Vertical and horizontal land deformation due to fluid withdrawal

A non-linear distribution of vertical displacement versus aquifer depth is calculated in the case of a partially penertrating well. For a fully penetrating well, however, a linear distribution is observed. The solution exhibits a vertically uniform horizontal displacement in the case of a fully penetrating well and, for a partially penetrating well, the maximum horizontal displacement occurs at the elevation of the well bottom.     

Commensurability of earthquake occurrence

During recent years huge earthquakes frequently occurred and caused surprise attack on many places of the globe. Frequent exceptional strong disasters of earthquakes remind that we must strengthen our research on cause of formation, mechanism, prediction and forecast of earthquakes, and achieve the goal of advancing the development of Earth science and mitigation of seismic disasters. The commensurability of earthquake occurrences has been studied by means of the commensurability revealed by the Titius–Bode law in the paper. The studied results show that the earthquakes basically all occur at the commensurable point of its time axis, respectively. It also shows that occurrence of the earthquakes is not accidental, showing certain patterns and inevitability, and the commensurable value is different for earthquakes occurring in different areas.     

Application of neural network and ANFIS model for earthquake occurrence in Iran

This study examined the spatial-temporal variations in seismicity parameters for the September 10^th, 2008 Qeshm earthquake in south Iran. To this aim, artificial neural networks and Adaptive Neural Fuzzy Inference System (ANFIS) were applied. The supervised Radial Basis Function (RBF) network and ANFIS model were implemented because they have shown the efficiency in classification and prediction problems. The eight seismicity parameters were calculated to analyze spatial and temporal seismicity pattern. The data preprocessing that included normalization and Principal Component Analysis (PCA) techniques was led before the data was fed into the RBF network and ANFIS model. Although the accuracy of RBF network and ANFIS model could be evaluated rather similar, the RBF exhibited a higher performance than the ANFIS for prediction of the epicenter area and time of occurrence of the 2008 Qeshm main shock. A proper training on the basis of RBF network and ANFIS model might adopt the physical understanding between seismic data and generate more effective results than conventional prediction approaches. The results of the present study indicated that the RBF neural networks and the ANFIS models could be suitable tools for accurate prediction of epicenteral area as well as time of occurrence of forthcoming strong earthquakes in active seismogenic areas.     

Physical and stochastic models of earthquake clustering

The phenomenon of earthquake clustering, i.e., the increase of occurrence probability for seismic events close in space and time to other previous earthquakes, has been modeled both by statistical and physical processes.From a statistical viewpoint the so-called epidemic model (ETAS) introduced by Ogata in 1988 and its variations have become fairly well known in the seismological community. Tests on real seismicity and comparison with a plain time-independent Poissonian model through likelihood-based methods have reliably proved their validity.On the other hand, in the last decade many papers have been published on the so-called Coulomb stress change principle, based on the theory of elasticity, showing qualitatively that an increase of the Coulomb stress in a given area is usually associated with an increase of seismic activity. More specifically, the rate-and-state theory developed by Dieterich in the ′90s has been able to give a physical justification to the phenomenon known as Omori law. According to this law, a mainshock is followed by a series of aftershocks whose frequency decreases in time as an inverse power law.In this study we give an outline of the above-mentioned stochastic and physical models, and build up an approach by which these models can be merged in a single algorithm and statistically tested. The application to the seismicity of Japan from 1970 to 2003 shows that the new model incorporating the physical concept of the rate-and-state theory performs not worse than the purely stochastic model with two free parameters only. The numerical results obtained in these applications are related to physical characters of the model as the stress change produced by an earthquake close to its edges and to the A and σ parameters of the rate-and-state constitutive law.     

A stochastic model of sedimentation

A mathematical model is presented which describes the origin of the earth's geological record in terms of a stochastic process involving random events of sedimentation and erosion. The model yields quantitative predictions of the percentages of the earth's land area in which sediments of one geological period directly overlie those of any given earlier period. It also predicts the total amount of sediment dating from each geological period, and the percentage of the earth's surface marked by outcrops of this sediment. These computed quantities are shown to correlate well with corresponding quantities derived from empirical investigation.     

