Explaining the physical origin of Båth's law

Båth's law is one of the three well-known scaling laws for earthquakes. It states that the difference in magnitudes of the mainshock and its largest aftershock is approximately constant, independent of the magnitude of the mainshock. Despite the progress in understanding the nature of Båth's law, the question of whether this law has a physical basis, or is simply a consequence of basic statistical features of aftershock sequences, has remained controversial. In this article we show that Båth's law can be derived within the Cosserat continuum theory from equations describing fault interaction. Our equations can describe both (1) the interacting mainshocks and aftershocks, and (2) the interacting foreshocks and mainshocks. We also derive (1) spatial extension of Båth's law to the normalized distance between the locations of the interacting mainshocks and aftershocks (or foreshocks and mainshocks), and (2) temporal extension of Båth's law to the difference between the time of the interacting mainshocks and aftershocks (or foreshocks and mainshocks).     

2012年苏门答腊Mw8.6地震成因及与周边大震关系

巽他海沟西侧地壳北向运动的差异性是2012年苏门答腊地震发生的动力学成因.库仑应力计算表明,2004年和2005年苏门答腊2次特大逆冲型地震对本次地震具有显著的触发作用.有记录以来至2011年,本次地震的发震断裂带没有发生过7级以上地震,震源区附近存在5级地震空区,2004年大震后该空区被打破.震前6年、4.5年和3个月发生了3组前震活动,其中最显著的是震前3个月发生的7.2级直接前震.      

Foreshock activity as a precursor of strong earthquakes in Corinthos Gulf,Central Greece

Foreshock activity preceding strong (M_s ≥ 5) main shocks in the Corinthos Gulf, Central Greece, is examined from primarily a data set of 1970–1998 and supplementary from data sets of 1785–1910 and 1911–1969. It has been found that foreshock activity appears at time T ≤ 4 months before the main shock. In general there is no apparent tendency of foreshock epicenters to move towards the main shock epicenter. The last 10 days of the foreshock period is the most important phase since the probability for the main shock occurrence at any time within that time window is very high exceeding 0.83. The duration of the foreshock period as well as the largest foreshock magnitude are both independent of the main shock magnitude. Obtained results are important for inclusion in probabilistic earthquake predictions in the Corinthos Gulf.     

On the validity of time-predictable model for earthquake generation in north-east India

North-east India is seismically very active and has experienced many widelydistributed shallow, large earthquakes. Earthquake generation model for the region was studied using seismicity data [(1906–1984) prepared by National Geophysical Data Centre (NGDC), Boulder Colorado, USA]. For establishing statistical relations surface wave magnitudes (M _s≥5·5) have been considered. In the region four seismogenic sources have been identified which show the occurrences of atleast three earthquakes of magnitude 5·5≤M _s≤7·5 giving two repeat times. It is observed that the time interval between the two consecutive main shock depends on the preceding main shock magnitude (M _p) and not on the following main shock magnitude (M _f) revealing the validity of time predictable model for the region. Linear relation between logarithm of repeat time (T) and preceding main shock magnitude (M _p) is established in the form of logT=cM _p+a. The values ofc anda are estimated to be 0–36 and 1–23, respectively. The relation may be used for seismic hazard evaluation in the region.     

Aftershocks of the june 20, 1978, Greece earthquake: A multimode faulting sequence

A 10-station portable seismograph network was deployed in northern Greece to study aftershocks of the magnitude (m_b) 6.4 earthquake of June 20, 1978. The main shock occurred (in a graben) about 25 km northeast of the city of Thessaloniki and caused an east-west zone of surface rupturing 14 km long that splayed to 7 km wide at the west end. The hypocenters for 116 aftershocks in the magnitude range from 2.5 to 4.5 were determined. The epicenters for these events cover an area 30 km (east-west) by 18 km (north-south), and focal depths ranges from 4 to 12 km. Most of the aftershocks in the east half of the aftershock zone are north of the surface rupture and north of the graben. Those in the west half are located within the boundaries of the graben. Composite focalmechanism solutions for selected aftershocks indicate reactivation of geologically mapped normal faults in the area. Also, strike-slip and dip-slip faults that splay off the western end of the zone of surface ruptures may have been activated.The epicenters for four large (M 4.8) foreshocks and the main shock were relocated using the method of joint epicenter determination. Collectively, those five epicenters form an arcuate pattern convex southward, that is north of and 5 km distant from the surface rupturing. The 5-km separation, along with a focal depth of 8 km (average aftershock depth) or 16 km (NEIS main-shock depth), implies that the fault plane dips northward 58° or 73°, respectively. A preferred nodal-plane dip of 36° was determined by B.C. Papazachos and his colleagues in 1979 from a focal-mechanism solution for the main shock. If this dip is valid for the causal fault and that fault projects to the zone of surface rupturing, a decrease of dip with depth is required.     

