Statistical properties of seismicity of fault zones at different evolutionary stages

We perform a systematic parameter space study of the seismic response of a large fault with different levels of heterogeneity, using a 3-D elastic framework within the continuum limit. The fault is governed by rate-and-state friction and simulations are performed for model realizations with frictional and large scale properties characterized by different ranges of size scales. We use a number of seismicity and stress functions to characterize different types of seismic responses and test the correlation between hypocenter locations and the employed distributions of model parameters. The simulated hypocenters are found to correlate significantly with small L values of the rate-and-state friction. The final sizes of earthquakes are correlated with physical properties at their nucleation sites. The obtained stacked scaling relations are overall self-similar and have good correspondence with properties of natural earthquakes.     

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.     

A dislocation model of microplate boundary ruptures n the presence of a viscoelastic asthenosphere

Summary. A microplate is modelled as an elastic plate with two long strike-slip boundaries, lying over a Maxwell-type viscoelastic asthenosphere. The microplate is subjected to a constant and uniform shear strain rate by the opposite motions of two adjoining larger plates. After the occurrence of an earthquake at one of the microplate boundaries, the time evolution of shear stress at the other boundary is studied. It is found that stress build-up at the second boundary is delayed due to stress diffusion governed by the asthenosphere relaxation. Earthquake occurrence at this latter boundary would be delayed depending upon both the microplate width and the ratio between the Maxwell relaxation time of the asthenosphere and a characteristic time required for tectonic strain to recover rupture conditions. It turns out that the parameters which determine the occurrence of seismic activity along the microplate boundaries are more strictly constrained in the presence of a viscoelastic asthenosphere than in the case of an elastic half-pace model.     

Stress drops, wave spectra and recurrence intervals of great earthquakes — implications of the Etorofu earthquake of 1958 November 6

Summary . The great Etorofu earthquake of 1958 November 6 is characterized by a relatively small aftershock area (70 × 150 km²) and an extremely large felt area. The felt area is more extensive than those of any other large earthquakes which have occurred in the southern Kurile to northern Japan arc since the beginning of this century. The mechanism is a pure thrust fault typical of most great earthquakes in island arcs. A body wave magnitude of m _b = 8.2 is obtained at periods around 6 s using more than 40 observations, although an m _b value of only 7.6–7.7 would be expected empirically from the observed surface wave magnitude of M _s= 8.1–8.2. Both an unusually large felt area and a high m _b indicate a dominance of high-frequency components in the seismic waves. A seismic moment of M _o= 4.4 × 10²⁸ dyne cm is determined from long-period surface waves from which a high stress drop of Δσ = 78 bar is obtained using a relatively small aftershock area. Historic data indicate an anomalously long time interval between the 1958 event and any earlier great earthquake from the same source region. The observed high stress drop can be interpreted as a consequence of this long intervening period through which strain built up. The dominance of the high-frequency seismic waves can then be interpreted as a result of this high stress drop. Stress drops, seismic wave spectra and recurrence intervals of great earthquakes are in this way closely related to each other. The 1958 event may represent a high strength extreme of stochastic fluctuation of fracture strength relevant to great earthquakes.     

Local and regional components of western Aegean deformation extracted from 100 years of geodetic displacement measurements

Our objectives are as follows. First, we wish to develop a methodology to recover the long-term component of deformation from any set of distributed, time-averaged geodetic strain measurements that were subject to seismic disturbance, given a catalogue of local seismicity that occurred during the measurement period. Second, using seismic and geodetic data sets that span approximately 100 years, we apply this technique in the western Aegean to assess the role of local seismicity in regional deformation. The methodology is developed using a model for crustal deformation constructed from a long-term, smooth regional strain field combined with instantaneous, local perturbations from upper-crustal earthquakes approximated by static elastic dislocations. By inverting geodetic displacements for the smooth field while simultaneously floating influential but uncertain earthquake source parameters, an estimate of the regional component of deformation that is approximately independent of the seismicity can be made. In the western Aegean we find that the horizontal component of regional deformation can be described with minor inaccuracy by a quadratic relative displacement field. The principal horizontal extensional axes calculated from the regionally smooth displacement field agree in orientation with the T-axes of earthquakes in the region. These observations indicate that the instantaneous elastic strain of the 10 km thick seismogenic layer is driven by a stress field that is smooth on the scale of the geodetic network as a whole, 200-300 km.     

