Doubly Stochastic Earthquake Source Model: “Omega-Square” Spectrum and Low High-Frequency Directivity Revealed by Numerical Experiments

Since its formulation in 1967–1970, the classical ω ^?2 model of earthquake source spectrum awaits a consistent theoretical foundation. To obtain one, stochastic elements are incorporated both into the final structure of the fault and into the mode of rupture propagation. The main components of the proposed “doubly stochastic” model are: (1) the Andrews’s concept, that local stress drop over a fault is a random self-similar field; (2) the concept of rupture with running slip pulse, after Heaton; (3) the hypothesis that a rupture front is a tortuous, multiply connected (“lacy”) fractal polyline that occupies a strip of finite width close to the slip-pulse width; and (4) the assumption that the propagation distance of fault-guided, mostly Rayleigh waves from a failing spot on a fault is determined by the slip-pulse width. Waveforms produced by this model are determined based on the fault asperity failure model after Das and Kostrov. Properties of the model are studied by numerical experiments. At high frequency, simulated source spectra behave as ω ^?2, and acceleration spectra are flat. Their level, at a given seismic moment and rms stress drop, is inversely related to the relative width of the slip pulse. When this width is relatively low, a well-defined second corner frequency (lower cutoff of acceleration spectrum) is seen. The model shows clear dependence of propagation-related directivity on frequency. Between the first and the second corner frequency, amplitude spectra are strongly enhanced for the forward direction; whereas, above the second corner frequency, directivity is significantly reduced. Still, it is not inhibited totally, suggesting incomplete incoherence of the simulated radiator at high frequencies.     

Characterization of the Heterogeneous Source Model of Intraslab Earthquakes Toward Strong Ground Motion Prediction

We characterize the heterogeneous source slip model of intraslab earthquakes to compare source scaling properties with those of inland crustal and subduction-zone plate-boundary earthquakes. We extracted rupture area (S), total area of asperity (S _a), average slip (D) and average slip on asperity (D _a) of eleven intraslab earthquakes following the procedure proposed by Somerville et al. (Seism Res Lett 70:59?C80, 1999) and proposed the empirical scaling relationship formula of S, S _a, and D for intraslab earthquakes. Under the same seismic moment, an intraslab earthquake has a smaller rupture area and total area of asperity, and smaller average slip than an inland crustal earthquake. The area ratio of asperity area and total rupture area of intraslab earthquakes are similar to those of inland crustal earthquakes. The strong motion generation area (SMGA) scaling of intraslab earthquakes appears self-similar, and those results support the idea the characterized source model of intraslab earthquakes can be modeled in a manner similar to that of inland crustal earthquakes.     

Scaling Transition in Earthquake Sources: A Possible Link Between Seismic and Laboratory Measurements

We estimate the corner frequencies of 20 crustal seismic events from mainshock–aftershock sequences in different tectonic environments (mainshocks 5.7 < M _W < 7.6) using the well-established seismic coda ratio technique (Mayeda et al. in Geophys Res Lett 34:L11303, 2007; Mayeda and Malagnini in Geophys Res Lett, 2010), which provides optimal stability and does not require path or site corrections. For each sequence, we assumed the Brune source model and estimated all the events’ corner frequencies and associated apparent stresses following the MDAC spectral formulation of Walter and Taylor (A revised magnitude and distance amplitude correction (MDAC2) procedure for regional seismic discriminants, 2001), which allows for the possibility of non-self-similar source scaling. Within each sequence, we observe a systematic deviation from the self-similar \( M_{0} \propto \mathop f\nolimits_{\text{c}}^{ - 3} \) line, all data being rather compatible with \( M_{0} \propto \mathop f\nolimits_{\text{c}}^{ - (3 + \varepsilon )} \) , where ε > 0 (Kanamori and Rivera in Bull Seismol Soc Am 94:314–319, 2004). The deviation from a strict self-similar behavior within each earthquake sequence of our collection is indicated by a systematic increase in the estimated average static stress drop and apparent stress with increasing seismic moment (moment magnitude). Our favored physical interpretation for the increased apparent stress with earthquake size is a progressive frictional weakening for increasing seismic slip, in agreement with recent results obtained in laboratory experiments performed on state-of-the-art apparatuses at slip rates of the order of 1 m/s or larger. At smaller magnitudes (M _W < 5.5), the overall data set is characterized by a variability in apparent stress of almost three orders of magnitude, mostly from the scatter observed in strike-slip sequences. Larger events (M _W > 5.5) show much less variability: about one order of magnitude. It appears that the apparent stress (and static stress drop) does not grow indefinitely at larger magnitudes: for example, in the case of the Chi–Chi sequence (the best sampled sequence between M _W 5 and 6.5), some roughly constant stress parameters characterize earthquakes larger than M _W ~ 5.5. A representative fault slip for M _W 5.5 is a few tens of centimeters (e.g., Ide and Takeo in J Geophys Res 102:27379–27391, 1997), which corresponds to the slip amount at which effective lubrication is observed, according to recent laboratory friction experiments performed at seismic slip velocities (V ~ 1 m/s) and normal stresses representative of crustal depths (Di Toro et al. in Nature in press, 2011, and references therein). If the observed deviation from self-similar scaling is explained in terms of an asymptotic increase in apparent stress (Malagnini et al. in Pure Appl Geophys, 2014, this volume), which is directly related to dynamic stress drop on the fault, one interpretation is that for a seismic slip of a few tens of centimeters (M _W ~ 5.5) or larger, a fully lubricated frictional state may be asymptotically approached.     