The 1983, M 5.9 earthquake of Heze,Shandong Province,with its short-term and imminent precursory phenomena

An earthquake (M = 5.9) occurred on November 7, 1983 in the Heze area, Shandong Province (35°17′ N, 115°17∃, H = 12 km). This earthquake belongs to the isolated type of earthquakes. There were no foreshocks; the aftershocks were few in number with their energy decreasing quickly.Within the area surrounding the main shock and up to about 200 km from the epicenter, several types of short-term and imminent anomalies were observed. The major characteristics of the anomalies are as follows:The short-term and imminent anomalies are relatively few in number. The maximum radius of the area where the anomalies occur is about 150–200 km from the epicenter. The time durations of what have been called short-term and imminent anomalies here are small, being

• 1.(1) from 10–20 days to 3–4 months and
• 2.(2) from 1–2 hours to 2–3 days, respectively. The premonitory information was scanty.

Finally, the procedure to recognize the indications of a moderate earthquake is discussed.     

Regional time-predictable modeling in the Hindukush–Pamir–Himalayas region

The seismic characteristic of Hindukush–Pamir–Himalaya (HPH) and its vicinity is very peculiar and has experienced many widely distributed large earthquakes. Recent work on the time-dependent seismicity in the Hindukush–Pamir–Himalayas is mainly based on the so-called “regional time-predictable model”, which is expressed by the relation log T=cM_p+a, where T is the inter-event time between two successive main shocks of a region and M_p is the magnitude of the preceded main shock. Parameter a is a function of the magnitude of the minimum earthquake considered and of the tectonic loading and c is positive (0.3) constant. In 90% of the cases with sufficient data, parameter c was found to be positive, which strongly supports the validity of the model. In the present study, a different approach, which assumes no prior regionalization of the area, is attempted to check the validity of the model. Nine seismic sources were defined within the considered region and the inter-event time of strong shallow main shock were determined and used for each source in an attempt at long-term prediction, which show the clustering and occurrence of at least three earthquakes of magnitude 5.5≤M_s≤7.5 giving two repeat times, satisfying the necessary and sufficient conditions of time-predictable model (TP model). Further, using the global applicability of the regional time- and magnitude-predictable model, the following relations have been obtained: log T_t=0.19 M_min+0.52M_p+0.29 log m₀−10.63 and M_f=1.31M_min−0.60M_p−0.72 log m₀+21.01, where T_t is the inter-event time, measured in years; M_min the surface wave magnitude of the smallest main shock considered; M_p the magnitude of preceding main shock; M_f the magnitude of the following main shock; and m₀ the moment rate in each source per year.

These relations may be used for seismic hazard assessment in the region. Based on these relations and taking into account the time of occurrence and the magnitude of the last main shock in each seismogenic source, time-dependent conditional probabilities for the occurrence of the next large (M_s≥5.5) shallow main shocks during the next 20 years as well as the magnitudes of the expected main shocks are determined.     

The Friuli earthquake (1976–1977)

The results of seismic studies on the Friuli May 6, 1976 earthquake based on historical and seismological data collected by the OGS are presented. The epicenter and hypocenter distributions reconstructed from the Friuli networks and from Trieste WWSS Station are examined. The earthquakes of Latisana (1975–1976) are interpreted as the foreshocks of the main shock of May 6. Parameters of larger shocks are calculated. At the end a correlation between the hypocenters and the involved geodynamic structure of the region is proposed.     

Statistical Completeness Analysis of Seismic Data

Earthquakes constitute one of the most powerful forces to which most civil engineering structures and historical constructions will ever be subjected; and thus designing and preserving structures to resist these forces is of utmost importance. The goal of earthquake-resistant design is to produce a structure or facility that can withstand a certain level of shaking without excessive damage. Seismic hazard analyses involve the quantitative estimation of ground shaking hazards at a particular site.The main objective of this study is to develop a homogeneous earthquake catalogue for the low seismic region Warangal from 1800 to 2016 by considering a circular radius of 500 km. The catalogue is declustered using the algorithm proposed by Uhrhammer (1986) for removal of foreshocks and aftershocks. All the events have been converted to moment magnitude scale for homogenization. Completeness analysis has been carried out using the method proposed by Stepp (1972) to determine the time interval in which the data is complete over different magnitude ranges. The analysis shows that for the magnitude range of 3.0 ≤ M ≤ 3.49, 3.5 ≤ M ≤ 3.99, 4.0 ≤ M ≤ 4.49, 4.5 ≤ M ≤ 4.99, 5.0 ≤ M ≤ 5.49 and M ≤ 5.49, the data is complete for the last 50 years (1967-2016), 60 years (1957-2016), 140 years (1867-2016) and 180 years (1837-2016) respectively. This study will provide a significant under-standing in distribution of earthquakes in Warangal region as well as the assessment of seismic hazard for the region.     

