Aftershock Rate Research Articles

A Quantitative Estimate of the Effects of Sea Tides on Aftershock Activity: Kamchatka

The issue of whether tidal forces really affect seismicity has been raised many times in the literature. Nevertheless, even though there seems to be a kind of consensus that such effects do exist, no quantitative estimates are available to relate tide parameters to changes in the level of seismic activity. Such estimation for aftershocks of large earthquakes near Kamchatka is the goal of the present study. We consider the influence on seismicity due to ocean tides only, because their effects are stronger than those of solid earth tides. Accordingly, we only consider earthquakes that occurred in the ocean. One important feature that distinguishes the present study from most other such research consists in the fact that we study the height of ocean tides and its derivative rather than tidal phases as the decisive factors. We considered 16 aftershock sequences of earthquakes near Kamchatka with magnitudes of 6 or greater. We also examined shallow background earthquakes along the coast of Kamchatka. Our basic model of aftershock rate was the Omori–Utsu law. The background seismicity distribution was assumed to be uniform over time. In both of these cases we used the actual distributions in space. The heights of sea tides were estimated using the FES 2004 model (Lyard et al., 2006). The variation in activity from what the basic model assumes in relation to tidal wave height and its time derivative was estimated by the method of differential probability gain. The main practical result of this study consists in estimates of averaged differential probability gain functions for aftershock rate with respect to both of the considered factors. These estimates can be used for earthquake hazard assessment from aftershocks with ocean tides incorporated. The results of our analysis show a persistent tendency of aftershock rate increasing during periods when the ocean tide decreased at a high rate. For the background events, we found a typical tendency of events rate increasing when the ocean tide decreased with high tidal amplitudes. The difference in the main factors that affect aftershocks and background seismicity suggest the inference that the effects of tides on aftershocks are more likely to be direct dynamic initiation of events during high strain rates, while the effects on the background events were static in character.

The Effect of a Mainshock on the Size Distribution of the Aftershocks

AbstractA systematic decay of the aftershock rate over time is one of the most fundamental empirical laws in Earth science. However, the equally fundamental effect of a mainshock on the size distribution of subsequent earthquakes has still not been quantified today and is therefore not used in earthquake hazard assessment. We apply a stacking approach to well‐recorded earthquake sequences to extract this effect. Immediately after a mainshock, the mean size distribution of events, orbvalue, increases by 20–30%, considerably decreasing the chance of subsequent larger events. This increase is strongest in the immediate vicinity of the mainshock, decreasing rapidly with distance but only gradually over time. We present a model that explains these observations as a consequence of the stress changes in the surrounding area caused by the mainshocks slip. Our results have substantial implications for how seismic risk during earthquake sequences is assessed.

The Omori Law: The 150-Year Birthday Jubilee of Fusakichi Omori

The outstanding Japanese seismologist Fusakichi Omori was born 150 years ago, on October 30, 1868. He discovered his first law in earthquake physics that now bears his name when he was 26. Essentially, Omori’s law tells us that the decay of aftershock rate follows a hyperbolic law. This paper provides a brief account of how that discovery was made. Attention is focused on two approaches in an attempt at generalizing Omori’s law. One of these has been known for many years and to many researchers. It is based on the concept that the aftershock rate depends on time as a power law. The other approach was discovered recently by using a formal analogy between the decay of aftershock activity in the lithosphere and the recombination of charged particles in the ionosphere. A differential equation for aftershocks has been proposed. The general solution to the equation retains the hyperbolic structure of Omori’s law, but also enables a flexible simulation of rock instability at the earthquake source that is “cooling down” after the main shock. The general solution also incorporates the non-monotonic function that describes the time-dependent decay of aftershock rate, which occurs when an earthquake source is acted on by endogenous and exogenous triggers. The aftershock equation is used to formulate the inverse problem in earthquake source physics.

