Earthquake Aftershocks Research Articles

Volumetric Structure of the Bachat Earthquake (Kuzbass) Aftershock Area and Stress State of Rock Mass under Open-Pit Mine

Abstract —The Bachat earthquake (M = 6.1) with the epicenter coordinates of 54.29° N, 86.17° E occurred on June, 18 2013 near the Bachatsky coal strip mine, is the world’s largest earthquake induced while mining solid minerals. More than 5000 aftershocks were registered and the spatial volumetric structure of the aftershock area was investigated. The Bachat coal field is located in the Salair zone of the Kuznetsk Depression and is represented by a brachysynclinal fold of a very complex structure characterized by the damage and fracturing behaviors of rocks. The main event is confined to the coal-mine pit wall, with the greatest density of aftershocks observed in its middle portion. In the cross section, aftershocks form a wide area with its deepened portion shifted towards the Kuznetsk Depression, while large faults bounding the depression dip down under the Salair Ridge. In the exposed pit wall, at a depth of 4 km, the activated area resembles a rhombus whose horizontal diagonal line runs across the entire length of the mine pit and decreases both in upward and downward directions. The area is seismically activated to a depth of 6 km, with more intense activation of rock mass observed within the 1–3 km depth interval. Results of the study of the mechanisms of aftershock sources revealed a disagreement between the stress state of rock mass of the Bachatsky open-pit coal mine modeled from the mechanisms of aftershocks, and the mainshock mechanism of the Bachat earthquake.

The 6 February 2023 Türkiye Earthquake Sequence as Detected in the Ionosphere

AbstractOn 6 February 2023, a series of large earthquakes struck Turkey and Northern Syria. The main earthquake of Mw 7.8 occurred at 01:17:34 UTC and was followed by the three notable (Mw > 5.5) aftershocks within the next 18 min. Then, ∼9 hr later, the biggest aftershock with magnitude Mw 7.5 and a Mw 6.0 earthquake occurred to the north‐east from the first main earthquake. In this work, we use data of ground‐based Global Navigation Satellite Systems (GNSS) receivers in Turkey, Israel and Cyprus to analyze the ionospheric response to this series of earthquakes. We separate these events in two groups: the first sequence of earthquakes (at 01–02 UTC) and the second sequence (at 10–11 UTC). For the first sequence, we observe a clear N‐shaped total electron content (TEC) response after the Mw 7.8 mainshock earthquake and Mw 6.7 aftershock, and a smaller TEC disturbance that is, most likely, caused by the Mw 5.6 earthquake. The latter is now the smallest earthquake detected by using ionospheric GNSS data. The co‐seismic ionospheric disturbances (CSID) propagated from the epicentral area in the south‐west direction with velocities of about 750–830 m/s. For the second sequence, we observed the response to the Mw 7.5 aftershock earthquake and the Mw 6.0 aftershock. The CSID propagated both to the south‐west and the north‐west to the epicentral area, with velocities of about 950–1,100 m/s.

Aftershocks and Fluctuating Diffusivity.

The Omori-Utsu law shows the temporal power-law-like decrease of the frequency of earthquake aftershocks and, interestingly, is found in a variety of complex systems/phenomena exhibiting catastrophes. Now, it may be interpreted as a characteristic response of such systems to large events. Here, hierarchical dynamics with the fast and slow degrees of freedom is studied on the basis of the Fokker-Planck theory for the load-state distribution to formulate the law as a relaxation process, in which diffusion coefficient in the space of the load state is treated as a fluctuating slow variable. The evolution equation reduced from the full Fokker-Planck equation and its Green's function are analyzed for the subdynamics governing the load state as the fast degree of freedom. It is shown that the subsystem has the temporal translational invariance in the logarithmic time, not in the conventional time, and consequently the aging phenomenon appears.