Stress Release and Source Scaling of the 2010–2011 Canterbury,New Zealand Earthquake Sequence from Spectral Inversion of Ground Motion Data

The Canterbury earthquake sequence beginning with the 2010 M _W 7.2 Darfield earthquake is one of the most notable and well-recorded crustal earthquake sequences in a low-strain-rate region worldwide and as such provides a unique opportunity to better understand earthquake source physics and ground motion generation in such a tectonic setting. Ground motions during this sequence ranged up to extreme values of 2.2 g, recorded during the February 2011 M _W 6.2 event beneath the city of Christchurch. A better understanding of the seismic source signature of this sequence, in particular the stress release and its scaling with earthquake size, is crucial for future ground motion prediction and hazard assessment in Canterbury, but also of high interest for other low-to-moderate seismicity regions where high-quality records of large earthquakes are lacking. Here we present a source parameter study of more than 200 events of the Canterbury sequence, covering the magnitude range M _W 3–7.2. Source spectra were derived using a generalized spectral inversion technique and found to be well characterized by the ω ^?2 source model. We find that stress drops range between 1 and 20 MPa with a median value of 5 MPa, which is a factor of 5 larger than the median stress drop previously estimated with the same method for crustal earthquakes in much more seismically active Japan. Stress drop scaling with earthquake size is nearly self-similar, and we identify lateral variations throughout Canterbury, in particular high stress drops at the fault edges of the two major events, the M _W 7.2 Darfield and M _W 6.2 Christchurch earthquakes.     

Near-Field Tsunami Edge Waves and Complex Earthquake Rupture

The effect of distributed coseismic slip on progressive, near-field edge waves is examined for continental shelf tsunamis. Detailed observations of edge waves are difficult to separate from the other tsunami phases that are observed on tide gauge records. In this study, analytic methods are used to compute tsunami edge waves distributed over a finite number of modes and for uniformly sloping bathymetry. Coseismic displacements from static elastic theory are introduced as initial conditions in calculating the evolution of progressive edge-waves. Both simple crack representations (constant stress drop) and stochastic slip models (heterogeneous stress drop) are tested on a fault with geometry similar to that of the M _w = 8.8 2010 Chile earthquake. Crack-like ruptures that are beneath or that span the shoreline result in similar longshore patterns of maximum edge-wave amplitude. Ruptures located farther offshore result in reduced edge-wave excitation, consistent with previous studies. Introduction of stress-drop heterogeneity by way of stochastic slip models results in significantly more variability in longshore edge-wave patterns compared to crack-like ruptures for the same offshore source position. In some cases, regions of high slip that are spatially distinct will yield sub-events, in terms of tsunami generation. Constructive interference of both non-trapped and trapped waves can yield significantly larger tsunamis than those that produced by simple earthquake characterizations.     

