Secondary Aftershocks Research Articles

State of stress in the northern Tabas block, east-central Iran, as inferred from focal mechanisms of the 1978 Tabas earthquake sequence

Abstract In this paper, the state of stress in the northern Tabas block in east-central Iran is analyzed based on the systematic inversion of aftershock focal mechanisms from the 1978.09.16 Tabas earthquake, to characterise the stress regime that controls most earthquakes in this area. Here, stress inversions of double-couple focal mechanisms of earthquakes recorded during the 30 days following the main shock have been carried out. The calculated average stress regime indicates dominant major 226° to 237° trending compression for the Tabas region. The dominating regime in east-central Iran is thrusting with a minimum stress axis, σ 3, close to vertical. The reconstruction of the main seismotectonic stress in east-central Iran with a NE-SW compression is consistent with independent information of the active plate convergence related to Arabia-Eurasia convergence. Most earthquakes in the mentioned area occur near or around concealed Quaternary thrust faults with their activity being controlled by the NE-SW compression. Where ϕ, the ratio of principal stress differences, is 0.5, a small difference between σ 2; σ 3 and σ 1 and small amounts of deviatoric stress is indicated. Therefore, for small deviatoric horizontal σ 1 it is not possible to increase and reactivate small sections of basement thrust faults and create secondary basement aftershocks. Reconstructed stress regimes in this study for sedimentary cover (237) and basement (226) of Tabas are similar. Therefore, it seems that the basement and cover were coupled together, possibly along the 2–4 km of upper Precambrian low-grade metamorphic rocks. Then these segments of the fold-and-thrust belt were involved in similar seismic activity under a similar stress regime.

Markov-modulated Hawkes process with stepwise decay

This paper proposes a new model—the Markov-modulated Hawkes process with stepwise decay (MMHPSD)—to investigate the variation in seismicity rate during a series of earthquake sequences including multiple main shocks. The MMHPSD is a self-exciting process which switches among different states, in each of which the process has distinguishable background seismicity and decay rates. Parameter estimation is developed via the expectation maximization algorithm. The model is applied to data from the Landers–Hector Mine earthquake sequence, demonstrating that it is useful for modelling changes in the temporal patterns of seismicity. The states in the model can capture the behavior of main shocks, large aftershocks, secondary aftershocks, and a period of quiescence with different background rates and decay rates.

Investigations on the aftershock sequence of the great Assam earthquake of August 15, 1950

The strain release curve of the aftershock sequence of the great Assam earthquake of August 15, 1950 exhibits three linear segments. A secondary aftershock sequence has also been reported; the strain release curve in this case is also linear. The b value, using the maximum likelihood method of Utsu, for the sequence is 0.52 ± 0.095. The fault plane solution shows that the fault strikes almost cast-west and dips northward at an angle of 80°; the motion is predominently strike slip (right lateral type). The spatial distribution of aftershocks shows two main centers of activity at the two ends of the probable fault.

Recent earthquake activity in Trichonis region and its tectonic significance

SUMMARY. - The aftershock activity associated with the central Greece (Trichonis Lake) earthquake of |une-Dec. 1975, has been studied, with emphasis on the time and magnitude distribution. It has been found that the value of b, in Gutenberg - R i c h t e r ' s relationship was near the same for the primary as well as the secondary or second order aftershocks of the sequences, but depends upon the focal depth. A correlation between the calculated focal mechanisms and the associated stress components to the distribution pattern of meizoseismic effects as well as to the geological structure of the seismic region was found. The seismic region lies at the top of an anticline which was found moving downwards, apparently due to compressional stresses. Within the series of three earthquakes the progress of the destruction of the buildings was observed and reported. The interest is concentrated to modern buildings out of reinforced concrete and infill brick walls. The relatively unexpected rather bad performance of the later case of buildings was compared to that of the traditional small houses out of brick or stone masonry, the behaviour of which may be considered as better from what it was expected.

