Modified Omori Law Research Articles

Properties of the Aftershock Sequences of the 2003 Bingöl, M D = 6.4, (Turkey) Earthquake

Aftershock sequences of the magnitude MW ¼6.4 Bingol earthquake of 1 May, 2003 (Turkey) are studied to analyze the spatial and temporal variability of seismicity parameters of the b value of the frequency- magnitude distribution and the p value describing the temporal decay rate of aftershocks. The catalog taken from the KOERI contains 516 events and one month's time interval. The b value is found as 1.49 ± 0.07 with Mc ¼3.2. Considering the error limits, b value is very close to the maximum b value stated in the literature. This larger value may be caused by the paucity of the larger aftershocks with magnitude MD C 5.0. Also, the aftershock area is divided into four parts in order to detect the differences in b value and the changes illustrate the heterogeneity of the aftershock region. The p value is calculated as 0.86 ± 0.11, relatively small. This small p value may be a result of the slow decay rate of the aftershock activity and the small number of aftershocks. For the fitting of a suitable model and estimation of correct values of decay parameters, the sequence is also modeled as a background seismicty rate model. Constant background activity does not appear to be important during the first month of the Bingol aftershock sequences and this result is coherent with an average estimation of pre- existing seismicity. The results show that usage of simple modified Omori law is reasonable for the analysis. The spatial variability in b value is between 1.2 and 1.8 and p value varies from 0.6 to 1.2. Although the physical interpretation of the spatial variability of these seismicity parameters is not straightforward, the variation of b and p values can be related to the stress and slip distribution after the mainshock, respectively. The lower b values are observed in the high stress regions and to a certain extent, the largest b values are related to Holocene alluvium. The larger p values are found in some part of the aftershock area although no slip occurred after the main shock and it is interpreted that this situation may be caused by the alluvium structure of the region. These results indicate that the spatial distribution in b and p values are generally related to the rupture mechanism and material properties of an aftershock area.

The 9th of July 1998 Faial Island (Azores, North Atlantic) seismic sequence

The Faial earthquake (ML 5.8) that occurred on the 9th of July, 1998, in the Azores region (north Atlantic), caused nine casualties and severe destruction affecting more than 5,000 people. The main shock was located at sea, 10 km NE of the Faial Island, and triggered a seismic sequence that lasted for several weeks and was characterized by an unusual high p-value of 1.40 for the modified Omori law. We present here the results of a joint inversion of hypocenters and 1D velocity model performed on the data collected by the permanent network complemented with a temporary network installed shortly after the occurrence of the main event. The 1D velocity model shows a heterogeneous upper crust, testified by the observed differences in site effects at the stations, while the middle crust from ∼2.5 to 8 km in depth is quite homogeneous. The Moho is located at a depth of about 12–13 km and the Vp/Vs ratio is found to be around 1.78. The events at depth are mainly concentrated in the middle-lower crust (8–12 km), while their spatial distribution shows a main cluster, visible after relocation, SSE trending. This direction of elongation is consistent with one of the fault planes (N151°E) of the centroid moment tensor (CMT) solution for the main shock. The same plane is the preferred main shock fault plane inferred after a Coulomb failure function analysis on the aftershock distribution. The main event relocation points to a focal depth shallower than 5 km. The aftershocks pattern shows that several fault systems were reactivated by the stress perturbation induced by the main shock. Besides the two main tectonic directions, trending WNW–ESE and NNW–SSE, observed in the tectonics of Faial, Pico, and S. Jorge, there is also evidence of a new tectonic direction trending WSW–ENE.

