Modified Omori Law Research Articles

Transient postseismic slip and aftershock triggering: A case study of the 2008 MW7.9 Wenchuan Earthquake, China

In this study, we investigate how a stress variation generated by a fault that experiences transient postseismic slip (TPS) affects the rate of aftershocks. First, we show that the postseismic slip from Rubin-Ampuero model is a TPS that can occur on the main fault with a velocity-weakening frictional motion, that the resultant slip function is similar to the generalized Jeffreys-Lomnitz creep law, and that the TPS can be explained by a continuous creep process undergoing reloading. Second, we obtain an approximate solution based on the Helmstetter-Shaw seismicity model relating the rate of aftershocks to such TPS. For the Wenchuan sequence, we perform a numerical fitting of the cumulative number of aftershocks using the Modified Omori Law (MOL), the Dieterich model, and the specific TPS model. The fitting curves indicate that the data can be better explained by the TPS model with a B/A ratio of approximately 1.12, where A and B are the parameters in the rate- and state-dependent friction law respectively. Moreover, the p and c that appear in the MOL can be interpreted by the B/A and the critical slip distance, respectively. Because the B/A ratio in the current model is always larger than 1, the model could become a possible candidate to explain aftershock rate commonly decay as a power law with a p-value larger than 1. Finally, the influence of the background seismicity rate r on parameters is studied; the results show that except for the apparent aftershock duration, other parameters are insensitive to r.

Testing the forecasting skills of aftershock models using a Bayesian framework

The Epidemic Type Aftershock Sequence (ETAS) model and the modified Omori law (MOL) are two aftershock rate models that are used for operational earthquake/aftershock forecasting. Previous studies have investigated the relative performance of the two models for specific case studies. However, a rigorous comparative evaluation of the forecasting performance of the basic aftershock rate models for several different earthquake sequences has not been done before. In this study, forecasts of five prominent aftershock sequences from multiple catalogs are computed using the Bayesian predictive distribution, which fully accounts for the uncertainties in the model parameters. This is done by the Markov Chain Monte Carlo (MCMC) sampling of the model parameters and forward simulation of the ETAS or MOL models to compute the aftershock forecasts. The forecasting results are evaluated using five different statistical tests, including two comparison tests. The forecasting skill tests indicate that the ETAS model tends to perform consistently well on the first three tests. The MOL fails the same tests for certain forecasting time intervals. However, in the comparison tests, it is not definite whether the ETAS model is the better performing model. This work demonstrates the use of forecast testing for different catalogs, which is also applicable to catalogs with a higher magnitude of completeness.

Hazard Model: Epidemic-Type Aftershock Sequence (ETAS) Model for Hungary

In this article we present a space–time epidemic-type aftershock sequence (ETAS) model for the area of Hungary, motivated by the goal of its application in insurance risk models. High-quality recent instrumental data from the period 1996–2021 are used for model parameterization, including data from the recent nearby Zagreb and Petrinja event sequences. In the earthquake-triggering equations of our ETAS model, we replace the commonly used modified Omori law with the more recently proposed stretched exponential time response form, and a Gaussian space response function is applied with a variance add-on for epicenter error. After this model was tested against the observations, an appropriate overall fit for magnitudes M≥3.0 was found, which is sufficient for insurance applications, although the tests also show deviations at the M=2.5 threshold. Since the data used for parameterization are dominated by Croatian earthquake sequences, we also downscale the model to regional zones via parameter adjustments. In the downscaling older historical data are incorporated for a better representation of the key events within Hungary itself. Comparison of long-term large event numbers in simulated catalogues versus historical data shows that the model fit by zone is improved by the downscaling.