Diverse Volumetric Faulting Patterns in the San Jacinto Fault Zone

AbstractWe examine locations, magnitudes, and faulting types of post‐2000 earthquakes in the trifurcation area of San Jacinto fault zone to clarify basic aspects of failure processes in the area. Most M ≥ 3.5 events have strike‐slip mechanisms, occur within 1 km of the main faults (Clark, Buck Ridge, and Coyote Creek), and have hypocenter depths of 10–13 km. In contrast, many smaller events have normal source mechanisms and hypocenters in intrafault areas deeper than 13 km. Additional small events with hypocenter depth <13 km occur in off‐fault regions and have complex geometries including lineations normal to the main faults. Five moderate earthquakes with M 4.7–5.4 have high aftershock rates (~150 M ≥ 1.5 events within 1 day from the mainshock). To obtain more details on aftershock sequences of these earthquakes, we detect and locate additional events with the matched filter method. There are almost no aftershocks within 1 km from the mainshocks, consistent with large mainshock stress drops and low residual stress. The five aftershock sequences have almost no spatial overlap. While the mainshocks are on the main faults, most aftershocks are located in intrafault and off‐fault regions. Their locations and spatial distribution reflect the mainshock rupture directions, and many also follow structures normal to the main faults. The significant diversity of observed features highlights the essential volumetric character of failure patterns in the area. The increasing rate of moderate events, productive aftershock sequences, and large inferred stress drops may reflect processes near the end of a large earthquake cycle.

Seismicity of the 2016 ML 5.8 Gyeongju earthquake and aftershocks in South Korea

Since the modern seismograph network by the Korea Meteorological Administration (KMA) had been operated from 1978, the largest earthquake (ML 5.8) occurred in Gyeongju, South Korea on 12 September 2016. ML 5.1 and 5.8 earthquakes occurred successively and damaged mostly old building structures around Gyeongju. Aftershocks continued to occur, clustering around the epicenters of the two events. Number of observed aftershocks with ML ≥ 0.1 was 3,376 from 12 September 2016 to 31 March 2017 and these aftershocks were located by manual procedure. Since the origin time of the ML 5.8 earthquake, 339 and 672 aftershocks (ML ≥ 0.1) occurred on 12 and 13 September 2016, respectively. The occurrence rate of aftershocks decreased exponentially with time after 16 September. It is observed that the seismicity of the 2016 Gyeongju earthquake and aftershock sequences is dominant in the Yangsan Fault System. The distribution of aftershocks is NNE-SSW direction along the Yangsan Fault System, which agrees with the fault plane solutions of main shock and foreshock showing the strike-slip faulting. These aftershocks concentrate within the epicentral distance of 5 km from main shock and the depth distribution of aftershocks is mainly around 11–15 km with vertical trends. With regard to the seismicity of the 2016 Gyeongju earthquake’s aftershocks the full catalog with ML ≥ 1.2 based on Mc is suggested in this study. Finally the distribution of aftershock sequence correlated to the focal mechanisms can provide specific seismicity in the Gyeongsang Basin.

Seismicity Controlled by a Frictional Afterslip During a Small‐Magnitude Seismic Sequence (ML < 5) on the Chihshang Fault, Taiwan

AbstractWe report evidence for frictional afterslip at shallow depths (about 5 to 7 km) during a small‐magnitude seismic sequence (with ML<5) along the Chihshang Fault, a main active structure of the Longitudinal Valley, in southeast Taiwan. The afterslip, which was recorded by a nearby borehole dilatometer, lasted about a month with a cumulative geodetic moment magnitude of 4.8 ± 0.2. The afterslip comprised two stages and controlled the aftershock sequence. The first postseismic stage, which followed a ML 4.6 earthquake, lasted about 6 h and mostly controlled the ruptures of neighboring asperities (e.g., multiplets) near the hypocenter. Then, a 4 week duration large afterslip event following a ML 4.9 earthquake controlled the rate of aftershocks during its first 2 days through brittle creep. The study presents a rare case of simultaneous seismological and geodetic observations for afterslip following earthquakes with magnitude lower than 5. Furthermore, the geodetic moment of the postseismic phase is at least equivalent to the coseismic moment of the sequence.