Seismic radiation from dynamic coalescence, and the reconstruction of dynamic source parameters on a planar fault

The dynamic coalescence of two mode II cracks on a planar fault is simulated here using the elastodynamic boundary integral equation method. We focus on the complexity of the resultant slip rate and seismic radiation in the crack coalescence model (CCM) and on the reconstruction of a single crack model (SCM) that can reproduce the CCM waveforms from heterogeneous source parameters rather than coalescence. Simulation results reveal that localized higher slip rates are generated by coalescence as a result of stress interaction between the approaching crack tips. The synthesized seismic radiation exhibits a distinct coalescence phase that has striking similarities to stopping phases in the radiation and propagation properties. The corresponding SCM yields a singular increase in the stress drop distribution, which is accompanied by a sudden decrease in it across the point of coalescence in the CCM. This implies that the generation of high-frequency radiation is more efficient from coalescence than from stopping, although both phenomena exhibit the same strong  ω⁻²  -type displacement spectra.     

A crack model of creep processes on deep sections of faults

A crack model in antiplane shear configuration is shown representing creep processes interpreted in terms of 'viscous' deformation of a narrow plastic layer, characterized by inhomogeneous rheological properties, embedded within a homogeneous elastic medium. The evolution in time of slip and stress over the crack plane is studied through a truncated expansion in Chebyshev polynomials, and convergence is proved to be fast in the simple examples considered. Finite-stress solutions are found which are compatible with constitutive relations of elasto-plastic materials and furthermore these allow us to simulate creep propagation and stress transfer between locked and unlocked fault segments. This model provides a simple interpretation of the shallow depth of the seismogenic layer observed in several areas of the world and lends itself to modelling creep processes during either post-seismic rebound or pre-seismic stress buildup. Stress transfer is accomplished mostly by the slow extension of the creeping section. During a seismic cycle it is envisaged that different regimes dominate over deep, intermediate and shallow sections of faults: (i) slow pre-seismic stress build-up accompanied by creep and stress migration toward intermediate depths; (ii) brittle fracture over shallow and intermediate sections of faults; (iii) post-seismic rebound over intermediate and deep sections of faults. The present crack model, while providing finite-stress solutions, allows a better understanding of how stress may accommodate at different depths over a fault plane during a seismic cycle.     

Double-planed deep seismic zone and upper-mantle structure in the Northeastern Japan Arc

Summary. The ScSp wave converted from the ScS wave at the boundary between the descending lithospheric slab and the mantle above it was clearly observed from a nearby deep earthquake with magnitude 7.7 at some stations of the seismic network of Tohoku University which covers the Tohoku District, the northeastern part of Honshu, Japan. By applying the three-dimensional seismic-ray tracing method, the location of this boundary was determined from the difference in arrival time between the ScS and ScSp waves. The result shows that the upper boundary of the descending slab lies exactly on the upper plane of the double-planed deep seismic zone found in the Northeastern Japan Arc.
There is an additional evidence that the boundary is located on the upper plane of the double-planed deep seismic zone. The hypocentre distribution of intermediate-depth earthquakes located by the small-scale seismic-array observation is extremely different from that obtained by the relatively large-scale seismic network. The discrepancy in the distribution of hypocentres of the same earthquake independently located is well explained by the inclined lithospheric slab model derived from the difference in arrival time between the ScS and ScSp waves.
The earthquakes with reverse faulting or with down-dip compressional stresses occur at the upper boundary of the descending slab. Within the descending slab, the earthquakes with down-dip extensional stresses also occur in a very narrow zone from 30 to 40 km below the dipping boundary in the depth range from 50 to about 200 km, and these shocks form the lower plane of the double-planed deep seismic zone.     