Precursory predictors of the onset of stick-slip frictional instability

Defining precursory phenomena that forewarn the onset of stick slip events remains an elusive but central goal in earthquake and other failure forecasting. We present a method to define the timing of instability by separately decoupling velocity and inertial effects in a spring-slider system. System state is defined in phase-space by velocity and inertia that in turn control critical stiffness and define the onset of instability while sliding velocity V = VLk/(k + dF/du) remains finite. A general energy analysis defines velocity and inertial effects (coefficients) that act against each other to promote/suppress instability by respectively increasing/decreasing critical stiffness. Repetitive stick-slip experiments define features of stick-slip cycles and identify a precursory trend in accelerating slip that precedes the onset of unstable sliding. We represent this precursory acceleration (dV/dt) immediately preceding instability by a general power-law relation dV/dt = AVα that reduces to V = B(ci + ti-t)-β. This represents the “true” timing of the onset of stick slip, ti relative to that “projected” from the linearization of the precursory data, tf, with tf=ci + ti. ci represents the small offset between the “predicted” and “true” timing of the onset of stick slip resulting from velocity and inertial effects and may be considered as the error in prediction. This error is one-order of magnitude smaller (∼3 ms) than the lead-time that forewarns of the event (∼40 ms) in our experiments and thus is useful as a predictor. Three independent methods using power-law, linear and criticality relationships confirm the fidelity of the timing of the slip instability transition evident in the stick slip data. This theoretical treatment suggests that the underlying physical meaning of the parameter c in the modified Omori law R∼(c + tM-t)-q is the time of the main shock in advance of the timing of the singularity predicted for an ideal response.

Mw ≥ 5 aftershocks of the 2008 Sichuan earthquake: Analysis of temporal variation of Omori Law p-value

Strong to great earthquakes considerably weaken the structural strength of the subsurface strata and civil constructions. The occurrence of Mw ≥ 5 aftershocks further contributes to the loss of human lives and damage to property. Therefore, the estimate of the duration of such aftershocks occurring near a metropolitan area is of major concern. In a previous study (Gupta et al., 2008), aftershocks for the destructive Sichuan earthquake, China (12 May 2008 Mw 7.9) for 23 days were used to estimatep-value and it was proposed that the M ≥ 5 aftershocks may continue for 7 months. In the present study, we analyze aftershock activity of Mw≥ 5 for 2-year duration within an area of 300 km radius from the epicenter, using modified Omori Law, which is well-known for analyzing aftershock rate and duration. We compare our results with the duration of aftershocks estimated using the exponential scaling law for the M ≥ 5 aftershock duration for major to great Himalayan earthquakes. Our analysis suggests that a highp-value (>1) indicates a slow decay of aftershocks as observed. As thep-value changes with time, the estimates of the duration of the occurrence of aftershocks of M ≥ 5 may change. Using a dynamic approach, the data of the first 100 days has been used in this study and the duration of occurrence of Mw ≥ 5 earthquakes is estimated to be ∼300 days, which is found to be true. Our analysis suggests that the temporal variation of thep-value from the onset of the mainshock and the slope of its variation are the key elements in comprehending the duration of the occurrence of the aftershocks of a certain magnitude. We infer that a highp-value (p>1) after the main earthquake, indicates a longer duration of larger aftershocks, which has been found in the case of the Sichuan earthquake. Thep-value decreases with time, however, an intermittent increase in thep-value could be an indicator of an increased chance for the occurrence of a higher magnitude aftershock. The proposed dynamic approach to estimating temporalp-values may help in forecasting the occurrence of stronger aftershocks more effectively. We believe that this is the first time, where the temporal variation ofp-values is estimated and related to the occurrence of aftershocks.