The earthquakes on 12 April 1998 and 12 July 2004 in Krn Mountains (NW Slovenia) – time distribution of aftershocks and magnitude-frequency relation

Earthquakes on 12 April 1998 (ML=5.6) and 12. July 2004 (ML =4.9) in Krn Mountains were followed by extensive aftershock sequences with several thousand of shocks which lasted for more than one year. In 400 days the first earthquake was followed by 104 and the second one by 89 aftershocks with ML≥2,0. Both strongest aftershocks had magnitudes smaller for 1.4 and 1.3 with respect to the mainshocks, which is slightly more than published values (1.2). Analysis of time distribution of aftershocks with maximum likelihood estimate has shown that the parameters of modified Omori's law, which describes the hyperbolic decay of aftershock activity with time, are very similar. This corresponds to the fact that both earthquakes occurred in the same hypocentral area. The value of p parameter is around 1.02. Aftershocks in 1998 clearly show secondary aftershock sequence which started with strongest aftershock on 6 May 1998 (ML=4.2), but there was no secondary sequence in 2004. Analysis of magnitude- frequency (Gutenberg-Richter's) relation with least squares and maximum likelihood estimate has given the value of b parameter for 1998 aftershock sequence between 0.77 and 0.83 and for 2004 sequence between 0.97 and 0.98. This means that the first earthquake was followed by more stronger aftershocks. Obtained parameters of modified Omori's law and Gutenberg-Richter's relation are in good agreement with values published for similar aftershock sequences.

Fluid‐induced rupture experiment on Fontainebleau sandstone: Premonitory activity, rupture propagation, and aftershocks

A 14% porosity Fontainebleau sandstone sample (diameter = 40 mm, length = 88 mm) was loaded tri‐axially, under 100 MPa confining pressure and 240 MPa differential stress. In drained conditions and under constant load, pore pressure (water) was raised until failure was triggered. During the experiment, elastic wave velocities and permeability were monitored while more than 3000 Acoustic Emissions (AE) were located prior and after failure. AE locations show that macroscopic fracture propagated from a large nucleation patch at speeds comprised between 0.1 and 4 m/s. Number of AE hits per second followed Omori's law, with exponents of 0.92 and 1.18 pre‐ and post‐failure respectively. No quiescence was observed post failure, except where rupture initially nucleated from. Fast depressurization of the pore space induced secondary aftershocks located within the fracture plane, possibly indicating a heterogeneous fault geometry after rupture, of lower permeability, that compacted during the release of pore pressure.

Analysis of relaxation temporal patterns in Greece through the RETAS model approach

The temporal decay of eight aftershock sequences in the area of Greece after 1975 was examined with main shocks magnitudes of M w ≥ 6.6. The analysis was done through the restricted epidemic type aftershock sequence (RETAS) stochastic model, which enables the possibility to recognize the prevailing clustering pattern of the relaxation process in the examined areas. In four of the cases the analysis selected the epidemic type aftershock sequence (ETAS) model to offer the most appropriate depiction of the aftershock temporal distribution which presumes that all shocks to the smallest ones in the sample can cause secondary aftershocks, while for the rest of the sequences triggering potential seems to have aftershocks above a certain magnitude threshold (RETAS model) and they are expected to induce secondary activity. The models, developed on aftershock data, were also applied to forecast real seismicity after the conclusion of the aftershock sequences. For four out of eight cases, we obtained promising estimations of ensuing seismicity after the end of the sequences with models based only on aftershock data. Some features of the RETAS model simulation were also studied, like simulating magnitudes, revealing that it is reasonable to consider in the model the temporal behavior of the aftershocks’ magnitudes as well. Stochastic modeling was also applied to estimate the duration of the relaxation process, assuming that the end of each sequence is marked by the divergence of real seismicity from the modified Omori formula (MOF) model, the latter known to represent pure aftershock activity. The obtained results give an indication that possibly low stressing rate results in longer duration of the relaxation process in a region.

BASS, an alternative to ETAS

The epidemic type aftershock sequence (ETAS) model has been widely used to model the statistics of seismicity. An essential feature of the ETAS model is the concept of generations of aftershocks. A mainshock has primary aftershocks, the primary aftershocks have secondary aftershocks, and so forth. In this paper, we introduce the branching aftershock sequence (BASS) model as an alternative to ETAS. The BASS model is fully self‐similar whereas the ETAS model is not. Furthermore, the ETAS model requires the specification of branching (parent‐daughter) ratios, while the BASS model instead utilizes Båth's law. We also show that the branching statistics in the BASS model are identical to the self‐similar Tokunaga statistics of drainage networks.