Fractal variogram-based time–space of aftershock sequences analysis—case study: the May 21, 2003 Boumerdes–Algeria earthquake, M w = 6.8

The most of shallow earthquakes are followed, just after the main shock, by increased residual seismicity known as “aftershocks” or “aftershock sequences”. Because of their disparity in time and space, aftershock sequences are more or less obvious and their productivity is spread out in time. Several studies have been regularly proposed to explain or to understand the mechanisms of the occurrence and the behaviour of these small earthquakes. In a theoretical context, many factors can induce the aftershock triggering: residual friction, subcritical crack growth, pore fluid flow etc. Just after the occurrence of the most destructive main shock of the 21 May 2003 Boumerdes (Algeria) earthquake, a wide sequence of aftershocks was recorded at different geographical locations and with various magnitudes. Based on the fact that the region of Boumerdes (40 km east of the capital Algiers) did not develop major earthquakes in the past, a geostatistical investigation of the data for this aftershock sequence is a valuable input for better seismogeological identification of this area. In the present analysis, after an overview of the geological factors in the likely occurrence of the earthquake, fundamental statistical parameters were chosen: the b value from the Gutenberg–Richter law, the p factor of the extracted respectively from the b value and the fractal variogram defined as a graphic tool to describe the continuity or the roughness of data. Jointly to the geostatistical parameters provided by the variogram like the fractal dimension. The main objective of the calculation and interpretation of these parameters is oriented towards a better understanding of the seismicity of the region of Boumerdes (Algeria) now classified as seismogenic zone.     

Application of time- and magnitude-predictable model for long-term earthquake prediction in Iran

The regional time- and magnitude-predictable model has been applied successfully in diverse regions of the world to describe the occurrence of main shocks. In the current study, the model has been calibrated against the historical and instrumental catalog of Iranian earthquakes. The Iranian plateau is divided into 15 seismogenic provinces; then, the interevent times for strong main shocks have been determined for each one. The empirical relations reported by Papazachos et al. (Tectonophysics 271:295–323, 1997a) for the Alpine–Himalayan belt (including Iran) were adopted except for the constant terms that were calculated separately for every seismotectonic area. By using the calibrated equations developed for the study area and taking into account the occurrence time and magnitude of the last main shocks in each seismogenic source, the time-dependent conditional probabilities of occurrence P(?t) of the next main shocks during next 10, 20, 30, 40 and 50 years as well as the magnitude of the expected main shocks (M _f) have been estimated. The immediate probability (within next 10 years) of a large main shock is estimated to be high and moderate (>35 %) in all regions except zones 9 (M _f = 5.8) and 15 (M _f = 6.1). However, it should be noted that the probabilities have been estimated for different M _f values in 15 regions. Comparing the model predictions with the actual earthquake occurrence rates shows the good performance of the model for Iranian plateau.     

The foreshock sequence of haicheng earthquake and earthquake swarm—the use of foreshock sequences in earthquake prediction

We have compared the Haicheng foreshock sequence with several earthquake swarms which occurred in its neighborhood. The spatial distribution of the earthquakes is relatively concentrated. For the most part, the events occurred within a few kilometers of each other. The focal mechanisms are comparatively stable. However, there are several swarms in which the variations of focal mechanisms are quite obvious after the occurrence of the largest event of the sequence, which would allow it to be recognized as a swarm. However, there are also swarms whose focal mechanisms are no less stable throughout the sequence compared to the Haicheng foreshock sequence. This feature could thus not be used to identify a foreshock sequence. The temporal distributions of foreshocks and swarms are quite similar in some cases. This is again not a definite criterion for identifying foreshocks, but is worthy of further study. Thus, no definite criterion for identifying foreshock sequences has been found. However, some earthquake swarms may be recognized in their later stage.Finally, we introduced a magnitude sequence with gaps which can be used to see whether a large event is still forthcoming. This method (in conjunction with other methods) could be used in areas prone to large earthquakes, immediately before a large event, to improve the probability of predicting the occurrence of a large event. We also report that the temporal distribution of all the sequences showed a 12-hour recurrence pattern that corresponded with the earth tides, indicating that tidal forces might be influencing foreshocks and earthquake swarm occurrence.     

