Aftershock Decay Rate Research Articles

Spatiotemporal characteristics and earthquake statistics of the 2020 and 2022 adjacent earthquake sequences in North Aegean Sea (Greece)

The two moderate earthquakes that occurred close and to the north of the North Aegean Trough (NAT) on 26 September 2020 (Mw5.3) and 16 January 2022 (Mw5.4), both followed by aftershock activity, are examined. Seismic activity along the NAT and its parallel branches is continuous and remarkable, with numerous strong instrumental (M≥6.0) earthquakes. Yet, the frequency of moderate (5.0≤M<6.0) earthquakes outside these major fault branches is rather rare and therefore their investigation provides the optimal means to decipher the seismotectonic properties of the broader area. The temporal and spatial proximity of the two seismic excitations from late September of 2020 through early 2022, intrigues for exhaustive investigation of seismic activity with the employment of earthquake relocation techniques, moment tensor solutions and statistical analysis. Our research revealed that this seismic activity purely falls inside the Mainshock – Aftershock type, with fast aftershock decay rates and moderate productivity. According to our findings, the two seismic sequences, despite their close proximity, exhibit distinctive features as a result of the intricate stress field generated at the western termination of the NAF system in an extensional domain.

Analysis of the Fractal Dimension, b-value, Slip Ratio, and Decay Rate of Aftershock Seismicity Following the 6 February 2023 (Mw 7.8 and 7.5) Türkiye Earthquakes

On 6 February 2023, Türkiye experienced a pair of consecutive earthquakes with magnitudes of Mw 7.8 and 7.5, and accompanied by an intense aftershock sequence. These seismic events were particularly impactful on the segments of the East Anatolian Fault Zone (EAFZ), causing extensive damage to both human life and urban centers in Türkiye and Syria. This study explores the analysis of a dataset spanning almost one year following the Turkiye mainshocks, including 471 events with a magnitude of completeness (Mc) ≥ 4.4. We employed the maximum likelihood approach to estimate the b-value and Omori-Utsu parameters (K, c, and p-values). The estimated b-value is 1.21 ± 0.1, indicating that the mainshocks occurred in a region characterized by elevated stress levels, leading to a sequence of aftershocks of larger magnitudes due to notable irregularities in the rupture zone. The aftershock decay rate (p-value = 1.1 ± 0.04) indicates a rapid decrease in stress levels following the main shocks. However, the c-value of 0.204 ± 0.058 would indicate a relatively moderate or low initial productivity of aftershocks. Furthermore, the k-value of 76.75 ± 8.84 suggests that the decay of aftershock activity commenced within a range of approximately 68 to 86 days following the mainshocks. The fractal dimension (Dc) was assessed using the correlation integral method, yielding a value of 0.99 ± 0.03. This implies a tendency toward clustering in the aftershock seismicity and a linear configuration of the epicenters. The slip ratio during the aftershock activity was determined to be 0.75, signifying that 75% of the total slip occurred in the primary rupture, with the remaining fraction distributed among secondary faults. The methodologies and insights acquired in this research can be extended to assist in forecasting aftershock occurrences for future earthquakes, thus offering crucial data for future risk assessment.

Analysis of the b, p values, and the fractal dimension of aftershocks sequences following two major earthquakes in central Himalaya

On April 25 of 2015, earthquake of 7.6 ML struck the central Himalayan region having epicenter at Barpak village in the Gorkha district of Nepal. The event was followed by 7.0 ML earthquake known as Dolakha earthquake, epicenter on the border of Dolakha and Sindhupalchowk. In this study, the b-value, aftershock decay rate p-value, and correlation fractal dimension were estimated for the aftershock sequences. The data used were obtained from the National Earthquake Monitoring and Research Centre (NEMRC), Nepal. The b–values 0.89 ± 0.05 and 0.90 ± 0.07 were computed for aftershocks after Gorkha and Dolakha event, respectively. A significant increase in b-values were reported following the Gorkha earthquake and Dolakha earthquake. The slip procured in the primary fault is respectively 60 % and 56 % after the events. The aftershocks sequences after both events were modelled by the Omori-Utsu law with p = 1.2 ± 0.11 and p = 0.76 ± 0.04. The observed b and p values after the earthquake sequences may correlate well with the large slip experienced by the seismogenic fault. This study sheds light on the mechanism behind the preparation of the significant earthquakes in the tectonic regions of the Himalaya.

