Statistical study of the occurrence of shallow earthquakes

Summary. The time—space-magnitude interaction of shallow earthquakes has been investigated for three catalogues: worldwide ( M ≥ 7.0), Southern and Northern California ( M ≥ 4.0) and Central California ( M ≥ 1.5). The earthquake sequences are considered as a multi-dimensional stochastic point process; the estimates of the parameters for a branching model of the seismic process are obtained by a maximum-likelihood procedure. After applying magnitude—time and magnitude—distance scaling, the pattern of relationship among earthquakes of different magnitude ranges is almost identical. The number of foreshocks diminishes as the magnitude difference between the main shock and the foreshocks increases, while the magnitude distribution of aftershocks has the opposite property. The strongest aftershocks are likely to occur at the beginning of the sequence; later they migrate away with velocities of the order of km/day. The sequences which are composed of smaller aftershocks last longer and there are indications that they remain essentially in the focal region. Foreshocks also appear to migrate, but in this case, toward the main shock. The rate of occurrence of dependent shocks increases as t ^-1 as the origin time of the main shock is approached, effectively making every earthquake a multi-shock event. This interaction of earthquakes was modelled by a Monte-Carlo simulation technique. The statistical inversion of simulated catalogues was undertaken to derive the information we would be able to retrieve from actual data, as well as possible errors of estimates. The possibility of using these results as a tool for seismic risk prediction is discussed and evaluated.     

A Branching Poisson-Markov Model of Earthquake Occurrences

Summary. The Markov process is re-examined as a possible model for aftershock occurrences. In this model, ɛ the state variable is assumed to be the accumulated strain energy. The transition in the energy state is related directly to the magnitude of the aftershock. The known empirical relations on the decay of aftershock sequences and frequency-magnitude law, are incorporated in determining suitable functions for the rate [λ(ɛ)] and transition probabilities [ T ( X |ɛ)] of the Markov process. A computer simulation of the process using a random number generator verified that the empirical relations were properly duplicated with these functions.
To model a complete earthquake catalog, including the main events and aftershocks, two processes are combined by assuming that: (1) independent earthquakes occur as a stationary Poisson process, and (2) they trigger aftershock sequences by channelling a fixed portion of their energy into the Markov process. A synthetic earthquake-aftershock catalogue is generated by simulating the branching Poisson-Markov process and is found to be fairly realistic.     

Non-Poissonian earthquake occurrence in coupled stress release models and its effect on seismic hazard

Most seismic hazard estimations are based on the assumption of a Poisson process for earthquake occurrence, even though both observations and models indicate a departure of real seismic sequences from this simplistic assumption. Instrumental earthquake catalogues show earthquake clustering on regional scales while the elastic rebound theory predicts a periodic recurrence of characteristic earthquakes on longer timescales for individual events. Recent implementations of time-dependent hazard calculations in California and Japan are based on quasi-periodic recurrences of fault ruptures according to renewal models such as the Brownian Passage Time model. However, these renewal models neglect earthquake interactions and the dependence on the stressing history which might destroy any regularity of earthquake recurrences in reality. To explore this, we investigate the (coupled) stress release model, a stochastic version of the elastic rebound hypothesis. In particular, we are interested in the time-variability of the occurrence of large earthquakes and its sensitivity to the occurrence of Gutenberg–Richter type earthquake activity and fault interactions. Our results show that in general large earthquakes occur quasi-periodically in the model: the occurrence probability of large earthquakes is strongly decreased shortly after a strong event and becomes constant on longer timescales. Although possible stress-interaction between adjacent fault zones does not affect the recurrence time distributions in each zone significantly, it leads to a temporal clustering of events on larger regional scales. The non-random characteristics, especially the quasi-periodic behaviour of large earthquakes, are even more pronounced if stress changes due to small earthquakes are less important. The recurrence-time distribution for the largest events is characterized by a coefficient of variation from 0.6 to 0.84 depending on the relative importance of small earthquakes.     

