Constant Stress Drop Research Articles

An Enhanced Catalog of Repeating Earthquakes on the 1980 Irpinia Fault System, Southern Italy

A pilot study employing a template-matching approach on the detection of repeating earthquakes (or repeaters) in a small volume of the Irpinia fault (Southern Italy) is presented here. A catalog of repeaters nucleating over about a decade with local magnitudes ranging between ML 0.4 and ML 1.7 is generated. The events nucleate at depths of about 11 km over a fault patch with a size of about 600 m. Assuming a constant stress drop for all repeaters, the yearly coseismic slip rate of the patch is estimated in the range of 1–4.8 mm with a mean value of about 3.4 mm, which is close to the fault slip rate estimated by geodetic approaches. Given the mechanical properties of the medium in the source region of the repeaters revealed by previous tomographic studies, and in particular the high Vp/Vs ratio (close to 1.95), it is postulated that these events are fluid triggered, consistently with the mechanism proposed for the generation of most of the microseismicity in the area. The encouraging outcomes of this study suggest to focus future measurement campaigns on this area and open perspectives to extend this approach to other segments of the Irpinia fault to reveal small-scale frictional properties in an area capable to generate M7 earthquakes.

A Source Model for Earthquakes near the Nucleation Dimension

ABSTRACT Earthquake self-similarity is a controversial topic, both observationally and theoretically. Theory predicts a finite nucleation dimension, implying a break of self-similarity below a certain magnitude. Although observations of non-self-similar earthquake behavior have been reported, their interpretation is challenging due to trade-offs between source and path effects and assumptions on the underlying source model. Here, I introduce a source model for earthquake nucleation and quantify the resulting scaling relations between source properties (far-field pulse duration, seismic moment, stress drop). I derive an equation of motion based on fracture mechanics for a circular rupture obeying rate–state friction and a simpler model with constant stress drop and fracture energy. The latter provides a good approximation to the rate–state model and leads to analytical expressions for far-field displacement pulses and spectra. The onset of ground motion is characterized by exponential growth with characteristic timescale t0=R0/vf, with R0 the nucleation dimension and vf a limit rupture velocity. Therefore, normalized displacements have a constant duration, proportional to the nucleation length rather than the source dimension. For ray paths normal to the fault, the exponential growth results in a Boatwright spectrum with n = 1, γ=2 and corner frequency ωc=1/t0. For other orientations, the spectrum has an additional sinc(·) term with a corner frequency related to the travel-time delay across the asperity. Seismic moments scale as M0∼R(R−R0)R0, in which R is the size of asperity, becoming vanishingly small as R→R0. Therefore, stress drops estimated from M0 and fc are smaller than the nominal stress drop, and they increase with magnitude up to a constant value, consistent with several seismological studies. The constant earthquake duration is also in agreement with reported microseismicity: for 0<Mw<2 events studied by Lin et al. (2016) in Taiwan, the observed durations imply a nucleation length between 45 and 80 m.

Time Domain Source Parameter Estimation of Natural and Man-Induced Microearthquakes at the Geysers Geothermal Field