The Effect of Seismic Sequences in Probabilistic Seismic Hazard Analysis

ABSTRACTTraditionally, probabilistic seismic hazard analysis (PSHA) considers only mainshock events and models their temporal occurrence through a homogeneous Poisson process. Thus, it disregards foreshocks and aftershocks, assuming they have a minor effect on PSHA. However, recent earthquake sequences, such as those in 2016–2017 in Central Italy and 2010–2011 in Christchurch, New Zealand, exposed the shortcomings of such a universally used but unconservative approach. Our efforts to quantify the bias in seismic hazard and risk estimates follow from these considerations. Herein, we investigate the epidemic-type aftershock sequence (ETAS) model’s ability to reproduce the statistical features of long-term historical seismicity in Italy in two different regions.In addition, we calculate and compare the seismic hazard at two sites in Central Italy using different approaches: (1) with seismicity clustering modeled using the ETAS model; (2) with only mainshocks modeled by means of the Poissonian approach; and (3) with seismicity clustering modeled via a combination of Poisson and modified Omori law. We consider two cases: (1) the “unconditional case,” which uses years of varying seismicity as initial conditions and, therefore, can be considered as a tool for predicting the long-term average hazard, and (2) “conditional case,” in which the hazard is estimated after a specific period, in our case higher than average seismicity. We scrutinize the different modeling assumptions during the process and investigate the effect of using different declustering methods in Poisson-based models. As expected, we find that using the mainshock-only seismicity models yields lower hazard estimates compared to those obtained with the Omori and ETAS model. In addition, we show that Omori and ETAS model predict similar results in the unconditional case, but the Omori model considerably underpredicts the hazard in the conditional case, for a site close to the sequences, when temporal variations in seismic hazard are accounted for.

Properties of the Zagreb 22 March 2020 earthquake sequence

Although strong and damaging earthquakes have hit Zagreb in the past, the 22 March 2020 earthquake (Mw 5.4) is the first one that was recorded by a modern digital local seismic network, and which could be analysed not only by macroseismic methods, but also by microseismic ones. Herewith we used the 3003 carefully analysed and located events from the first year of the aftershock sequence to learn more about the aftershock rate decay, their magnitude distribution, focal mechanisms and hypocentral locations. The aftershock activity rate was found to closely follow the modified Omori law, and fault-plane solutions for 10 events indicated prevailing pure-reverse faulting. Our analyses suggest that the reverse North Medvednica boundary fault (NMBF) was the causative fault, as it fits with the focal mechanisms and with the geometry of aftershock locations. The epicentral area was of a triangular shape with the mainshock in one vertex, and the opposite side of the triangle lying parallel to the surface trace of the NMBF. The hypocentres of aftershocks were predominantly located in the hanging wall of the fault. No surface break was observed, so the rupture is assumed to be buried. These facts were interpreted as a combination of the effect of conservation of mass (seismic flow) requiring some fault-parallel stress redistribution and transfer of material, and the fault loading and activation in the compressive environment controlled by the stress partition at the brittle-ductile transition zone within the crust. The later process involves compression within the hanging wall during the interseismic stage when the fault segment in the brittle crust is locked, followed by sudden dilatation during the rupture phase.

Sequence-based hazard analysis for Italy considering a grid seismic source model

Earthquakes are usually clustered in both time and space and, within each cluster, the event of highest magnitude is conventionally identified as the mainshock, while the foreshocks and the aftershocks are the events that occur before and after it, respectively. Mainshocks are the earthquakes considered in the classical formulation of the probabilistic seismic hazard analysis (PSHA), where the contribution of foreshocks and aftershocks is usually neglected. In fact, it has been shown that it is possible to rigorously, within the hypotheses of the model, account for the effect of mainshock-aftershocks sequences by means of the sequence-based PSHA (i.e., SPSHA). SPSHA extends the usability of the homogeneous Poisson process, adopted for mainshocks within PSHA, to also describe the occurrence of clusters maintaining the same input data of PSHA; i.e., the seismic rates derived by a declustered catalog. The aftershocks’ occurrences are accounted for by means of conditional non-homogeneous Poisson processes based on the modified Omori law. The seismic source model for Italy has been recently investigated, and the objective of the study herein presented is to include and evaluate the effect of aftershocks, by means of SPSHA, based on a new grid model. In the paper, the results of PSHA and SPSHA are compared, considering the spectral and return periods that are of typical interest for earthquake engineering. Finally, a comparison with the SPSHA map based on a well- established source model for Italy is also provided.

