frequency contents are due to source processes, not path effects. The LFEs’ amplitude and spectra variations are consistent with a linear moment-duration scaling: the same scaling observed among slow slip events. The similar scaling suggests that tremor and slow slip events are governed by the same fault zone process and that when we attempt to identify the process creating slow earthquakes, we should focus on processes which allow higher slip rates on smaller faults.

Huang and Hawthorne present new evidence supporting that tremor and slow slip are linked by the same moment-duration scaling. First-order implications would include that tremor and slow slip are likely generated by the same fault zone process.

The High-Frequency Signature of Slow and Fast Laboratory Earthquakes

Tectonic faults fail through a spectrum of slip modes, ranging from slow aseismic creep to rapid slip during earthquakes. Understanding the seismic radiation emitted during these slip modes is key for advancing earthquake science and earthquake hazard assessment. In this work, we use laboratory friction experiments instrumented with ultrasonic sensors to document the seismic radiation properties of slow and fast laboratory earthquakes. Stick-slip experiments were conducted at a constant loading rate of 8 μm/s and the normal stress was systematically increased from 7 to 15 MPa. We produced a full spectrum of slip modes by modulating the loading stiffness in tandem with the fault zone normal stress. Acoustic emission data were recorded continuously at 5 MHz. We demonstrate that the full continuum of slip modes radiate measurable high-frequency energy between 100 and 500 kHz, including the slowest events that have peak fault slip rates <100 μm/s. The peak amplitude of the high-frequency time-domain signals scales systematically with fault slip velocity. Stable sliding experiments further support the connection between fault slip rate and high-frequency radiation. Experiments demonstrate that the origin of the high-frequency energy is fundamentally linked to changes in fault slip rate, shear strain, and breaking of contact junctions within the fault gouge. Our results suggest that having measurements close to the fault zone may be key for documenting seismic radiation properties and fully understanding the connection between different slip modes.

Imaging evolution of Cascadia slow-slip event using high-rate GPS

The slip history of short-term slow slip event (SSE) is typically inferred from daily Global Positioning System (GPS) data, which, however, cannot image the sub-daily processes, leaving the underlying mechanisms of SSEs elusive. To address the temporal resolution issue, we attempted to employ the kinematic subdaily GPS analysis, which has never been applied to SSE studies because its signal-to-noise ratio has been believed too low. By carefully post-processing sub-daily positions to remove non-tectonic position fluctuation, our 30-min kinematic data clearly exhibits the transient motion of a few mm during one Cascadia SSE. A spatiotemporal slip image by inverting the 30-min data exhibits a multi-stage evolution; it consists of an isotropic growth of SSE followed by an along-strike migration and termination within the rheologically controlled down-dip width. This transition at the slip growth mode is similar to the rupture growth of regular earthquakes, implying the presence of common mechanical factors behind the two distinct slip phenomena. The comparison with a slip inversion of the daily GPS demonstrates the current performance and limitation of the subdaily data in the SSE detection and imaging. Better understanding of the non-tectonic noise in the kinematic GPS analysis will further improve the temporal resolution of SSE.

Probing the seismic cycle timing with coseismic twisting of subduction margins

Assessing the timing of great megathrust earthquakes is together crucial for seismic hazard analysis and deemed impossible. Geodetic instrumentation of subduction zones has revealed unexpected deformation patterns at subduction segments adjacent to those that hosted recent mega-earthquakes: coastal sites move landward with faster velocities than before the earthquake. Here, we show observations from the largest and best-monitored megathrust earthquakes, and from a scaled analog model, to reveal that these events create coseismic and postseismic deformation patterns typical of a complete gear-like rotation about a vertical axis, hereafter called twisting. We find that such twisting alters the interseismic velocity field of adjacent subduction segments depending on the time since the last earthquake. Early interactions accelerate while late interactions decelerate local kinematics. This finding opens the possibility of using megathrust earthquakes, the characteristics of the twisting pattern, and the ensuing geodetic velocity changes, as a proxy for estimating the timing of the seismic cycle at unruptured segments along the margin.