Water injection in geothermal areas is the preferential strategy to sustain the natural production of geothermal resources. In this context, monitoring microearthquakes is a fundamental tool to track changes in the reservoirs in terms of soil composition, response to injections, and resource exploitation with space and time. Therefore, refined source characterization is crucial to better estimate the size, source mechanism, and rupture process of microearthquakes, as they are possibly related to industrial activities, and to identify any potential variation in the background seismicity. Standard approaches for source parameter estimation are ordinarily based on the modelling of Fourier displacement spectra and its characteristic parameters: the low-frequency spectral level and corner frequency. Here, we apply an innovative time domain technique that uses the curves of P-wave amplitude vs. time along the seismogram. This methodology allows estimation of seismic moment, source radius, and stress release from the plateau level and the corner time of the average logarithm of P-wave displacement versus time with the assumption of a triangular moment rate function, uniform rupture speed, and a constant/frequency-independent Q-factor. In the current paper, this time domain methodology is implemented on a selected catalog of microearthquakes consisting of 83 events with a moment magnitude ranging between 1.0 and 1.5 that occurred during a 7-year period (2007–2014) of fluid extraction/injection around Prati-9 and Prati-29 wells at The Geysers geothermal field. The results show that the time domain technique provides accurate seismic moment (moment magnitude) and rupture duration/radius estimates of microearthquakes down to the explored limit (M 1) while accounting for the anelastic attenuation effect in the radiated high-frequency wavefield. The retrieved source radius vs. moment scaling is consistent with a self-similar, constant stress drop scaling model, which proves an appropriate attenuation correction and the validity of the assumed, triangular moment rate function for microearthquake ruptures. Two alternative mechanical models are proposed to explain the observed difference (about two orders of magnitude) in the retrieved average stress release estimates between the time and frequency domain methods. We argue that the two quantities may not refer to the same physical quantity representing the stress release of earthquake ruptures. Either the smaller stress release values from the time domain method may indicate a larger fracture area (by a factor of 20) radiating the observed P-waveforms than the one estimated from the corner frequencies, or the frequency domain estimate is a proxy for dynamic stress release while the time domain is more representative of the static release. The latter is associated with a much lower dynamic friction value than static friction value at the fault during the rupture process.

Extension of Aseismic Slip Propagation Theory to Slow Earthquake Migration

AbstractNatural faults host various types of migrating slow earthquake phenomena, with migration speeds much lower than seismic wave speeds and different moment‐duration scaling from regular earthquakes. To advance the obtained quantitative understanding of the migration process and long duration of slow earthquakes, I study a chain reaction model in a population of brittle asperities based on a rate‐ and state‐dependent friction on a 3‐D subduction plate boundary. Simulation results show that the migration speed is quantitatively related to frictional properties by an analytical relation derived here. By assuming that local pore water in front of the migration drives rapid tremor reversal and is so local as to hold a constant stress drop, the application of the analytical solution to observational results suggests that (a) the temporal changes of observed migration speeds for the rapid tremor reversal could be explained by about 70% reduction of the effective normal stress; (b) effective normal stress for the deeper extension of seismogenic segment in the western part of Shikoku is about 1.5 times greater than that in the central part. Applying rupture time delay between slow earthquake asperities for the duration longer than regular earthquake, I also conclude that (c) the characteristic slip distance of rate‐and‐state friction for low‐frequency earthquakes is roughly between 30 µm and 30 mm; (d) the stress and strength drops of very low‐frequency earthquakes is much smaller than 1 MPa.

Source parameter estimation of acoustic emissions induced by hydraulic fracturing in the laboratory

SUMMARYThe hydraulic fracturing technique is used for resource production, such as in shale gas/oil extraction and enhanced geothermal systems. The effects of fracturing are often monitored via induced earthquakes, and obtaining as much information as possible from those earthquakes is desirable. The stress drop—calculated from the seismic moment Mo and corner frequency fc—is an earthquake-related parameter that can help identify additional characteristics of the seismicity. To investigate the relationship between stress drops and hydraulically induced seismic events, we estimated the Mo and fc of acoustic emission (AE) events during hydraulic fracturing experiments performed in the laboratory in previous studies using 2 Eagle Ford shale and 10 Kurokami-jima granite samples. We estimated Mo by fitting the theoretical spectra to the observed spectra after correcting for the following effects: (1) frequency response of AE transducers under the installation method used in the fracturing experiment, including differences in sensitivity across every transducer used in each experiment; and (2) the difference in radiation pattern coefficients, which depends on the focal mechanisms of each AE event. This analysis used 46 857 focal mechanisms obtained from moment tensor solutions estimated using a deep learning technique. The range of the resultant Mo was found to be 2.8 × 10–5 ≤ Mo ≤ 4.5 × 10–1 [N·m], corresponding to −9.1 ≤ Mw ≤ −6.3, where Mw is the moment magnitude. We also estimated fc using the multiple-empirical Green's function method, reducing the influence of modelling errors in the AE sensor response and transfer function of the medium. Out of the 1053 events whose Mo and fc were estimated, 465 events (44.2 per cent)—regardless of their focal mechanisms—were found to have Mo and fc values consistent with the constant stress drop scaling of shear failure (i.e. shear failures have 0.1–100 MPa stress drops independent of their magnitude) that has been repeatedly confirmed in many previous studies. The remaining events showed lower fc values than those expected from the scaling law. This indicates that high pore pressure in a source region induced by fluid stimulation contributes to the occurrence of low-frequency earthquakes. Overall, we demonstrated that source parameter estimation was possible for laboratory AEs induced by hydraulic fracturing, which can improve our understanding of the characteristics of fluid-induced earthquakes.