A study of Guptkashi,Uttarakhand earthquake of 6 February 2017 (<Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript>5.3) in the Himalayan arc and implications for ground motion estimation

The 2017 Guptkashi earthquake occurred in a segment of the Himalayan arc with high potential for a strong earthquake in the near future. In this context, a careful analysis of the earthquake is important as it may shed light on source and ground motion characteristics during future earthquakes. Using the earthquake recording on a single broadband strong-motion seismograph installed at the epicenter, we estimate the earthquake’s location (30.546° N, 79.063° E), depth (H?=?19 km), the seismic moment (M₀?=?1.12×10¹⁷ Nm, M _w 5.3), the focal mechanism (φ?=?280°, δ?=?14°, λ?=?84°), the source radius (a?=?1.3 km), and the static stress drop (Δσ _s ~22 MPa). The event occurred just above the Main Himalayan Thrust. S-wave spectra of the earthquake at hard sites in the arc are well approximated (assuming ω^?2 source model) by attenuation parameters Q(f)?=?500f^0.9, κ?=?0.04 s, and f_max?=?infinite, and a stress drop of Δσ?=?70 MPa. Observed and computed peak ground motions, using stochastic method along with parameters inferred from spectral analysis, agree well with each other. These attenuation parameters are also reasonable for the observed spectra and/or peak ground motion parameters in the arc at distances ≤?200 km during five other earthquakes in the region (4.6?≤?M _w ?≤?6.9). The estimated stress drop of the six events ranges from 20 to 120 MPa. Our analysis suggests that attenuation parameters given above may be used for ground motion estimation at hard sites in the Himalayan arc via the stochastic method.     

Slip-Weakening Models of the 2011 Tohoku-Oki Earthquake and Constraints on Stress Drop and Fracture Energy

We present 2D dynamic rupture models of the 2011 Tohoku-Oki earthquake based on linear slip-weakening friction. We use different types of available observations to constrain our model parameters. The distribution of stress drop is determined by the final slip distribution from slip inversions. As three groups of along-dip slip distribution are suggested by different slip inversions, we present three slip-weakening models. In each model, we assume uniform critical slip distance eastward from the hypocenter, but several asperities with smaller critical slip distance westward from the hypocenter. The values of critical slip distance are constrained by the ratio of deep to shallow high-frequency slip-rate power inferred from back projection source imaging. Our slip-weakening models are consistent with the final slip, slip rate, rupture velocity and high-frequency power ratio inferred for this earthquake. The average static stress drop calculated from the models is in the range of 4.5–7 MPa, though large spatial variations of static stress drop exist. To prevent high-frequency radiation in the region eastward from the hypocenter, the fracture energy needed there is in the order of 10 MJ/m², and the average up-dip rupture speed cannot exceed 2 km/s. The radiation efficiency calculated from our models is higher than that inferred from seismic data, suggesting the role of additional dissipation processes. We find that the structure of the subduction wedge contributes significantly to the up-dip rupture propagation and the resulting large slip at shallow depth.     

Source process of the 14 November 2001 western Kunlun Mountain <Emphasis Type="Italic">M</Emphasis><Subscript>S</Subscript>=8.1 earthquake

Based on digital teleseismic P-wave seismograms recorded by 28 long-period seismograph stations of the global seismic network, source process of the November 14, 2001 western Kunlun Mountain M _S=8.1 (M _W=7.8) earthquake is estimated by a new inversion method. The result shows that the earthquake is a very complex rupture event. The source rupture initiated at the hypocenter (35.95°N, 90.54°E, focal depth 10 km, by USGS NEIC), and propagated to the west at first. Then, in several minutes to a hundred minutes and over a large spatial range, several rupture growth points emerged in succession at the eastern end and in the central part of the finite fault. And then the source rupture propagated from these rupture growth points successively and, finally, stopped in the area within 50 km to the east of the centroid position (35.80°N, 92.91°E, focal depth 15 km, by Harvard CMT). The entire rupture lasted for 142 s, and the source process could be roughly separated into three stages: The first stage started at the 0 s and ended at the 52 s, lasting for 52 s and releasing approximately 24.4% of the total moment; The second stage started at the 55 s and ended at the 113 s, lasting for 58 s and releasing approximately 56.5% of the total moment; The third stage started at the 122 s and ended at the 142 s, lasting for 20 s and releasing approximately 19.1% of the total moment. The length of the ruptured fault plane is about 490 km. The maximum width of the ruptured fault plane is about 45 km. The rupture mainly occurred within 30 km in depth under the surface of the Earth. The average static slip in the underground rocky crust is about 1.2 m with the maximum static slip 3.6 m. The average static stress drop is about 5 MPa with the maximum static stress drop 18 MPa. The maximum static slip and the maximum stress drop occurred in an area within 50 km to the east of the centroid position.     