Statistical analysis of time-dependent earthquake occurrence and its impact on hazard in the low seismicity region Lower Rhine Embayment

The time-dependence of earthquake occurrence is mostly ignored in standard seismic hazard assessment even though earthquake clustering is well known. In this work, we attempt to quantify the impact of more realistic dynamics on the seismic hazard estimations. We include the time and space dependences between earthquakes into the hazard analysis via Monte Carlo simulations. Our target region is the Lower Rhine Embayment, a low seismicity area in Germany. Including aftershock sequences by using the epidemic type aftershock-sequence (ETAS) model, we find that on average the hypothesis of uncorrelated random earthquake activity underestimates the hazard by 5–10 per cent. Furthermore, we show that aftershock activity of past large earthquakes can locally increase the hazard even centuries later. We also analyse the impact of the so-called long-term behaviour, assuming a quasi-periodic occurrence of main events on a major fault in that region. We found that a significant impact on hazard is only expected for the special case of a very regular recurrence of the main shocks.     

Seismic reflection studies using local earthquake sources

Summary. A method is presented for processing three-component digital recordings of micro-earthquakes to obtain near-vertical reflection profiles in regions of shallow seismicity. The processing includes magnitude and focal-depth normalization and event stacking, where stacking is by small localized groups, with ray theoretical time and distance corrections applied to compensate for varying focal depths. In areas with high seismicity, this procedure allows earthquakes to be treated as "controlled" sources to probe layered structures of the deep crust and upper mantle. The validity of our approach is demonstrated using S-waves from aftershocks of the Borah Peak, Idaho, earthquake (Ms = 7.3) of 1983.     

Statistical discrimination of foreshocks from other earthquake clusters

When earthquake activity begins, it may be a foreshock sequence to a larger earthquake, a swarm, or a simple main-shock-aftershock sequence. This paper is concerned with the conditional probability that it will be foreshock activity of a later larger earthquake, depending on the occurrence pattern of some early events in the sequence. The earthquake catalogue of the Japan Meteorological Agency (1926-1993, M_J≥4) is decomposed into a large number of clusters in time and space in order to compare statistical features of foreshocks with those of swarms and aftershocks. Using such a data set, Ogata, Utsu & Katsura (1995) revealed some discriminating features of foreshocks relative to the other types of clusters, for example the events' closer proximity in time and space, and a tendency towards chronologically increasing magnitudes, which encouraged us to construct models which forecast the probability of the earthquakes being foreshocks. Specifically, the probability is a function of the history of magnitude differences, spans between origin times and distances between epicentres within a cluster. For purposes of illustration, the models were fitted to the early part of the data (1926-1975) and the validity of the forecasting procedure was checked on data from the later period (1976-1993). Two procedures for evaluating the performance of the probability forecast are suggested. Furthermore, for the case where only a single event is available (i.e. either it is the first event in a cluster or an isolated event), we also forecast the probability of the event being a foreshock as a function of its geographic location. Then, the validity of the forecast is demonstrated in a similar manner. Finally, making use of the multi-element prediction formula, we show that the forecasting performance is enhanced by the joint use of the information in the location of the first event, and that in the subsequent interevent history in the cluster.     

Evidence of spatial variations of attenuation in the western Pyrenean range

Summary. Spectral attenuation of coda waves has been studied in the range 2–40 Hz from local events recorded in the western Pyrenean range from 1980 to 1982. Q _c was obtained using a single scattering model of S -waves for different segments of the coda. An increase of Q _c with lapse time was found and attributed to a rapid increase of Q _β with depth.
Three groups of events were selected from distinct focal areas. Two data sets are mainly composed of aftershocks of moderate earthquakes of magnitude 5.1 and 4.8, respectively. No moderate earthquake occurred in the third area in the few years preceding or following the selected events. Use of stations close to epicentres allowed sampling of the coda at very short lapse times and then study of small, distinct scattering volumes. Noticeable differences were found between the three studied areas and attributed to spatial rather than temporal variations.
The Q _c frequency dependence was studied according to Q _c= qf ^α. α is found to range from 0.7 to 1.1 and q from 30 to 140. These values are in agreement with those found in other tectonic areas. It is shown that scattering is the dominant attenuation process below 10Hz.     