Source Properties of Hydraulic‐Fracturing‐Induced Earthquakes in the Kiskatinaw Area, British Columbia, Canada

AbstractThis work presents a high resolution source property study of hydraulic fracturing induced earthquakes in the Montney Formation, a low‐permeability tight shale reservoir in the Kiskatinaw area, northeast British Columbia, Canada. We estimate source parameters, including focal mechanism solutions (FMSs), seismic moment, spectral corner frequency, and static stress drop values of earthquakes recorded between July 2017 and July 2020. Waveform‐similarity‐based event classification of 8,283 earthquakes yields 52 event families (clusters) and 1,014 isolated events (individuals). We calculate a total of 64 FMSs of events ML > 2.5 with high‐quality waveforms. Of the 64 solutions, 54 come from events within families, and are used to infer an additional 3,500 focal mechanisms of smaller‐magnitude events with similar waveforms. The other 10 are isolated events. The dominant faulting style inferred from FMSs highlights multiple cascading, shallow, strike‐slip events and generally isolated, larger‐magnitude reverse‐style events in close proximity to the Fort St. John Graben system. Inferred nodal planes of strike‐slip events are at low‐angles to regional SHmax, suggesting optimally oriented, left‐lateral faults. Reverse faulting nodal planes are roughly perpendicular to SHmax and have an orientation consistent with the reactivation of pre‐existing normal basement faults. Source spectral analysis using three approaches, including spectral‐ratio fitting, suggests a constant stress drop of 1–10 MPa and self‐similarity for induced events. Constant stress drop scaling breaks down at magnitudes smaller than ∼ML 2.0, likely due to observational bandwidth limitations.

Spatio‐Temporal Evolution of Earthquake Static Stress Drop Values in the 2016–2017 Central Italy Seismic Sequence

AbstractThe static stress drop of an earthquake is an indicator of the stress state of a specific fault before rupture initiation. The stress state is primarily controlled by the ambient stress field, fault strength, fault complexity, and the presence of fluids. This study aims to investigate the spatio‐temporal distribution of static stress drop values of the 2016–2017 multi‐fault rupture seismic sequence in central Italy, which includes three earthquakes with Mw ≥ 5.9 (Amatrice, Visso, and Norcia earthquakes), and over 95,000 aftershocks (M 0.5–6.5). We estimate stress drop values using a circular crack model with corner frequency and seismic moment estimates from single‐spectra fitting, a cluster‐event method, and spectral‐ratio fitting. The temporal distribution of stress drop values shows an apparent increase of stress drop following a large earthquake (Mw ≥ 5.9). The spatial distribution shows comparably high stress drop values for early aftershocks surrounding the mainshock rupture area. High stress drop events correlate with fault complexity, such as fault intersections at depth and reactivated thrust fronts. We observe a constant stress drop for Mw ≥ ∼3, in contrast to previous studies. Instrument response and signal‐to‐noise bandwidth limitations likely govern the observed decrease in stress drop with decreasing magnitude for events with Mw ≤ 3. The spatio‐temporal distribution of stress drop values in a complex seismic sequence could support a more complete understanding of the earthquake rupture process and the evolution of seismic sequences. It could also highlight areas where stress loading is focused, which would have implications for short and intermediate term seismic hazard estimates.

