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.     

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.     

The spatial stability of alcohol outlets and crime in post‐disaster Christchurch,New Zealand

The devastating Canterbury Earthquakes of 2010 and 2011 left an indelible mark on the city of Christchurch. The social and economic upheaval that immediately followed the Earthquakes has, in time, been replaced with a period of rebuild and transformation. In this study we investigate the effects that the Canterbury Earthquakes had on two important and inter‐related phenomena in the city: alcohol availability and crime. More specifically, we investigate how alcohol outlets and crime across six different categories changed in magnitude and spatial distribution pre‐ (end‐2009) and post‐ (end‐2014) earthquake. We do this using a variety of geospatial techniques including a relatively new method: the spatial point pattern test which allows for the identification of changes in spatial patterns at the local level. Results indicate that both alcohol outlets and crime have decreased in magnitude since the Canterbury Earthquakes. Using the spatial point pattern test we found statistically significant differences in spatial point patterns for both alcohol outlets and all crime types pre‐ to post‐earthquake. The similarity in the differences of the spatial distributions of alcohol outlets and crime provides a first empirical clue of their potential association in the city post‐earthquake.     

A comparison of scenario-based hybrid bilevel and multi-objective location-allocation models for earthquake emergency shelters: a case study in the central area of Beijing,China

The accurate location and allocation of disaster emergency shelters are key components of effective urban planning and emergency management. Various models have been developed to solve the location-allocation problem, but gaps remain with regard to model realism and associated applicability. For the available location and allocation models of earthquake emergency shelters, uncertainty with respect to earthquake hazard, population exposure, rate of damage to buildings and the effects of evacuee behavior are often neglected or oversimplified. Moreover, modifying the models can be an alternative means of improving the solution quality when the optimization algorithm has difficulty coping with a complex, high-dimensional problem. This article develops a scenario-based hybrid bilevel model that addresses the concerns related to high-dimensional complexity and provides a higher degree of realism by incorporating the uncertainties of population dynamics and earthquake damage scenarios into location-allocation problems for earthquake emergency shelters. A modified particle swarm optimization algorithm combined with a simulated annealing algorithm was applied to derive solutions using the hybrid bilevel model and a conventional multi-objective model, and the solutions obtained using the two models were then compared. The novel features of the study include the hybrid bilevel model that considers the dynamic number of evacuees and its implementation for earthquake emergency shelter location and allocation. The results show that the solutions significantly differ between daytime and nighttime. When applied to the multi-objective model, the optimization algorithm is time consuming and may only find the local optima and provide suboptimal solutions in the considered scenarios with more evacuees. By contrast, the hybrid bilevel model shows more desirable performance because it significantly reduces the dimensionality of the location-allocation problem based on a two-step-to-reach approach. The proposed hybrid bilevel model is proven to be useful for optimal shelter allocation, and the presented results can be used as a reference for balancing the interests of the government and residents during the planning of shelters in Beijing.     

Tectonics of the Marmara Sea region of Turkey: new evidence from microearthquake fault plane solutions

Summary. Composite and single-event fault plane solutions for microearthquakes in the Izmit Bay area of the Marmara Sea indicate right-lateral strike-slip motion and tension on this extension of the North Anatolian Fault. This interpretation is consistent with teleseismically determined fault-plane solutions obtained for large earthquakes on the Marmara Sea seismic lineation. Consideration of the microplate geometry of north-western Turkey, inferred from seismicity as well as earthquake mechanisms, suggests that the region comprises two seismotectonic units with differing styles of deformation. The (Anatolid) structures of south- and central-western Anatolia are undergoing major extension, whereas the (Pontid) structures of the Marmara Sea region are being sheared, resulting in a mixed regime of both strike-slip and extensional faulting.     

A modified particle swarm optimization algorithm for optimal allocation of earthquake emergency shelters

Allocation for earthquake emergency shelters is a complicated geographic optimization problem because it involves multiple sites, strict constraints, and discrete feasible domain. Huge solution space makes the problem computationally intractable. Traditional brute-force methods can obtain exact optimal solutions. However, it is not sophisticated enough to solve the complex optimization problem with reasonable time especially in high-dimensional solution space. Artificial intelligent algorithms hold the promise of improving the effectiveness of location search. This article proposes a modified particle swarm optimization (PSO) algorithm to deal with the allocation problem of earthquake emergency shelter. A new discrete PSO and the feasibility-based rule are incorporated according to the discrete solution space and strict constraints. In addition, for enhancing search capability, simulated annealing (SA) algorithm is employed to escape from local optima. The modified algorithm has been applied to the allocation of earthquake emergency shelters in the Zhuguang Block of Guangzhou City, China. The experiments have shown that the algorithm can identify the number and locations of emergency shelters. The modified PSO algorithm shows a better performance than other hybrid algorithms presented in the article, and is an effective approach for the allocation problem of earthquake emergency shelters.     