Seismicity pattern in north Sumatra-Great Nicobar region: In search of precursor for the 26 December 2004 earthquake

We analyse the seismicity pattern including b-value in the north Sumatra-Great Nicobar region from 1976 to 2004. The analysis suggests that there were a number of significant, intermediate and short-term precursors before the magnitude 7.6 earthquake of 2 November 2002. However, they were not found to be so prominent prior to the magnitude 9.0 earthquake of 26 December 2004 though downward migration of activity and a 50-day short-term quiescence was observed before the event. The various precursors identified include post-seismic and intermediate-term quiescence of 13 and 10 years respectively, between the 1976 (magnitude 6.3) and 2002 earthquakes with two years (1990–1991) of increase in background seismicity; renewed seismicity, downward migration of seismic activity and foreshocks in 2002, just before the mainshock. Spatial variation in b-value with time indicates precursory changes in the form of high b-value zone near the epicenter preceding the mainshocks of 2004 and 2002 and temporal rise in b-value in the epicentral area before the 2002 earthquake.     

基于集集强震群序列地震特征的地震追踪预测

分析集集强震群前余震序列的 7年 (1993/ 0 9/ 2 1— 2 0 0 0 / 0 9/ 2 0 )中震级规模在M =3 0以上的地震目录 ,可以找到前震类型、孕震空区特征、孕震条带特征、前震丛集性活动与信号震特征、主震前平静以及余震序列的二次余震等至少 6项清楚的地震序列特征。利用已发展出的年度强震趋势分析步骤的经验 ,佐以依据地震序列特征进一步加以追踪的观念 ,以集集地震序列分析为例 ,试图将地震趋势分析由年的时间尺度 ,追踪到更短的月的时间范围 ;并尝试建立台湾地区西部地震带浅源强震的追踪分析步骤 ,并为以测震学为基础的地震预测提供逼近短临时间尺度的分析方法。     

Seismicity assessment in and around Syria based on instrumental data: application of Gumbel distributions and Gutenberg-Richter relationship

An instrumental earthquake catalog covering the time span between 1903 and 2007 and for the area bounded by 32°N–38°N and 35°E–43°E has been compiled in this research. The catalog has a magnitude of completeness (M _c ) with 3.5. Least squares and statistical probability Gumbel’s techniques with different approaches have been applied on the instrumental events in order to assess the average recurrence time periods for different earthquake magnitudes. The constants a and b of Gutenberg-Richter and the average recurrence times have been computed firstly for the study area and secondly for the central and northern parts of Dead Sea fault system. The different statistical computations using Knopoff and Kagan formalism are generally in agreement and suggest an average recurrence time of 203 years for an earthquake of magnitude 7 for the region. The occurrence of large well-documented historical earthquakes in Lebanon and western Syria, the existence of active fault segments, the absence of large earthquakes during the study period, the increasing number of the low-magnitude earthquakes, and the continued accumulation of the strain since 1900 indicate therefore the probability of an earthquake occurrence of a large magnitude. This should be permanently taken into consideration in seismic hazard assessment on the local and regional scales.     

Migration of seismicity and pore pressure diffusion for five decades long Koyna–Warna sequence and precursory nucleation process for earthquake forecasting

The continued reservoir-triggered seismicity for five decades in Koyna area has been attributed to southward migration of seismicity (during 1967–1992 near and south of Koyna dam and from 1993 onwards mostly near the new Warna reservoir). Spread of seismicity in the vicinity of reservoirs is attributed to pore-pressure diffusion. Moderate size Koyna–Warna earthquakes are found to nucleate at shallow depth (≤ 3 km) due to pore pressure caused by water level fluctuation of reservoir(s). The nucleation zone deepens along the critically stressed permeable fault zone to cause the occurrence of mainshock at the base of seismogenic layer (i.e. 5–10 km). The clustering of foreshocks up to 500 hr prior to several moderate size Koyna earthquakes of magnitude Mw 4–5 has been detected and used for quantifying the nucleation process. A static stress transfer by means of cascade model from one foreshock to next for the generation of foreshocks has been proposed for nucleation model. The nucleation process can be considered as an immediate earthquake precursor for the Koyna-Warna region.     

Large earthquakes in the Baikal region as response to bifurcations in nonlinear resonance hysteresis

The hypothesis that large earthquakes in the Baikal region are a response to bifurcations in nonlinear resonance hysteresis in a system consisting of three oscillators, attractor structures of riftogenesis, is substantiated. The hypothesis is confirmed by the spatial-temporal and magnitude distribution of large earthquakes: all the pairs of earthquakes with magnitude M _LH > 5.5 that took place in the region within a small time period but were remote from one another show fair agreement with the main theoretical conclusions.