A study of geomagnetic storms

Summary. An attempt is made to find interplanetary magnetic field and solar-wind parameters which control the development of geomagnetic storms. For this purpose, the interplanetary energy flux is estimated in terms of the Poynting flux ( E × B /4π), and its time variations are compared with the rate of energy dissipation in terms of the ring-current particle injection u _i( t ), Joule dissipation in the ionosphere u_j ( t ) and auroral particle injection u_p ( t ) for 15 major geomagnetic storms.
It is shown that the growth of geomagnetic storms, namely the time variations of the rate of the total energy dissipation, u ( t ) = u _i( t ) + u _j( t ) + u _p( t ), is closely related to the Poynting flux by the following relation:
where l ₀≅ 7 R _E and θ' is a measure of the angle between the interplanetary magnetic field vector and the magnetospheric field vector at the front of the magnetosphere in the equatorial plane. Further, it is shown that within a factor of 2 for each storm period.
A large increase of u ( t ) is associated with substorm activity. Thus, the energy flux ɛ( t ) entering the magnetosphere is dissipated through magneto-spheric substorm processes within the magnetosphere, and their accumulated effects can be understood as geomagnetic storm phenomena.     

The 2004 May 28 Baladeh earthquake (Mw 6.2) in the Alborz, Iran: overthrusting the South Caspian Basin margin, partitioning of oblique convergence and the seismic hazard of Tehran

We use teleseismic waveform analysis and locally recorded aftershock data to investigate the source processes of the 2004 Baladeh earthquake, which is the only substantial earthquake to have occurred in the central Alborz mountains of Iran in the modern instrumental era. The earthquake involved slip at 10–30 km depth, with a south-dipping aftershock zone also restricted to the range 10–30 km, which is unusually deep for Iran. These observations are consistent with co-seismic slip on a south-dipping thrust that projects to the surface at the sharp topographic front on the north side of the Alborz. This line is often called the Khazar Fault, and is assumed to be a south-dipping thrust which bounds the north side of the Alborz range and the south side of the South Caspian Basin, though its actual structure and significance are not well understood. The lack of shallower aftershocks may be due to the thick pile of saturated, overpressured sediments in the South Caspian basin that are being overthrust by the Alborz. A well-determined earthquake slip vector, in a direction different from the overall shortening direction across the range determined by GPS, confirms a spatial separation ('partitioning') of left-lateral strike-slip and thrust faulting in the Alborz. These strike-slip and thrust fault systems do not intersect within the seismogenic layer on the north side, though they may do so on the south. The earthquake affected the capital, Tehran, and reveals a seismic threat posed by earthquakes north of the Alborz, located on south-dipping thrusts, as well as by earthquakes on the south side of the range, closer to the city.     

Rayleigh-wave amplitudes from earthquakes in the range 0–150°

Summary . Vertical component Rayleigh-wave amplitudes from 1461 shallow earthquakes recorded in the distance range 0–150° are analysed to separate the effects of earthquake size, epicentral distance (Δ) and recording station.
The estimated decay of amplitude with distance has the form of a theoretical curve for the decay of Rayleigh waves with distance if the assumption is made that the decay due to dispersion for the data analysed is that of an Airy phase. Writing the decay due to anelastic attenuation as exp (- k Δ), k is estimated to be 0.676/rad over the whole range of distance. If the distance effects are represented by a straight line of the form h log Δ+ constant, h is estimated to be 1.15. The calibration function for computing M _s derived from the estimated distance effects is very similar to that of Marshall & Basham.
Station effects on Rayleigh-wave amplitudes though statistically significant are small, and can probably be ignored in the computation of M _s.
Comparing the estimated surface-wave magnitudes (earthquake size) obtained in this study with the long and short period body-wave magnitudes ( m ^LP_b and m ^SP_b respectively) obtained by Booth, Marshall & Young for the same earthquake shows that m ^LP_b is about equal to M _s over the magnitude range of interest (˜4.0–7.0). The m ^LP_b and M_s relationship shows that the greater the long-period energy radiated by an earthquake the smaller proportionately is the short-period energy.     

Simulations of strong ground motion for earthquakes in the Mexicali–Imperial Valley region