Seismic regime and features of geophysical fields in the epicentral area of the Andrey-Tas earthquake (seismotectonic zone of the Chersky Randge, northeast Yakutia)

This paper describes the strong Andrey-Tass earthquake (Mѡ=6.1), which occurred in 2008 on the northeastern flank of the seismotectonic zone of the Chersky Randge in the region of the interaction of the Eurasian and North American lithospheric plates. Geophysical fields were using to elucidate structural and tectonic features of the study area and their relationship with seismicity. Using data from digital maps of magnetic and gravity field anomalies, it was possible to clarify the kinematic parameters of the western end of the Ilin-Tas fault, where the epicenter of the Andrey-Tas earthquake occurred. This fault separates the Indigiro-Zyrian Trough from the Momskii Randge and Andrei Tas Locke elevations and is traced by gradient zones of transition from negative to positive ΔTa and Δg values. The main seismic shock is confining to thickening of Δg isoanomalies, which form a gravitational step, within which gravity values decrease from south to north. The entire epicentral field with aftershocks covers the western slope of the Andrei Tas Locke. The development of the seismic process during three stages was analyzed: 1963-2007 (before the event), 2008 (the event with aftershocks), 2009-2020 (after the event). We plotted the recurrence of the aftershocks of the Andrei Tas earthquake. Information obtained because of study of Andrei Tas earthquake aftershocks enables us to detail manifestations of local seismic activity.

Fragility curves for reinforced concrete (RC)/steel vertical hybrid frame structure under mainshock–aftershock sequences

ABSTRACT A reinforced concrete (RC)/steel vertical hybrid frame structure usually consists of a lower concrete structure and an upper steel structure connected in series. This study aims to derive fragility curves for RC/steel vertical hybrid frame structures under mainshock–aftershock sequences. For this purpose, a double incremental dynamic analysis (D-IDA) approach is performed to derive fragility curves for a five-story RC/steel vertical hybrid frame (a three‐story RC frame at the bottom + a two‐story steel frame at the top) under 14 real mainshock– aftershock earthquake ground motions. The fragility curves obtained for RC/steel frame are also compared with fragility curves for a five‐story purely RC frame. Also, residual capacity diagrams are provided for RC/steel and purely RC frames based on the D-IDA results. The results show that RC/steel frame structure has larger collapse capacity than that of the purely RC frame structure, and can diminish collapse probability by 33% compared to purely RC frame structure.

Seismicity and Fault Interaction in the Gulf of Aqaba

The Gulf of Aqaba is considered one of the most seismotectonically active regions in the Middle East. This study analyzes the seismic activity from 1983 to 2018 to investigate the spatio-temporal distribution of the events in the Gulf’s three basins. The seismic activity is characterized by conventional mainshock–aftershock sequences and swarm activity. Most activity is located in the Aragonese basin, while the Dakar basin shows less seismic activity. The b-value was calculated for the three basins from the declustered catalogue, representing the fingerprint of the transform fault. Within the Aragonese, three significant earthquakes occurred in 1993, 1995, and 2015 with moment magnitude (Mw) of 5.8, 7.2, and 5.2, respectively. An intermediate seismic quiescence preceded the three earthquakes. The quiescence time for the 1995 earthquake began at the tail of the aftershocks of the 1993 mainshock, suggesting that the two earthquakes were not entirely independent. At the tail of the 1995 earthquake aftershocks, the seismic activity spread across the Gulf, increasing in frequency and decreasing in magnitude. A similar pattern was observed for the seismic quiescence preceding the 2015 mainshock. The occurrence of the three significant and proximal earthquakes in the Aragonese region over a 22-year interval, with the described similarities, suggests a link between these earthquakes. Finally, the Coulomb stress transfer shows that the 1993 source fault seems to increase the stress loading on the 1995 left-lateral strike-slip fault, and the latter would also increase the stress transfer on the 2015 left-lateral strike-slip fault.

Forecasting Strong Subsequent Earthquakes in Greece with the Machine Learning Algorithm NESTORE.

Aftershocks of earthquakes can destroy many urban infrastructures and exacerbate the damage already inflicted upon weak structures. Therefore, it is important to have a method to forecast the probability of occurrence of stronger earthquakes in order to mitigate their effects. In this work, we applied the NESTORE machine learning approach to Greek seismicity from 1995 to 2022 to forecast the probability of a strong aftershock. Depending on the magnitude difference between the mainshock and the strongest aftershock, NESTORE classifies clusters into two types, Type A and Type B. Type A clusters are the most dangerous clusters, characterized by a smaller difference. The algorithm requires region-dependent training as input and evaluates performance on an independent test set. In our tests, we obtained the best results 6 h after the mainshock, as we correctly forecasted 92% of clusters corresponding to 100% of Type A clusters and more than 90% of Type B clusters. These results were also obtained thanks to an accurate analysis of cluster detection in a large part of Greece. The successful overall results show that the algorithm can be applied in this area. The approach is particularly attractive for seismic risk mitigation due to the short time required for forecasting.