Spatiotemporal variations in seismic activity in and around the focal region of the 2021 [formula omitted]7.3 and 2022 [formula omitted]7.4 Fukushima-Oki earthquakes, Japan

The spatiotemporal evolution of seismic activity is presented for a broad region surrounding the focal areas of the 2021 M7.3 and 2022 M7.4 Fukushima-Oki earthquakes, which occurred within the subducting slab off the Pacific coast of Fukushima Prefecture, northeastern Japan. This study investigates the spatiotemporal variations in seismic activity during the periods before the 2021 M7.3 earthquake, between the 2021 M7.3 and 2022 M7.4 earthquakes, and after the 2022 M7.4 earthquake using the b-value of the Gutenberg–Richter relation, the aftershock decay rate (p-value), and changes in the seismicity rate (Z-value). The study area is also divided into two depth sections to investigate the depth variations in these seismicity parameters relative to the plate interface. The b-values in the deeper section (intraslab) are generally lower than those in the shallower section (around the plate interface) throughout the entire analysis period, including the hypocentral areas of the M7.3 and M7.4 earthquakes. The aftershock decay rates for the M7.3 and M7.4 earthquakes also show depth-dependent characteristics, with a slower decay rate (p < 1.0) at many grid nodes in the deeper section than in the shallower section. Furthermore, seismic quiescence was noted in the hypocentral area of the M7.3 earthquake about two years before the occurrence of this mainshock. The locations of the M7.3 and M7.4 earthquakes around the down-dip edge of the slip area of the 2011 M9.0 Tohoku earthquake suggests that the variations in seismic activity detected in this study mainly reflect stress increases due to the coseismic slip and postseismic deformation of this great earthquake. The present study suggests that the effect of viscoelastic relaxation is a dominant factor in the deeper section. Furthermore, the variations in seismicity may also reflect heterogeneous structures within the slab.

Dynamics between earthquakes, volcanic eruptions, and geothermal energy exploitation in Japan

Intruding magma brings high temperatures close to the surface, thus offering possibilities for harnessing large amounts of heat for geothermal exploitation. Mount Aso in southern Japan showed frequent volcanic activity during 2016, accompanied by significant earthquake activities with tens of thousands of aftershocks (Kumamoto sequence). Here we investigate the influence of earthquake/volcanic activity on the future productivity of nearby geothermal power plants to determine whether the activity is detrimental or beneficial to energy exploitation. Model results show an increase in {text {CO}}_2 pressure and temperature with a spatio-temporal correlation between modeled earthquake locations and aftershock decay rates along the entire sequence, showing that seismic activity opened pre-existing vertical cracks providing pathways for the ascending magma. Interestingly, the minor but still significant eruption of Mount Aso in October 2021 may have enhanced future geothermal power generation, indicating a vigorous and active system, possibly increasing the future geothermal power production.

Stochastic Modeling of the Al Hoceima (Morocco) Aftershock Sequences of 1994, 2004 and 2016

The three aftershock sequences that occurred in Al Hoceima, Morocco, in May 1994 (Mw 6.0), February 2004 (Mw 6.4) and January 2016 (Mw 6.3) were stochastically modeled to investigate their temporal and energetic behavior. A form of the restricted trigger model known as the restricted epidemic type aftershock sequence (RETAS) was used for the temporal analysis of the selected series. The best-determined fit models for each sequence differ based on the Akaike information criteria. The revealed discrepancies suggest that, although the activated fault systems are close (within 10 to 20 km), their stress regimes change and shift across each series. In addition, a stochastic model was presented to study the strain release following a specific strong earthquake. This model was constructed using a compound Poisson process and depicted the progression of the strain release during the aftershock sequence. The proposed model was then applied to the data. After the RETAS model was used to evaluate the behavior of the aftershock decay rate, the best-fit model was obtained and integrated into the strain-release stochastic analysis. By detecting the potential disparities between the observed data and model, the applied stochastic model of strain release allows for a more comprehensive examination. Furthermore, comparing the observed and expected cumulative energy release numbers revealed some variations at the start of all three sequences. This demonstrates that significant aftershock clusters occur more frequently shortly after the mainshock at the start of the sequence rather than if they are assumed to occur randomly.