Induced Earthquakes Before and After Cessation of Long‐Term Injections in Rongchang Gas Field

AbstractFor more than three decades, the depleted Rongchang gas reservoir in China's Sichuan Basin was used for the disposal of unwanted water, which resulted in induced earthquakes, with magnitudes as high as 5.2. After all wells were closed, the frequency of seismic activity was observed to decay following a modified Omori law, and since April 2015, seismic activity again began to increase, and a M4.9 earthquake occurred on 27 December. The results of an epidemic‐type aftershock sequence (ETAS) model analysis show that forced seismicity accounted for more than 70% of the total events. For most M ≥ 3.5 earthquakes, including two M ≥ 4 events, the estimated overpressure was lower than the maximum injection pressure. These results, coupled with the fact that postinjection seismic activity has similar characteristics to seismicity during injection, indicate that the injected overpressure fluid was still the driving factor for postinjection seismic activity.

Classes of sustained microfracturing produced after formation of hydraulic fractures

Aftershocks were observed to occur after hydraulic fracturing tests on mortar blocks at the laboratory scale. Five aftershocks sequences were recorded and fitted with the original and modified Omori laws. The modified Omori law was found to be a better model for the aftershock sequences studied. Both the estimated decay exponent p and the time shift c fall in the range found from observations of the geological aftershocks. The statistical similarity between the geological and the laboratory aftershocks suggests that there is a common underlying mechanism governing the generation of aftershocks across the scale. In this mechanism the aftershocks correspond to crack production by the mechanism of static fatigue. The power law decay of aftershock frequency (modified Omori law) is explained by the residual stress relaxation caused by the reduction of deformation moduli produced by crack accumulation. Two types of decay exponents p (exponents of the modified Omori's law) were observed: (1) p > 1 caused by static fatigue fracturing of initially non-fractured zones (bridges) within the fracture; (2) p < 1 caused by static fatigue production of parallel cracks outside the fracture surface.

Ensembles of ETAS Models Provide Optimal Operational Earthquake Forecasting During Swarms: Insights from the 2015 San Ramon, California Swarm

Abstract Earthquake swarms, typically modeled as time‐varying changes in background seismicity, which are driven by external processes such as fluid flow or aseismic creep, present challenges for operational earthquake forecasting. Although the time decay of aftershock sequences can be estimated with the modified Omori law, it is difficult to forecast the temporal behavior of seismicity rates during a swarm. To explore these issues, we apply the epidemic‐type aftershock sequence (ETAS) model (Ogata, 1988) to the 2015 San Ramon, California swarm, which lasted several weeks and had almost 100 2≤M≤3.6 earthquakes. We develop three‐day forecasts during the swarm based on an ETAS model fit to all prior seismicity in the region as well as an ETAS model fit only to previous swarms in the region, which is better at capturing the higher background rate during the swarm. We also explore forecasts in which the background rate is updated periodically during the swarm using data over different lookback windows and find generally these models perform better than the models in which the background rate is fixed. Finally, we construct ensemble forecasts by combining the different models weighted according to their performance. The ensemble forecasts outperform all of the individual models and allow us to avoid making arbitrary choices at the outset of a swarm as to which single model will perform the best.