Rougher Faults May Generate More Earthquake Aftershocks

Lab experiments on pieces of granite reflect natural aftershock dynamics and highlight the role of rock roughness along a fault.

Analysis of Aftershock Earthquake Decay in Mamberamo on September 10, 2022 using GEOSTAT V2.0 Software

There was an earthquake on September 10, 2022 with a magnitude of 6.2 with a depth of 16 km in Mamberamo Raya, Papua. This earthquake is located at coordinates 2.04° South Latitude - 138.26° East Longitude. This earthquake produced 93 aftershocks since seven days after the mainshock. This study aims to determine the end time of aftershock decay. This study uses the Mogi I, Mogi II, Utsu and Omori methods contained in the GEOSTAT V2.0 software. The approach of observational data in real time is carried out to validate the selected calculation method. This aftershock decay analysis aims to mitigate earthquake disasters to the public in the form of information on the estimated decay time of aftershocks. The calculation of the Mogi I method shows that the aftershock experienced a decay on the 9th day of September 18, 2022 (r = -0.94157). The calculation of the Mogi II method shows that the aftershock experienced a decay on the 7th day of September 17, 2022 (r = -089415). While the calculation of the Omori method shows that the aftershock earthquake experienced decay on the 6th day of September 16, 2022 (r = 081628) and the calculation method of the Utsu method showed that the aftershock experienced decay on the 9th day of September 18 2022 (r = -094154). The calculation method that is close to BMKG real time observation is the Utsu method with a decay time on the 9th day of September 18, 2022 (r = -0.94154).

Hidden jerk in universal creep and aftershocks.

Most materials exhibit creep memory under the action of a constant load. The memory behavior is governed by Andrade's creep law, which also has an inherent connection with the Omori-Utsu law of earthquake aftershocks. Both empirical laws lack a deterministic interpretation. Coincidentally, the Andrade law is similar to the time-varying part of the creep compliance of the fractional dashpot in anomalous viscoelastic modeling. Consequently, fractional derivatives are invoked, but since they lack a physical interpretation, the physical parameters of the two laws extracted from curve fit lack confidence. In this Letter, we establish an analogous linear physical mechanism that underlies both laws and relates its parameters with the material's macroscopic properties. Surprisingly, the explanation does not require the property of viscosity. Instead, it necessitates the existence of a rheological property that relates strain with the first order time derivative of stress, which involves jerk. Further, we justify the constant quality factor model of acoustic attenuation in complex media. The obtained results are validated in light of the established observations.

Comparative Analysis of Multistorey RCC and Semi-Rigid Steel Frame with Cross Bracings Subjected to Mainshock and Aftershock Earthquake Sequence

Strong Ground Motions have a significant impact on structural analysis and design. Seismic evaluation is deemed necessary for the quality, reliability, and feasibility of existing and developing structures. Earthquakes are even more disastrous when a mainshock is succeeded and preceded by aftershocks of higher magnitude. Most of the time, these aftershocks are ignored during analysis. In the last few decades, steel buildings have been crucial to the construction sector. On the other hand, RCC frames are commonly designed structures for commercial purposes and cost-effectiveness. IS 1893 (Part:1)-2002 Criteria for Earthquake Resistant Design of Structures and IS 13920-2016 Ductile Detailing of RC Structures Subjected to Seismic Reactions are majorly used for Seismic Analysis. Steel bracings in the structural system increase the ductility and stiffness of the frame structure. That can be arranged in a variety of ways, such as X, diagonally, alternatively, V, inverted V, K, etc. Cross bracings are used in this paper for the design of a typical multi-story (G+9) semi-rigid steel frame and a typical RCC frame is designed of the same dimensions. Both the frames are modelled and compared using ETABS software and a static nonlinear Time History analysis is executed to examine the performance of both the frames under the Mainshock and Aftershock of Chamoli earthquake. The Mainshock and Aftershock results of the Chamoli earthquake are extracted from the Centre for Engineering Strong Motion Research Ground Motion Database. Base shear, joint displacement, kinetic energy, and story displacement are a few of the variables of Time History Analysis that affect how well a building performs during mainshock and aftershock earthquakes. When analysing the outcomes, it is important to take into account that each of these factors significantly affects how a building responds to seismic loads.