Focal Mechanism of the Koyna, India Earthquake of 1967, December 10

One of the two alternate fault plane solutions determined in this study for the Koyna earthquake of 1967 December 10 shows a component of normal faulting. This possibility remained unnoticed in previous focal mechanism studies. Both solutions show left lateral motion along the nodal plane striking towards north-north-east. The origin of the tectonic stress causing the earthquake is believed to be related to the collision of Indian and Eurasian continents, following which the entire Indian Peninsula may be under a state of left lateral shear.     

Coseismic rotation changes from the 2004 Sumatra earthquake: the effects of Earth's compressibility versus earthquake induced topography

Polar motion is modelled for the large 2004 Sumatra earthquake via dislocation theory for an incompressible elastic earth model, where inertia perturbations are due to earthquake-triggered topography of density–contrast interfaces, and for a compressible model, where inertia perturbation due to compression-dilatation of Earth's material is included; density and elastic parameters are based on a multilayered reference Earth. Both models are based on analytical Green's functions, propagated from the centre to the Earth's surface. Preliminary and updated seismological solutions are considered in elucidating the effects of improving earthquake parameters on polar motion. The large Sumatra thrust earthquake was particularly efficient in driving polar motion since it was responsible for large material displacements occurring orthogonally to the strike of the earthquake and to the Earth's surface, as imaged by GRACE gravity anomalies over the earthquake area. The effects of earthquake-induced topography are four times larger than the effects of Earth's compressibility, for l = 2 geopotential components. For varying compressional Earth properties and seismic solution, modelled polar motion ranges from 8.6 to 9.4 cm in amplitude and between 117° and 130° east longitude in direction. The close relationship between polar motion direction, earthquake longitude and thrust nature of the event, are established in terms of basic physical concepts.     

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.     

An improved method for the determination of the tectonic stress field from focal mechanism data

All conventional stress inversion methods, when applied to earthquake focal mechanism data, suffer from uncertainty as to which plane is the true fault plane. This paper deals with several problems in stress inversion brought about by this uncertainty. Our analysis shows that the direction of shear stress on the auxiliary plane does not coincide with the hypothetical slip direction unless the B -axis is parallel to one of the three principal stress directions. Based on this simple fact, we propose a new algorithm dealing with the ambiguity in fault/auxiliary plane identification. We also propose a method to handle the inhomogeneity problem of data quality, which is common and unique for focal mechanism data. Different inversion methods and algorithms are applied to two sets of 'focal mechanism' data simulated from field fault-slip measurement data. The inversion results show that, among the four stress parameters inverted, the stress ratio suffers the most from the ambiguity in fault/auxiliary plane identity, whereas the solutions for the principal stress directions are surprisingly good. The errors in inversion solutions resulting from the fault/auxiliary plane ambiguity can be significantly reduced by controlling subjectively the sample variance of the measurement errors. Our results also suggest that the fault plane cannot be distinguished correctly from the auxiliary plane with a high probability on the basis of the stress inversion alone.     

The two-point correlation function of the seismic moment tensor

Summary. We use the invariants of the two-point correlation function of the seismic moment to investigate the degree of irregularity of an earthquake fault, i.e. to study the rapidity with which a complex fault changes its direction of orientation. The two-point correlation function is a fourth-order tensor which has three scalar invariants in the isotropic case. Although the accuracy of present-day catalogues of fault plane solutions is rather low for our purpose, nevertheless the invariants of these correlation tensors confirm the generally     

A fault plane solution using theoretical P seismograms

We use the method of Hudson and Douglas, Hudson & Blarney to compute seismograms which simulate the codas of 10 short period P -wave seismograms from a shallow earthquake. The polarities and relative amplitudes of P and pP measured from seven of the observed seismograms are used to compute a fault plane solution with confidence limits, assuming that the source radiates as a double couple. This solution is in approximate agreement with that given for the same earthquake by Sykes & Sbar, who used only the onset polarities of short-period P waves. The small difference between the two solutions can be explained by interference between the true first motion of P and microseismic noise at two stations.
The results show that, for some shallow earthquakes, the relative amplitude method has the following advantages over the first motions method. First, a P/pP amplitude ratio (with appropriate confidence limits) can always be measured, even in seismograms which are so noisy that the first motion of P is uncertain. Second, the fault plane solutions obtained from relative amplitudes have known confidence limits. Finally, by using more information from each seismogram, the relative amplitude method requires considerably fewer seismograms than the first motions method.     

