A test of the precursory accelerating moment release model on some recent New Zealand earthquakes

The proposal that the moment release rate increases in a systematic way in a large region around a forthcoming large earthquake is tested using three recent, large New Zealand events. The three events, 1993–1995, magnitudes 6.7–7.0, occurred in varied tectonic settings. For all three events, a circular precursory region can be found such that the moment release rate of the included seismicity is modelled significantly better by the proposed accelerating model than by a linear moment release model, although in one case the result is dubious. The 'best' such regions have radii from 122 to 167 km, roughly in accord with previous observations world-wide, but are offset by 50–60 km from the associated main shock epicentre. A grid-search procedure is used to test whether these three earthquakes could have been forecast using the accelerating moment release model. For two of the earthquakes the result is positive in terms of location, but the main shock times are only loosely constrained.     

Coseismic slip model of the 2007 August Pisco earthquake (Peru) as constrained by Wide Swath radar observations

The Pisco earthquake ( M _w 8.0; 2007 August 15) occurred offshore of Peru's southern coast at the subduction interface between the Nazca and South American plates. It ruptured a previously identified seismic gap along the Peruvian margin. We use Wide Swath InSAR observations acquired by the Envisat satellite in descending and ascending orbits to constrain coseismic slip distribution of this subduction earthquake. The data show movement of the coastal regions by as much as 85 cm in the line-of-sight of the satellite. Distributed-slip model indicates that the coseismic slip reaches values of about 5.5 m at a depth of ∼18–20 km. The slip is confined to less than 40 km depth, with most of the moment release located on the shallow parts of the interface above 30 km depth. The region with maximum coseismic slip in the InSAR model is located offshore, close to the seismic moment centroid location. The geodetic estimate of seismic moment is 1.23 × 10²¹ Nm ( M _w 8.06), consistent with seismic estimates. The slip model inferred from the InSAR observations suggests that the Pisco earthquake ruptured only a portion of the seismic gap zone in Peru between 13.5° S and 14.5° S, hence there is still a significant seismic gap to the south of the 2007 event that has not experienced a large earthquake since at least 1687.     

Earthquake sequences on a frictional fault model with non-uniform strengths and relaxation times

Summary. The space and time characteristics of earthquake sequences, including a main shock, aftershocks and the recurrence of major shocks in a long time range, are investigated on a frictional fault model with non-uniform strengths and relaxation times, which is subjected to a time-dependent shear stress. Aftershocks with low stress drop take place successively in spaced regions so as to fill the gaps which have not yet been ruptured since the main shock, while those with high stress drop occur in and around the regions left unruptured during the main faulting. The frequency decay of aftershocks with time follows a hyperbolic law with the rates p consistent with observations. There are good linear relations in logarithmic scales for source area versus frequency and seismic moment versus frequency of the generated aftershocks. The b -value obtained in the present experiments appears slightly larger than that for observations. It was found that more heterogeneous distribution of the fault strength give smaller p and larger b -values. The recurrence of major shocks, particularly of very large shocks with high stress drop, is often preceded by a completely silent period of activity or very low activity with a small number of foreshocks. The major shocks take place successively in adjacent unruptured regions and sometimes show slow-speed migrations. These results provide explanations to various observations of earthquake sequences.     

Simulating a seismic series using geostatistical and stochastic methods: application to the seismic series in the Alborán Sea (1997 June 24–?)

Seismic series can be taken as examples of correlated unstationary sets of time-stochastic sequences. We investigate the possibility of estimating what is most probable to occur subsequently, if we know the events that have occurred up to a given moment.
The stochastic methods can be used with data of the seismic series, irrespective of their genesis and origin. Using three stochastic methods, namely (1) simulating the likelihood of occurrence by conditional geostatistical simulation; (2) developing a stochastic analysis of the energy release by means of energy packages; and (3) calculating the occurrence time of the most probable next earthquake, we were able to simulate the occurrence of earthquakes that took place during the Alborán Sea seismic series (1997–1998).
We conclude that it is possible to set limits on the time of occurrence and energy release, understood as the magnitude of the most probable earthquake, during the development of a seismic sequence and prior to the actual occurrence of the earthquake.     