Satellite geodesy and downscaled laboratory experiments reveal that great subduction earthquakes trigger step changes in kinematics of neighboring segments. This signal is potentially informative of the timing of the seismic cycle.

Afterslip Moment Scaling and Variability From a Global Compilation of Estimates

Aseismic afterslip is postseismic fault sliding that may significantly redistribute crustal stresses and drive aftershock sequences. Afterslip is typically modeled through geodetic observations of surface deformation on a case-by-case basis, thus questions of how and why the afterslip moment varies between earthquakes remain largely unaddressed. We compile 148 afterslip studies following 53 M _w 6.0-9.1 earthquakes, and formally analyze a subset of 88 well-constrained kinematic models. Afterslip and coseismic moments scale near-linearly, with a median Spearman's rank correlation coefficient (CC) of 0.91 after bootstrapping (95% range: 0.89-0.93). We infer that afterslip area and average slip scale with coseismic moment as M o 2 / 3 and M o 1 / 3 , respectively. The ratio of afterslip to coseismic moment (M _rel ) varies from <1% to >300% (interquartile range: 9%-32%). M _rel weakly correlates with M _o (CC: -0.21, attributed to a publication bias), rupture aspect ratio (CC: -0.31), and fault slip rate (CC: 0.26, treated as a proxy for fault maturity), indicating that these factors affect afterslip. M _rel does not correlate with mainshock dip, rake, or depth. Given the power-law decay of afterslip, we expected studies that started earlier and spanned longer timescales to capture more afterslip, but M _rel does not correlate with observation start time or duration. Because M _rel estimates for a single earthquake can vary by an order of magnitude, we propose that modeling uncertainty currently presents a challenge for systematic afterslip analysis. Standardizing modeling practices may improve model comparability, and eventually allow for predictive afterslip models that account for mainshock and fault zone factors to be incorporated into aftershock hazard models.

InSAR data reveal that the largest hydraulic fracturing-induced earthquake in Canada, to date, is a slow-slip event

For tectonic earthquakes, slip rate spans a continuum from creep to supershear earthquakes, where slow slip events (SSEs) are important in releasing stress without radiating damaging seismic energy. Industrial-scale subsurface fluid injection has caused induced earthquakes, but the role of SSEs in fault activation is currently unclear. Ground-deformation observations, measured by satellite radar, show that SSEs up to magnitude 5.0 occurred during hydraulic fracturing (HF) operations in northwestern Canada, corroborated by reported deformation of the steel well casing. Although the magnitude 5.0 SSE exceeded the magnitude of the largest induced earthquake in this region (magnitude 4.55), it was undetected by seismograph networks. The observed SSEs occurred within a buried thrust belt and their magnitude and duration are consistent with scaling behavior of SSEs in unbounded natural systems, e.g. slab interfaces in subduction zones.

Segmentation of Shallow Slow Slip Events at the Hikurangi Subduction Zone Explained by Along-Strike Changes in Fault Geometry and Plate Convergence Rates

Over the last two decades, geodetic and seismic observations have revealed a spectrum of slow earthquakes along the Hikurangi subduction zone in New Zealand. Of those, shallow slow slip events (SSEs) that occur at depths of less than 15 km along the plate interface show a strong along-strike segmentation in their recurrence intervals, which vary from ∼1 yr from offshore Tolaga Bay in the northeast to ∼5 yr offshore Cape Turnagain ∼300 km to the southwest. To understand the factors that control this segmentation, we conduct numerical simulations of SSEs incorporating laboratory-derived rate-and-state friction laws with both planar and non-planar fault geometries. We find that a relatively simple model assuming a realistic non-planar fault geometry reproduces the characteristics of shallow SSEs as constrained by geodetic observations. Our preferred model captures the magnitudes and durations of SSEs, as well as the northward decrease of their recurrence intervals. Our results indicate that the segmentation of SSE recurrence intervals is favored by along-strike changes in both the plate convergence rate and the downdip width of the SSE source region. Modeled SSEs with longer recurrence intervals concentrate in the southern part of the fault (offshore Cape Turnagain), where the plate convergence rate is lowest and the source region of SSEs is widest due to the shallower slab dip angle. Notably, the observed segmentation of shallow SSEs cannot be reproduced with a simple planar fault model, which indicates that a realistic plate interface is an important factor to account for in modeling SSEs.