Dependences of the Omori and Gutenberg–Richter parameters

Laboratory experiments on studying the aftershock regime are carried out with sandstone specimens under different axial loading and uniform compression and constant pore pressure. The aftershock sequences are modeled by the scenario of stepwise increasing axial loading of a specimen with strain control ensuring regular generation of aftershock sequences. The experiments are conducted on intact specimens and on the specimens with preliminarily formed shear macrofractures simulating natural faults. The experiments were conducted with multichannel recording of the acoustic emission (AE) signals which made it possible to locate the AE sources. Several types of the dependence of the acoustic activity relaxation parameters (parameters p and c of the modified Omori law and the Gutenberg–Richter b-value) on the level of acting stresses are revealed. The b-value decreases with the growth of axial stresses at all levels of uniform compression. In the case of fracture on the preexisting fault, the Omori relaxation parameter p increases with the growth of axial stresses whereas parameter c (the time delay before the onset of relaxation) decreases with the growth of axial stresses and increases with the rise of the level of uniform compression. In the case of a fracture of an undamaged specimen, parameter p remains unchanged as the axial stresses grow, whereas parameter c increases slightly. Parameter variations in the case of a complex stress state with both varying deviatoric (differential stresses) and spherical parts (effective pressure) of the stress tensor take on a unified form when expressed in terms of Coulomb stresses. It is hypothesized that the time delay of the aftershock activity relaxation is determined by the kinetics of fracture in accordance with the kinetic concept of strength in solids. This hypothesis is supported by exponential dependence of parameter c on stresses and on the effective strength of the medium revealed in the experiments. Under this hypothesis, the dependences of parameter c on the Coulomb stresses can be unified for different effective strength values with the use of Zhurkov’s formula for durability of materials. The obtained parameter estimates for the dependence of c on strength and stresses suggest that the c value is determined by the difference of the strength and the acting stresses, indicating how far the stress state of the medium is from the critical state corresponding to the ultimate strength.

Laboratory Modeling of Aftershock Sequences: Stress Dependences of the Omori and Gutenberg–Richter Parameters

Laboratory experiments on studying the aftershock regime are carried out on sandstone specimens at different levels of axial loading and uniform compression and at constant pore pressure. The aftershock sequences are modeled by the scenario of stepwise increasing axial loading of a specimen with strain control, which ensures the regular generation of aftershock sequences. The experiments are conducted on intact specimens and on those with preliminarily formed shear macrofractures simulating natural faults. The multichannel recording of the signals of acoustic emission (AE) during the experiments allowed locating the AE sources. Several types of the dependence of the parameters of relaxation of the acoustic activity—parameters p and c of the modified Omori law and the Gutenberg–Richter b-value—on the level of acting stresses are revealed. The b-value decreases with the growth of axial stresses at all levels of uniform compression. In the case of a fracture on the preexisting fault, the Omori relaxation parameter p increases with the growth of axial stresses; parameter c—the time delay before the onset of relaxation—decreases with the growth of axial stresses and increases with the rise of the level of uniform compression. In the case of a fracture of an undamaged specimen, parameter p remains unchanged with the growth of axial stresses, whereas parameter c increases slightly. Parameter variations in the case of a complex stress state with both varying deviatoric (differential stresses) and spherical parts (effective pressure) of the stress tensor take on a unified form when expressed in terms of Coulomb stresses. It is hypothesized that the time delay of the relaxation of the aftershock activity is determined by the kinetics of a fracture in accordance with the kinetic concept of strength in solids. This hypothesis is supported by the exponential dependences of parameter c on stresses and the effective strength of the medium which are revealed in the experiments. Under this hypothesis, based on Zhurkov’s formula for the durability of materials, it is possible to unify the dependences of parameter c on the Coulomb stresses at different effective strength values. The obtained parameter estimates for the dependence of c on strength and stresses suggest that the c value is determined by the difference of the strength and the acting stresses, thus indicating how far the stress state of the medium is from critically corresponding to the ultimate strength.

Analysis of rock mass stability according to power-law attenuation characteristics of acoustic emission and microseismic activities

Under the influence of many factors, including complicated geological condition, high stress environment and strong disturbance by blasting, rock mass failure, and in some cases, dynamic failures would occur. Therefore, it is important to investigate and to understand rock mass stability during mining. In this study, Modified Omori Law (MOL) was applied to analyze the acoustic emission (AE) and microseismic (MS) sequence power-law attenuation characteristics in the laboratory and in situ. The MOL parameters, during the period of constant stress at lower stress level was much different with that at higher stress level, can reflect the stress level in rock. Before failure of the two rock specimens, the MOL is not applicable, indicating that the rock was close to the critical instability state. During the mining process, rock mass would be strongly disturbed by blasting. The AE sequence monitored from a ramp near the stope, and the MS sequence monitored from the whole rock mass near the stope all exhibited distinct power-law attenuation characteristics. The changes of MOL parameters, i.e., p, c and A, are very complex and related to many factors and it should cooperative analyze the three parameters to evaluate rock mass stability during the mining process.