Introduction to the special section for the 2005 West Off Fukuoka Prefecture Earthquake

On 20 March 2005, the 2005 West Off Fukuoka Prefecture earthquake with Japan Meteorological Agency magnitude (MJMA) of 7.0 occurred in the offshore region of Fukuoka Prefecture, in northern Kyushu, Japan. This earthquake caused more than 1,000 casualties and damaged many buildings in the surrounding area, especially on Genkai Island as well as in and around Fukuoka City. Because the 2005 West Off Fukuoka Prefecture earthquake was one of the largest intraplate earthquakes in recorder history occurring ages at the junction of the Southwestern Japan Arc and the Ryukyu Arc, intensive seismological and geodetic studies were carried out in its aftermath. Ten papers from these studies were published as the special section for the 2005 West Off Fukuoka Prefecture earthquake (1) of Earth, Planets and Space, Vol. 58, No.1, 2006. In addition, eight papers are published in the special section (2) of this issue. These studies have revealed important characteristics of the earthquake as summarized in the following paragraphs. The mainshock and aftershocks were mainly aligned NW-SE in an approximately 25 km long trend, and the hypocenters of the aftershock region were distributed on a nearly vertical plane at depths of 2–16 km. The mainshock was located near the central part of the aftershock region, with a depth of 9.5 km. These findings suggest that the strike and dip of the fault plane of the earthquake are approximately N60◦W and 90◦, respectively, and the length and width of the fault are about 25 km and 14 km, respectively. The largest aftershock of MJMA 5.8 occurred near the SE edge of the main aftershock region, and the aftershock region extended about 5 km in the SE direction based on the secondary aftershock activity, which had a different strike angle from that of most of the aftershocks. Following the most intense aftershock activity, there was no distinct enlargement of the aftershock region, and the aftershock activity gradually declined (Shimizu et al., 2006). The fault structure has been discussed in detail on the basis of precise analyses of aftershock distribution based on onshore and offshore seismic observations made with densely located ocean bottom seismometers (Uehira et al., 2006). The fault plane is bent near both the NW and SE

Aftershock seismicity and fault structure of the 2005 West Off Fukuoka Prefecture Earthquake (MJMA7.0) derived from urgent joint observations

Abstract On March 20, 2005, a large M JMA7.0 earthquake occurred in the offshore area, west of Fukuoka prefecture, northern Kyushu, Japan. A series of joint observations were carried out by teams from several universities in Japan with the aim of investigating the aftershock activity. Six online telemetered and 17 offline recording seismic stations were installed on land around the aftershock area immediately followed the occurrence of the mainshock. Because aftershocks were located mainly in offshore regions, we also installed 11 ocean bottom seismometers (OBSs) just above the aftershock region and its vicinity in order to obtain accurate locations of hypocenters. The OBS observation was carried out from March 27 to April 13, 2005. We further conducted temporary GPS observations in which ten GPS receivers were deployed around the aftershock region. The aftershocks were mainly aligned along an approximately 25-km-long NW-SE trend, and the hypocenters of the main aftershock region were distributed on a nearly vertical plane at depths of 2–16 km. The mainshock was located near the central part of the main aftershock region at a depth of approximately 10 km. The largest aftershock of M JMA5.8 occurred near the southeastern edge of the main aftershock region, and the aftershock region subsequently extended about 5 km in the SE direction as defined by secondary aftershock activity. Enlargement of the aftershock region did not occur after the peak in aftershock activity, and the aftershock activity gradually declined. The distribution of hypocenters and seismogenic stress as defined by aftershocks suggest that the 2005 West Off Fukuoka Prefecture Earthquake occurred on the fault that is the NW extension of the Kego fault, which extends NW-SE through the Fukuoka metropolitan area, and that the largest aftershock occurred at the northwestern tip of the Kego fault.

Bibliographic and Intellectual Control: why it matters

When the Cellulose Acetate Microfilm forum was set up just over two years ago one of its first activities was to carry out in-depth surveys of the condition of microfilm in the collections of the libraries involved. To a greater or lesser degree the libraries found evidence of deterioration in their stocks of acetate film. Many libraries, especially those which had collections dating from more recent decades, had no significant problems with the condition of the microfilm stock in their care. But for almost all of the libraries there was a secondary aftershock, as it were, after the first earthquake. This shock came to those who are responsible for listing and cataloguing the materials, and showed up considerable gaps in the recording of details of the surrogate microfilms in the library collections. In this paper I will describe the extent of the problem, suggest the causes and possible solutions, and conclude with a look towards some strategic possibilities for coping in the future.