Frictional changes induced by seismic slip on a non-planar fault

We propose a model which describes the formation of a strong asperity on a fault. We consider a fault surface which differs slightly from a plane due to a jog-like topographic variation. The fault is placed in an elastic space and is subject to a uniform stress field. The orientation of the fault is such that the normal traction (which is compressive) is greater on the topographic variation, determining a higher static friction and hence an asperity. The value of friction on this asperity depends on the magnitude of shear stress. For times of seismological interest, the increase in shear stress, at rates typical of tectonic processes, does not produce a sensible increase in friction with respect to the adjacent fault segments. A considerable increase in friction and the formation of a strong asperity (or even a barrier) can occur due to repeated seismic-slip episodes on the fault. Slip results in an elastic medium deformation, causing an increase in normal traction on the asperity and hence in friction. This process is described with the aid of a tensile Somigliana dislocation. Regions with high friction undergo partial fracturing of the fault-face material, which can produce fault gouge. The tensile dislocation introduces a small non-double-couple component in the seismic moment of the seismic event, the magnitude of this component depending mainly on the relative size of the asperity.     

Implications of stress concentration on a strike-slip fault in an elastic plate subject to basal shear stress

Summary We consider a long strike-slip fault in a lithosphere modelled as an elastic slab. To the base of the slab a shear stress distribution is applied which simulates the viscous drag exerted by the asthenosphere. The resulant stress on the fault plane may directly fracture the lithosphere in its brittle upper portion; alternatively it may give rise at first to a stable aseismic sliding in the lower portion. In the latter case, stress concentration due to the deep aseismic slip is the relevant feature of the pre-seismic stress acting on the upper section of the lithosphere. The two cases are examined by use of dislocation theory and their observable effects compared. Different depths of the aseismic slip zone and the presence or absence of a uniform friction on the seismic fault are allowed for. If the model is applied to the San Andreas fault region, where a steady sliding condition actually seems to be present at shallow depth, it turns out that the slip amplitudes commonly associated with large earthquakes are consistent with average basal stress values which can be substantially lower than a few bars, a value often quoted as the steady state basal stress due to a velocity gradient in the upper asthenosphere.     

New classification system for mass transport complexes in offshore Trinidad

This paper delineates our use of 10 708 km² of three‐dimensional (3D) seismic data from the continental margin of Trinidad and Tobago West Indies to describe a series of mass transport complexes (MTCs) that were deposited during the Plio‐Pleistocene. This area, situated along the obliquely converging boundary of the Caribbean/South American plates and proximal to the Orinoco Delta, is characterized by catastrophic shelf‐margin processes, intrusive/extrusive mobile shales and active tectonism. Extensive mapping of different stratigraphic intervals of the 3D seismic survey reveals several MTCs that range in area from 11.3 to 2017 km². Three types of MTCs are identified: (1) shelf‐attached systems that were fed by shelf‐edge deltas whose sediment input is controlled by sea‐level fluctuations and sedimentation rates; (2) slope‐attached systems, which occur when upper‐slope sediments catastrophically fail owing to gas‐hydrate disruptions and/or earthquakes and (3) locally detached systems, formed when local instabilities in the seafloor trigger relatively small collapses. Such classification of the relationship between slope mass failures and sourcing regions enables a better understanding of the nature of initiation, length of development history and petrography of such MTCs. 3D seismic enables more accurate calculation of deposit volumes, improves deposit imaging, and, thus, increases the accuracy of physical and computer simulations of mass failure processes.     

The growing spherical seismic source

Summary. A solution is found for the seismic radiation from an arbitrarily growing spherical source in an inhomogeneously prestressed elastic medium. The general problem of the growing seismic source in a prestressed medium is formulated as a boundary value problem. For the special case of the growing spherical source, an expansion in vector spherical harmonics reduces the problem to a set of one-dimensional Volterra integral equations. The equations can be easily formed through the use of Bessel function recursion relations. The integral equations for a growing spherical cavity are solved numerically. Waveforms are then computed for homogeneous and inhomogeneous stress fields for several growth histories. The resulting waveforms are similar to the waveforms of the corresponding instantaneous problem, but stretched out in time and reduced in amplitude. The effects of diffraction and the overshoot of equilibrium are reduced with a reduction in growth rate. The effects caused by inhomogeneity of the stress field are quite strong for the growing as well as for the instantaneous seismic source.     