Improved Scaling Relationships for Seismic Moment and Average Slip of Strike-Slip Earthquakes Incorporating Fault-Slip Rate, Fault Width, and Stress Drop

ABSTRACT We develop a self-consistent scaling model relating magnitude Mw to surface rupture length (LE), surface displacement DE, and rupture width WE, for strike-slip faults. Knowledge of the long-term fault-slip rate SF improves magnitude estimates. Data are collected for 55 ground-rupturing strike-slip earthquakes that have geological estimates of LE, DE, and SF, and geophysical estimates of WE. We begin with the model of Anderson et al. (2017), which uses a closed form equation for the seismic moment of a surface-rupturing strike-slip fault of arbitrary aspect ratio and given stress drop, ΔτC. Using WE estimates does not improve Mw estimates. However, measurements of DE plus the relationship between ΔτC and surface slip provide an alternate approach to study WE. A grid of plausible stress drop and width pairs were used to predict displacement and earthquake magnitude. A likelihood function was computed from within the uncertainty ranges of the corresponding observed Mw and DE values. After maximizing likelihoods over earthquakes in length bins, we found the most likely values of WE for constant stress drop; these depend on the rupture length. The best-fitting model has the surprising form WE∝logLE—a gentle increase in width with rupture length. Residuals from this model are convincingly correlated to the fault-slip rate and also show a weak correlation with the crustal thickness. The resulting model thus supports a constant stress drop for ruptures of all lengths, consistent with teleseismic observation. The approach can be extended to test other observable factors that might improve the predictability of magnitude from a mapped fault for seismic hazard analyses.

Inferring Hydraulic Pressure Changes from Induced Seismicity Observations: Three Showcases from Geothermal Reservoirs

We apply a recently developed approach for inferring in situ fluid pressure changes from induced seismicity observations to datasets from geothermal reservoirs at St. Gallen (Switzerland), Paralana (Australia), and Cooper Basin (Australia), respectively. The approach, referred to as seismohydraulic pressure mapping (SHPM), is based on mapping the seismic moment of induced earthquakes. Relative fluid pressure changes are inferred from the stress deficit of fracture patches slipping repeatedly. The SHPM approach was developed for the specific scenario, where induced earthquakes occur on a single, larger-scale plane with slip being driven by the regional stress field. We demonstrate that this scenario applies to the three datasets under investigation, indicating that geothermal systems in crystalline rock could typically be fault-dominated. For all datasets, individual earthquake source geometry could not be determined from source spectra due to the attenuation of the high signal frequencies. Instead, SHPM was applied assuming a constant stress drop in a circular crack model. Absolute values of inferred pressure change scale with the assumed stress drop while the spatiotemporal pattern of pressure changes remains similar even when varying stress drop by one order of magnitude. We demonstrate how the associated mismapping of seismic moment tends to average out when hypocentres are densely spaced. Our results indicate that SHPM could provide important information for calibrating numerical reservoir models.

Spatiotemporal Clustering of Seismicity During the 2018 Kilauea Volcanic Eruption

AbstractThe intense volcanic and seismic activity at Kilauea volcano, Hawaii in 2018 provides an opportunity to understand the characteristics and driving forces of volcano earthquake clusters. Nearest neighbor distance analysis of a high‐resolution earthquake catalog reveals two modes of clustering: M1 and M2. M1 clusters focus on events within short space and time windows, and are concentrated within isolated fault patches. Examination of three structures shows a gradual increase of source radius (assuming a constant stress drop) and spatial migration of seismicity, likely representing aseismic growth of peripheral faults. M2 clusters focus on temporal clustering of all seismicity within the caldera and most clusters represent complete seismicity cycles between major collapse events. Beginning in late June, the M2 cluster duration gradually increased. The event numbers show a strong linear relationship with the tilt rates on the transverse component, suggesting earthquake rates are controlled by the deformation rate within the caldera.