Statistical Properties of Aftershocks for Ahar-Varzeghan Twin Earthquakes on 11 August 2012, NW Iran, and Investigation of Seismicity of North Tabriz Fault

Two earthquakes occurred on 11 August 2012 in East Azerbaijan province, NW Iran with Mw 6.3 at 12:23:15.9 and Mw 6.1; 11 minutes after the first shock at 12:34:34.8 GMT time. In this study, we concentrated on the properties of the aftershock sequences in a duration of 7.5-month time-period data after the main shocks, recorded by Broadband Iranian Network (BIN). We obtained p, c and K parameters with the maximum likelihood method and the occurrence rate was modeled by the modified Omori formula. Besides, we showed that aftershocks of the aftershock in 7 Nov. 2012 (M = 5.6) also decay according to the modified Omori law. We investigated the spatial and temporal variations of b-values before and after the twin earthquakes with Mw 6.3 and Mw 6.1 approximately 20 km around North Tabriz Fault (NTF) in the region from 1996 to 2013 using Iranian Seismological Center (IRSC). We believed that a research of the past 17 years has clearly established that spatial b-value changes and seismicity rate are highly significant and meaningful. Moreover, our research led to a warning for a probable strong motion along NTF for the coming couple of years.

Engineering Applications Using Probabilistic Aftershock Hazard Analyses: Aftershock Hazard Map and Load Combination of Aftershocks and Tsunamis

After the Tohoku earthquake in 2011, we observed that aftershocks tended to occur in a wide region after such a large earthquake. These aftershocks resulted in secondary damage or delayed rescue and recovery activities. In addition, it has been reported that there are regions where the intensity of the vibrations owing to the aftershocks was much stronger than those associated with the main shock. Therefore, it is necessary to consider the seismic risk associated with aftershocks. We used the data regarding aftershocks that was obtained from the Tohoku earthquake and various other historically large earthquakes. We investigated the spatial and temporal distribution of the aftershocks using the Gutenberg–Richter law and the modified Omori law. Subsequently, we previously proposed a probabilistic aftershock occurrence model that is expected to be useful to develop plans for recovery activities after future large earthquakes. In this study, the probabilistic aftershock hazard analysis is used to create aftershock hazard maps. We propose a hazard map focusing on the probability of aftershocks on the scale of the main shock for use with a recovery activity plan. Following the lessons learned from the 2011 Tohoku earthquake, we focus on the simultaneous occurrence of tsunamis and aftershocks just after a great subduction earthquake. The probabilistic aftershock hazard analysis is used to derive load combination equations of the load and resistance factor design. This design is intended to simultaneously consider tsunamis and aftershocks for tsunami-resistant designs of tsunami evacuation buildings.

Probabilistic aftershock hazard analysis, two case studies in West and Northwest Iran

Aftershock hazard maps contain the essential information for search and rescue process, and re-occupation after a main-shock. Accordingly, the main purposes of this article are to study the aftershock decay parameters and to estimate the expected high-frequency ground motions (i.e., Peak Ground Acceleration (PGA)) for recent large earthquakes in the Iranian plateau. For this aim, the Ahar-Varzaghan doublet earthquake (August 11, 2012; M N =6.5, M N =6.3), and the Ilam (Murmuri) earthquake (August 18, 2014 ; M N =6.2) have been selected. The earthquake catalogue has been collected based on the Gardner and Knopoff (Bull Seismol Soc Am 64(5), 1363-1367, 1974) temporal and spatial windowing technique. The magnitude of completeness and the seismicity parameters (a, b) and the modified Omori law parameters (P, K, C) have been determined for these two earthquakes in the 14, 30, and 60 days after the mainshocks. Also, the temporal changes of parameters (a, b, P, K, C) have been studied. The aftershock hazard maps for the probability of exceedance (33%) have been computed in the time periods of 14, 30, and 60 days after the Ahar-Varzaghan and Ilam (Murmuri) earthquakes. For calculating the expected PGA of aftershocks, the regional and global ground motion prediction equations have been utilized. Amplification factor based on the site classes has also been implied in the calculation of PGA. These aftershock hazard maps show an agreement between the PGAs of large aftershocks and the forecasted PGAs. Also, the significant role of b parameter in the Ilam (Murmuri) probabilistic aftershock hazard maps has been investigated.