Source history of the 1905 great Mongolian earthquakes (Tsetserleg, Bolnay)

Two great Mongolian earthquakes, Tsetserleg and Bolnay, occurred on 1905 July 9 and 23. We determined the source history of these events using body waveform inversion. The Tsetserleg rupture (azimuth N60°) correspond to a N60° oriented branch of the long EW oriented Bolnay fault.
Historical seismograms recorded by Wiechert instruments are digitized and corrected for the geometrical deformation due to the recording system. We use predictive filters to recover the signals lost at the minute marks.
The total rupture length for the Tsetserleg earthquake may reach up to 190 km, in order to explain the width of the recorded body waves. This implies adding 60 km to the previously mapped fault. The rupture propagation is mainly eastward. It starts at the southwest of the central subsegment, showing a left lateral strike-slip with a reverse component. The total duration of the modelled source function is 65 s. The seismic moment deduced from the inversion is 10²¹ N m, giving a magnitude   M _w = 8  .
The nucleation of the Bolnay earthquake was at the intersection between the main fault (375 km left lateral strike-slip) and the Teregtiin fault (N160°, 80 km long right lateral strike-slip with a vertical component near the main fault). The rupture was bilateral along the main fault: 100 km to the west and 275 km to east. It also propagated 80 km to the southeast along the Teregtiin fault. The source duration was 115 s. The moment magnitude Mw varies between 8.3 and 8.5.
The nucleation and rupture depths remain uncertain. We tested three cases: (1) nucleation and rupture depth limited to the seismogenic zone; (2) nucleation in the seismogenic zone and rupture propagation going to the base of the crust and (3) nucleation within the crust–upper mantle interface and rupture propagation within the upper mantle.     

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.     

Applicability of time-to-failure analysis to accelerated strain before earthquakes and volcanic eruptions

We examine quantitatively the ranges of applicability of the equation Ω= A+B [1− t/t _f ] ^m for predicting 'system-sized' failure times t _f in the Earth. In applications Ω is a proxy measure for strain or crack length, and A , B and the index m are model parameters determined by curve fitting. We consider constitutive rules derived from (a) Charles' law for subcritical crack growth; (b) Voight's equation; and (c) a simple percolation model, and show in each case that this equation holds only when m < 0. When m > 0, the general solution takes the form Ω = A + B [1 + t / T  ] ^m , where T   is a positive time constant, and no failure time can be defined. Reported values for volcanic precursors based on rate data are found to be within the range of applicability of time-to-failure analysis ( m < 0). The same applies to seismic moment release before earthquakes, at the expense of poor retrospective predictability of the time of the a posteriori -defined main shock. In contrast, reported values based on increasing cumulative Benioff strain occur in the region where a system-sized failure time cannot be defined ( m > 0; commonly m ≈ 0.3). We conclude on physical grounds that cumulative seismic moment is preferred as the most direct measure of seismic strain. If cumulative Benioff strain is to be retained on empirical grounds, then it is important that these data either be re-examined with the independent constraint m < 0, or that for the case 0 < m + 1 < 1, a specific correction for the time-integration of cumulative data be applied, of the form ΣΩ = At + B '{1 − [1 − t/t _f ] ^m+1 }.     

Candidate precursors: pulse-like geoelectric signals possibly related to recent seismic activity in Japan

Telemetric network observations of pulse-like geoelectric charge signals using a vertical dipole buried under the ground were undertaken at various observation sites over a wide area in Japan from April 1996. From continuous records of the signals during the six months following that, we attempted to select anomalous signals, possibly related to seismic electric activity. Special attention was paid to the elimination of noise resulting from industrial and meteorological electric activity, comparison with other electromagnetic signals in the VLF band and the relation between the precursor period and the distance from the eventual main shock that occurred in Japan. Four candidate precursor electric signals, which were not contaminated by industrial and meteorological electric activity, were then selected, of which the second appeared before the Akita-ken Nairiku-nanbu earthquake swarm, for which the maximum M = 5.9 occurred on 1996 August 11, and the third and fourth before the Chiba-ken Toho-oki earthquake, M = 6.6, on 1996 September 11. A tentative qualitative model explaining why the candidate precursory signal is related to stress building up before an earthquake is presented in terms of the electrification of gases released from fracturing rocks immediately prior to the main shock.     