Postseismic relaxation associated with transient creep rheology

Perfettini and Avouac (2004) postulated that both the aftershock rate (assumed proportional to the local stressing rate) and the postseismic relaxation are driven by the loading imposed by postseismic slip on the brittle creep fault zone (BCFZ), the downdip extension of the fault zone below the coseismic rupture. I explore the consequences of that hypothesis for a long, strike‐slip fault in the case where the BCFZ rheology is compatible with ordinary transient creep (creep strain proportional to loge(1 + t/τ2)). Because the important relaxation occurs near the bottom of the coseismic rupture, I calculate the postearthquake response with a model in which the BCFZ is represented by a viscoelastic half‐space below the coseismic rupture. I find that both the predicted postseismic relaxation and the cumulative number of aftershocks can be approximated by the same temporal dependence NMO(t) = aMO(1−(1 + t/τ)1−p)/(p − 1), where t is the time after the earthquake and aMO, τ, and p are the constants chosen to fit either data set. Notice that dNMO(t)/dt = (aMO/τ)/(1 + t/τ)p is the modified Omori law used to describe the rate of aftershock occurrence. Thus, the modified Omori law can be understood as a consequence of the Perfettini–Avouac hypothesis (aftershocks driven by slip on the BCFZ) and a BCFZ rheology compatible with ordinary transient creep. Moreover, the temporal dependence NMO(t) has been shown to fit postseismic surface deformation following at least 9 earthquakes. I also show that the conventional, one‐dimensional, spring‐block model of a BFCZ with a rheology compatible with ordinary transient creep leads to the same temporal dependence (NMO(t)).

Postearthquake Relaxation and Aftershock Accumulation Linearly Related after the 2003 M 6.5 Chengkung, Taiwan, and the 2004 M 6.0 Parkfield, California, Earthquakes

We treat both the number of earthquakes and the deformation following a mainshock as the superposition of a steady background accumulation and the postearthquake process. The preseismic displacement and seismicity rates r u and r E are used as estimates of the background rates. Let t be the time after the mainshock, u ( t ) + u 0 the postseismic displacement less the background accumulation r u t , and Δ N ( t ) the observed cumulative number of postseismic earthquakes less the background accumulation r E t . For the first 160 days (duration limited by the occurrence of another nearby earthquake) following the Chengkung ( M 6.5, 10 December 2003, eastern Taiwan) and the first 560 days following the Parkfield ( M 6.0, 28 September 2004, central California) earthquakes u ( t ) + u 0 is a linear function of Δ N ( t ). The aftershock accumulation Δ N ( t ) for both earthquakes is described by the modified Omori Law d Δ N / dt ∝ (1 + t / τ ) − p with p = 0.96 and τ = 0.03 days. Although the Chengkung earthquake involved sinistral, reverse slip on a moderately dipping fault and the Parkfield earthquake right-lateral slip on a near-vertical fault, the earthquakes share an unusual feature: both occurred on faults exhibiting interseismic fault creep at the surface. The source of the observed postseismic deformation appears to be afterslip on the coseismic rupture. The linear relation between u ( t ) + u 0 and N ( t ) suggests that this afterslip also generates the aftershocks. The linear relation between u ( t ) + u 0 and Δ N ( t ) obtains after neither the 1999 M 7.1 Hector Mine (southern California) nor the 1999 M 7.6 Chi-Chi (central Taiwan) earthquakes, neither of which occurred on fault segments exhibiting fault creep.

Properties of the aftershocks sequences of the 2000 and 2002 earthquakes in Aksehir-Afyon graben, west-central Anatolia, Turkey

The b-value of the Gutenberg–Richter’s frequency–magnitude relation and the p-value of the modified Omori law, which describes the decay rate of aftershock activity, were investigated for more than 500 aftershocks in the Aksehir-Afyon graben (AAG) following the 15 December 2000 Sultandagi–Aksehir and the 3 February 2002 Cay–Eber and Cobanlar earthquakes. We used the Kandilli Observatory’s catalog, which contains records of aftershocks with magnitudes ≥2.5. For the Cobanlar earthquake, the estimated b-values for three aftershock sequences are in the range 0.34 ≤ b ≤ 2.85, with the exception of the one that occurred during the first hour (4.77), while the obtained p-values are in the range 0.44 ≤ p ≤ 1.77. The aftershocks of the Sultandagi earthquake have a high p-value, indicating fast decay of the aftershock activity. A regular increase of b can be observed, with b < 1.0 after 0.208 days for the Cay–Eber earthquake. A systematic and similar increase and decrease pattern exists for the b- and p-values of the Cobanlar earthquakes during the first 5 days.