Secondary Aftershocks and Their Importance for Aftershock Forecasting

The potential locations of aftershocks, which can be large and damaging, are often forecast by calculating where the mainshock increased stress. We find, however, that the mainshock-induced stress field is often rapidly altered by aftershock-induced stresses. We find that the percentage of aftershocks that are secondary aftershocks, or aftershocks triggered by previous aftershocks, increases with time after the mainshock. If we only consider aftershock sequences in which all aftershocks are smaller than the mainshock, the percentage of aftershocks that are secondary also increases with mainshock magnitude. Using the California earthquake catalog and Monte Carlo trials we estimate that on average more than 50% of aftershocks produced 8 or more days after M ≥5 mainshocks, and more than 50% of all aftershocks produced by M ≥7 mainshocks that have aftershock sequences lasting at least 15 days, are triggered by previous aftershocks. These results suggest that previous aftershock times and locations may be important predictors for new aftershocks. We find that for four large aftershock sequences in California, an updated forecast method using previous aftershock data (and neglecting mainshock-induced stress changes) can outperform forecasts made by calculating the static Coulomb stress change induced solely by the mainshock. Manuscript received 20 November 2002.

Failure-Time Remapping in Compound Aftershock Sequences

Compound aftershock sequences are of special interest because the decay of secondary aftershocks contains information about the mechanisms that generate all earthquakes. If earthquakes nucleate as a result of accelerating slip, growing cracks, or any similar failure process, then the rate of decay of aftershock sequences is a direct result of that failure process, as influenced by local material properties. The aftershocks are then triggered by the mainshock, moved closer to failure, and concentrated on the curved part of loading curve, occurring earlier than they would have if the mainshock had not occurred. Secondary aftershocks, which are themselves triggered by an aftershock, are promoted toward failure twice and consequently should decay differently than primary aftershocks do. The theory behind this concept is developed, explored with numerical models, and tested with a study of the aftershocks of the Hector Mine earthquake of 1999. Because the Hector Mine mainshock occurred during the aftershock sequence of the Landers 1992 earthquake, failure-time remapping predicts a slightly different temporal distribution for the Hector Mine aftershocks than they would have had without the influence of the Landers mainshock. This prediction is testable. In this work, three different types of aftershock decay relations are applied to 94 spatial subsets of aftershocks and evaluated with two different statistical measures. Remapped aftershock decay models were superior for almost all the cases studied, regardless of the type of aftershock decay model used or the statistical measure. These results confirm previous work suggesting that the majority of aftershocks are not caused by their mainshock, only promoted toward failure, and most earthquakes nucleate through a failure process such as velocity-dependent friction or stress corrosion cracking. Manuscript received 15 July 2002.

When and where the aftershock activity was depressed: Contrasting decay patterns of the proximate large earthquakes in southern California

Seismic quiescence has attracted attention as a possible precursor to a large earthquake. However, sensitive detection of quiescence requires accurate modeling of normal aftershock activity. We apply the epidemic‐type aftershock sequence (ETAS) model that is a natural extension of the modified Omori formula for aftershock decay, allowing further clusters (secondary aftershocks) within an aftershock sequence. The Hector Mine aftershock activity has been normal, relative to the decay predicted by the ETAS model during the 14 months of available data. In contrast, although the aftershock sequence of the 1992 Landers earthquake (M = 7.3), including the 1992 Big Bear earthquake (M = 6.4) and its aftershocks, fits very well to the ETAS up until about 6 months after the main shock, the activity showed clear lowering relative to the modeled rate (relative quiescence) and lasted nearly 7 years, leading up to the Hector Mine earthquake (M = 7.1) in 1999. Specifically, the relative quiescence occurred only in the shallow aftershock activity, down to depths of 5–6 km. The sequence of deeper events showed clear, normal aftershock activity well fitted to the ETAS throughout the whole period. We argue several physical explanations for these results. Among them, we strongly suspect aseismic slips within the Hector Mine rupture source that could inhibit the crustal relaxation process within “shadow zones” of the Coulomb's failure stress change. Furthermore, the aftershock activity of the 1992 Joshua Tree earthquake (M = 6.1) sharply lowered in the same day of the main shock, which can be explained by a similar scenario.

Regularity and complexity of aftershock occurrence due to mechanical interactions between fault slip and fluid flow

SUMMARY A sequence of aftershocks is modelled assuming fluid migration in a narrow, porous fault zone formed along a vertical strike-slip fault in a semi-infinite elastic medium. The principle of the effective stress coupled to the Coulomb failure criterion introduces mechanical coupling between fault slip and pore fluid. The fluid is assumed to flow out of localized high-pressure fluid compartments in the fault zone at the instant of the main shock occurrence. We successfully simulate both regularity and complexity observed for aftershocks in a unified way. For example, we can simulate both the Omori law and the Gutenberg‐Richter relation, which are the most outstanding regularity observed seismologically. A large majority of simulated aftershocks are shown to consist of repeated slips, that is, slips on fault segments that have experienced slips earlier in the aftershock sequence. Our calculations show that the emergence of the Gutenberg‐ Richter relation is closely related to the occurrence of these repeated slips. Complexity is also a striking feature of aftershocks. One of the examples is the occurrence of secondary aftershocks, which can also be simulated successfully if we assume several high-pressure fluid compartments formed in a fault zone or a significant change in the permeability caused by the rupture occurrence.

