不同模型下地震位错理论的对比 及其应用进展综述

对半空间和球位错理论在理论和应用研究方面的进展进行了综合评述, 讨论了地震位错理论在海啸方面的相关研究进展和位错理论与粒子群算法结合在断层反演方面的研究进展, 对比分析了不同位错模型的优缺点, 总结了位错模型在应用中的影响因素. 本文认为不同位错理论的应用受地球分层的影响最大, 其次是重力、 曲率的影响, 而受地形、 震源深度及断层倾角等因素的影响则较小, 在实际应用中应予以综合考虑.      

Piezomagnetic fields produced by dislocation sources

Tectonomagnetic modeling based on the linear piezomagnetic effect is reviewed with special attention to dislocation models. Stacey's scheme was the prototype for such modeling, as proposed in his first seismomagnetic calculations in 1964. The linear piezomagnetic law is presented, in which the stress-induced magnetization is expressed as a linear combination of stress components. The Gauss law for magnetic field and the Cauchy-Navier equation for static elastic equilibrium are combined through linear piezomagnetism and the Hooke law to yield the basic equation for piezomagnetic potential. A representation theorem for its solution is given by surface integrals of the displacement and its normal derivative over the strained body.A Green's function method is developed to compute the piezomagnetic field produced by a dislocation surface in an elastic half-space. Volterra's formula for piezomagnetic potential is derived by modifying Stacey's scheme for tectonomagnetic modeling. The Green's functions for the problem are called elementary piezomagnetic potentials, which are defined as potentials produced by elementary dislocations. Special consideration is required to construct the elementary piezomagnetic potentials, because the stress field around a point dislocation has a singularity of orderr ^–3. The integral representing elementary piezomagnetic potentials is not uniformly convergent. Owing to inappropriate convergency, the Green's functions obtained in an earlier study led to a puzzling outcome. Revised Green's functions give consistent results with those obtained so far by numerical integrations. Generally the piezomagnetic field produced by dislocation sources is weak in the case of a homogeneous earth model. Two enhancement effects for piezomagnetic signals are suggested: one due to inhomogeneous magnetization and the other via bore-hole observations.     

诱发地震中的非双力偶震源

在诱发地震的研究中，用小孔径地震台网在近场观测，其震源机制的Ｐ波初动除Ⅲ象限分布的双力偶外，还有不是Ⅲ象限分布的非双力偶震源机制。双力偶震源机制是剪切破裂机制。非双力偶震源机制为向内源炸型和张破裂机制，以及在适当方向上两个以上双力偶迭加的结果。     

Renewal models for earthquake predictability

The new Database of Italy’s Seismogenic Sources (Basili et al. 2008) identifies areas with a degree of homogeneity in earthquake generation mechanism judged sufficiently high. Nevertheless, their seismic sequences show rather long and regular interoccurrence times mixed with irregularly distributed short interoccurrence times. Accordingly, the following question could naturally arise: do sequences consist of nearly periodic events perturbed by a kind of noise; are they Poissonian; or short interoccurrence times predominate like in a cluster model? The relative reliability of these hypotheses is at present a matter of discussion (Faenza et al., Geophys J Int 155:521–531, 2003; Corral, Proc Geoph 12:89–100, 2005, Tectonophysics 424:177–193, 2006). In our regions, a statistical validation is not feasible because of the paucity of data. Moreover, the classical tests do not clearly suggest which one among different proposed models must be favoured. In this paper, we adopt a model of interoccurrence times able to interpret the three different hypotheses, ranging from exponential to Weibull distributions, in a scenario of increasing degree of predictability. In order to judge which one of these hypotheses is favoured, we adopt, instead of the classical tests, a more selective indicator measuring the error in respect to the chosen panorama of possible truths. The earthquake prediction is here simply defined and calculated through the conditional probability of occurrence depending on the elapsed time t₀ since the last earthquake. Short-term and medium-term predictions are performed for all the Italian seismic zones on the basis of datasets built in the context of the National Projects INGV-DPC 2004–2006, in the frame of which this research was developed. The mathematical model of interoccurrence times (mixture of exponential and Weibull distributions) is justified in its analytical structure. A dimensionless procedure is used in order to reduce the number of parameters and to make comparisons easier. Three different procedures are taken into consideration for the estimation of the parameter values; in most of the cases, they give comparable results. The degree of credibility of the proposed methods is evaluated. Their robustness as well as their sensitivity are discussed. The comparison of the probability of occurrence of a Maw >5.3 event in the next 5 and 30 years from January 1, 2003, conditional to the time elapsed since the last event, shows that the relative ranking of impending rupture in 5 years is roughly maintained in a 30-year perspective with higher probabilities and large fluctuations between sources belonging to the same macro region.     

Evaluation of numerical earthquake forecasting models

Evaluation of numerical earthquake forecasting models needs to consider two issues of equal importance: the application scenario of the simulation, and the complexity of the model. Criterion of the evaluation-based model selection faces some interesting problems in need of discussion.     