Are triggering rates of labquakes universal? Inferring triggering rates from incomplete information

The acoustic emission activity associated with recent rock fracture experiments under different conditions has indicated that some features of event-event triggering are independent of the details of the experiment and the materials used and are often even indistinguishable from tectonic earthquakes. While the event-event triggering rates or aftershock rates behave pretty much identical for all rock fracture experiments at short times, this is not the case for later times. Here, we discuss how these differences can be a consequence of the aftershock identification method used and show that the true aftershock rates might have two distinct regimes. Specifically, tests on a modified Epidemic Type Aftershock Sequence model show that the model rates cannot be correctly inferred at late times based on temporal information only if the activity rates or the branching ratio are high. We also discuss both the effect of the two distinct regimes in the aftershock rates and the effect of the background rate on the inter-event time distribution. Our findings should be applicable for inferring event-event triggering rates for many other types of triggering and branching processes as well.

Forecasting the (Un)Productivity of the 2014 M 6.0 South Napa Aftershock Sequence

ABSTRACT The 24 August 2014 M w 6.0 South Napa mainshock produced fewer aftershocks than expected for a California earthquake of its magnitude. In the first 4.5 days, only 59 M ≥1.8 aftershocks occurred, the largest of which was an M 3.9 that happened a little over two days after the mainshock. We investigate the aftershock productivity of the South Napa sequence and compare it with other M ≥5.5 California strike‐slip mainshock–aftershock sequences. While the productivity of the South Napa sequence is among the lowest, northern California mainshocks generally have fewer aftershocks than mainshocks further south, although the productivities vary widely in both regions. An epidemic‐type aftershock sequence (ETAS) model (Ogata, 1988) fit to Napa seismicity from 1980 to 23 August 2014 fits the sequence well and suggests that low‐productivity sequences are typical of this area. Utilizing regional variations in productivity could improve operational earthquake forecasting (OEF) by improving the model used immediately after the mainshock. We show this by comparing the daily rate of M ≥2 aftershocks to forecasts made with the generic California model (Reasenberg and Jones, 1989; hereafter, RJ89), RJ89 models with productivity updated daily, a generic California ETAS model, an ETAS model based on premainshock seismicity, and ETAS models updated daily following the mainshock. RJ89 models for which only the productivity is updated provide better forecasts than the generic RJ89 California model, and the Napa‐specific ETAS models forecast the aftershock rates more accurately than either generic model. Therefore, forecasts that use localized initial parameters and that rapidly update the productivity may be better for OEF than using a generic model and/or updating all parameters.

Long-Delayed Aftershocks in New Zealand and the 2016 M7.8 Kaikoura Earthquake

We study aftershock sequences of six major earthquakes in New Zealand, including the 2016 M7.8 Kaikaoura and 2016 M7.1 North Island earthquakes. For Kaikaoura earthquake, we assess the expected number of long-delayed large aftershocks of M5+ and M5.5+ in two periods, 0.5 and 3 years after the main shocks, using 75 days of available data. We compare results with obtained for other sequences using same 75-days period. We estimate the errors by considering a set of magnitude thresholds and corresponding periods of data completeness and consistency. To avoid overestimation of the expected rates of large aftershocks, we presume a break of slope of the magnitude–frequency relation in the aftershock sequences, and compare two models, with and without the break of slope. Comparing estimations to the actual number of long-delayed large aftershocks, we observe, in general, a significant underestimation of their expected number. We can suppose that the long-delayed aftershocks may reflect larger-scale processes, including interaction of faults, that complement an isolated relaxation process. In the spirit of this hypothesis, we search for symptoms of the capacity of the aftershock zone to generate large events months after the major earthquake. We adapt an algorithm EAST, studying statistics of early aftershocks, to the case of secondary aftershocks within aftershock sequences of major earthquakes. In retrospective application to the considered cases, the algorithm demonstrates an ability to detect in advance long-delayed aftershocks both in time and space domains. Application of the EAST algorithm to the 2016 M7.8 Kaikoura earthquake zone indicates that the most likely area for a delayed aftershock of M5.5+ or M6+ is at the northern end of the zone in Cook Strait.