量子地震模型:对汶川地震的解释

从大量的地震参数分析可知,在由同一主震引发的所有的余震发生的位置都不同。在发生地震之前,地震的震中位置都是一些相互独立、互不连续且发生了弹性应变的单元个体,笔者称这些独立不连续的弹性应变单元称为应变量子。综合前人研究成果,笔者建立了一个地震模型。运用该模型对2008年5月12日发生在中国汶川地震作了解释:由于在龙门山断裂带周围形成了许多的应变量子,这些应变量子的形成阻碍了龙门山断裂的运动,产生滑移亏损,从而造成在地震前测量到的龙门山断裂带速度场变化很不显著。2008年5月12日14时28分时,在龙门山断裂周围已形成应变量子中的其中一应变量子最先达到它的最大储能,释放它所储存的应变能,引发了汶川Ms8.0地震。此次地震产生的地震波引发了龙门山断裂周围地壳应力的重分布,使得其他应变量子提前达到最大储能,释放出能量,于是触发成千上万次余震。此外,我们或许可以通过观测断裂滑移速率的变化情况来预测断裂周围应变量子的形成,从而来预测该断裂是否存在潜在地震的可能。     

A stochastic model of soil erosion

The erosion model computes the rill and inter-rill flow over a surface with random roughness, and the erosion caused by this flow. The measured roughness of a surface is analysed and used to generate random surfaces for the simulation process. Computations are carried out over a number of time intervals; the steady state condition is assumed for each interval. Changes in the surface geometry due to erosion during an interval are used to revise the surface for the subsequent interval. The model includes simplified mechanisms to simulate ponding, deposition and failure of side slopes of rills.     

A way to synchronize models with seismic faults for earthquake forecasting: Insights from a simple stochastic model

Numerical models are starting to be used for determining the future behaviour of seismic faults and fault networks. Their final goal would be to forecast future large earthquakes. In order to use them for this task, it is necessary to synchronize each model with the current status of the actual fault or fault network it simulates (just as, for example, meteorologists synchronize their models with the atmosphere by incorporating current atmospheric data in them). However, lithospheric dynamics is largely unobservable: important parameters cannot (or can rarely) be measured in Nature. Earthquakes, though, provide indirect but measurable clues of the stress and strain status in the lithosphere, which should be helpful for the synchronization of the models.The rupture area is one of the measurable parameters of earthquakes. Here we explore how it can be used to at least synchronize fault models between themselves and forecast synthetic earthquakes. Our purpose here is to forecast synthetic earthquakes in a simple but stochastic (random) fault model. By imposing the rupture area of the synthetic earthquakes of this model on other models, the latter become partially synchronized with the first one. We use these partially synchronized models to successfully forecast most of the largest earthquakes generated by the first model. This forecasting strategy outperforms others that only take into account the earthquake series. Our results suggest that probably a good way to synchronize more detailed models with real faults is to force them to reproduce the sequence of previous earthquake ruptures on the faults. This hypothesis could be tested in the future with more detailed models and actual seismic data.     

A physico-rheological model for the large tangshan earthquake

Space-time distributions of the epicenters of earthquakes with M_L 3 from 1966 to 1976 and of historic earthquakes with M 6 have been studied. It is suggested that they mainly occur in seismic belts running N45°E and N47°W, which form a rectangular grid, and the largest earthquakes occurred in the nodal regions of this grid. A theoretical analysis is presented to support these findings.Various types of precursors such as land deformations, changes in gravity, anomalies in the magnetic field and electrical resistivity and waterlevels in deep wells have been studied in correlation with epicenter distribution. The possibility of magma intrusion and its consequences are studied. The first author concludes that stresses must have accumulated, obviously in the regions of intersection. Two different mechanisms of stress accumulation are suggested. He presents a preliminary evaluation of the precursory data with relation to the Russian IPE (Institute of Physics of the Earth) model and the DD (Dilatancy Diffusion model) and propose a physico-rheological model for the Tangshan earthquake. In this new model an attempt is made to take account of such factors as the rheological behaviour of the crust and seismic belts, the mechanisms of stress accumulation, the local stress field, the long-term weakening of the crust, the time-dependent volume dilatancy and the possibility of magma intrusion.     

Post-seismic deformation associated with the 2001 Bhuj earthquake

We report the results of GPS measurements of post-seismic deformation due to the 2001 Bhuj earthquake in the Kachchh region, western India. The estimated horizontal velocity vectors in ITRF05 are in the range of 48?C49?mm/year in N46?C50°E. The observed velocity at the Gandhinagar permanent site, a far off site from the earthquake source region and probably unaffected by the post-seismic deformation, is 49?±?1?mm/year in N47°E, which is consistent with the predicted motion of Indian plate at Gandhinagar. At other sites in the source region, transient post-seismic deformation is found to be low; it attenuated rapidly within 3?C4?years of the earthquake and is much low now. Our results support the idea that mantle rheology is weak in the region.     