Aftershock decay, productivity, and stress rates in Hawaii: Indicators of temperature and stress from magma sources

We examined dozens of aftershock sequences in Hawaii in terms of Gutenberg‐Richter and modified Omori law parameters. We studied p, the rate of aftershock decay; Ap, the aftershock productivity, defined as the observed divided by the expected number of aftershocks; and c, the time delay when aftershock rates begin to fall. We found that for earthquakes shallower than 20 km, p values &gt;1.2 are near active magma centers. We associate this high decay rate with higher temperatures and faster stress relaxation near magma reservoirs. Deep earthquakes near Kilauea's inferred magma transport path show a range of p values, suggesting the absence of a large, deep magma reservoir. Aftershock productivity is &gt;4.0 for flank earthquakes known to be triggered by intrusions but is normal (0.25 to 4.0) for isolated main shocks. We infer that continuing, post‐main shock stress from the intrusion adds to the main shock's stress step and causes higher Ap. High Ap in other zones suggests less obvious intrusions and pulsing magma pressure near Kilauea's feeding conduit. We calculate stress rates and stress rate changes from pre‐main shock and aftershock rates. Stress rate increased after many intrusions but decreased after large M7–8 earthquakes. Stress rates are highest in the seismically active volcano flanks and lowest in areas far from volcanic centers. We found sequences triggered by intrusions tend to have high Ap, high (&gt;0.10 day) c values, a stress rate increase, and sometimes a peak in aftershock rate hours after the main shock. We interpret these values as indicating continuing intrusive stress after the main shock.

Physics of the Omori law: Inferences from interevent time distributions and pore pressure diffusion modeling

Empirical laws and statistics of earthquakes are valuable as a basis for a better understanding of the earthquake cycle. In this paper we focus on the postseismic phase and the physics of aftershock sequences. Using interevent time distributions for a catalogue of Icelandic seismicity, we infer that the parameter C 2 in the Omori law, often considered to represent incomplete detection of aftershocks, is at least in part related to the physics of the earthquake process. We investigate the role of postseismic pore pressure diffusion after two Icelandic earthquakes on the rate of aftershocks and what we can infer about the physical meaning of C 2 from the diffusion process. Using the Mohr–Coulomb failure criterion we obtain a rate of triggered points in our diffusion model that agrees with the modified Omori law, with a value of C 2 that is consistent with data. Our pore pressure diffusion model suggests that C 2 is related to the process of reducing high pore pressure gradients existing across a fault zone at short times after a main shock.

Earthquake activity related to seismic cycles in a model for a heterogeneous strike-slip fault

We investigate the evolution of seismicity within large earthquake cycles in a model of a discrete strike-slip fault in elastic solid. The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of regions around the fault, static/kinetic friction and dislocation creep along the fault, and 3D elastic stress transfer. The fault consists of brittle parts which fail during earthquakes and undergo small creep deformation between events, and aseismic creep cells which are characterized by high ongoing creep motion. This mixture of brittle and creep cells is found to generate realistic aftershock sequences which follow the modified Omori law and scale with the mainshock size. Furthermore, we find that the distribution of interevent times of the simulated earthquakes is in good agreement with observations. The temporal occurrence, however, is magnitude-dependent; in particular, the small events are clustered in time, whereas the largest earthquakes occur quasiperiodically. Averaging the seismicity before several large earthquakes, we observe an increase of activity and a broadening scaling range of magnitudes when the time of the next mainshock is approached. These results are characteristics of a critical point behavior. The presence of critical point dynamics is further supported by the evolution of the stress field in the model, which is compatible with the observation of accelerating moment release in natural fault systems.