Rapid estimation of the hazard posed by strong aftershocks for Kamchatka and the Kuril Islands

This paper deals with the rapid estimation of the hazard posed by strong aftershocks for Kamchatka and the Kuril Islands based on the 12-hour aftershocks, namely, their rate, time of expectation, and maximum magnitude. The data set consists of main shocks and aftershocks as reported in the Catalog of the Kamchatka Branch of the Geophysical Survey, Russian Academy of Sciences (GS RAS) for 1968–2016. We used both the Gutenberg–Richter relation and the Omori–Utsu law to find that the aftershock rates in two time intervals are connected by a relationship of proportionality, with the constant of proportionality being independent of the lowest magnitude of these earthquakes. With this property in mind, we calculated the constants of proportionality for estimating the rate of aftershocks with a magnitude above threshold values based on the data for the first 12 hours after the main shock. We have derived easily remembered rules for estimating the aftershock rates that can be expected for 5 days and for 1 month with magnitudes above a fixed value based on the 12-hour aftershock observations. We also derived empirical regression relations to estimate the magnitude of the largest aftershock that can be expected to occur during 1 year after the main shock and the time of the last aftershock to occur whose magnitude is 5.2 or greater.

Omori’s law: a note on the history of geophysics

In the late nineteenth century, the Japanese seismologist Omori discovered the first law of earthquake physics, which states that the rate of aftershocks decreases hyperbolically with time. Over the years since then, there has been a vast amount of literature on this law, and the significance of its discovery has been universally recognized. There is, however, a profound division of opinion as to the interpretation of the law. Some argue that Omori just proposed a simple data-fitting formula and replace this formula by a power-law one with a negative fractional exponent, whereas for others the Omori law makes physical sense. The paper describes the history and essence of Omori’s discovery, with special attention paid to interpretational questions. It is shown that Omori’s original formulation of the law correlates well with the current understanding of the rock destruction mechanism at the earthquake focus.

Foreshock Seismicity Suggests Gradual Differential Stress Increase in the Months Prior to the 3 September 2016Mw5.8 Pawnee Earthquake

ABSTRACT The 3 September 2016 M w 5.8 Pawnee earthquake was the largest earthquake in Oklahoma history. To determine the relationship with nearby seismic activity and whether there were any precursory foreshocks to the event, we analyze a dataset comprising regional seismometers throughout Oklahoma, including the Oklahoma Geological Survey statewide network. We use a matched‐filter technique to identify potential missing earthquakes before and after the mainshock. This technique utilizes cataloged waveforms as templates that, when correlated against continuous waveforms, are able to identify repeating or nearby earthquakes. As shown in other studies, the aftershocks roughly fall along an east‐southeast‐trending linear belt that illuminates a previously unknown fault. We utilize the augmented seismicity catalog to draw two main conclusions. From standard statistical seismological methods, we deduce that the b ‐value decreased prior to the Pawnee mainshock; previous work suggests that b ‐value and differential stress are anticorrelated. The b ‐value result suggests the differential stress along the fault that eventually ruptured was gradually increasing in the few months leading up to the mainshock. During the aftershock period, we infer an Omori–Utsu p ‐value close to 1, typical for most tectonic events. Although the prolonged seismicity in the months leading up to the event may be a hallmark of induced earthquakes and may help decipher induced earthquakes from natural earthquakes, the rate of aftershocks is indistinguishable from natural tectonic earthquakes though deficient in larger aftershocks.

Predicting crackling noise in compressional deformation

Compressional deformation of wood as a porous material is a test system for the prediction of avalanches. We analyze the predictability of ‘woodquakes’ or acoustic emission (AE) events from small wood samples, based on a geophysics analogy, the Omori production law. The main idea is that an enhanced aftershock rate leads to an increased event probability after a ‘main shock’ or an event that exceeds a pre-chosen energy threshold. We present an analysis of the resulting relation, and show that combined with an AE timeseries analysis procedure implemented on a fast signal processing setup this allows to confirm the ensuing prediction scheme. By maximizing the prediction efficiency by tuning the parameters of prediction trials like ‘when’, ‘for how long time’ and ‘for how big events’ aftershock probabilities up to close to 50% are realized and confirmed in on-line experiments. We also repeat the procedure for the main shock prediction utilizing a version of the Omori law for fore shocks. The implications of these trials are discussed in terms of the efficiency of avalanche prediction.