GIS空间动态模型组件的设计与实现

组件重用技术为GIS与空间模型的集成提供了新的解决方案。该文设计的空间动态模型的GIS组件 -Dy namicGC ,它在传统GIS数据模型的基础上 ,增加了表达空间动态系统的过程和关系 (流 )的数据模型和对象接口 ,为GIS环境下创建复杂动态过程模型提供了新的工具和解决方案。该组件基于微软组件对象模型 (COM/DCOM)实现 ,充分考虑了互操作性、模型建模语言以及模型系统的可获取性需求 ,由一系列支持动态数据计算的OLE自动化对象集组成 ,可支持VB、Dephi、VisualC 等通用开发环境 ,也支持VBA、VBSCRIPT、JAVASCRIPT等脚本语言环境。使用VBA创建了经典的“生命游戏”的元胞自动机模型的实现 ,作为该组件创建动态过程模型的应用实例。     

Far-field simulation of the 1946 Aleutian tsunami

We present hydrodynamic far-field simulations of the Aleutian tsunami of 1946 April 1, using both a dislocation source representing a slow earthquake and a dipolar one modelling a large landslide. The earthquake source is derived from the recent seismological study by López and Okal, while the landslide source was previously used to explain the exceptional run-up at Scotch Cap in the near field. The simulations are compared to a field data set previously compiled from testimonies of elderly witnesses at 27 far-field locations principally in the Austral and Marquesas Islands, with additional sites at Pitcairn, Easter and Juan Fernández. We find that the data set is modelled satisfactorily by the dislocation source, while the landslide fails to match the measured amplitudes, and to give a proper rendition of the physical interaction of the wavefield with the shore, in particular at Nuku Hiva, Marquesas. The emerging picture is that the event involved both a very slow earthquake, responsible for the far-field tsunami, and a major landslide explaining the near-field run-up, but with a negligible contribution in the far field.     

Comment on 'The use of velocity spectrum for stacking receiver functions and imaging upper mantle discontinuities' by H. Gurrola, J. B. Minster and T. Owens

In a recent paper, Gurrola, Minster & Owens (1994; hereafter referred to as GMO) introduced a technique for the analysis of seismic data and applied it to the records of station OBN in Russia. GMO claimed that this was a new technique in earthquake seismology, and that their results for OBN provided a new insight into the deep structure of the Russian platform. We have some comments on their techniques and results.     

Source process and tectonic implications of the great 1975 North Atlantic earthquake

Summary. The Atlantic segment of the Africa–Europe plate boundary has usually been interpreted as a transform boundary on the basis of the bathymetric expression of the Gloria fault and dextral strike-slip first-motion mechanisms aligned along the Azores–Gibraltar line of seismicity. The 1975 May 26 earthquake ( M _s=7.9) was assumed to fit into this framework because it occurred in the general area of this line and has a similar first-motion focal mechanism (strike=288°, dip=72°, slip angle=184°). However, several anomalies cast doubt on this picture: the event is abnormally large for an oceanic transform event; a sizeable tsunami was excited; the aftershock area is unusually small for such a large event; and most significantly, the epicentre is 200 km south of the presumed plate boundary. The Rayleigh wave radiation pattern indicates a change in focal mechanism to one with a significant dip-slip component. The short duration of the source time history (20 s, as deconvolved from long-period P -waves), the lack of directivity in the Rayleigh waves, and the small one-day aftershock area suggest a fault length less than 80 km. One nodal plane of the earthquake is approximately aligned with the trace of an ancient fracture zone.
We have compared the Pasadena 1-90 record of the 1975 earthquake to that of the 1941 North Atlantic strike-slip earthquake (200 km to the NNW) and confirmed the large size of the 1941 event ( M =8.2). The non-colinear relationship of the 1975 and 1941 events suggests that there is no well-defined plate boundary between the Azores and Gibraltar. This interpretation is supported by the intraplate nature of both the 1975 event and the large 1969 thrust event 650 km to the east. This study also implies that the largest oceanic strike-slip earthquakes occur in old lithosphere in a transitional tectonic regime.     

A detailed analysis of the February 1996 aftershock sequence in the eastern Pyrenees, France