Analysis of aftershocks in a lithospheric model with seismogenic zone governed by damage rheology

We perform analytical and numerical studies of aftershock sequences following abrupt steps of strain in a rheologically layered model of the lithosphere. The model consists of a weak sedimentary layer, over a seismogenic zone governed by a viscoelastic damage rheology, underlain by a viscoelastic upper mantle. The damage rheology accounts for fundamental irreversible aspects of brittle rock deformation and is constrained by laboratory data of fracture and friction experiments. A 1-D version of the viscoelastic damage rheology leads to an exponential analytical solution for aftershock rates. The corresponding solution for a 3-D volume is expected to be sum of exponentials. The exponential solution depends primarily on a material parameter R given by the ratio of timescale for damage increase to timescale for accumulation of gradual inelastic deformation, and to a lesser extent on the initial damage and a threshold strain state for material degradation. The parameter R is also inversely proportional to the degree of seismic coupling across the fault. Simplifying the governing equations leads to a solution following the modified Omori power-law decay with an analytical exponent p= 1. In addition, the results associated with the general exponential expression can be fitted for various values of R with the modified Omori law. The same holds for the decay rates of aftershocks simulated numerically using the 3-D layered lithospheric model. The results indicate that low R values (e.g. R≤ 1) corresponding to cold brittle material produce long Omori-type aftershock sequences with high event productivity, while high R values (e.g. R≥ 5) corresponding to hot viscous material produce short diffuse response with low event productivity. The frequency-size statistics of aftershocks simulated in 3-D cases with low R values follow the Gutenberg–Richter power law relation, while events simulated for high R values are concentrated in a narrow magnitude range. Increasing thickness of the weak sedimentary cover produces results that are similar to those associated with higher R values. Increasing the assumed geothermal gradient reduces the depth extent of the simulated earthquakes. The magnitude of the largest simulated aftershocks is compatible with the Båth law for a range of values of a dynamic damage-weakening parameter. The results provide a physical basis for interpreting the main observed features of aftershock sequences in terms of basic structural and material properties.

Long-term seismicity of the Reykjanes Ridge (North Atlantic) recorded by a regional hydrophone array

The seismicity of the northern Mid-Atlantic Ridge was recorded by two hydrophone networks moored in the sound fixing and ranging (SOFAR) channel, on the flanks of the Mid-Atlantic Ridge, north and south of the Azores. During its period of operation (05/2002–09/2003), the northern ‘SIRENA’ network, deployed between latitudes 40° 20′N and 50° 30′N, recorded acoustic signals generated by 809 earthquakes on the hotspot-influenced Reykjanes Ridge. This activity was distributed between five spatio-temporal event clusters, each initiated by a moderate-to-large magnitude (4.0–5.6 M) earthquake. The rate of earthquake occurrence within the initial portion of the largest sequence (which began on 2002 October 6) is described adequately by a modified Omori law aftershock model. Although this is consistent with triggering by tectonic processes, none of the Reykjanes Ridge sequences are dominated by a single large-magnitude earthquake, and they appear to be of relatively short duration (0.35–4.5 d) when compared to previously described mid-ocean ridge aftershock sequences. The occurrence of several near-equal magnitude events distributed throughout each sequence is inconsistent with the simple relaxation of mainshock-induced stresses and may reflect the involvement of magmatic or fluid processes along this deep (>2000 m) section of the Reykjanes Ridge.

Aftershocks resulting from creeping sections in a heterogeneous fault

We show that realistic aftershock sequences with space‐time characteristics compatible with observations are generated by a model consisting of brittle fault segments separated by creeping zones. The dynamics of the brittle regions is governed by static/kinetic friction, 3D elastic stress transfer and small creep deformation. The creeping parts are characterized by high ongoing creep velocities. These regions store stress during earthquake failures and then release it in the interseismic periods. The resulting postseismic deformation leads to aftershock sequences following the modified Omori law. The ratio of creep coefficients in the brittle and creeping sections determines the duration of the postseismic transients and the exponent p of the modified Omori law.