Gorkha earthquake (MW7.8) and aftershock sequence: A fractal approach

On April 25, 2015, Nepal was struck by the MW7.8 Gorkha earthquake followed by an intense aftershock sequence. It was one of the most destructive earthquakes in the Himalayan arc, causing more than 8900 fatalities. In this study, we analyzed the dataset (429 events, magnitude of completeness (Mc) ≥ 4.2 local magnitude) of the first 45 days after the Gorkha earthquake to estimate the seismicity parameters b-value, D-value, and p-value. We used the maximum likelihood method to estimate the b-value and Omori-Utsu parameters, whereas the correlation integral method was applied to estimate the fractal dimension (D-value). The analysis was carried out using running and sliding window techniques. The lowest b-value (0.57 ± 0.04) and the highest D-value (1.65 ± 0.02) were computed at the time of the Gorkha earthquake, after which the b-value significantly increased to a maximum of 1.57. It again dropped to 0.93 at the time of the major aftershock on May 12, 2015. The D-value showed an initial quick drop and then decreased in a wavy pattern until the end of the study period, indicating the clustering and scattering of earthquakes in a fault region. The b-value contour map identified the eastern part of the study area as a high stress region (b = ∼0.8), implying that the stress shifted to that region. The D-value contour map reveals that the seismogenic structure shifted from linear to planar in the region. The rate of aftershock decay (p = 0.86 ± 0.04) for a short period reflects that the level of stress decreased rapidly. This study helps to understand the level of stress and seismicity pattern of a region, which could be useful for aftershock studies.

Aftershock sequence of 22 September 2016, Manica-Zinave earthquake (Mw5.6),Mozambique

The occurrence of the September 22, 2016 Manica-Zinave earthquake (Mw5.6) and its subsequent aftershocks provided data to study the physics of earthquakes along the southern end of the East African Rift System (EARS). The event occurred in the southern part of Mozambique, less than 40 km from the epicentre of the Mw7.0 Machaze earthquake, which occurred on February 22, 2006. About 320 aftershocks were recorded within a period of 6 months. The analysis of the Manica-Zinave event and its aftershocks was done to understand the tectonics of the region. The aftershocks were relocated using the double difference method. The focal mechanism for this event shows normal faulting, which is consistent with most events along the EARS. Statistical analysis of the aftershock sequence was performed for the calculation of the b-value and the aftershock decay rate p-value. The b-value and p-value obtained for this sequence are 1.02 and 0.86 respectively. These values are typical of aftershock sequences of heterogeneous stressed regions. Due to its proximity, the event might be an aftershock of the Machaze earthquake, which might have occurred due to stress readjustment within the area. The p-value obtained from the Omori law computation suggests that the region is highly stressed.

Aftershocks are fluid-driven and decay rates controlled by permeability dynamics

One aspect of earthquake physics not adequately addressed is why some earthquakes generate thousands of aftershocks while other earthquakes generate few, if any, aftershocks. It also remains unknown why aftershock rates decay as ~1/time. Here, I show that these two are linked, with a dearth of aftershocks reflecting the absence of high-pressure fluid sources at depth, while rich and long-lasting aftershock sequences reflect tapping high-pressure fluid reservoirs that drive aftershock sequences. Using a physical model that captures the dominant aspects of permeability dynamics in the crust, I show that the model generates superior fits to observations than widely used empirical fits such as the Omori-Utsu Law, and find a functional relationship between aftershock decay rates and the tectonic ability to heal the co- and post-seismically generated fracture networks. These results have far-reaching implications, and can help interpret other observations such as seismic velocity recovery, attenuation, and migration.