Universal Non-Extensive Statistical Physics Temporal Pattern of Major Subduction Zone Aftershock Sequences.

Large subduction-zone earthquakes generate long-lasting and wide-spread aftershock sequences. The physical and statistical patterns of these aftershock sequences are of considerable importance for better understanding earthquake dynamics and for seismic hazard assessments and earthquake risk mitigation. In this work, we analyzed the statistical properties of 42 aftershock sequences in terms of their temporal evolution. These aftershock sequences followed recent large subduction-zone earthquakes of M ≥ 7.0 with focal depths less than 70 km that have occurred worldwide since 1976. Their temporal properties were analyzed by investigating the probability distribution of the interevent times between successive aftershocks in terms of non-extensive statistical physics (NESP). We demonstrate the presence of a crossover behavior from power-law (q ≠ 1) to exponential (q = 1) scaling for greater interevent times. The estimated entropic q-values characterizing the observed distributions range from 1.67 to 1.83. The q-exponential behavior, along with the crossover behavior observed for greater interevent times, are further discussed in terms of superstatistics and in view of a stochastic mechanism with memory effects, which could generate the observed scaling patterns of the interevent time evolution in earthquake aftershock sequences.

Cascading Hazards in a Migrating Forearc‐Arc System: Earthquake and Eruption Triggering in Nicaragua

AbstractStrain partitioning in oblique convergent margins results in margin‐parallel shear in the overriding plate. Margin‐parallel shear is often accommodated by margin‐parallel strike‐slip faults proximal to active volcanic arcs. Along the Nicaraguan segment of the Central American Forearc (CAFA) in the Cocos‐Caribbean plate convergent margin, there are no well‐expressed right‐lateral faults that accommodate CA‐CAFA relative motion. Instead, historical earthquakes and mapped fault orientations indicate that the ∼12 mm/yr of dextral motion is accommodated on arc‐normal, left‐lateral faults (i.e., bookshelf faults). We investigate three upper‐plate earthquakes; the 10 April 2014 (Mw 6.1), 15 September 2016 (Mw 5.7), and 28 September 2016 (Mw 5.5), using Global Position System co‐seismic displacements and relocated earthquake aftershocks. Our analyses of the three earthquakes indicate that the 10 April 2014 earthquake ruptured an unmapped margin‐parallel right‐lateral fault in Lago Xolotlán (Managua) and the September 2016 earthquakes ruptured arc‐normal, left‐lateral and oblique‐slip faults. These earthquakes represent a triggered sequence whereby the 10 April 2014 earthquake promoted failure of the faults that ruptured in September 2016 by imparting a static Coulomb stress change (ΔCFS) of 0.02–0.07 MPa. Likewise, the 15 September 2016, earthquake additionally promoted failure (ΔCFS of 0.08–0.1 MPa) on sub‐parallel faults that ruptured in two subsequent earthquakes. We also present an instance of magma‐tectonic interaction whereby the 10 April 2014 earthquake dilated (10s of μStrain) the shallow magmatic system of Momotombo Volcano, which led to magma injection, ascent, and eruption on 1 December 2015, after ∼100 years of quiescence.

Shaking table test study on seismic performance of RC frame structure with NES

A new type of nonlinear vibration absorber NES (Nonlinear Energy Sink) studied in this paper belongs to the structural passive control technology, which consists of a horizontal track and an additional mass block. Acting as a damper absorb and dissipate energy, the NES completes the target energy transfer by generating a horizontal nonlinear restoring force and reduces the response of the main structure. In this paper theoretical analysis of the new NES was analyzed by the expression of the restoring force of the NES and the equation of motion of the additional NES system are deduced. Shaking table test was carried out on the 1:4 scale RC frame structure model installed with the new NES shock absorber, focusing on the research on the energy dissipation and shock absorption effect of the NES shock absorber, and whether it can improve the seismic performance of the RC frame structure damaged in the earthquake. The results show that the NES installed in the RC frame structure has sufficient nonlinear displacement and energy dissipation capacity under the moderate and strong earthquakes, showing a very good energy dissipation and shock absorption effect. The NES can reduce the top story displacement and acceleration response of the main structure under the action of earthquake; the top story displacement and absolute acceleration response are related to the natural frequency of the frame and the spectral characteristics of seismic waves, so that the vibration control effect is affected by the frequency spectrum of seismic waves. In the frequency domain analysis of the frame dynamic response, the nonlinear energy well exhibits the characteristics of broadband control. This type of NES significantly reduces the seismic response of damaged structures, improves the seismic performance of damaged structures under moderate to strong earthquakes, and decreases the risk of potential collapse and construction costs during earthquake aftershocks.