高地震烈度区堆积体边坡动力响应时程特征分析

考虑到在地震过程中,工程边坡的动安全系数最小值出现在某一瞬间,而用这个值评价边坡在地震荷载作用下的抗滑稳定性不合适宜。在简单分析地震荷载作用下边坡稳定性评价的主要方法及差异基础上,介绍了地震动力响应时程分析法的基本原理和计算过程,明确指出了边坡动力稳定分析时应注意的边界条件、材料参数等问题,建立了评价动力稳定性的有限元应力法表达式。基于地震动力时程反应,结合金安桥水电站库岸堆积体边坡工程,用动力有限元计算获得了边坡的动力响应在空间的变化规律(包括动应力和加速度等)和整体稳定性,计算成果合理地评价了其稳定性。     

Constraints on the frequency–magnitude relation and maximum magnitudes in the UK from observed seismicity and glacio-isostatic recovery rates

Earthquake populations have recently been shown to have many similarities with critical-point phenomena, with fractal scaling of source sizes (energy or seismic moment) corresponding to the observed Gutenberg–Richter (G–R) frequency–magnitude law holding at low magnitudes. At high magnitudes, the form of the distribution depends on the seismic moment release rate M˙ and the maximum magnitude m _max . The G–R law requires a sharp truncation at an absolute maximum magnitude for finite M˙ . In contrast, the gamma distribution has an exponential tail which allows a soft or 'credible' maximum to be determined by negligible contribution to the total seismic moment release. Here we apply both distributions to seismic hazard in the mainland UK and its immediate continental shelf, constrained by a mixture of instrumental, historical and neotectonic data. Tectonic moment release rates for the seismogenic part of the lithosphere are calculated from a flexural-plate model for glacio-isostatic recovery, constrained by vertical deformation rates from tide-gauge and geomorphological data. Earthquake focal mechanisms in the UK show near-vertical strike-slip faulting, with implied directions of maximum compressive stress approximately in the NNW–SSE direction, consistent with the tectonic model. Maximum magnitudes are found to be in the range 6.3–7.5 for the G–R law, or 7.0–8.2 m _L for the gamma distribution, which compare with a maximum observed in the time period of interest of 6.1 m _L . The upper bounds are conservative estimates, based on 100 per cent seismic release of the observed vertical neotectonic deformation. Glacio-isostatic recovery is predominantly an elastic rather than a seismic process, so the true value of m _max is likely to be nearer the lower end of the quoted range.     

Fault-plane solutions and hypocentral distribution of some 1977 Friuli aftershocks

Summary. The polarity of first-arrivals of P -waves recorded by the vertical-component seismometers of the Friuli telemetric network of the Osservatorio Geofisico Sperimentale, Trieste have been used to fmd a number of cumulative fault-plane solutions of aftershocks of the large 1976 May Friuli earthquake. In spite of its poor quality, the cumulative solution for the whole period 1977 May—September is similar to the greatest majority of partial cumulative solutions which exhibit much better quality. The polarities of opposite sign, characterizing the first-arrivals of seismic rays which have travelled along subparallel paths and which are responsible for reducing the quality of the solutions, seem to be due mainly to variations in the direction of slip on faults with constant orientation. The inversion of P - and T -axes revealed by the solutions, however, occurred in certain periods at particular hypocentral depths or in specific epicentral zones and has been responsible for the reversal of some polarities.
The almost constant orientation of the principal stresses, revealed by most fault-plane solutions, suggests that they represent the orientation of the regional tectonic stresses related to this phase of the earthquake. Although this orientation is similar to that of the 1976 May shock, an inversion of the P - and T -axes suggests that normal faulting has taken over from reverse faulting observed for the main shock. The reversal of the P - and T -axes may be due to the partial release of the stresses related to the earthquake or to the shift of location of the hypocentres, possibly associated with a different limb of a major thrust-fold.     

FIR filter effects and nucleation phases

The symmetric impulse response of linear phase Finite Impulse Response (FIR) filters most commonly used in modern seismic recording systems produces precursory signals to impulsive arrivals. These acausal filter-generated artefacts may result in misinterpretations of various onset properties. Prior to any onset interpretation, these effects have to be removed from the seismic record. This can be achieved without loss of bandwidth by post-filtration of the digital seismograms if the filter coefficients and the decimation ratios are known. We have analysed numerous signals from different instruments and sampling rates for precursory phases and found that—in contrast to commonly held beliefs—FIR-filter-related precursory signals are not always easy to recognize visually from their waveform signature. Furthermore, they can exhibit surprisingly similar properties to those reported for nucleation phases, although the majority of nucleation phases reported in the past have been obtained on instruments with a causal response. We demonstrate examples of filter-related precursory signals for events scanning nine orders of moment, from 10¹⁰ N m to 10¹⁹ N m. Surprisingly, the lower bound of the artefact durations as a function of seismic moment scales close to the cube root of the seismic moment. We interpret this as being caused by the fact that above a certain seismic moment, the attenuated source signal acts as a causal lowpass filter of a smaller bandwidth than the FIR filter. Assuming an ω^-2 source model, constant stress drop and an empirical relationship between the maximum artefact duration and the cut-off frequency of the FIR filter, the artefact durations are expected to scale proportional to the 1/2.5 power of the seismic moment, in comparison to 1/3 as proposed for nucleation phases.     