Remotely Triggered Seismicity in the Yellowstone National Park Region by the 2002 Mw 7.9 Denali Fault Earthquake, Alaska

Coincident with the arrival of low-frequency, large-amplitude surface waves of the Mw 7.9 Denali fault earthquake (DFE), an abrupt increase in seismicity was observed in the Yellowstone National Park region, despite the large epicentral distance of 3100 km. Within the first 24 hr following the DFE mainshock, we located more than 250 earthquakes, which occurred throughout the entire Yellowstone Na- tional Park region. The elevated seismicity rate continued for about 30 days and followed a modified Omori law decay with a P value of 1.02 ! 0.07. For a declus- tered earthquake catalog, the seismicity following the 2002 DFE uniquely stands out with a significance of 30r. The increase in seismicity occurred over all magnitude bands. In general, we observed that seismicity following the DFE outlined the spatial pattern of past seismicity routinely observed in the Yellowstone National Parkregion. However, we found significant differences in triggered seismicity inside and outside the caldera. Earthquakes inside the Yellowstone caldera occurred preferentially as clusters close to major hydrothermal systems, were of larger magnitude, and seis- micity decayed more rapidly. This suggests that either different trigger mechanisms were operating inside and outside the caldera or that the crust responded differently to the same trigger mechanism depending on its different mechanicalstate.Compared with other sites that experienced remote earthquake triggering following the 2002 DFE, Yellowstone showed the most vigorous earthquake activity. We attribute this to strong directivity effects of the DFE, which caused relatively large peak dynamic stresses (0.16-0.22 MPa) in Yellowstone, and to the volcanic nature of Yellowstone.

Spatial and temporal variations of the aftershock sequences of the 1999 İzmit and Düzce earthquakes

In this study the properties of the aftershock sequences in the first five months after the 17 August 1999 Izmit and 12 November 1999 Duzce earthquakes are investigated. For this purpose, the b-value of frequency-magnitude distribution of earthquakes and temporal decay rate of aftershocks as described by the p-value in the modified Omori law are calculated. The data taken from the website of the KOERI consist of 1841 events for the Izmit and 913 events for the Duzce activity, respectively. The b-value for the Izmit sequence is found as 1.10±0.03 with Mc = 2.6 and b = 1.16 ± 0.05 for the Duzce sequence with Mc = 2.8. Both b-values are close to 1 and typical for aftershock sequences. The p-values are calculated as 0.86 ± 0.05 for the Izmit and p = 1.34 ± 0.09 for Duzce aftershocks, respectively. Small p-value found in Izmit sequence may be a result of the background seismicity of the aftershock region. Because of the lower p-value for the Izmit activity than that of the Duzce sequence, the aftershocks show a relatively slow decay rate in the Izmit earthquake. Considerable spatial variability is found, b-values ranging from 0.8 to 1.6, and p-values ranging from 0.4 to 1.4. The spatial variations of b and p-values of an aftershock sequence may associate with the rupture mechanism and geological structure of an earthquake area. A good agreement between the slip and b-value for the Duzce sequence are found whereas we could not observe a linear relation between these parameters for the Izmit sequence. After the Izmit earthquake, the larger b-values correlate with the regions where the lower stress changes occurred whereas the lower b-values are in the areas with the larger stress variations. Also, the lower and higher b-values are related to the higher and lower P-wave velocity in general. Regarding the geological aspect, the larger b and p-values for the two sequences are related to Holocene alluvium structures which have low velocity. On the other hand, after the both earthquakes, the larger p-values correlate well with the regions on which the maximum slip is located and the lower p-values are related to the lower slip regions. However, the material properties seem more effective than the stress changes and slip distributions in the b-value variations and the slip distribution is the most significant factor on p-values in the both sequences.