Evidence for Fluid Migration During the 2016 Meinong, Taiwan, Aftershock Sequence

AbstractAn important question of earthquake science is to what extent fluids such as water play an important role in modulating seismicity. While many models of earthquake rupture assume that fluids are critical for dynamic weakening during slip and evidence for fluids is well documented for shallow injection‐induced or hydrothermally induced earthquakes, there has been limited conclusive evidence for the role of fluids for tectonic earthquakes in the middle‐to‐lower crust. Here, we provide evidence for fluid migration during the 2016 Meinong, Taiwan, aftershock sequence, occurring at 10–20 km depth within a classic fold‐and‐thrust belt. We find high Vp/Vs ratios, characteristic of highly fluid saturated regions, in the Meinong aftershock region and that the Vp/Vs ratios in the central aftershock region change with time during the aftershock sequence. The central aftershock sequence distinguishes itself from other aftershocks by having a swarm‐like magnitude distribution and aftershock decay rate, as well as a slower migration rate that may be related to fluid diffusion. The estimated permeability (~3.8 × 10−15 m2) and temporal changes in Vp/Vs suggest that moderate earthquakes may be able to strongly affect permeabilities in the midcrust. The results also suggest that fluid processes play a critical role in regulating seismicity in a classic continental collision tectonic setting and may also have a role in modifying earthquake hazards more generally.

Aftershock analysis of the 2015 Gorkha-Dolakha (Central Nepal) earthquake doublet

On 25 April 2015, a large earthquake with moment-magnitude (Mw) 7.8 occurred at Gorkha (latitude 28.23° N and longitude 84.73° E) in Central Nepal. Just 17 days later, another large earthquake of Mw 7.3 occurred at Dolakha (latitude 27.80° N and longitude 86.06° E), about 140 km away from the previous epicenter. In this study, we deal with the aftershocks of these two earthquakes that occurred in the region (27°–28.5°N, 84°–87°E) spanning the period from 25 April 2015 to 28 May 2016 to find the spatiotemporal distribution patterns, the size distribution (b-value), and the aftershock decay rate (p-value) of this sequence. Aftershock epicenters of the 2015 Gorkha-Dolakha earthquake doublet are distributed over an area approximately 170 km in length and 70 km in width and largely confined in a depth range from 5 to 25 km. The spatial distribution of epicenters and known geological structures in this study reveals that aftershocks are limited on the east by the surface trace of the Everest lineament and on the south side by the surface trace of the segment of the Main Boundary Thrust (MBT). The estimated b-and p-values of this seismic sequence are 0.93 ± 0.03 and 0.79 ± 0.24, respectively. This b-value is higher than the b-value estimated by the previous studies, while the p-value corresponds in general with the p-value obtained by recent study in the region.

Pore Pressure Pulse Drove the 2012 Emilia (Italy) Series of Earthquakes

AbstractThe 2012 Emilia earthquakes sequence is the first debated case in Italy of destructive event possibly induced by anthropic activity. During this sequence, two main earthquakes occurred separated by 9 days on contiguous thrust faults. Scientific commissions engaged by the Italian government reported complementary scenarios on the potential trigger mechanism ascribable to exploitation of a nearby oil field. In this study, we combine a refined geodetic source model constrained by precise aftershock locations and an improved tomographic model of the area to define the geometrical relation between the activated faults and investigate possible triggering mechanisms. An aftershock decay rate that deviates from the classical Omori‐like pattern and Vp/Vs changes along the fault system suggests that natural pore pressure pulse drove the space‐time evolution of seismicity and the activation of the second main shock.

Depth dependent stress revealed by aftershocks

Characterising the state of stress in the brittle upper-crust is essential in mechanics of faulting, industrial production processes, and operational earthquake forecasting. Nevertheless, unresolved questions concern the variation of pore-fluid with depth and the absolute strength on tectonically active faults. Here we show that, along the San Andreas fault system, the time-delay before the onset of the power-law aftershock decay rate (the c-value) varies by three orders of magnitude in the first 20 km below the surface. Despite the influence of the lithostatic stress, there is no continuous change in c-value with depth. Instead, two decay phases are separated by an abrupt increase at an intermediate depth range of 2–5 km. This transitional regime is the only one observed in fluid-injection-induced seismic areas. This provides strong evidence for the role of fluid and a porosity reduction mechanism at depth of few kilometres in active fault zones. Aftershock statistics can then be used to predict changes in differential shear stress with depth until the brittle-ductile transition is reached.