The Marmara Sea region: Seismic behaviour in time and the likelihood of another large earthquake near Istanbul (Turkey)

The North Anatolian Fault (NAF) extends for about 1500 km from Karliova to the east, to the Egean Sea in the west. The Marmara region, located near the western end of the NAF, is a tectonically active zone characterized by the transition between a strike slip stress regime and an extensional one in the Aegean Sea. Microseismic studies performed around the Marmara Sea in 1995 [Tectonophysics 316, 2000, 1], and just before the 1999 Izmit Earthquake Bull. Seism. Soc. Am. 92, 2002a, 361;J. Seismol. 6, 2002b, 287) permitted the analysis of the evolution of seismicity connected to this destructive earthquake and its sequels. Several observations indicate that the aftershock distribution fits well the EW orientation of the NAF, but the ruptures are not simple and linear as a first glance would suggest. Instead they are segmented in at least five pieces as shown by the slip variation and aftershock clusters, showing complexity at different scales (Bull. Seism. Soc. Am. 92, 2002a, 361). There is still a gap, across the northern border of the Marmara Sea that has not ruptured, and this is the only sector that did not break on the NAF since the 1939 great Erzincan earthquake. Will it rupture as a whole with a large magnitude earthquake, or by segments with smaller magnitude events? The Hurst analysis of the overall behaviour of the seismicity in the Marmara region since historical times shows that if a large earthquake occurs in the near future, it might break the complete gap. The Hurst character of the time variation of seismicity is persistent with H= 0.82. The aftershocks of the 1999 Izmit earthquake can be analyzed by using the Hurst method, showing an exceptionally high persistent memory.     

G: Fracture energy,friction and dissipation in earthquakes

Recent estimates of fracture energy G ^′ in earthquakes show a power-law dependence with slip u which can be summarized as G ^′ ∝ u ^a where a is a positive real slightly larger than one. For cracks with sliding friction, fracture energy can be equated to G _f : the post-failure integral of the dynamic weakening curve. If the dominant dissipative process in earthquakes is friction, G ^′ and G _f should be comparable and show a similar scaling with slip. We test this hypothesis by analyzing experiments performed on various cohesive and non-cohesive rock types, under wet and dry conditions, with imposed deformation typical of seismic slip (normal stress of tens of MPa, target slip velocity > 1 m/s and fast accelerations ≈ 6.5 m/s²). The resulting fracture energy G _f is similar to the seismological estimates, with G _f and G ^′ being comparable over most of the slip range. However, G _f appears to saturate after several meters of slip, while in most of the reported earthquake sequences, G ^′ appears to increase further and surpasses G _f at large magnitudes. We analyze several possible causes of such discrepancy, in particular, additional off-fault damage in large natural earthquakes.     

The Lemnos 8 January 2013 (M w = 5.7) earthquake: fault slip,aftershock properties and static stress transfer modeling in the north Aegean Sea

We investigate mainshock slip distribution and aftershock activity of the 8 January 2013 M _w?=?5.7 Lemnos earthquake, north Aegean Sea. We analyse the seismic waveforms to better understand the spatio-temporal characteristics of earthquake rupture within the seismogenic layer of the crust. Peak slip values range from 50 to 64 cm and mean slip values range from 10 to 12 cm. The slip patches of the event extend over an area of dimensions 16?×?16 km². We also relocate aftershock catalog locations to image seismic fault dimensions and test earthquake transfer models. The relocated events allowed us to identify the active faults in this area of the north Aegean Sea by locating two, NE–SW linear patterns of aftershocks. The aftershock distribution of the mainshock event clearly reveals a NE–SW striking fault about 40 km offshore Lemnos Island that extends from 2 km up to a depth of 14 km. After the mainshock most of the seismic activity migrated to the east and to the north of the hypocenter due to (a) rupture directivity towards the NE and (b) Coulomb stress transfer. A stress inversion analysis based on 14 focal mechanisms of aftershocks showed that the maximum horizontal stress is compressional at N84°E. The static stress transfer analysis for all post-1943 major events in the North Aegean shows no evidence for triggering of the 2013 event. We suggest that the 2013 event occurred due to tectonic loading of the North Aegean crust.     