The 1997 Kagoshima (Japan) earthquake doublet: A quantitative analysis of aftershock rate changes

We quantitatively map relative rate changes for the aftershock sequence following the second mainshock of the 1997 earthquake doublet (MW = 6.1, MW = 6.0) in the Kagoshima province (Japan). Using the spatial distribution of the modified Omori law parameters for aftershocks that occurred during the 47.8 days between the two mainshocks, we forecast the aftershock activity in the next 50 days and compare it to the actually observed rates. The relative rate change map reveals four regions with statistically significant relative rate changes ‐ three negative and one positive. “Our analysis suggests that the coseismic rate changes for off‐fault aftershocks could be explained by changes in static stress. However, to explain the activation and deactivation of on‐fault seismicity, other mechanism such as unusual crustal properties and the presence of abundant crustal fluids are required.”

Refining earthquake clustering models

Assuming that earthquakes are the realization of a stochastic point process and that the magnitude distribution of all earthquakes is described by the Gutenberg‐Richter law with a constant b value, we model the occurrence rate density of earthquakes in space and time by means of an epidemic model. The occurrence rate density is computed by the sum of two terms, one representing the independent, or spontaneous activity, and the other representing the activity induced by previous earthquakes. While the first term depends only on space, the second one is factored into three terms that include the magnitude, time, and location, respectively, of the past earthquakes. In this paper we use the modified Omori law for the time term, focusing our investigation on the magnitude and space terms. We formulate two different hypotheses for each of them, and we find the respective maximum likelihood parameters on the basis of the catalog of instrumental seismicity recorded in Italy from 1987 to 2000. The comparison of the respective likelihood computed for the seismicity recorded in 2001 provides a way for choosing the best model. The confidence level of our choice is then assessed by means of a Monte Carlo simulation on the various hypotheses. Our study shows that an inverse power density function is more reliable than a normal density function for the space distribution and that the hypothesis of scale invariance of aftershock productivity with respect to magnitude can be rejected with high confidence level. The final model is suitable for computing earthquake occurrence probability in real circumstances.

How do asperities fracture? An experimental study of unbroken asperities

The fracture of a shear fault containing several unbroken asperities in a granitic porphyry is examined in detail via acoustic emission (AE) data collected by a high-speed multi-channel waveform recording system. The experimental results reveal that a quasi-static nucleation of the shear faulting corresponds to the fracture of coupled asperities on the fault plan. AEs caused by the fracture of individual asperities exhibit similar characteristics to the sequence for natural earthquakes, including foreshock, mainshock, and aftershock events. Foreshocks, initiated at the edge of the asperity, occur with an event rate that increases according to a power law of the temporal distance to the mainshock, and with a decreasing b-value (from ∼1.1 to ∼0.5). One or a few mainshocks then initiate at the edge of the asperity or the front of the foreshocks. The aftershock period is characterized by a remarkable increase and subsequent gradual decrease in b-value and a decreasing event rate obeying the modified Omori law, which has been well established for earthquakes. The fracture of neighboring asperities is then initiated after the mainshock of a particular asperity, presumably due to redistribution of the strain energy accumulated within an asperity, which is released by the mainshock, resulting in enhancement of the stress concentration around the nearest neighboring intact asperities. The progressive fracturing of multiple, coupled asperities during the nucleation of shear faulting results in short-term precursory fluctuations in both b-value and event rate, which may prove useful information in the prediction of failure of the main fault plane of seismic earthquakes.

A Stochastic Two-node Stress Transfer Model Reproducing Omori's Law

— We present an alternative to the epidemic type aftershock sequence (ETAS) model of Ogata (1988). The continuous time two-node network stress release/transfer Markov model is able to reproduce the (modified) Omori law for aftershock frequencies. One node (denoted by A) is loaded by external tectonic forces at a constant rate, with `events' (main shocks) occurring at random instances with risk given by a function of the `stress level' at the node. Each event is a random (negative) jump of the stress level, and adds (or removes) a random amount of stress to the second node (B), which experiences `events' in a similar way, but with another risk function (of the stress level at that node only). When that risk function satisfies certain simple conditions (it may, in particular, be exponential), the frequency of jumps (aftershocks) at node B, in the absence of any new events at node A, follows Omori's law \((\prpto (c + t)^{-1})\) for aftershock squenc es. When node B is allowed tectonic input, which may be negative, i.e., aseismic slip, the frequency of events takes on a decay form that parallels the constitutive law derived by Dieterich (1994), which fits very well to the modified Omori law. We illustrate the model by fitting it to aftershock data from California post-1973, and from the Valparaiso earthquake of March 3 1985.