基于随机介质理论的采水地面变形时空分布

采用随机介质理论计算规模采水引起的地面下沉和水平位移。分析了采水引起的地面位移机制,采用有效应力原理推导微单元体的沉降;利用非稳定流理论Theis模型计算单井定流量采水时平面径向流引起的降深;利用现场观测数据,通过反分析法确定模型参数;由于模型的边界动态变化,故分时段采用数学近似法和变边界数值逼近法处理。在此基础上建立单元盆地在降落漏斗区域的时空分布积分方程,引入柱坐标系进行解答。工程实例分析表明,随机介质理论适用于计算采水引起的地面变形;结合非稳定流理论和数值计算方法能较好地预测地面随时间的变形规律。     

Vertical and horizontal deformation of an inhomogeneous elastic half-space

Vertical and horizontal deformations of surface footings have been studied for an inhomogeneous elastic half-space in which the shear modulus increases with an arbitrary power of depth, n, and Poisson's ratio is constant. A general solution for displacements has been obtained first for point loads applied in vertical and horizontal directions. These are then used in obtaining closed-form solutions for displacements of uniformly loaded circular and rectangular footings. Finally, a numerical method is described that can be used to analyse a rigid footing of an arbitrary shape, and results for rigid rectangular footings are given.     

Stein estimation for SIR-predictable models of earthquake occurrence

It is usually accepted that a time-predictable model of earthquake occurrences is better than the so-called slip-predictable model. Here a size-interval relation (SIR)-predictable model is proposed which combines the features of the time-predictable and slip-predictable models. Unlike a constant, and hence nonpredictive, relation between the size of the next earthquake and the inter-event interval, given by the so-called slip-predictable model, the SIR-predictable model prescribes such a relation contingent upon the size of the previous earthquake. Unlike the time-predictable model, instead of predicting the time interval, it proposes a size-interval relation. Using data about a seismogenic source called Cephalonia in Greece, the superiority of the SIR-predictable model over the time-predictable model is illustrated. The SIR-predictable model can be made more efficient by employing two-stage nonlinear estimation procedures motivated by the initial work by Stein. Introducing these procedures to seismologists is an independent objective of this paper. Also, Stein estimators have a dimensionality threshold. This work discusses two techniques of threshold extension.     

渗透性水平向各向异性导致椭圆形地面沉降漏斗的一个性质

水平向渗透系数各向异性会导致抽水产生的水位降深等值线呈现椭圆形,进而产生椭圆形地面沉降漏斗,这种椭圆形地面沉降漏斗的现象在现实中广泛存在。渗透系数均质各向同性的圆形地面沉降漏斗中,地面某点沉降值s与该点至漏斗中心的距离r之间符合s- 线性关系,渗透性水平向各向异性导致的椭圆形地面沉降漏斗也具有s- 线性关系规律。应用地下水动力学相关理论,经过理论推导,得出了椭圆形地面沉降漏斗各径向线上半对数线性关系式 中常数项 、 与径向线方位角θ之间的函数关系式,即 、 与 或 的平方呈正比,该函数关系式得到中国、美国和印度共6个区域性地面沉降漏斗实例的有力验证。对公式验证回归所得的12个相关系数中,1个为87.19%,其余11个都在90%以上。以上渗透性水平向各向异性导致的区域性椭圆形地面沉降漏斗的性质,公式简单实用,可方便应用于椭圆形地面沉降漏斗中非监测点的沉降值推测,利于全面了解椭圆形沉降漏斗信息,具有广泛应用价值。     

巽他弧北部掸邦高原地壳变形、长期块体运动和发震过程:来自大地测量研究结果的约束

本文通过约束大地测量研究来探索掸邦高原及其周围地区现今的地壳变形和长期块体运动,以期提供该地区地球动力学和相关地震危险状况的最新状态。掸邦高原在横向上由西侧的萨干(Sagaing)断裂和东侧的红河断裂这两条主要断裂包围。其中,青藏高原地壳的韧性流挤压被认为是该夹层变形单元变形的主要因素。大地测量清楚地表明,萨干断裂和红河断裂段分别具有约18 mm/a和约45 mm/a右旋运动走滑速率。此外,掸邦高原内部断层体系大地滑移累积表现为1213 mm/a的整体左旋运动速率。我们认为相对于刚性巽他古陆,研究区域的形变分布和长期块体运动主要受区域书架型断层作用控制,其原因是掸邦高原两侧的主断裂(萨干断裂和红河断裂)存在差异性断裂活动。     

Structure of earthquake occurrence in space,time and magnitude

Distributions of time between consecutive earthquakes verify an approximately universal scaling law for stationary seismicity. The shape of these distributions is shown to arise as a mixture of one distribution for short‐distance events and an exponential distribution for far‐off events, the distinction from short and long distances being relative to the size of the region studied. The distributions of consecutive distances show a double power law decay and verify an approximate scaling law which guarantees the simultaneous fulfillment of the scaling laws for time. The interplay between space and time can be seen as well by looking at the distribution of distances for a fixed time separation. These results suggest that seismicity can be understood as a series of intertwined independent continuous‐time random walks, with power law‐distributed waiting times and Lévy‐flight jumps. However, a simple model based on these ideas does not capture the invariance of seismicity under renormalization.     