Lower-crustal rifting in the Rukwa Graben, East Africa

An M_w 5.9 earthquake occurred in the Lake Rukwa rift, Tanzania, on 1994 August 18, and was well recorded by 20 broad-band seismic stations at distances of 160 to 800 km and 21 broad-band stations at teleseismic distances. The regional and teleseismic waveforms have been used to investigate the source characteristics of the main shock, and also to locate aftershocks that occurred within three weeks of the main shock. Teleseismic body-wave modelling yields the following source parameters for the main shock: source depth of 25 ± 2 km, a normal fault orientation, with a horizontal tension axis striking NE-SW and an almost vertical pressure axis (Nodal Plane I: strike 126°–142°, dip 63°–66°, and rake 280°–290°; Nodal Plane II: strike 273°–289°, dip 28°–31°, and rake 235°–245°), a scalar moment of 4.1 times 10¹⁷ N m, and a 2 s impulsive source time function. Four of the largest aftershocks also nucleated at depths of 25 km, as deduced from regional sPmp–Pmp times. The nodal planes are broadly consistent with the orientation of both the Lupa and Ufipa faults, which bound the Rukwa rift to the northeast and southwest, respectively. The rupture radius of the main shock, assuming a circular fault, is estimated to be 4 km with a corresponding stress drop of 6.5 MPa. Published estimates of crustal thickness beneath the Rukwa rift indicate that the foci of the main shock and aftershocks lie at least 10 km above the Moho. The presence of lower-crustal seismicity beneath the Rukwa rift suggests that the pre-rift thermal structure of the rifted crust has not been strongly modified by the rifting, at least to depths of 25 km.     

Determination of the polynomial moments of the seismic moment rate density distribution with positivity constraints

We present a new formulation of the inverse problem of determining the temporal and spatial power moments of the seismic moment rate density distribution, in which its positivity is enforced through a set of linear conditions. To test and demonstrate the method, we apply it to artificial data for the great 1994 deep Bolivian earthquake. We use two different kinds of faulting models to generate the artificial data. One is the Haskell-type of faulting model. The other consists of a collection of a few isolated points releasing moment on a fault, as was proposed in recent studies of this earthquake. The positions of 13 teleseismic stations for which P - and SH -wave data are actually available for this earthquake are used. The numerical experiments illustrate the importance of the positivity constraints without which incorrect solutions are obtained. We also show that the Green functions associated with the problem must be approximated with a low approximation error to obtain reliable solutions. This is achieved by using a more uniform approximation than Taylor's series. We also find that it is necessary to use relatively long-period data first to obtain the low- (0th and 1st) degree moments. Using the insight obtained into the size and duration of the process from the first-degree moments, we can decrease the integration region, substitute these low-degree moments into the problem and use higher-frequency data to find the higher-power moments, so as to obtain more reliable estimates of the spatial and temporal source dimensions. At the higher frequencies, it is necessary to divide the region in which we approximate the Green functions into small pieces and approximate the Green functions separately in each piece to achieve a low approximation error. A derivation showing that the mixed spatio-temporal moments of second degree represent the average speeds of the centroids in the corresponding direction is given.     

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.     

Source tomography by simulated annealing using broad-band surface waves and geodetic data: application to the Mw= 8.1 Chile 1995 event

We invert surface-wave and geodetic data for the spatio-temporal complexity of slip during the M _w =8.1 Chile 1995 event by simulated annealing. This quasi-global inversion method allows for a wide exploration of model space, and retains the non-linearity of the source tomography problem. Complex source spectra are obtained from 5 to 45 mHz from first- and second-orbit fundamental-mode Rayleigh waves using an empirical Green's function cross-correlation technique. Coseismic displacement vectors were measured at 10 GPS sites near Antofagasta. They are part of a French-Chilean experiment which monitors the Northern Chile seismic gap. The spectra, together with the geodetic data, are inverted for the moment distribution on a 2-D dipping fault, under the physical constraints of slip positivity and causality. Marginal a posteriori distributions of the model parameters are obtained from several independently inverted solutions. In general, features of the slip model are well resolved. Data are well fitted by a purely unilateral southward rupture with a nearly uniform velocity around 2.5–3.0 km s⁻¹, and a total duration of 65 s. Several regions of moment release were imaged, one near the hypocentre, a major one 80 km south of it and a minor one 160 km south of it. The major patch of moment release seemed to have propagated to relatively shallow depths near the trench, 100 km SSW of the epicentre. The region of major slip is located updip of the 1987, M _w =7.5 earthquake, suggesting a causal relationship. Most of the slip occurred updip of the hypocentre (36 km), but the entire coupled plate interface (20–40 km) ruptured during the Chile 1995 event.     