Triggering of the 1999 MW 7.1 Hector Mine earthquake by aftershocks of the 1992 MW 7.3 Landers earthquake

There is strong observational evidence that the 1999 MW 7.1 Hector Mine earthquake in the Mojave Desert, California, was triggered by the nearby 1992 MW 7.3 Landers earthquake. Many authors have proposed that the Landers earthquake directly stressed the Hector Mine fault. Our model of the Landers aftershock sequence, however, suggests there is an 85% chance that the Hector Mine hypocenter was actually triggered by a chain of smaller earthquakes that was initiated by the Landers main shock. We perform our model simulations using the Monte Carlo method based on the Gutenberg‐Richter relationship, Omori's law, Båth's law, and assumptions that all earthquakes, including aftershocks, are capable of producing aftershocks and that aftershocks produce their own aftershocks at the same rate that other earthquakes do. In general, our simulations show that if it has been more than several days since an M ≥ 7 main shock, most new aftershocks will be the result of secondary triggering. These secondary aftershocks are not physically constrained to occur where the original main shock increased stress. This may explain the significant fraction of aftershocks that have been found to occur in main shock stress shadows in static Coulomb stress triggering studies.

Temporal characteristics of some aftershock sequences in Bulgaria

We apply statistical analysis to study the temporal distribution of aftershocks in aftershock sequences of five earthquakes which occurred in Bulgaria. We use the maximum likelihood method to estimate the parameters of the modified Omori formula for aftershock sequences which is directly based on a time series. We find that: the maximum likelihood estimates of the parameter p show a regional variation, with lower values of the decay rate in North Bulgaria; the modified Omori formula provides an appropriate representation of temporal variation of the aftershock activity in North Bulgaria; the aftershock sequences in South Bulgaria are best modeled by the combination of an ordinary aftershock sequence with secondary aftershock activity. A plot of the cumulative number of events versus the frequency-linearized time t clearly demonstrates a transition from aftershock to foreshock activity prior to the second 1986 Strazhitsa (North Bulgaria) earthquake.

Temporal characteristics of some earthquake sequences in Greece

Temporal features of the aftershock activities following some moderate shallow earthquakes in Greece have been studied by making use of the modified Omori formula and Akaike's Information Criterion (AIC). Although the main shocks occurred in different seismogenic regions in Greece, the aftershock activities show almost the same anomalous pattern. In most cases, the secondary aftershocks of the aftershock activity of the main event are preceded by seismic quiescence. Also, in some cases, the aftershock activity recovers to a normal level or increases beyond it prior to the occurrence of the large aftershock. The observed temporal pattern may be useful in predicting a large aftershock which might be as large and destructive as the main shock, if the aftershock activity is monitored immediately after the occurrence of the main shock.

Transition from aftershock to normal activity: The 1965 Rat Islands earthquake aftershock sequence

A transition from aftershock to normal activity is identified 2200 days after the occurrence of the 1965 Rat Islands earthquake of Mw = 8.7. After this time, we observe a significant departure of the seismicity in the focal region from the extrapolated trend of the aftershock activity predicted by the modified Omori formula proposed by Utsu in 1961. The maximum likelihood estimate of the parameters for the formula and the selection of a statistical model based on the Akaike Information Criterion show that the whole aftershock sequence is best modeled by the combination of an ordinary aftershock sequence and secondary aftershock activity associated with the largest aftershock. Fitting of the activity after the transition period to the modified Omori formula results in an unusually low value of the decay constant. We interpret that this activity represents normal or background seismicity and not another secondary aftershock sequence. Defining background activity in a focal region of a large earthquake is essential for detection of seismic quiescence prior to the next major event.

Estimation of the parameters in the modified omori formula for aftershock frequencies by the maximum likelihood procedure.

This paper proposes the maximum likelihood method to estimate the parameters of the modified Omori formula for aftershock sequences directly based on a time series of aftershocks. The likelihood function is derived by assuming that the aftershocks are distributed according to a certain non-stationary Poisson process. This method incidentally provides the asymptotic error distribution of the estimates. Statistical comparison of the characteristic parameters between two aftershock sequences, parameter estimation in case of the existence of the secondary aftershocks and other related problems are also discussed. As illustrative examples of calculations, some aftershock data are analyzed.