Source Parameters of Moderate-To-Large Chinese Earthquakes From the Time Evolution of P-Wave Peak Displacement on Strong Motion Recordings

In this work we propose and apply a straightforward methodology for the automatic characterization of the extended earthquake source, based on the progressive measurement of the P-wave displacement amplitude at the available stations deployed around the source. Specifically, we averaged the P-wave peak displacement measurements among all the available stations and corrected the observed amplitude for distance attenuation effect to build the logarithm of amplitude vs. time function, named LPDT curve. The curves have an exponential growth shape, with an initial increase and a final plateau level. By analyzing and modelling the LPDT curves, the information about earthquake rupture process and earthquake magnitude can be obtained. We applied this method to the Chinese strong motion data from 2007 to 2015 with Ms ranging between 4 and 8. We used a refined model to reproduce the shape of the curves and different source models based on magnitude to infer the source-related parameters for the study dataset. Our study shows that the plateau level of LPDT curves has a clear scaling with magnitude, with no saturation effect for large events. By assuming a rupture velocity of 0.9 Vs, we found a consistent self-similar, constant stress drop scaling law for earthquakes in China with stress drop mainly distributed at a lower level (0.2 MPa) and a higher level (3.7 MPa). The derived relation between the magnitude and rupture length may be feasible for real-time applications of Earthquake Early Warning systems.

On the heterogeneity of the earthquake rupture

SUMMARYThe scaling of earthquake parameters with seismic moment and its interpretation in terms of self-similarity is still debated in the literature. We address this question by examining a worldwide compilation of corner frequency-based and elastic rebound theory (ERT)-based fault slip, area and stress drop values for earthquakes ranging in magnitude from −0.7 to 7.8. We find that corner frequency estimates of slip (and stress drop) scale differently than those inferred from the ERT approach, where the latter deviates from the generally accepted constant stress drop behaviour of so-called self-similar scaling models. We also find that average slips from finite-source models are consistent with corner frequency scaling, whereas peak slip values are more consistent with the ERT scaling. The different scaling of corner frequency- and ERT-based estimates of slip and stress drop with earthquake size is interpreted in terms of heterogeneity of the rupture process. ERT-based estimates of stress drop decrease with seismic moment suggesting a self-affine behaviour. Despite the inferred heterogeneity at all scales, we do not observe a clear effect on the Brune stress drop scaling with earthquake size.

Well Proximity Governing Stress Drop Variation and Seismic Attenuation Associated With Hydraulic Fracturing Induced Earthquakes

AbstractWe use broadband seismic data collected within 3 km of a hydraulic fracturing (HF) well in northeast British Columbia, Canada, to estimate the stress drop values of HF‐induced earthquakes and their spatial variation. Applying both spectral ratio and clustered single‐spectra fitting methods to 484 induced earthquakes (M‐1.0 to 3.0), we find that earthquakes close to the injection well have lower stress drop values than those at greater distance. Stress drop values are generally invariant within clusters either proximal (~0.1–1 MPa) or distal (~1–10 MPa) to the well, suggesting that dynamic ruptures in rocks with similar rheological properties tend to have relatively constant stress drop values. Clustered single spectrum fitting also suggests that the seismic quality factor (Q) is lower proximal to the well. We interpret the lower stress drop values and higher seismic attenuation proximal to the well as a result of higher fracture density and/or elevated pore pressure in the rock matrix due to hydraulic stimulation.