Application of conditional geostatistical simulation to calculate the probability of occurrence of earthquakes belonging to a seismic series

Geostatistics offers various techniques of estimation and simulation that have been satisfactorily applied in solving geological problems. In this sense, conditional geostatistical simulation is applied to calculate the probability of occurrence of an earthquake with a lower than or equal magnitude to one determined during a seismic series. It is possible to calculate the energy of the next most probable earthquake from a specific time, given knowledge of the structure existing among earthquakes occurring prior to a specific moment.     

地震灾害死亡人口快速评估方法对比研究

中国是世界上地震活动最为频繁的国家之一,属于地震多发区。在收集分析国内外关于地震灾害死亡人口评估模型的基础上,选取10种模型以2000年以来中国典型地震灾害为案例验证其适用性。结果表明：① 对于5.7级（含）以下地震,10种模型的评估结果基本都在合理范围内,可采用各评估结果的区间值来支撑应急决策;5.7~6.6级（含）地震,10种评估方法得到的结果表现出不同程度的偏差,可采用多数评估结果指向的死亡人口数量级来支撑应急决策;6.6级以上地震,则只能采用有特定适用范围的基于结构易损性的评估结果来支撑应急决策,且也存在较大的不确定性。② 从地震灾害人员伤亡动态评估方法、地震—地质灾害死亡人口快速评估方法和快速评估软件系统方面进行了相关讨论。此研究可为地震灾害死亡人口快速评估模型的改进与发展提供借鉴。     

Temporal and spatial variations of post-seismic deformation following the 1999 Chi-Chi, Taiwan earthquake

We use GPS displacements collected in the 15 months after the 1999 Chi-Chi, Taiwan earthquake  ( M _w 7.6)  to evaluate whether post-seismic deformation is better explained by afterslip or viscoelastic relaxation of the lower crust and upper mantle. We find that all viscoelastic models tested fail to fit the general features in the post-seismic GPS displacements, in contrast to the satisfactory fit obtained with afterslip models. We conclude that afterslip is the dominant mechanism in the 15-month period, and invert for the space–time distribution of afterslip, using the Extended Network Inversion Filter. Our results show high slip rates surrounding the region of greatest coseismic slip. The slip-rate distribution remains roughly stationary over the 15-month period. In contrast to the limited coseismic slip on the décollement, afterslip is prominent there. Maximum afterslip of 0.57 m occurs downdip and to the east of the hypocentral region. Afterslip at hypocentral depths is limited to the southern part of the main shock rupture, with little or no slip on the northern section where coseismic slip was greatest. Whether this results from along strike variations in frictional properties or dynamic conditions that locally favour stable sliding is not clear. In general, afterslip surrounds the area of greatest coseismic slip, consistent with post-seismic slip driven by the main shock stress change. The total accumulated geodetic afterslip moment is  3.8 × 10¹⁹ N m  , significantly more than the seismic moment released by aftershocks,  6.6 × 10¹⁸ N m  . Afterslip and aftershocks appear to have different temporal evolutions and some spatial correlations, suggesting that aftershock rates may not be completely controlled by the rate of afterslip.     

An improved region–time–length algorithm applied to the 1999 Chi-Chi, Taiwan earthquake

By means of the region–time–length (RTL) algorithm, which is widely used for investigating the precursory seismicity changes in China, Italy, Japan, Russia and Turkey, we examine the precursory seismic activity occurred prior to the 1999, M _w = 7.6, Chi-Chi earthquake around its epicentre. Based on our calculation of the RTL values, the epicentral area has been found to strongly exhibit the signature of anomalous activity, associated with the seismic quiescence and activation, before the main shock. Also proposed in this study is a helpful method for determining two important parameters used in the RTL analysis, the characteristic time and distance. Such method will largely reduce the ambiguity in the original RTL algorithm.