Following the 1996 February 18 M _L = 5.2 earthquake in the Agly massif in the eastern French Pyrenees, we installed a temporary network of seismometers around the epicentre. In this paper, we analyse 336 well-located aftershocks recorded from February 19 to February 23 by 18 temporary stations and two permanent stations located less than 35  km from the epicentre. Most aftershocks have been located with an accuracy better than 1.5  km in both horizontal and vertical positions. Their spatial distribution suggests the reactivation of a known fault system. We determined 39 fault-plane solutions using P -wave first motions. Despite their diversity, the focal mechanisms yield an E–W subhorizontal T-axis. We also determined fault-plane solutions and principal stress axes using the method developed by Rivera & Cisternas (1990 ) for the 15 best-recorded events. We obtain a pure-shear-rupture tectonic regime under N–S subhorizontal compression and E–W subhorizontal extension. These principal stress axes, which explain the focal mechanisms for at least 75 per cent of the 39 aftershocks, are different from the axes deduced from the main shock. The post-earthquake stress field caused by the main-shock rupture, modelled as sinistral strike slip on three vertical fault segments, is computed for various orientations and magnitudes of the regional stress field, assumed to be horizontal. The aftershock distribution is best explained for a compressive stress field oriented N30°E. Most aftershocks concentrate where the Coulomb failure stress change increases by more than 0.2  MPa. The diversity of aftershock focal mechanisms, poorly explained by this model, may reflect the great diversity in the orientations of pre-existing fractures in the Agly massif.     

Applying the relative hypocentre location approach: where was the 1980 November 23 Irpinia earthquake?

The purpose of this work is to evaluate under what conditions it is feasible and with what accuracy it is possible to locate the nucleation point of a large earthquake, given the availability of aftershocks located with high precision by the deployment of a local network. We experiment with several approaches and apply them lo the location of the epicentre of the 1980 November 23 Irpinia earthquake ( M ^w= 6.9).
First we use local P ^g phases selected to optimize the azimuthal coverage, obtaining a well-constrained location with a small statistical error, which typically underestimates the true hypocentre uncertainty.
We then exploit the relative location technique, obtaining stable, almost coincident solutions under three conditions: (1) using multiple independent master events to derive an average epicentre; (2) fitting simultaneously the larger data set for all available master events, using a forward approach; (3) conducting an a priori evaluation of the statistics of station and master events to separate model uncertainties and improve the statistical accuracy of the relative locations. Moreover, only by introducing station statistics can we achieve the desired accuracy of ≅ 1 km in constraining the rupture nucleation point of this large earthquake, and we show that the application of the relative location technique to uncleaned, unweighted data for a single master event provides only a crude epicentre with a confidence ellipse deceivingly smaller than the true hypocentre uncertainty.
The revised epicentre for the 1980 November 23 Irpinia earthquake (48.803 °N-15.302°E) validates the class of multidisciplinary reconstructions of the source process such as the model of Valensise et al. (1989), based on the hypocentre of Westaway & Jackson (1987), and is shifted by almost 13 km to the NW of the epicentre recently proposed by Westaway (1992).     

Likelihood analysis of earthquake catalogues

We apply several classes of stochastic multidimensional models to statistical analysis of earthquake catalogues using likelihood methods. We investigate the importance of including different earthquake parameters in the model: epicentral coordinates, hypocentral depth, time limits for interearthquake interaction, and especially spatial distribution of earthquakes as well as spatial aftershock patterns. Results of this study combined with other investigations, suggest that most distributions controlling earthquake interaction have a fractal or scale-invariant form. Developed models are used for statistical analysis of several earthquake catalogues to evaluate parameters of earthquake occurrence. These parameters are shown to be similar for shallow earthquakes of different magnitude ranges and seismogenic regions, confirming self-similarity of the earthquake process. Whereas intermediate earthquakes seem to emulate the pattern of shallow earthquake occurrence, albeit at a much smaller aftershock rate, deep earthquakes differ significantly in their properties. Predictability of standard shallow earthquake catalogues has been analysed; we present evidence that for the best available catalogues the predictability is close to 10 bits per earthquake. Several synthetic earthquake catalogues have been created and processed through the likelihood inversion scheme. The results from likelihood analysis of these catalogues confirm our approach.     

Geodetic inversion for space–time distribution of fault slip with time-varying smoothing regularization

We have developed a new geodetic inversion method for space–time distribution of fault slip velocity with time-varying smoothing regularization in order to reconstruct accurate time histories of aseismic fault slip transients. We introduce a temporal smoothing regularization on slip and slip velocity through a Bayesian state space approach in which the strength of regularization (temporal smoothness of slip velocity) is controlled by a hyperparameter. The time-varying smoothing regularization is realized by treating the hyperparameter as a time-dependent stochastic variable and adopting a hierarchical Bayesian state space model, in which a prior distribution on the hyperparameter is introduced in addition to a conventional Bayesian state space model. We have tested this inversion method on two synthetic data sets generated by simulated aseismic slip transients. Results show that our method reproduces well both rapid changes of slip velocity and steady-state velocity without significant oversmoothing and undersmoothing, which has been hard to overcome by the conventional Bayesian approach with time-independent smoothing regularization. Application of this method to transient deformation in 2002 caused by a silent earthquake off the Boso peninsula, Japan, also shows similar advantages of this method over the conventional approach.