Summary. In this paper computer modelling is used to test simple approximations for simulating strong ground motions for moderate and large earthquakes in the Mexicali–Imperial Valley region. Initially, we represent an earthquake rupture process as a series of many independent small earthquakes distributed in a somewhat random manner in both space and time along the rupture surface. By summing real seismograms for small earthquakes (used as empirical Green's functions), strong ground motions at specific sites near a fault are calculated. Alternatively, theoretical Green's functions that include frequencies up to 20 Hz are used in essentially similar simulations. The model uses random numbers to emulate some of the non-deterministic irregularities associated with real earthquakes, due either to complexities in the rupture process itself and/or strong variations in the material properties of the medium. Simulations of the 1980 June 9 Victoria, Baja California earthquake ( M _L= 6.1) approximately agree with the duration of shaking, the maximum ground acceleration, and the frequency content of strong ground motion records obtained at distances of up to 35 km for this moderate earthquake. In the initial stages of modelling we do not introduce any scaling of spectral shape with magnitude, in order to see at what stage the data require it. Surprisingly, such scaling is not critical in going from M = 4–5 events to the M = 6.1 Victoria earthquake. However, it is clearly required by the El Centro accelerogram for the Imperial Valley 1940 earthquake, which had a much higher moment ( Ms ∼ 7). We derive the spectral modification function for this event. The resulting model for this magnitude ∼ 7 earthquake is then used to predict the ground motions at short distances from the fault. Predicted peak horizontal accelerations for the M ∼ 7 event are about 25–50 per cent higher than those observed for the M = 6.1 Victoria event.     

The 2003 Mw 7.2 Fiordland subduction earthquake, New Zealand: aftershock distribution, main shock fault plane and static stress changes on the overlying Alpine Fault

The 2003 August 21 Fiordland earthquake ( M _L7.0, M _W7.2) was the largest earthquake to occur in New Zealand for 35 yr and the fifth of M6+ associated with shallow subduction in Fiordland in the last 15 yr. The aftershocks are diffuse and do not distinguish between the two possible main shock fault planes implied by the Harvard CMT solution, one corresponding to subduction interface thrusting and the other corresponding to steeply seaward dipping thrusting. The distinction is important for calculating the induced stress changes on the overlying Alpine Fault which has a history of very large earthquakes, the last possibly in 1717. We have relocated the aftershocks, using data from temporary seismographs in the epicentral region and the double difference technique. We then use the correlation between aftershock hypocentres and regions of positive changes in Coulomb Failure Stress (CFS) due to various candidate main shock fault planes to argue for concentrated slip on the shallow landward dipping subduction interface. Average changes in CFS on the offshore segments of the Alpine Fault are then negative, retarding any future large events. In our models the change in CFS is evaluated on faults of optimal orientation in the regional stress field as determined by inversion of P -wave polarities.     

The mechanisms of shallow earthquakes and the monitoring of a comprehensive test ban

The ability of seismological criteria to identify earthquakes from underground explosions depends partly on the orientation of the earthquake source. Well-determined double-couple moment tensor solutions for a large number of earthquakes have been published in the Harvard centroid moment tensor (CMT) and United Slates Geological Survey (USGS) catalogues. Statistical analyses of these catalogues indicate that the distribution of the orientation of earthquake mechanisms is not random. The distribution of the T axes shows significant clustering around the downward vertical, indicating that a larger number of earthquake mechanisms radiate compressional P -wave energy to teleseismic distances from near the maximum of the radiation pattern than is predicted if earthquake sources are randomly oriented double couples. The clustered T axes correspond to compressional dip-slip mechanisms, and it is this type of mechanism which is believed to cause both the m _b: M _s (the ratio of body-wave to surface-wave magnitude) and first-motion criteria to misidentify an earthquake as an explosion.     

云南地震地质灾害与资源环境效应问题的初步研究

在对历史震害资料浅析的基础上，利用最近40年有现场调查的地震记录，分析了云南省各类地震地质灾害与资源环境破坏影响的一些特征，并结合云南地震时空活动特性，对云南有仪测地震资料近百年间的地震地质灾害与资源环境效应问题进行了反演，表明：（1）云南地区地震地质灾害与资源环境破坏影响具有群体分区特征。（2）云南地区存在时间进程上连续的中强地震活跃背景：地震对资源环境的作用影响具有强度为2级的高背景值。（3）云南资源环境地震破坏影响具有多侧面、长时效和渐微影响的特征。地震对资源环境的破坏，必将恶化人类生存条件，阻碍社会经济的长期与可持续发展。这是资源环境安全防震减灾所面临的新课题。     

Spatial distribution of earthquakes: the two-point correlation function

Summary. The distribution of distances between pairs of earthquake epicentres and hypocentres has been determined for four local and two world-wide catalogues. These spatial correlation functions shows that the number of events per unit volume at distance R from any earthquake is proportional to R ^-α, where a is close to 1.0 for shallow earthquakes and increases to 1.5 or possibly larger for deeper events. This distribution of earthquakes is independent of magnitude and independent of the dimensions of the region under consideration. These results place limits on possible models of earthquake fault geometries.     