Source Scaling of Inland Crustal Earthquake Sequences in Japan Using the S-Wave Coda Spectral Ratio Method

We estimate corner frequencies and stress drops for 298 events ranging from M _w 3.2–7.0 in 17 inland crustal earthquake sequences in Japan to investigate the source scaling and variation in stress drops. We obtain the source spectral ratio from observed records by the S-wave coda spectral ratio method. The advantage of using the S-wave coda is in obtaining much more stable source spectral ratios than using direct S-waves. We carefully examine the common shape of the decay of coda envelopes between event pair records. The corner frequency and stress drop are estimated by modeling the observed source spectral ratio with the omega-square source spectral model. We investigate the dependences of stress drops on some tectonic effects such as regionality, focal mechanism, and source depth. The principal findings are as follows: (1) a break in self-similar source scaling is found in our dataset. Events larger than M _w 4.5 show larger stress drops than those of smaller events. (2) Stress drops of aftershocks are mostly smaller than those of mainshocks in each sequence. (3) There are no systematic differences between stress drops of events occurring inside and outside the Niigata-Kobe Tectonic Zone in Japan. (4) Clear dependence of the faulting type on stress drops cannot be seen. (5) Stress drops of aftershocks depend on their source depth. (6) The crack size obtained from the corner frequency corresponds to the total rupture area of heterogeneous slip models for large events.     

Inferred fault geometry and slip distribution of the 2010 Jiashian,Taiwan, earthquake is consistent with a thick-skinned deformation model

We invert measurements of coseismic displacements from 139 continuously recorded GPS sites from the 2010, Jiashian, Taiwan earthquake to solve for fault geometry and slip distribution using an elastic uniform stress drop inversion. The earthquake occurred at a depth of ~ 23 km in an area between the Western Foothills fold-and-thrust belt and the crystalline high mountains of the Central Range, providing an opportunity to examine the deep fault structure under Taiwan. The inferred rupture plane is oblique to the prominent orientation of thrust faults and parallel to several previously recognized NW-striking transfer zones that appear to connect stepping thrusts. We find that a fault striking 318°–344° with dip of 26°–41° fits the observations well with oblique reverse-sinistral slip under a low stress drop of about 0.5 MPa. The derived geodetic moment of 2.92 × 10¹⁸ N-m is equivalent to a M_w = 6.24 earthquake. Coseismic slip is largely concentrated within a circular patch with a 10-km radius at the depth between 10 and 24 km and maximum slip of 190 mm. We suggest this earthquake ruptured the NW-striking Chishan transfer fault zone, which we interpret as a listric NE-dipping lateral ramp with oblique slip connecting stepping thrust faults (ramps). The inferred slip on the lateral ramp is considerably deeper than the 7–15 km deep detachment identified in previous studies of western Taiwan. We infer an active basal detachment under western Taiwan at a depth of at least ~ 20–23 km based on these inversion results. The earthquake may have nucleated at the base of the lateral ramp near the intersection with the basal detachment. Coulomb stress change calculations suggest that this earthquake moved several NE-striking active thrust faults in western Taiwan nearer to failure.     

Joint inversion of GNSS and teleseismic data for the rupture process of the 2017 <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript>6.5 Jiuzhaigou,China, earthquake

The spatio-temporal slip distribution of the earthquake that occurred on 8 August 2017 in Jiuzhaigou, China, was estimated from the teleseismic body wave and near-field Global Navigation Satellite System (GNSS) data (coseismic displacements and high-rate GPS data) based on a finite fault model. Compared with the inversion results from the teleseismic body waves, the near-field GNSS data can better restrain the rupture area, the maximum slip, the source time function, and the surface rupture. The results show that the maximum slip of the earthquake approaches 1.4 m, the scalar seismic moment is ~ 8.0 × 10¹⁸ N·m (M_w?≈?6.5), and the centroid depth is ~ 15 km. The slip is mainly driven by the left-lateral strike-slip and it is initially inferred that the seismogenic fault occurs in the south branch of the Tazang fault or an undetectable fault, a NW-trending left-lateral strike-slip fault, and belongs to one of the tail structures at the easternmost end of the eastern Kunlun fault zone. The earthquake rupture is mainly concentrated at depths of 5–15 km, which results in the complete rupture of the seismic gap left by the previous four earthquakes with magnitudes >?6.0 in 1973 and 1976. Therefore, the possibility of a strong aftershock on the Huya fault is low. The source duration is ~ 30 s and there are two major ruptures. The main rupture occurs in the first 10 s, 4 s after the earthquake; the second rupture peak arrives in ~ 17 s. In addition, the Coulomb stress study shows that the epicenter of the earthquake is located in the area where the static Coulomb stress change increased because of the 12 May 2017 M_w7.9 Wenchuan, China, earthquake. Therefore, the Wenchuan earthquake promoted the occurrence of the 8 August 2017 Jiuzhaigou earthquake.     