基于GIS的二维非结构化剖分网格优化

非结构化网格剖分是数值模拟的关键技术之一,网格质量直接影响到计算的收敛性和精确度。在GIS辅助建立非结构化网格空间拓扑关系的基础上,针对GIS和实际研究问题给出Spring-Laplace方法——一种新的单元尺度函数定义,在GIS空间算法下利用该方法优化节点位置,并基于推进阵面算法的思想,结合空间邻近拓扑关系实现了三角剖分节点和网格的重新编号算法,方便了开边界条件的赋值,提高了计算效率。实例表明,该方法大大提高了网格生成质量,能适应FVCOM数值模型对非结构化网格剖分的要求,其收敛速度快,具有较高的运算效率。     

Quasi-static crack models and the frictional stress threshold criterion for slip arrest

Summary. Two-dimensional crack problems in elastic homogeneous isotropic media are considered which describe rupture over a fault surface characterized by non-uniform stress drop. Solutions can be found in which the stress field is finite at the crack tips and the rupture surface is not assigned a priori , but is part of the solution. These crack models are found to be consistent with the frictional stress threshold criterion for slip arrest over pre-existing fault surfaces. A crack is found to stop when its contribution to the stress field is opposite to the stress drop at the crack tips. The quasi-static propagation of a crack up to the arrest configuration is studied in terms of the minimum energy principle. The crack spontaneously propagates in such a way as to make the value of the stress intensity factor at one tip equal to the value at the other tip. Furthermore a tip propagating in a region with higher friction is found to move more slowly than the other tip propagating in a region with lower friction. Simple criteria for fracture arrest are derived, in terms of a properly averaged stress drop. Piecewise constant stress drop profiles are explicitly considered yielding a variety of solutions which can be applied to modelling asperities or barriers over a fault plane. The evaluation of the amount of the energy released during the quasi-static crack propagation shows that stopping phases cannot be efficiently radiated if the crack comes to rest in a low friction region.     

Evidence for different scaling of earthquake source parameters for large earthquakes depending on faulting mechanism

Scaling relationships between seismic moment, rupture length, and rupture width have been examined. For this purpose, the data from several previous studies have been merged into a database containing more than 550 events. For large earthquakes, a dependence of scaling on faulting mechanism has been found. Whereas small and large dip-slip earthquakes scale in the same way, the self-similarity of earthquakes breaks down for large strike-slip events. Furthermore, no significant differences in scaling could be found between normal and reverse earthquakes and between earthquakes from different regions. Since the thickness of the seismogenic layer limits fault widths, most strike-slip earthquakes are limited to rupture widths of between 15 and 30 km while the rupture length is not limited. The aspect ratio of dip-slip earthquakes is similar for all earthquake sizes. Hence, the limitation in rupture width seems to control the maximum possible rupture length for these events. The different behaviour of strike-slip and dip-slip earthquakes can be explained by rupture dynamics and geological fault growth. If faults are segmented, with the thickness of the seismogenic layer controlling the length of each segment, strike-slip earthquakes might rupture connected segments more easily than dip-slip events, and thus could produce longer ruptures than dip-slip events of the same width     

Seismic evidence for a sharp lithospheric base persisting to the lowermost mantle beneath the Caribbean

Broad-band data from South American earthquakes recorded by Californian seismic networks are analysed using a newly developed seismic wave migration method—the slowness backazimuth weighted migration (SBWM). Using the SBWM, out-of-plane seismic P -wave reflections have been observed. The reflection locations extend throughout the Earth's lower mantle, down to the core–mantle boundary (CMB) and coincide with the edges of tomographically mapped high seismic velocities. Modelling using synthetic seismograms suggests that a narrow (10–15 km) low- or high-velocity lamella with about 2 per cent velocity contrast can reproduce the observed reflected waveforms, but other explanations may exist. Considering the reflection locations and synthetic modelling, the observed out-of-plane energy is well explained by underside reflections off a sharp reflector at the base of the subducted lithosphere. We also detect weaker reflections corresponding to the tomographically mapped top of the slab, which may arise from the boundary between the Nazca plate and the overlying former basaltic oceanic crust. The joint interpretation of the waveform modelling and geodynamic considerations indicate mass flux of the former oceanic lithosphere and basaltic crust across the 660 km discontinuity, linking processes and structure at the top and bottom of the Earth's mantle, supporting the idea of whole mantle convection.     