The earthquake arrest zone

SUMMARY Earthquake ruptures are generally considered to be cracks that propagate as fracture or frictional slip on pre-existing faults. Crack models have been used to describe the spatial distribution of fault offset and the associated static stress changes along a fault, and have implications for friction evolution and the underlying physics of rupture processes. However, field measurements that could help refine idealized crack models are rare. Here, we describe large-scale laboratory earthquake experiments, where all rupture processes were contained within a 3-m long saw-cut granite fault, and we propose an analytical crack model that fits our measurements. Similar to natural earthquakes, laboratory measurements show coseismic slip that gradually tapers near the rupture tips. Measured stress changes show roughly constant stress drop in the centre of the ruptured region, a maximum stress increase near the rupture tips and a smooth transition in between, in a region we describe as the earthquake arrest zone. The proposed model generalizes the widely used elliptical crack model by adding gradually tapered slip at the ends of the rupture. Different from the cohesive zone described by fracture mechanics, we propose that the transition in stress changes and the corresponding linear taper observed in the earthquake arrest zone are the result of rupture termination conditions primarily controlled by the initial stress distribution. It is the heterogeneous initial stress distribution that controls the arrest of laboratory earthquakes, and the features of static stress changes. We also performed dynamic rupture simulations that confirm how arrest conditions can affect slip taper and static stress changes. If applicable to larger natural earthquakes, this distinction between an earthquake arrest zone (that depends on stress conditions) and a cohesive zone (that depends primarily on strength evolution) has important implications for how seismic observations of earthquake fracture energy should be interpreted.

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.

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.

Moment–Area Scaling Relationship Assuming Constant Stress Drop for Crustal Earthquakes

ABSTRACTFor crustal earthquakes, the scaling relationship between the seismic moment M0 and rupture area S varies with the size of the earthquake, due to the limited thickness of the seismogenic layer. In those M0–S scaling relations, in most cases, the calculated static stress drop is altered with the size of earthquake, although the change depends on the assumed fault model. However, it is not clear whether the dependence of the stress drop on M0 is physically reasonable. In this study, the scaling relation between M0 and S, which assumes a constant stress drop over a wide M0 range, is discussed based on the analytical stress drop formula of a rectangular strike-slip fault. In the proposed relation, M0 is proportional to S3/2 for small and medium faults and to S1 for long faults. In addition, the relation between M0 and S varies in the intermediate range, depending on the aspect ratio. The scaling relation showed good agreement with past event data when the saturated rupture width was set to around 15–20 km and the stress drop was set to about 3 MPa.

A Review on Scaling of Earthquake Source Spectra

In this review paper, the theoretical and observational studies of scaling of earthquake source displacement spectra (abbreviated as source spectra) are compiled and discussed. The earlier studies, including the kinetic models proposed by several authors [including Haskell (Bull Seismol Soc Am 56:125–140, 1966) and Aki (J Geophys Res 72:1217–1231, 1967), provided the so-called ω−1, ω-square, and ω-cube models. Aki (1967) favored the ω-square model and also assumed constant stress drop, Δσ, and self-similarity of earthquakes. Some observations agree to one of the two models, but others do not. Hence, numerous alternative forms of the three scaling models to interpret the observations have been made by seismologists. For the corner frequencies, fc, the seismic moment Mo scales with fc in the form of Mo ~ f c −3 . For fcP of the P-waves and fcS of the S-waves, fcP > fcS is more reasonable than fcP < fcS. Mo scales as T D 3 , where TD is the duration time of source rupture and inversely related to fc, for both small and large events. The second corner frequency or cut-off frequency, fmax, at higher ω, that exists in the source spectra could be yielded by source, path, and site effects. The mechanisms to cause the patch corner frequency are still open. Analytical and numerical studies of the scaling laws based on the dislocation (e.g., Aki 1967), cracks (e.g., Walter and Brune in J Geophys Res 98(B3):4449–4459, 1993), spring-slider (e.g., Shaw in Geophys Res Lett 20:643–646, 1993), and statistical physics models (e.g., Hanks in J Geophys Res 84:2235–2242, 1997), including self-organized criticality (e.g., Bak et al. in Phys Rev Lett 59:381–384, 1987), show different scaling laws under various physical conditions.