Temporal Delineation and Quantification of Short Term Clustered Mining Seismicity

The assessment of the temporal characteristics of seismicity is fundamental to understanding and quantifying the seismic hazard associated with mining, the effectiveness of strategies and tactics used to manage seismic hazard, and the relationship between seismicity and changes to the mining environment. This article aims to improve the accuracy and precision in which the temporal dimension of seismic responses can be quantified and delineated. We present a review and discussion on the occurrence of time-dependent mining seismicity with a specific focus on temporal modelling and the modified Omori law (MOL). This forms the basis for the development of a simple weighted metric that allows for the consistent temporal delineation and quantification of a seismic response. The optimisation of this metric allows for the selection of the most appropriate modelling interval given the temporal attributes of time-dependent mining seismicity. We evaluate the performance weighted metric for the modelling of a synthetic seismic dataset. This assessment shows that seismic responses can be quantified and delineated by the MOL, with reasonable accuracy and precision, when the modelling is optimised by evaluating the weighted MLE metric. Furthermore, this assessment highlights that decreased weighted MLE metric performance can be expected if there is a lack of contrast between the temporal characteristics of events associated with different processes.

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.

Statistical analysis of aftershock sequences related with two major Nepal earthquakes: April 25, 2015, MW 7.8, and May 12, 2015, MW 7.2

Present study describes the statistical properties of aftershock sequences related with two major Nepal earthquakes (April 25, 2015, MW 7.8, and May 12, 2015, MW 7.2) and their correlations with the tectonics of Nepal Himalaya. The established empirical scaling laws such as the Gutenberg–Richter (GR) relation, the modified Omori law, and the fractal dimension for both the aftershock sequences of Nepal earthquakes have been investigated to assess the spatio-temporal characteristics of these sequences. For this purpose, the homogenized earthquake catalog in moment magnitude, MW is compiled from International Seismological Center (ISC) and Global Centroid Moment Tensor (GCMT) databases during the period from April 25 to October 31, 2015. The magnitude of completeness, MC, a and b-values of Gutenberg–Richter relationship for the first aftershock sequence are found to be 3.0, 4.74, 0.75 (±0.03) respectively whereas the MC, a and b-values of the same relationship for the second aftershock sequence are calculated to be 3.3, 5.46, 0.90 (±0.04) respectively. The observed low b-values for both the sequences, as compared to the global mean of 1.0 indicate the presence of high differential stress accumulations within the fractured rock mass of Nepal Himalaya. The calculated p-values of 1.01 ± 0.05 and 0.95 ± 0.04 respectively for both the aftershock sequences also imply that the aftershock sequence of first main-shock exhibits relatively faster temporal decay pattern than the aftershock sequence of second main-shock. The fractal dimensions, DC values of 1.84 ± 0.05 and 1.91 ± 0.05 respectively for both the aftershock sequences of Nepal earthquakes also reveal the clustering pattern of earthquakes and signifies that the aftershocks are scattered all around the two dimensional space of fractured fault systems of the Nepal region. The low b-value and low DC observed in the temporal variations of b-value and DC before the investigated earthquake (MW 7.2) suggest the presence of high-stress concentrations in the thrusting regimes of the Nepal region before the failure of faults. Moreover, the decrease of b-value with the corresponding decrease of DC observed in their temporal variations can primarily act as an indicator for possible prediction of major earthquakes in the study region.