Site-dependent models of earthquake ground motion

Random vibration analyses of structural systems subjected to seismic loading are dependent upon the characterization of earthquake ground motion as a stochastic process. The response of structural systems to earthquakes is dependent strongly on the local geological conditions, which should be incorporated into seismological models of ground motion. In the study presented herein, three previously developed ground-motion models are adapted to incorporate site-dependent characteristics. Records obtained from two recording stations in California are used as a basis for the ground-motion models. Single-degree-of-freedom (SDOF) oscillators are subjected to ensembles of accelerograms generated from these models, and both elastic and inelastic response are considered. Response statistics are compared to those generated by the analysis of structural response to ensembles of recorded motion from the two sites. The important features of the ground motion for effective reproduction of response statistics are identified, and observations are made on the sensitivity of specific response parameters to site-dependent characteristics of the ground motion.     

Efficient testing of earthquake forecasting models

Computationally efficient alternatives are proposed to the likelihood-based tests employed by the Collaboratory for the Study of Earthquake Predictability for assessing the performance of earthquake likelihood models in the earthquake forecast testing centers. For the conditional L-test, which tests the consistency of the earthquake catalogue with a model, an exact test using convolutions of distributions is available when the number of earthquakes in the test period is small, and the central limit theorem provides an approximate test when the number of earthquakes is large. Similar methods are available for the R-test, which compares the likelihoods of two competing models. However, the R-test, like the N-test and L-test, is fundamentally a test of consistency of data with a model. We propose an alternative test, based on the classical paired t-test, to more directly compare the likelihoods of two models. Although approximate and predicated on a normality assumption, this new T-test is not computer-intensive, is easier to interpret than the R-test, and becomes increasingly dependable as the number of earthquakes increases.     

Physical models of earthquake instability and precursory processes

This paper selectively reviews physical models of earthquake instability. In these models, instability arises as a result of interaction of a fault constitutive relation with deformation of the surrounding material that occurs in response to remote tectonic loading. In contrast to kinematic models in which the fault slip is imposed, it is calculated in physical models and, consequently, these models are essential for understanding precursory processes. Some kind of weakening behavior for the fault constitutive relation is required to produce an instability analogous to an earthquake. Two commonly employed idealizations discussed here are rate-independent slip weakening and rate/state-dependent friction. When these constitutive models are employed on surfaces embedded in elastic half-spaces or layers, possibly coupled to a viscoelastic substrate, the results are capable of simulating realistically some aspects of earthquake occurrence. Common to all models is the prediction that earthquake instability is preceded by precursory slip which produces a departure of surface strain-rate from the background level. Near the epicenter of a moderate to large earthquake, the magnitude of this departure appears to be well within the range of current geodetic measurement accuracy, and its duration is of the order of months to years. However, details depend on a variety of factors, including the modelling of the constitutive relation near peak stress, coupling of elastic crust to the asthenosphere, and coupling of deformation with pore fluid diffusion.     

Constraining potential earthquake sources from the geophysical data

The spatial models describing the physico-mechanical properties of the rocks within the seismically active segment of the Altai–Sayan region are constructed from the ground-based geophysical data. The comparative analysis of their probability density functions at the nodes of the spatial grid covering the studied domain and at the hypocenters of the previous earthquakes shows that the bulk and shear moduli are the most efficient markers of the weakened crustal zones, which are prone to earthquakes. The algorithm for constraining the potential earthquake sources based on the spatial distributions of the elastic moduli of the rocks is suggested. When applied to the Taellin segment of the Altai–Sayan region, this algorithm has localized four echelons of the potential source zones of earthquakes at different depths in the crust. The horizontal positions of two of these zones were delineated by the previous studies based on the ground observations of seismicity, whereas the other two zones have been identified by the suggested algorithm for the first time.     

Arma models for earthquake ground motions

This paper outlines the use of discrete, autoregressive/moving-average (ARMA) models for identification and estimation of parameters in models derived from analysis of uniformly digitized earthquake ground motion acceleration data. Such models are of equal generality as compared to continuous-time models and have a number of significant advantages for purposes of digital analysis and simulation. The structure of ARMA models is briefly described, their relation to continuous models noted, and results of their application to a number of recorded accelerograms summarized.     

Structural identification using linear models and earthquake records

The problem of determining linear models of structures from seismic response data is investigated using ideas from the theory of system identification. The approach is to determine the optimal estimates of the model parameters by minimizing a selected measure-of-fit between the responses of the structure and the model. Because earthquake records are normally available from only a small number of locations in a structure, and because of noise in the records, it is necessary in practice to estimate parameters of the dominant modes in the records, rather than the stiffness and damping matrices of the linear model. A new algorithm is developed to determine the optimal estimates of the modal parameters. After tests with simulated data, the method is applied to a multi-storey building using records from the 1971 San Fernando earthquake in California. New information is obtained concerning the properties of the lower modes of the building and the time-varying character of the equivalent linear parameters.     