Numerical simulation on the influences of Wenchuan earthquake on the surrounding faults

On 12 May 2008, the devastating Wenchuan earthquake struck the Longmenshan fault zone, which comprised the eastern margin of the Tibetan Plateau, and this fault zone was predominantly a convergent boundary with a right-lateral strike-slip component. After such a large-magnitude earthquake, it was crucial to analyze the influences of the earthquake on the surrounding faults and the potential seismic activity. In this paper, a complex viscoelastic model of western Sichuan and eastern Tibet regions was constructed including the topography. Based on the findings of co-seismic static slip distribution, we calculated the stress change caused by the Wenchuan earthquake with the post-seismic relaxation into consideration. Our preliminary results indicated that: (1) The tectonic stressing rate was relatively high in Kunlun mountain pass-Jiangcuo, Ganzi-Yushu, Xianshuihe and Zemuhe faults; while in the east Kunlun and Longriba was medium; also the value was less in the Minjiang, Longmenshan, Anninghe and Huya faults. As to the Longmenshan fault, the value was 0.28×10^-3 MPa/a to 0.35×10^-3 MPa/a, which is coincident with the previous long recurrence interval of Wenchuan earthquake; (2) The Wenchuan earthquake not only caused the Coulomb stress decrease in the source region, but also the stress increase in the two terminals, especially the northeastern segment, which is comparatively consistent with the aftershock distribution. Meanwhile, the high concentration areas of the static slip distribution were corresponding to the Coulomb stress reductions; (3) The Coulomb stress change caused by Wenchuan earthquake showed significant increase on five major faults, which were northwestern segment of Xianshuihe fault, eastern Kunlun fault, Longriba fault, Minjiang fault and Huya fault respectively; also the Coulomb stress on the fault plane of the Yushu earthquake was faintly increased; (4) We defined the recurrence interval as the time needed to accumulate the magnitude of the stress drop, and the recurrence interval of Wenchuan earthquake was estimated about 1 714 a to 2 143 a correspondingly.     

Complete process of rock failure and the complete course of seismogeny

Conclusion Based on the analysis about the law of deformation rate, the concepts of the deformation rate of precursor, and its stress drop, and the stress drop of instability are discussed. According to the obtained deformationu ₀ corresponding to the maximum stress, the unstable pointu ₁ and the stable pointu ₂ of equilibrium, the complete process of rock failure can be divided into four stages quantitatively, corresponding to “the steady stage I”, “the precursor stage II”, “the unstable stage III” and “the later stage IV” of rock failure respectively, which can be used to simulate the complete course of earthquake. This kind of similarity between the complete process of rock failure and the complete course of earthquake suggests clearly the direction to reveal the law being of universal significance for the simulation of the earthquake in the laboratory experiments. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,13, 517–521, 1991.     

Strong ground motion simulation for the 2013 Lushan M W6.6 earthquake,Sichuan, China,based on the inverted and synthetic slip models

It is well known that quantitative estimation of slip distributions on fault plane is one of the most important issues for earthquake source inversion related to the fault rupture process. The characteristics of slip distribution on the main fault play a fundamental role to control strong ground motion pattern. A large amount of works have also suggested that variable slip models inverted from longer period ground motion recordings are relevant for the prediction of higher frequency ground motions. Zhang et al. (Chin J Geophys 56:1412–1417, 2013) and Wang et al. (Chin J Geophys 56:1408–1411, 2013) published their source inversions for the fault rupturing process soon after the April 20, 2013 Lushan earthquake in Sichuan, China. In this study, first, we synthesize two forward source slip models: the value of maximum slip, fault dimension, size, and dimension of major asperities, and corner wave number obtained from Wang’s model is adopted to constrain the generation of k ^?2 model and crack model. Next, both inverted and synthetic slip models are employed to simulate the ground motions for the Lushan earthquake based on the stochastic finite-fault method. In addition, for a comparison purpose, a stochastic slip model and another k ^?2 model (k ^?2 model II) with 2 times value of corner wave number of the original k ^?2 model (k ^?2 model I) are also employed for simulation for Lushan event. The simulated results characterized by Modified Mercalli Intensity (MMI) show that the source slip models based on the inverted and synthetic slip distributions could capture many basic features associated with the ground motion patterns. Moreover, the simulated MMI distributions reflect the rupture directivity effect and the influence of the shallow velocity structure well. On the other hand, the simulated MMI by stochastic slip model and k ^?2 model II is apparently higher than observed intensity. By contrast, our simulation results show that the higher frequency ground motion is sensitive to the degree of slip roughness; therefore, we suggest that, for realistic ground‐motion simulations due to future earthquake, it is imperative to properly estimate the slip roughness distribution.     