Spatio-temporal evolution of aftershock energy release following the 1989, MW6.9, LOMA Prieta earthquake in California

We apply a stochastic model to study Benioff strain release after the Mw6.9 October 18, 1989 Loma Prieta strong earthquake in north California, USA. The model is developed, following a compound Poisson process and contours the evolution of strain release during the aftershock sequence following the main shock occurrence. First, the temporal evolution of the aftershock decay rate was modeled by the Restricted Epidemic Type Aftershock Sequence (RETAS) model and after that the recognized best fit model is integrated into the strain release stochastic analysis. The applied stochastic model of Benioff strain release empowers a more detailed study by detecting possible deviations between observed data and model. Real values of the cumulative Benioff strain release surpass the expected modeled ones, indicating, that large aftershocks cluster at the beginning of the Loma Prieta sequence immediately after the occurrence of the main shock. Strain release spatial analysis reveals release patterns, which change during the aftershock sequence.

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

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

Power-law rheology controls aftershock triggering and decay.

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

Aftershock Decay Rates in the Iranian Plateau

Motivated by the desire to have more information following the occurrence of damaging events, the main purpose of this article is to study aftershock sequence parameters in the Iranian plateau. To this end, the catalogue of the Iranian earthquakes between 2002 to the end of 2013 has been collected and homogenized among which 15 earthquakes have been selected to study their aftershock decay rates. For different tectonic provinces, the completeness magnitudes (Mc) of the earthquake catalogue have been calculated in different time intervals. Also, the Mc variability in spatial and temporal windows has been determined for each selected event. For major Iranian earthquakes, catalogue of aftershocks has been collected thanks to three declustering methods: first, the classical windowing method of Gardner and Knopoff (Bull Seismol Soc Am 64:1363–1367, 1974); second, a modified version of this using spatial windowing based on the Wells and Coppersmith (Bull Seismol Soc Am 84:974–1002, 1994) relations; and third, the Burkhard and Grunthal (Swiss J Geosci 102:149–188, 2009) scheme. Effects of the temporal windows also have been investigated using the time periods of 1 month, 100 days, and 1 year in the declustering method of Gardner and Knopoff (Bull Seismol Soc Am 64:1363–1367, 1974). In the next step, the modified Omori law coefficients have been calculated for the 15 selected earthquakes. The calibrated regional generic model describing the temporal and magnitude distribution of aftershocks is of interest for time-dependent seismic hazard forecasts. The regional characteristics of the aftershock decay rates have been studied for the selected Iranian earthquakes in the Alborz, Zagros and Central Iran regions considering their different seismotectonics regimes. However, due to the lack of sufficient data, no results have been reported for the Kopeh-Dagh and Makran seismotectonic regions.

Revisiting the 1894 Omori Aftershock Dataset with the Stretched Exponential Function

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

Modeling aftershocks as a stretched exponential relaxation

AbstractThe decay rate of aftershocks has been modeled as a power law since the pioneering work of Omori in the late nineteenth century. Although other expressions have been proposed in recent decades to describe the temporal behavior of aftershocks, the number of model comparisons remains limited. After reviewing the aftershock models published from the late nineteenth century until today, I solely compare the power law, pure exponential and stretched exponential expressions defined in their simplest forms. By applying statistical methods recommended recently in applied mathematics, I show that all aftershock sequences tested in three regional earthquake catalogs (Southern and Northern California, Taiwan) and with three declustering techniques (nearest‐neighbor, second‐order moment, window methods) follow a stretched exponential instead of a power law. These results infer that aftershocks are due to a simple relaxation process, in accordance with most other relaxation processes observed in Nature.

Common dependence on stress for the statistics of granular avalanches and earthquakes.

Both earthquake size-distributions and aftershock decay rates obey power laws. Recent studies have demonstrated the sensibility of their parameters to faulting properties such as focal mechanism, rupture speed or fault complexity. The faulting style dependence may be related to the magnitude of the differential stress, but no model so far has been able to reproduce this behaviour. Here we investigate the statistical properties of avalanches in a dissipative, bimodal particulate system under slow shear. We find that the event size-distribution obeys a power law only in the proximity of a critical volume fraction, whereas power-law aftershock decay rates are observed at all volume fractions accessible in the model. Then, we show that both the exponent of the event size-distribution and the time delay before the onset of the power-law aftershock decay rate are decreasing functions of the shear stress. These results are consistent with recent seismological observations of earthquake size-distribution and aftershock statistics.