Crack Models of Repeating Earthquakes Predict Observed Moment‐Recurrence Scaling

AbstractSmall repeating earthquakes are thought to represent rupture of isolated asperities loaded by surrounding creep. The observed scaling between recurrence interval and seismic moment, Tr∼M1/6, contrasts with expectation assuming constant stress drop and no aseismic slip (Tr∼M1/3). Here we demonstrate that simple crack models of velocity‐weakening asperities in a velocity‐strengthening fault predict the M1/6 scaling; however, the mechanism depends on asperity radius, R. For small asperities ( , where is the nucleation radius) numerical simulations with rate‐state friction show interseismic creep penetrating inward from the edge, and earthquakes nucleate in the center and rupture the entire asperity. Creep penetration accounts for ∼25% of the slip budget, the nucleation phase takes up a larger fraction of slip. Stress drop increases with increasing R; the lack of self‐similarity being due to the finite nucleation dimension. For simulations exhibit simple cycles with ruptures nucleating from the edge. Asperities with exhibit complex cycles of partial and full ruptures. Here Tr is explained by an energy criterion: full rupture requires that the energy release rate everywhere on the asperity at least equals the fracture energy, leading to the scaling Tr∼M1/6. Remarkably, in spite of the variability in behavior with source dimension, the scaling of Tr with stress drop Δτ, nucleation length and creep rate vpl is the same across all regimes: . This supports the use of repeating earthquakes as creepmeters and provides a physical interpretation for the scaling observed in nature.

Testing stress shadowing effects at the South American subduction zone

The seismic gap hypothesis assumes that a characteristic earthquake is followed by a long period with a reduced occurrence probability for the next large event on the same fault segment, as a consequence of the induced stress shadow. The gap model is commonly accepted by geologists and is often used for time-dependent seismic hazard estimations. However, systematic and rigorous tests to verify the seismic gap model have often failed so far, which might be partially related to limited data and too tight model assumptions. In this study, we relax the assumption of a characteristic size and location of repeating earthquakes and analyse one of the best available data sets, namely the historical record of major earthquakes along a 3000 km long linear segment of the South American subduction zone. To test whether a stress shadow effect is observable, we compiled a comprehensive catalogue of mega-thrust earthquakes along this plate boundary from 1520 to 2015 containing 174 earthquakes with Mw > 6.5. In our new testing approach, we analyse the time span between an earthquake and the last event that ruptured the epicentre location, where we consider the impact of the uncertainties of epicentres and rupture extensions. Assuming uniform boundary conditions along the trench, we compare the distribution of these recurrence times with simple recurrence models. We find that the distribution is in all cases almost exponentially distributed corresponding to a random (Poissonian) process; despite some tendencies for clustering of the Mw ≥ 7 events and a weak quasi-periodicity of the Mw ≥ 8 earthquakes, respectively. To verify whether the absence of a clear stress shadow signal is related to physical assumptions or data uncertainties, we perform simulations of a physics-based stochastic earthquake model considering rate and state-dependent earthquake nucleation, which are adapted to the observations with regard to the number of events, spatial extend, size distribution and involved uncertainties. Our simulations show that the catalogue uncertainties lead to a significant blurring of the theoretically peaked distribution, but the distribution would be still distinguishable from the observed one for Mw ≥ 7 events. However, considering the stress transfer to adjacent fault segments and heterogeneous instead of constant stress drop within the rupture zone can explain the observed recurrence time distribution. We conclude that simplified recurrence models, ignoring the complexity of the underlying physical process, cannot be applied for forecasting the Mw ≥ 7 earthquake occurrence at this plate boundary.