Fluid-injection-induced earthquakes characterized by hybrid-frequency waveforms manifest the transition from aseismic to seismic slip

Aseismic slip loading has recently been proposed as a complementary mechanism to induce moderate-sized earthquakes located within a few kilometers of the wellbore over the timescales of hydraulic stimulation. However, aseismic slip signals linked to injection-induced earthquakes remain largely undocumented to date. Here we report a new type of earthquake characterized by hybrid-frequency waveforms (EHWs). Distinguishing features from typical induced earthquakes include broader P and S-pulses and relatively lower-frequency coda content. Both features may be causally related to lower corner frequencies, implying longer source durations, thus, either slower rupture speeds, lower stress drop values, or a combination of both. The source characteristics of EHWs are identical to those of low-frequency earthquakes widely documented in plate boundary fault transition zones. The distribution of EHWs further suggests a possible role of aseismic slip in fault loading. EHWs could thus represent the manifestation of slow rupture transitioning from aseismic to seismic slip.

The slow self-arresting nature of low-frequency earthquakes

Low-frequency earthquakes are a series of recurring small earthquakes that are thought to compose tectonic tremors. Compared with regular earthquakes of the same magnitude, low-frequency earthquakes have longer source durations and smaller stress drops and slip rates. The mechanism that drives their unusual type of stress accumulation and release processes is unknown. Here, we use phase diagrams of rupture dynamics to explore the connection between low-frequency earthquakes and regular earthquakes. By comparing the source parameters of low-frequency earthquakes from 2001 to 2016 in Parkfield, on the San Andreas Fault, with those from numerical simulations, we conclude that low-frequency earthquakes are earthquakes that self-arrest within the rupture patch without any introduced interference. We also explain the scaling property of low-frequency earthquakes. Our findings suggest a framework for fault deformation in which nucleation asperities can release stress through slow self-arrest processes.

The source scaling and seismic productivity of slow slip transients

Slow slip events (SSEs) represent a slow faulting process leading to aseismic strain release often accompanied by seismic tremor or earthquake swarms. The larger SSEs last longer and are often associated with intense and energetic tremor activity, suggesting that aseismic slip controls tremor genesis. A similar pattern has been observed for SSEs that trigger earthquake swarms, although no comparative studies exist on the source parameters of SSEs and tremor or earthquake swarms. We analyze the source scaling of SSEs and associated tremor- or swarm-like seismicity through our newly compiled dataset. We find a correlation between the aseismic and seismic moment release indicating that the shallower SSEs produce larger seismic moment release than deeper SSEs. The scaling may arise from the heterogeneous frictional and rheological properties of faults prone to SSEs and is mainly controlled by temperature. Our results indicate that similar physical phenomena govern tremor and earthquake swarms during SSEs.

Minimal model for the onset of slip pulses in frictional rupture

We present a minimal one-dimensional continuum model for the transition from cracklike to pulselike propagation of frictional rupture. In its nondimensional form, the model depends on only two free parameters: the nondimensional prestress and an elasticity ratio that accounts for the finite height of the system. The model predicts stable slip pulse solutions for slip boundary conditions, and unstable slip pulse solutions for stress boundary conditions. The results demonstrate that a mechanism based solely on elastic relaxation and redistribution of initial prestress can cause pulselike rupture, without any particular rate or slip dependences of dynamic friction. This means that pulselike propagation along frictional interfaces is likely a generic feature that can occur in systems of finite thickness over a wide range of friction constitutive laws.

Fault zone heterogeneities explain depth-dependent pattern and evolution of slow earthquakes in Cascadia

Slow earthquakes including tremor and slow-slip events are recent additions to the conventional earthquake family and have a close link to megathrust earthquakes. Slow earthquakes along the Cascadia subduction zone display a diverse behavior at different spatiotemporal scales and an intriguing increase of events frequency with depth. However, what causes such variability, especially the depth-dependent behavior is not well understood. Here we build on a heterogeneous asperities-in-matrix fault model that incorporates differential pore pressure in a rate-and-state friction framework to investigate the underlying processes of the observed episodic tremor and slow-slip (ETS) variability. We find that the variations of effective normal stress (pore pressure) is one important factor in controlling ETS behavior. Our model reproduces the full complexity of ETS patterns and the depth-frequency scaling that agree quantitatively well with observations, suggesting that fault zone heterogeneities can be one viable mechanism to explain a broad spectrum of transient fault behaviors.