Fault Zone Imaging With Distributed Acoustic Sensing: Body‐To‐Surface Wave Scattering

AbstractFault zone structures at many scales largely dictate earthquake ruptures and are controlled by the geologic setting and slip history. Characterizations of these structures at diverse scales inform better understandings of earthquake hazards and earthquake phenomenology. However, characterizing fault zones at sub‐kilometer scales has historically been challenging, and these challenges are exacerbated in urban areas, where locating and characterizing faults is critical for hazard assessment. We present a new procedure for characterizing fault zones at sub‐kilometer scales using distributed acoustic sensing (DAS). This technique involves the backprojection of the DAS‐measured scattered wavefield generated by natural earthquakes. This framework provides a measure of the strength of scattering along a DAS array and thus constrains the positions and properties of local scatterers. The high spatial sampling of DAS arrays makes possible the resolution of these scatterers at the scale of tens of meters over distances of kilometers. We test this methodology using a DAS array in Ridgecrest, CA which recorded much of the 2019 Mw7.1 Ridgecrest earthquake aftershock sequence. We show that peaks in scattering along the DAS array are spatially correlated with mapped faults in the region and that the strength of scattering is frequency‐dependent. We present a model of these scatterers as shallow, low‐velocity zones that is consistent with how we may expect faults to perturb the local velocity structure. We show that the fault zone geometry can be constrained by comparing our observations with synthetic tests.

Seismic response and aftershock fragility curves for Non-ductile Mid-rise buildings comprised of reinforced concrete frame with masonry infill

The 2010/2011 Canterbury, New Zealand earthquake sequences showed that aftershock earthquakes can be more destructive to existing buildings than the mainshock earthquake, particularly for buildings that were designed prior to the adoption of ductility requirements. Following the Canterbury earthquakes it was observed by post-earthquake reconnaissance teams that the level of damage for a number of non-ductile masonry infill buildings had increased from minor damage in the mainshock to moderate and major damage in the aftershocks. The majority of these non-ductile masonry infill buildings were constructed before the establishment of the New Zealand Standard (NZS) 4203 in 1976, and it was found that these buildings were constructed using low grade undeformed (smooth) longitudinal reinforcement and incorporated seismic detailing that was assessed as inadequate when compared to current design practice. The reported study was conducted to investigate the behaviour of non-ductile mid-rise masonry infill buildings when subjected to a combined mainshock-aftershock earthquake sequence, with the associated development of fragility curves that can be used to forecast the potential for building damage and collapse. Incremental Dynamic Analysis (IDA) was undertaken to seismically assess these non-ductile mid-rise masonry infill buildings, and a set of aftershock fragility curves was generated for different damage states following mainshock shaking. It was established that as the Inter-storey Drift Ratio (IDR) of a mainshock-damaged building increased, further damage that derived from aftershock shaking occurred at a smaller spectral acceleration intensity, illustrating that these mainshock-damaged buildings were highly vulnerable when subjected to a smaller intensity of aftershock earthquakes.

Fine Structure of the Subducting Slab and the 2022 M 7.4 Fukushima–Oki Intraslab Earthquake

Abstract The 16 March 2022 M 7.4 Fukushima–Oki earthquake is the largest one among forearc intraslab earthquakes in Japan since 2000. These subcoast events can cause severe damage to the local society because of their proximity to inhabited areas. However, their generating mechanism is still not clear. Here, we present 3D high-resolution seismic tomography of the source zone of four large intraslab events (M ≥7.0) during 2003–2022 in northeast Japan, which is obtained by inverting high-quality arrival-time data recorded at both onshore and offshore seismic stations. Aftershocks of the subcoast intraslab earthquakes are mainly distributed in gaps of high-velocity bodies with high Poisson’s ratio and at the upper ∼20 km depth of the subducting Pacific slab. Our results indicate that the four large intraslab events were caused by rupturing of buried hydrated faults that formed at the outer rise and dehydration embrittlement on the fault planes.