Source process of the 14 November 2001 western Kunlun Mountain M S=8.1 earthquake

Based on digital teleseismic P-wave seismograms recorded by 28 long-period seismograph stations of the global seismic network, source process of the November 14, 2001 western Kunlun Mountain M _S=8.1 (M _W=7.8) earthquake is estimated by a new inversion method. The result shows that the earthquake is a very complex rupture event. The source rupture initiated at the hypocenter (35.95°N, 90.54°E, focal depth 10 km, by USGS NEIC), and propagated to the west at first. Then, in several minutes to a hundred minutes and over a large spatial range, several rupture growth points emerged in succession at the eastern end and in the central part of the finite fault. And then the source rupture propagated from these rupture growth points successively and, finally, stopped in the area within 50 km to the east of the centroid position (35.80°N, 92.91°E, focal depth 15 km, by Harvard CMT). The entire rupture lasted for 142 s, and the source process could be roughly separated into three stages: The first stage started at the 0 s and ended at the 52 s, lasting for 52 s and releasing approximately 24.4% of the total moment; The second stage started at the 55 s and ended at the 113 s, lasting for 58 s and releasing approximately 56.5% of the total moment; The third stage started at the 122 s and ended at the 142 s, lasting for 20 s and releasing approximately 19.1% of the total moment. The length of the ruptured fault plane is about 490 km. The maximum width of the ruptured fault plane is about 45 km. The rupture mainly occurred within 30 km in depth under the surface of the Earth. The average static slip in the underground rocky crust is about 1.2 m with the maximum static slip 3.6 m. The average static stress drop is about 5 MPa with the maximum static stress drop 18 MPa. The maximum static slip and the maximum stress drop occurred in an area within 50 km to the east of the centroid position. Foundation item: Joint Seismological Science Foundation of China (103066) and Foundation of the Seismic Pattern and Digital Seismic Data Application Research Office of Institute of Earthquake Science of the China Earthquake Administration.     

Characterization of Stress Drops on Asperities Estimated from the Heterogeneous Kinematic Slip Model for Strong Motion Prediction for Inland Crustal Earthquakes in Japan

Dense strong motion observation networks provided us with valuable data for studying strong motion generation from large earthquakes. From kinematic waveform inversion of seismic data, the slip distribution on the fault surface of large earthquakes is known to be spatially heterogeneous. Because heterogeneities in the slip and stress drop distributions control the generation of near-source ground motion, it is important to characterize these heterogeneities for past earthquakes in constructing a source model for reliable prediction of strong ground motion. The stress changes during large earthquakes on the faults recently occurring in Japan are estimated from the detailed slip models obtained by the kinematic waveform inversion. The stress drops on and off asperities are summarized on the basis of the stress change distributions obtained here. In this paper, we define the asperity to be a rectangular area whose slip is 1.5 or more times larger than the average slip over the fault according to the previous study for inland crustal earthquakes. The average static stress drops on the asperities of the earthquakes studied here are in the range 6?C23?MPa, whereas those off the asperities are below 3?MPa. We compiled the stress drop on the asperities together with a data set from previous studies of other inland earthquakes in Japan and elsewhere. The static stress drop on the asperity depends on its depth, and we obtained an empirical relationship between the static stress drop and the asperity??s depth. Moreover, surface-breaking asperities seemed to have smaller stress drops than buried asperities. Simple ground motion simulations using the characterized asperity source models reveal that deep asperities generate larger ground motion than shallow asperities, because of the different stress drops of the asperities. These characteristics can be used for advanced source modeling in strong ground motion prediction for inland crustal earthquakes.