The 1984 July 19 North Wales earthquake—a lower crustal continental event indicating brittle behaviour at an unusual depth

Summary. Attention has recently been focused on the structure and composition of the lower crust in continental areas. It is generally believed that, except in special circumstances, ductile behaviour below mid-crustal depths precludes the brittle processes that cause earthquakes. The 1984 July 19 earthquake in North Wales occurred at the unexpected depth of 23 km. We report here the location of the larger aftershocks and the relocation of the main shock with respect to one of them. The lower crustal depths of the events are confirmed by tests with a wide range of models. The occurrence of earthquakes at these depths may be related to low heat flow in the region.     

The fractal geometry of the surface ruptures of the 1999 Chi-Chi earthquake, Taiwan

The 1999 September 20 Chi-Chi earthquake is the largest seismic event which occurred in the island during the twentieth century. Available seismic data relative to this earthquake are of high quality, and surface ruptures identified as features associated to the Chelungpu fault can be clearly observed at the surface and precisely mapped. We calculated the fractal dimension ( D ) and b value of Gutenberg–Richter law for 6-month aftershocks of the Chi-Chi earthquake for the fault area, and find that the surface ruptures exhibit self-similar geometry only within specific ruler intervals. The D values of the surface ruptures reflect the fault slip and geometry at depth. More importantly, the small-size aftershocks seem more likely to occur within high D value and high b value areas, whereas small D value and small b value areas have a high potential for medium- and large-size aftershocks.     

A conjugate strike-slip fault system within the extensional tectonics of Western Turkey

Three main shocks M-1, M-2 and M-3 (17 October 2005 at 05:45 UTC, M _w 5.4; 17 October at 09:46 UTC, M _w 5.8 and 20 October at 21:40 UTC, M _w 5.9) and their associated aftershocks within the Gulf of S i ğac i k, 50 km southwest of Izmir, Turkey were studied in detail. A temporary seismic network deployed during the activity allowed the hypocentre of M-3 and subsequent aftershocks to be determined with high accuracy. A relative relocation technique was used to improve the epicentres of M-1 and M-2. All three main shocks have strike-slip mechanisms which agree with the linear trends of the aftershock locations. Two distinct zones were illuminated by the aftershock locations. The zones contain clear echelon patterns with slightly different orientations from the trend of the aftershock distribution. M-2 and M-3 ruptured along of the eastern rupture zone which aligns N45°E. However the strike direction of M-1 is not clearly identified. The alignment of the two rupture zones intersect at their southern terminus at an angle of 90°. The fault zones form conjugate pair system and static triggering is considered as a probable mechanism for the sequential west to east occurrence of M-1, M-2 and M-3. This earthquake sequence provides seismological evidence for conjugate strike-slip faulting co-existing within a region dominated by north–south extension and well-developed east–west trending normal faults.     

The evolution of the Gulf of Corinth (Greece): an aftershock study of the 1981 earthquakes

Summary. A preliminary study of the aftershocks of three earthquakes that occurred near to Corinth (Greece) in 1981 is combined with observations of the morphology and faulting to understand the evolution of the Eastern Gulf of Corinth. The well located aftershocks form a zone 60km long and 20km wide. They do not lie on the main fault planes and are mostly located between the north-dipping faulting on which the first two earthquakes occurred and the south-dipping faulting associated with the third event. A cluster of aftershocks also lies in the footwall of the eastern end of the south-dipping fault of the third event.
Morphologically, it is observed that in the evolution of the Eastern Gulf of Corinth, antithetic faulting apparently predates the appearance of the main faulting at the surface. This evolution can be explained by motion on a deep seated, shallow angle, aseismic normal fault. A model based on such a fault also accounts for the aftershock distribution of the 1981 earthquakes.     

云南省地震与太阳活动的统计关系研究

地震与太阳活动的关系是研究活动性和地震预测中有意义的课题。作者选取云南省及周边地区1965～2006年2级以上地震为样本,使用时间序列分析方法和相关分析方法对地震与太阳黑子、耀斑的相关性进行了研究,得到中小地震为主的样本与太阳活动不相关、大地震与太阳活动存在弱相关性的结论。作者的结论与以往研究者的结论不同,原因在于以往的研究者使用大震强震为样本,样本数少,得到的结论存在不可避免的偶然性。因此在一个地方具备发生大地震的内在条件时,关注太阳活动也是十分必要的。