Assessment of Quantitative Aftershock Productivity Potential in Mining-Induced Seismicity

Strong mining-induced earthquakes exhibit various aftershock patterns. The aftershock productivity is governed by the geomechanical properties of rock in the seismogenic zone, mining-induced stress and coseismic stress changes related to the main shock’s magnitude, source geometry and focal mechanism. In order to assess the quantitative aftershock productivity potential in the mining environment we apply a forecast model based on natural seismicity properties, namely constant tectonic loading and the Gutenberg-Richter frequency-magnitude distribution. Although previous studies proved that mining-induced seismicity does not obey the simple power law, here we apply it as an approximation of seismicity distribution to resolve the number of aftershocks, not considering their magnitudes. The model used forecasts the aftershock productivity based on the background seismicity level estimated from an average seismic moment released per earthquake and static stress changes caused by a main shock. Thus it accounts only for aftershocks directly triggered by coseismic process. In this study we use data from three different mines, Mponeng (South Africa), Rudna and Bobrek (Poland), representing different geology, exploitation methods and aftershock patterns. Each studied case is treated with individual parameterization adjusted to the data specifics. We propose the modification of the original model, i.e. including the non-uniformity of M0, resulting from spatial correlation of mining-induced seismicity with exploitation. The results show that, even when simplified seismicity distribution parameters are applied, the modified model predicts the number of aftershocks for each analyzed case well and accounts for variations between these values. Such results are thus another example showing that coseismic processes of mining-induced seismicity reflect features of natural seismicity and that similar models can be applied to study the aftershock rate in both the natural and the mining environment.

Seismogenesis and earthquake triggering during the 2010–2011 Rigan (Iran) earthquake sequence

This study assesses the aftershock activity of two earthquakes that occurred on December 20, 2010 with magnitude of MN 6.5 (Global CMT Mw 6.5) and January 27, 2011 with magnitude of MN 6.0 (Global CMT Mw 6.2) in the Rigan region of southeastern Iran. This study has been done by assessing the statistical properties of the aftershock sequences associated with each of these earthquakes, namely b-value of Gutenberg–Richter relation, partitioning of radiated seismic energy, p-value of modified Omori law and the DC-value associated with the fractal dimension. The b-values of b = 0.89 ± 0.08 and b = 0.88 ± 0.08 were calculated for first main shock and second main shock sequence respectively. This suggests that this region is characterized by large differential stress; the genesis of large aftershock activity in a short time interval gives power this. Further, 2.2% of the whole energy is related with the aftershocks activity for first main shock sequence while 97.8% is associated with main shock; for second sequence, 20% of the total energy is associated with the aftershocks activity while 80% is associated with main shock. The p-values of 1.1 ± 0.12 and 1.1 ± 0.1 were calculated for first and second main shocks sequence respectively, which imply fast decay rate of aftershocks and high surface heat flux. A value of the spatial fractal dimension (Dc) equal to 2.34 ± 0.03 and 2.54 ± 0.02 for first and second main shocks sequence respectively, which reveals random spatial distribution and source in a two-dimensional plane that is being filled-up by fractures. Moreover, we then use the models to calculate the Coulomb stress change to appraise coming seismic hazard by inspecting the static Coulomb stress field due to these two main shocks for the recognition of the conceivable regions of aftershocks activity. The first main shock increased stress by more than 0.866 bars at the hypocenter of the second main shock, thus promoting the failure. In addition, the cumulative coseismic Coulomb stress changes due to the reveals that most of the aftershocks happened in the region of increased Coulomb stress.

Power-law rheology controls aftershock triggering and decay.

The occurrence of aftershocks is a signature of physical systems exhibiting relaxation phenomena. They are observed in various natural or experimental systems and usually obey several non-trivial empirical laws. Here we consider a cellular automaton realization of a nonlinear viscoelastic slider-block model in order to infer the physical mechanisms of triggering responsible for the occurrence of aftershocks. We show that nonlinear viscoelasticity plays a critical role in the occurrence of aftershocks. The model reproduces several empirical laws describing the statistics of aftershocks. In case of earthquakes, the proposed model suggests that the power-law rheology of the fault gauge, underlying lower crust, and upper mantle controls the decay rate of aftershocks. This is verified by analysing several prominent aftershock sequences for which the rheological properties of the underlying crust and upper mantle were established.