Strain-geoelectric resistivity precursor and the virtual dislocation model to the Tangshan earthquake

The complete records of geoelectric resistivity before two earthquakes were analyzed, including 16 stations within 240 km around the Tangshan earthquake and 2 stations within 50–60 km from theM6.1 Datong earthquake. By eliminating various disturbances in the records and realizing the precursory anomalies to be reliable, the authors studied the distribution of the geoelectric precursor field, which proves to be physically related to the earthquake source stress field. Comparision of the sign distribution of coseismic resistivity changes with the solution of earthquake source mechanism indicates that, the coseismic resistivity changes are of opposite sign but similar spatial distribution with respect to the corresponding resistivity precursor changes. Therefore, from the resistivity observations we are of the opinion that the Tangshan earthquake is an elastic rebound process. A virtual dislocation model of geoelectric precursor for the Tangshan earthquake is proposed, in which the geoelectric precursors are supposed to be caused by the strain accumulation due to a virtual dislocation, which is opposite in sign to the actual slip taking place at the earthquake occurrence. Taking into account of the non-linear characteristics of the amplification factorK=(Δρ/ρ)/ɛ in a range of 10⁻⁷–10⁻⁵ strain changes, the theoretical distribution of geoelectric precursors for the Tangshan earthquake was calculated based on the theory of fracture mechanics and reasonably selected dislocation parameters. The results show that the semi-quantitative theoretical values are in good agreement with the observed, suggesting that the virtual dislocation model of the geoelectric precursor is appropriate to the Tangshan earthquake. Contribution No. 96A0023, Institute of Geophysics, SSB, China. This work was supported by the National Natural Science Foundation of China and the Science and Technology Department of SSB.     

Elasto-plastic earthquake shear-response of one-dimensional earth dam models

A simplified analysis procedure for the non-linear hysteretic earthquake-response of earth dams is presented. The dam is modelled as a one-dimensional hysteretic shear-wedge subjected to base excitation. The hysteretic stress-strain behaviour of the dam materials is modelled by using elasto-plastic constitutive equations based on multi-surface kinematic plasticity theory. The method is based on a Galerkin formulation of the equations of motion in which the solution is expanded using eigenmodes of the linearized problem defined over the spatial domain occupied by the dam. The technique is applied to analyse the non-linear dynamic response of an earth dam subject to two very different input ground motions. The following investigations are presented: (i) comparison between the results obtained using two soil models depicting different nonlinear properties, (ii) comparison between the results of the one-mode and the multi-mode solution expansions, (iii) comparison with the results obtained through an elaborate finite element representation of the dam, and finally, (iv) comparison with the results obtained through the Makdisi-Seed¹¹ iterative procedure for earth dam analysis. The comparisons show that the proposed technique can be used to determine adequately the transient earthquake response of long earth dams. Furthermore, the efficiency and low computational cost make the technique very attractive; it can easily and systematically be extended to two- and three-dimensional calculations of earth dam response.     

Attenuation models inferred from intraplate earthquake recordings

Strong-motion recordings at 87 sites from 56 different intraplate earthquakes from North America, Europe, China and Australia have been used through a two-step regression analysis to develop new attenuation models for peak ground acceleration, and for pseudo-relative velocity for frequencies of 0.25, 0.5, 1.0, 2.0, 5.0 and 10.0 Hz, all for 5 per cent of critical damping. The estimates are obtained along with an analysis of residuals and scatter. A similar regression analysis has been performed also for Fourier spectra of acceleration, in which case the coefficient for the anelastic term has been interpreted in terms of a frequency dependent quality factor Q. The resulting Q-model shows a strong frequency sensitivity with values around 600–700 at 1 Hz, around 2000 at 10 Hz and around 5200 at 25 Hz. These PGA, PSV and Q results depend, however, on the underlying assumption for geometrical spreading, in particular for low frequencies.     

Simulating earthquake evacuation using human behavior models

In classical earthquake risk assessment, the human behavior is actually not taken into account in risk assessment. Agent‐based modeling is a simulation technique that has been applied recently in several fields, such as emergency evacuation. The paper is proposing a methodology that includes in agent‐based models the human behavior, considering the anxiety effects generated by the crowd and their influence on the evacuation delays. The proposed model is able to take into account the interdependency between the earthquake evacuation process, and the corresponding damage of structural and non‐structural components that is expressed in term of fragility curves. The software REPAST HPC has been used to implement the model, and as a case study, the earthquake evacuation by a mall located in Oakland has been used. The human behavior model has been calibrated through a survey using a miscellaneous sample from different countries. The model can be used to test future scenarios and help local authorities in situations where the human behavior plays a key role. Copyright © 2017 John Wiley & Sons, Ltd.     

Matter-element models for comprehensive earthquake prediction and their applications

Extenics was a branch of mathematics for studying the incompatible problems. In this paper, basing on calculating the associative functions of all various indexes, we have obtained the quantitative assessment results of prediction indexes by introducing this theory into the comprehensive earthquake prediction through establishing the matter-element model for comprehensive prediction, so that the incompatible problems can be solved. The preliminary results demonstrate that this method has better prospects in comprehensive earthquake prediction. Foundation item: Chinese Joint Seismological Science Foundation (196006).