独龙江流域的地震地质环境

本文利用青藏高原东南边缘及其与印缅山弧交接地带的地震活动性、新构造运动以及地震构造特征等研究成果和实地考察资料，借以分析并初步阐明独龙江流域的地质地质环境，为该区的自然资源开发利用和地震地质灾害预测提供一些实际资料。     

Modelling the compliance of crustal rock—II. Response to temporal changes before earthquakes

There have been several claims that seismic shear waves respond to changes in stress before earthquakes. The companion paper develops a stress-sensitive model (APE) for the behaviour of low-porosity low-permeability crystalline rocks containing pervasive distributions of fluid-filled intergranular microcracks, and this paper uses APE to model the behaviour before earthquakes. Modelling with APE shows that the microgeometry and statistics of distributions of such fluid-filled microcracks respond almost immediately to changes in stress, and that the behaviour can be monitored by analysing seismic shear-wave splitting. The physical reasons for the coupling between shear-wave splitting and differential stress are discussed.
In this paper, we extend the model by using percolation theory to show that large crack densities are limited at the grain-scale level by the percolation threshold at which interacting crack clusters lead to pronounced increases in rock-matrix permeability. In the simplest formulation, the modelling is dimensionless and almost entirely constrained without free parameters. Nevertheless, APE modelling of the evolution of fluid-saturated rocks under stress reproduces the observed fracture criticality and the narrow range of shear-wave azimuthal anisotropy in crustal rocks. It also reproduces the behaviour of temporal variations in shear-wave splitting observed before and after the 1986, M = 6, North Palm Springs earthquake, Southern California, and several other smaller earthquakes.
The agreement of APE modelling with a wide range of observations confirms that fluid-saturated crystalline rocks are stress-sensitive and respond to changes in stress by critical fluid-rock interactions at the microscale level. This means that the effects of changes in stress and other parameters can be numerically modelled and monitored by appropriate observations of seismic shear waves.     

A multidisciplinary study of a slow-slipping fault for seismic hazard assessment: the example of the Middle Durance Fault (SE France)

Assessing seismic hazard in continental interiors is difficult because these regions are characterized by low strain rates and may be struck by infrequent destructive earthquakes. In this paper, we provide an example showing that interpretations of seismic cross sections combined with other kinds of studies such as analysis of microseismicity allow the whole seismogenic source area to be imaged in this type of region. The Middle Durance Fault (MDF) is an 80-km-long fault system located southeastern France that has a moderate but regular seismicity and some palaeoseismic evidence for larger events. It behaves as an oblique ramp with a left-lateral-reverse fault slip and has a low strain rate. MDF is one of the rare slow active fault system monitored by a dedicated dense velocimetric short period network. This study showed a fault system segmented in map and cross section views which consists of staircase basement faults topped by listric faults ramping off Triassic evaporitic beds. Seismic sections allowed the construction of a 3-D structural model used for accurate location of microseismicity. Southern part of MDF is mainly active in the sedimentary cover. In its northern part and in Alpine foreland, seismicity deeper than 8 km was also recorded meaning active faults within the crust cannot be excluded. Seismogenic potential of MDF was roughly assessed. Resulting source sizes and estimated slip rates imply that the magnitude upper limit ranges from 6.0 to 6.5 with a return period of a few thousand years. The present study shows that the coupling between 3-D fault geometry imaging and accurate location of microseismicity provides a robust approach to analyse active fault sources and consequently a more refined seismic hazard assessment.     

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.