Here, the authors combine the geological and seismological constraints of the Cascadia Subduction Zone and develop a 3D rate and state friction model. By considering depth-dependent variations of differential pore pressure following a simple linear profile, the model reproduces the full spectrum of the observed ETS complexity.

What's down there? The structures, materials and environment of deep-seated slow slip and tremor

Deep-seated slow slip and tremor (SST), including slow slip events, episodic tremor and slip, and low-frequency earthquakes, occur downdip of the seismogenic zone of numerous subduction megathrusts and plate boundary strike-slip faults. These events represent a fascinating and perplexing mode of fault failure that has greatly broadened our view of earthquake dynamics. In this contribution, we review constraints on SST deformation processes from both geophysical observations of active subduction zones and geological observations of exhumed field analogues. We first provide an overview of what has been learned about the environment, kinematics and dynamics of SST from geodetic and seismologic data. We then describe the materials, deformation mechanisms, and metamorphic and fluid pressure conditions that characterize exhumed rocks from SST source depths. Both the geophysical and geological records strongly suggest the importance of a fluid-rich and high fluid pressure habitat for the SST source region. Additionally, transient deformation features preserved in the rock record, involving combined frictional-viscous shear in regions of mixed lithology and near-lithostatic fluid pressures, may scale with the tremor component of SST. While several open questions remain, it is clear that improved constraints on the materials, environment, structure, and conditions of the plate interface from geophysical imaging and geologic observations will enhance model representations of the boundary conditions and geometry of the SST deformation process. This article is part of a discussion meeting issue 'Understanding earthquakes using the geological record'.

Initial effective stress controls the nature of earthquakes

Modern geophysics highlights that the slip behaviour response of faults is variable in space and time and can result in slow or fast ruptures. However, the origin of this variation of the rupture velocity in nature as well as the physics behind it is still debated. Here, we first highlight how the different types of fault slip observed in nature appear to stem from the same physical mechanism. Second, we reproduce at the scale of the laboratory the complete spectrum of rupture velocities observed in nature. Our results show that the rupture velocity can range from a few millimetres to kilometres per second, depending on the available energy at the onset of slip, in agreement with theoretical predictions. This combined set of observations bring a new explanation of the dominance of slow rupture fronts in the shallow part of the crust or in areas suspected to present large fluid pressure.

Excitation of San Andreas tremors by thermal instabilities below the seismogenic zone

The relative motion of tectonic plates is accommodated at boundary faults through slow and fast ruptures that encompass a wide range of source properties. Near the Parkfield segment of the San Andreas fault, low-frequency earthquakes and slow-slip events take place deeper than most seismicity, at temperature conditions typically associated with stable sliding. However, laboratory experiments indicate that the strength of granitic gouge decreases with increasing temperature above 350°C, providing a possible mechanism for weakening if temperature is to vary dynamically. Here, we argue that recurring low-frequency earthquakes and slow-slip transients at these depths may arise because of shear heating and the temperature dependence of frictional resistance. Recurring thermal instabilities can explain the recurrence pattern of the mid-crustal low-frequency earthquakes and their correlative slip distribution. Shear heating associated with slow slip is sufficient to generate pseudotachylyte veins in host rocks even when fault slip is dominantly aseismic.

An exponential build-up in seismic energy suggests a months-long nucleation of slow slip in Cascadia

Slow slip events result from the spontaneous weakening of the subduction megathrust and bear strong resemblance to earthquakes, only slower. This resemblance allows us to study fundamental aspects of nucleation that remain elusive for classic, fast earthquakes. We rely on machine learning algorithms to infer slow slip timing from statistics of seismic waveforms. We find that patterns in seismic power follow the 14-month slow slip cycle in Cascadia, arguing in favor of the predictability of slow slip rupture. Here, we show that seismic power exponentially increases as the slowly slipping portion of the subduction zone approaches failure, a behavior that shares a striking similarity with the increase in acoustic power observed prior to laboratory slow slip events. Our results suggest that the nucleation phase of Cascadia slow slip events may last from several weeks up to several months.