A multi-tiered earthquake hazard model for Australia

Earthquakes result from tectonic processes, and their distribution is strongly influenced by large-scale geology and the tectonic stress field. However, earthquake hazard estimates, particularly ground motion recurrence, have traditionally been computed using source models based primarily on instrumental and historical seismicity. In areas of low to moderate seismicity such as Australia, large earthquakes commonly occur in areas which have experienced little or no recent activity, making it difficult to develop source models based solely on seismicity.

The seismotectonic model developed for Australia that is presented here (AUS5) is based on geology, geophysics, tectonics and seismicity. The model was developed using a number of tiers of information, so that new information can easily be incorporated. The information used includes, but is not limited to, tectonic provinces, basins and ranges, gravity, magnetic, topography, and seismicity, all on a regional scale. On a local scale, for a site-specific earthquake hazard study, active faulting can be incorporated to provide fault source zones.

An earthquake hazard map showing peak ground acceleration with a 10% chance of exceedance in 50 years for southeastern Australia using the geologically defined seismotectonic model AUS5 is presented as an indication of how the model performs.     

A method for estimating earthquake occurrence probability using first- and multiple-order Markov chain models

It is valuable in earthquake prediction to determine the occurrence probability of major earthquakes by making use of data obtained from precursory phenomena up to the time of the evaluation. In this study, the time evolution of the state determined by earthquakes and precursory phenomena was modelled using Markov chains. Various probabilities suitable for earthquake prediction were derived from the transition probability of the Markov chain with a chosen length of memory time. As an example, earthquake sequence records for northern China, which covered a period of about two thousand years, were examined and the results were also obtained from modern scientific observations of the radon anomaly which covered a period of about 10 years.Assuming moderate-sized earthquakes of two magnitude ranges 4 3/4 M 5 3/4, 6 M 6 3/4 as precursors to large earthquakes of a magnitude range, 7 M 8 1/2, transition probabilities were calculated for a time interval from 2 to 40 yr. The results showed that the precursory time of moderate-sized earthquakes is mainly distributed in a time span of around several years and that the earthquake occurrence probability is considerably large when the precursory earthquakes occur successively. Furthermore, it was shown that a larger moderate-sized earthquake (4 3/4 M 5 3/4) is a more effective precursor than an entire moderate-sized earthquake (4 3/4 M 6 3/4).Second, a multiple precursor case was tried by means of simulation based on the radon anomaly data obtained during a limited observation period. Simultaneous occurrence of two precursors makes the earthquake occurrence probability increase by 1.5–2.0 for a reasonable choice of a mean recurrence interval of the radon anomaly compared with the case where only a moderate-sized earthquake was treated as the precursor. However, the probability is much the same if the average recurrence interval of the radon anomaly is the same through time, including the preparatory period before the earthquake.     

Statistics of ultimate strain of the earth's crust and probability of earthquake occurrence

Statistics of ultimate strain are improved by adding new data to the previous ones. The critical value for horizontal strain seems somewhat larger than that for vertical strain, although parameters of a Weibull distribution, which is customarily used for quality-control research and which fits in very well with the present statistics, are calculated for the whole set of data making no distinction between the two subsets because of their scantiness.On the basis of the parameters thus determined and strain rates obtained from geodetic data, probabilities of earthquake occurrence in a few regions in Japan and the U.S. are estimated. Probability of having an earthquake in an area southwest of Tokyo, where we had the 1923 earthquake (magnitude 7.9), at this time amounts to 20%, a value almost the same as that obtained in the previous papers. The probability will reach some 50 and 90% by 2000 and 2050, respectively. In the North Izu district, where an earthquake of magnitude 7.0 occurred in 1930, a shearing crustal motion is going on to an extent for which we have a probability for an earthquake recurring there in these 40 years amounting to 40%. By the end of this century, it will become as high as 85%.Similar estimates of such cumulative probabilities are made for the San Francisco and Fort Tejon regions, where great earthquakes occurred respectively in 1906 and 1857, yielding values of 30 and 80% at present. These probabilities are tentative because of possible errors in evaluating geodetic measurements and uncertainty of the ultimate crustal strain assigned to the San Andreas fault.