Emergence of a band‐limited power law in the aftershock decay rate of a slider‐block model

In order to elucidate how structural heterogeneities affect the aftershock decay rate, we examine the aftershock sequences produced by a slider‐block model of seismicity. In this model, the geometry of the seismic zone is the only free parameter and all aspects of the system are known. The power law aftershock decay rate holds only for smooth faults. A band‐limited power law emerges at intermediate fault complexity. For rough faults, only a transient regime toward an exponential decay is observed. In all fault geometries examined, a band‐limited power law model fits the synthetic aftershock decay rate better than the Modified Omori Law. Then, as the connected seismic elements form a simpler localised surface, we show that the power law aftershock decay rate extends over longer time, and that the power law exponent increases. These results support the inference that the correlation time of the power law aftershock decay rate increases as the deformation localises along dominant major faults.

The August–December 2000 earthquake swarm in NW Bohemia: the first results based on automatic processing of seismograms

Main features of the August–December 2000 earthquake swarm which occurred in the major focal area of the North-West Bohemia / Vogtland swarm region are presented. Seismograms from four stations of WEBNET were automatically processed to get arrival times, first motion amplitudes and hypocentre coordinates of a representative set of events. Altogether 7017 microearthquakes in the magnitude range of M L=0–3.3 were identified. It is shown the decay of activity of individual swarm phases followed the modified Omori law, which points to a partial similarity with aftershock sequences of tectonic earthquakes. The space-time distribution of a subset of 2913 events with low location residuals shows a strong space clustering of the earthquake hypocentres and their pronounced migration between individual swarm phases. Most of the activity took place along an elliptical, nearly vertically dipping, 6 km long N-S oriented fault plane in depths ranging from 10.5 to 6.5 km. The P and T axes were estimated by FOCMEC for the 782 strong events and three groups of earthquakes with similar faulting type were distinguished. In contrast to the normal and strike-slip faulting events that created the prevailing portion of the swarm and were distributed uniformly within the focal area, the reverse events were clustered in time and space.

Temporal limits of the power law aftershock decay rate

We compare the aftershock decay rate in natural data with predictions from a stochastic analytical model based on a Markov process with stationary transition rates. These transition rates vary according to the magnitude of a scalar representing the state of stress and defined as the overload. Thus, the aftershock decay rate in the model is a sum of independent exponential decay functions with different characteristic times. From different shapes of the overload distribution and different expressions of the transition rates, we discuss the magnitude of the exponent of the power law aftershock decay rate and the time interval over which we can expect to observe this regime. Before and after this time interval, we show that the decay is linear and exponential, respectively. From our analytical solutions, we deduce a model of aftershock decay rate in which a power law scaling exponent and two characteristic rates emerge. One rate is a short‐term linear decrease before the onset of the power law decay to account for a finite number of events at zero time, and the other one can be interpreted as an inverse correlation time, after which aftershocks no longer occur. Then, we interpret the empirical modified Omori law (MOL) and its parameters in the framework of our theoretical model. We suggest a technique to systematically estimate and interpret the temporal limits of the power law aftershock decay rate in real sequences. We approximate these temporal limits from data available from several well‐known aftershock sequences and show from an Akaike Information Criteria (AIC) that, in almost all cases examined here, our model fits better the aftershock decay rate than the MOL despite a quantitative penalty for the extra parameter required. From this work, we conclude that the time delay before the onset of the power law decay may be related to the recurrence time of an earthquake. Finally, we suggest that the power law decay rates extend over longer times according to the concentration of the deformation along dominant major faults.