Precursory Tidal Triggering of the 2011 Mw 9.0 Tohoku Aftershocks

Precursory earth tidal triggering is believed to influence earthquake timing preferentially when a region is critically stressed. However, whether and how the recurrence of aftershocks after a giant earthquake is affected by tidal triggering remains perplexing. To provide insight into this study, we utilized the Schuster test to explore the tidally induced stress variation correlated with the 2011 Mw 9.0 Tohoku earthquake aftershock sequence by determining the tidal phase angle at the occurrence time of events and the periodic characteristics of the aftershocks. Our results show that the aftershocks were triggered by short-period tides, including semidiurnal and diurnal tides. The rupture associated with the mainshock likely resulted in a critical stress state in the focal region, which is conducive to tidal triggering. We subdivided the aftershock catalog into several subsets, using a depth of 30 km and a magnitude of 5 as discriminators. The analysis of these subsets reveals that weaker and deeper earthquakes are best correlated with Earth tides, which will be helpful to investigate the mechanisms of tidal correlation.

Analysis of Multistorey RCC Frame subjected to Mainshock and Aftershock Earthquake

Abstract: Structure analysis and design are significantly influenced by earthquake. It is believed that seismic evaluation is required for the viability and serviceability of both present and future building structures. When a structure's base is subjected to a certain type of ground motion, a time history analysis is performed to examine the dynamic reaction of the structure at each time interval. The near-field earthquake ground motion verification may have specific impacts for both forward and backward directivity. The initial's velocity and displacement motions, respectively, exhibit pulse and fling-step characteristics. Therefore, it is crucial to assess how well structures built solely to withstand the primary shock would work through future aftershocks. Using modern seismic protection systems, such as base isolations or / and supplemental dampening devices, that significantly reduce building damages during main shocks and their related aftershocks is one of the appropriate solutions to this issue. Due to changes in both static and dynamic stress that take place during the earthquake process, aftershock events are set off by the primary shock. In order to better understand the ground motion features of a sizable collection of mainshock and subsequent aftershock ground motion data recorded in accelerograph stations around the region, this study reviews pertinent literature in the field. The G+9 RCC building will be used in this study to conduct a time history analysis of the mainshock and aftershock data of the Chamoli earthquake provided by the Centre for Engineering Strong Motion Research Ground Motion Database. For designing purposes, the IS 456-2000 code is taken into consideration. Live loads are measured in accordance with IS 875-part 1, and seismic zone IV is selected for analysis in accordance with IS 1893-2016. Storey drift, base shear, joint reactions, and storey displacement are just a few of the variables that can have an impact on how well a building performs. Since each of these variables has a significant impact on how a structure responds to seismic loads, they are also taken into account when evaluating the results.

Mainshock-aftershock effect on the seismic performance of multi-story CBFs equipped with SMA-friction damping braces

This paper aims to understand the effect of mainshock-aftershock earthquake sequences on the seismic performance of multi-story concentrically braced frames (CBFs) equipped with shape memory alloy (SMA) friction damping braces (SMAFDBs), based on a comparison with those equipped with buckling-restrained braces (BRBs). The SMAFDB is a serial connection of SMA damper and friction damper. The friction damper starts to slip and serves as the “fuse” element to protect the SMA damper under destructive earthquake events. Ten ground motion records corresponding to the maximum considered earthquake (MCE) hazard level are defined as the mainshock input, and the aftershock input is generated by appropriately scaling the mainshock input to four seismic hazard levels. To achieve a fair comparison, the considered CBFs are first designed to exhibit identical mean height-wise peak interstory drift ratios under the design-basis earthquake (DBE) ground motions. Then, these two frames are subjected to four suites of mainshock-aftershock earthquake sequences and their seismic responses are compared against each other. It indicates that both the peak and residual interstory drift ratios of the SMAFDB frame (SMAFDBF) are smaller than that of the BRB frame (BRBF) on average during the aftershock earthquakes, which is found primarily attributed to the fact that the former suffers from smaller post-mainshock residual deformation. The higher seismic capacity of the SMAFDBF over the BRBF is also confirmed by conducting fragility analysis. Finally, the recentering capacity under aftershock earthquakes are analyzed for both frames, based on the maximum residual interstory drift ratios.