Spatially inhomogeneous background rate estimators and uncertainty quantification for nonparametric Hawkes point process models of earthquake occurrences

Space–time Hawkes point process models for the conditional rate of earthquake occurrences traditionally make many parametric assumptions about the form of the triggering function for the rate of aftershocks following an earthquake. As an alternative, Marsan and Lengline [Science 319 (2008) 1076–1079] developed a completely nonparametric method that provides an estimate of a homogeneous background rate for mainshocks, and a histogram estimate of the triggering function. At each step of the procedure the model estimates rely on computing the probability each earthquake is a mainshock or aftershock of a previous event. The focus of this paper is the improvement and assessment of Marsan and Lengline’s method in the following ways: (a) the proposal of novel ways to incorporate a spatially inhomogeneous background rate; (b) adding error bars to the histogram estimates which quantify the sampling variability in the estimation of the underlying seismic process. A simulation study is designed to evaluate and validate the ability of our methods to recover the triggering function and spatially varying background rate. An application to earthquake data from the Tohoku District in Japan is discussed at the end, and the results are compared to a well-established parametric model of seismicity for this region.

Self-similar aftershock rates.

In many important systems exhibiting crackling noise-an intermittent avalanchelike relaxation response with power-law and, thus, self-similar distributed event sizes-the "laws" for the rate of activity after large events are not consistent with the overall self-similar behavior expected on theoretical grounds. This is particularly true for the case of seismicity, and a satisfying solution to this paradox has remained outstanding. Here, we propose a generalized description of the aftershock rates which is both self-similar and consistent with all other known self-similar features. Comparing our theoretical predictions with high-resolution earthquake data from Southern California we find excellent agreement, providing particularly clear evidence for a unified description of aftershocks and foreshocks. This may offer an improved framework for time-dependent seismic hazard assessment and earthquake forecasting.

Aftershocks triggered by fluid intrusion: Evidence for the aftershock sequence occurred 2014 in West Bohemia/Vogtland

AbstractThe West Bohemia/Vogtland region, central Europe, is well known for its repeating swarm activity. However, the latest activity in 2014, although spatially overlapping with previous swarm activity, consisted of three classical aftershock sequences triggered by ML3.5, 4.4, and 3.5 events. To decode the apparent system change from swarm‐type to mainshock‐aftershock characteristics, we have analyzed the details of the major ML4.4 sequence based on focal mechanisms and relocated earthquake data. Our analysis shows that the mainshock occurred with rotated mechanism in a step over region of the fault plane, unfavorably oriented to the regional stress field. Most of its intense aftershock activity occurred in‐plane with classical characteristics such as (i) the maximum magnitude of the aftershocks is significantly less than the mainshock magnitude and (ii) the decay can be well fitted by the Omori‐Utsu law. However, the absolute number of aftershocks and the fitted Omori‐Utsu c and p parameters are much larger than for typical sequences. By means of the epidemic‐type aftershock sequence model, we show that an additional aseismic source with an exponentially decaying strength triggered a large fraction of the aftershocks. Corresponding pore pressure simulations with an exponentially decreasing flow rate of the fluid source show a good agreement with the observed spatial migration front of the aftershocks extending approximately with . Thus, we conclude that the mainshock opened fluid pathways from a finite fluid source into the fault plane explaining the unusual high rate of aftershocks, the migration patterns, and the exponential decrease of the aseismic signal.

Revisiting the 1894 Omori Aftershock Dataset with the Stretched Exponential Function

In 1894, Fusakichi Omori published his landmark article on aftershocks in which he described the temporal decay rate of aftershocks as a power law. In this article, I show that the expression proposed by Omori does not hold when the proper visualization method is used (i.e., complementary cumulative density function in log–log plot) and that the choice of a stretched exponential function should have been preferred on physical grounds. I reproduce the emblematic aftershock sequence of the 1891 Great Nobi earthquake used by Omori and show that a stretched exponential expression describes the data better than a power law.