Using machine learning algorithms, the authors here identify slow slip precursors in the Cascadia subduction zone to last for months - which in turn argues for a much better predictability of slow slip rupture.

Connecting a broad spectrum of transient slip on the San Andreas fault

Strain accumulated on the deep extension of some faults is episodically released during transient slow-slip events, which can subsequently load the shallow seismogenic region. At the San Andreas fault, the characteristics of slow-slip events are difficult to constrain geodetically due to their small deformation signal. Slow-slip events (SSEs) are often accompanied by coincident tremor bursts composed of many low-frequency earthquakes. Here, we probabilistically estimate the spatiotemporal clustering properties of low-frequency earthquakes detected along the central San Andreas fault. We find that tremor bursts follow a power-law spatial and temporal decay similar to earthquake aftershock sequences. The low-frequency earthquake clusters reveal that the underlying slow-slip events have two modes of rupture velocity. Compared to regular earthquakes, these slow-slip events have smaller stress drop and rupture velocity but follow similar magnitude-frequency, moment-area, and moment-duration scaling. Our results connect a broad spectrum of transient fault slip that spans several orders of magnitude in rupture velocity.

The predictable chaos of slow earthquakes

Slow earthquakes, like regular earthquakes, result from unstable frictional slip. They produce little slip and can therefore repeat frequently. We assess their predictability using the slip history of the Cascadia subduction between 2007 and 2017, during which slow earthquakes have repeatedly ruptured multiple segments. We characterize the system dynamics using embedding theory and extreme value theory. The analysis reveals a low-dimensional (<5) nonlinear chaotic system rather than a stochastic system. We calculate properties of the underlying attractor like its correlation and instantaneous dimension, instantaneous persistence, and metric entropy. We infer that the system has a predictability horizon of the order of days weeks. For the better resolved segments, the onset of large slip events can be correctly forecasted by high values of the instantaneous dimension. Longer-term deterministic prediction seems intrinsically impossible. Regular earthquakes might similarly be predictable but with a limited predictable horizon of the order of their durations.

Slip bursts during coalescence of slow slip events in Cascadia

Both laboratory experiments and dynamic simulations suggest that earthquakes can be preceded by a precursory phase of slow slip. Observing processes leading to an acceleration or spreading of slow slip along faults is therefore key to understand the dynamics potentially leading to seismic ruptures. Here, we use continuous GPS measurements of the ground displacement to image the daily slip along the fault beneath Vancouver Island during a slow slip event in 2013. We image the coalescence of three originally distinct slow slip fronts merging together. We show that during coalescence phases lasting for 2 to 5 days, the rate of energy (moment) release significantly increases. This observation supports the view proposed by theoretical and experimental studies that the coalescence of slow slip fronts is a possible mechanism for initiating earthquakes.

Self-similarity of low-frequency earthquakes

Low-frequency earthquakes are a particular class of slow earthquakes that provide a unique source of information on the physical processes along a subduction zone during the preparation of large earthquakes. Despite increasing detection of these events in recent years, their source mechanisms are still poorly characterised, and the relation between their magnitude and size remains controversial. Here, we present the source characterisation of more than 10,000 low-frequency earthquakes that occurred during tremor sequences in 2012–2016 along the Nankai subduction zone in western Shikoku, Japan. We show that the scaling of seismic moment versus corner frequency for these events is compatible with an inverse of the cube law, as widely observed for regular earthquakes. Their radiation, however, appears depleted in high-frequency content when compared to regular earthquakes. The displacement spectrum decays beyond the corner frequency with an omega-cube power law. Our result is consistent with shear rupture as the source mechanism for low-frequency earthquakes, and suggests a self-similar rupture process and constant stress drop. When investigating the dependence of the stress drop value on the rupture speed, we found that low-frequency earthquakes might propagate at lower rupture velocity than regular earthquakes, releasing smaller stress drop.