Sensitivity analysis of the parameters of earthquake recurrence time power law scaling

The stability of the power law scaling of earthquake recurrence time distribution in a given space–time window is investigated, taking into account the magnitude of completeness and the effective starting time of aftershock sequences in earthquake catalogs from Southern California and Japan. A new method is introduced for sampling at different distances from a network of target events. This method allows the recurrence times to be sampled many times on the same area. Two power laws with unknown exponents are assumed to govern short- and long-recurrence-time ranges. This assumption is developed analytically and shown to imply simple correlation between these power laws. In practice, the results show that this correlation structure is not satisfied for short magnitude cutoffs (m _c = 2.5, 3.5, 4.5), and hence the recurrence time distribution departs from the power law scaling. The scaling parameters obtained from the stack of the distributions corresponding to different magnitude thresholds are quite different for different regions of study. It is also found that significantly different scaling parameters adjust the distribution for different magnitude thresholds. In particular, the power law exponents decrease when the magnitude cutoff increases, resulting in a slower decrease of the recurrence time distribution, especially for short time ranges. For example, in the case of Japan, the exponent p₂ of the power law scaling at large recurrence times follows roughly the relation: , where m _c is the magnitude cutoff. In case of Southern California, it is shown that Weibull distribution provides a better alternative fit to the data for moderate and large time scales.     

The earthquake recurrence law and energy balance of the seismic process

Relationships between the average seismic energy of strong and weak earthquakes in confined ranges are considered. These relationships are related to the earthquake recurrence (Gutenberg-Richter) law parameters. The theoretical foundation of the study is based on the results obtained by M.A. Sadovsky and V.F. Pisarenko in 1999, who described the indicated law as a ratio of the total seismic energy and maximum expected earthquake. Some empirical relationships obtained by the author on the basis of the Kamchatka and Sakhalin regional earthquake catalogs are reported. The determination of the recurrence law parameters on the basis of these relationships is shown to be efficient.     

利用地震复发周期考察汶川8．0级地震前兆异常

通过对汶川Ms8．0地震复发周期的时间和空间进行扫描,发现地震发生前,在时间上和空间上,地震复发周期均出现低值异常。因此,对地震发生的时间和地区进行异常判断,地震复发周期是一个可以参考利用的指标。     

Toward a physical undenstanding of earthquake scaling relations

In seismological literature, there exist two competing theories (the so-calledW model andL model) treating earthquake scaling relations between mean slip and rupture dimension and between seismic moment and rupture dimension. The core of arguments differentiating the two theories is whether the mean slip should scale with the rupture width or with the rupture length for large earthquakes. In this paper, we apply the elastic theory of dislocation to clarify the controversy. Several static dislocation models are used to simulate strike-slip earthquakes. Our results show that the mean slip scales linearly with the rupture width for small earthquakes with a rupture length smaller than the thickness of the seismogenic layer. However, for large earthquakes with a rupture length larger than the thickness of the seismogenic layer, our models show a more complicated scaling relation between mean slip and rupture dimension. When the rupture length is smaller than a cross-over length, the mean slip scales nearly linearly with the rupture length. When the rupture length is larger than a cross-over length, the mean slip approaches asymptotically a constant value and scales approximately with the rupture width. The cross-over length is a function of the rupture width and is about 75 km for earthquakes with a saturated rupture width of 15 km. We compare our theoretical predictions with observed source parameters of some large strike-slip earthquakes, and they match up well. Our results also suggest that when large earthquakes have a fixed aspect ratio of rupture length to rupture width (which seems to be the case for most subduction earthquakes) the mean slip scales with the rupture dimension in the same way as small earthquakes.     

A scaling law for the occurrence of aftershocks in southern California

A scaling law for the occurrence of aftershocks in southern California is proposed which suggests that the number of aftershocks is independent of the magnitude of the mainshock if aftershocks are counted in the magnitude interval from (Mm ? Δ) to Mm.     

Testing a theoretical resistance law for overland flow on a stony hillslope

Overland flow, sediments, and nutrients transported in runoff are important processes involved in soil erosion and water pollution. Modelling transport of sediments and chemicals requires accurate estimates of hydraulic resistance, which is one of the key variables characterizing runoff water depth and velocity. In this paper, a new theoretical power–velocity profile, originally deduced neglecting the impact effect of rainfall, was initially modified for taking into account the effect of rainfall intensity. Then a theoretical flow resistance law was obtained by integration of the new flow velocity distribution. This flow resistance law was tested using field measurements by Nearing for the condition of overland flow under simulated rainfall. Measurements of the Darcy–Weisbach friction factor, corresponding to flow Reynolds number ranging from 48 to 194, were obtained for simulated rainfall with two different rainfall intensity values (59 and 178 mm hr⁻¹). The database, including measurements of flow velocity, water depth, cross-sectional area, wetted perimeter, and bed slope, allowed for calibration of the relationship between the velocity profile parameter Γ, the slope steepness s, and the flow Froude number F, taking also into account the influence of rainfall intensity i. Results yielded the following conclusions: (a) The proposed theoretical flow resistance equation accurately estimated the Darcy–Weisbach friction factor for overland flow under simulated rainfall, (b) the flow resistance increased with rainfall intensity for laminar overland flow, and (c) the mean flow velocity was quasi-independent of the slope gradient.     

论地震的“发震时段”

用地震电磁波法作临震预报，发现地震的发震时间是有规律性的，仪器到的辽南发生的地方震和有些大地震，就是在预测的“发震时段”里发生的。     

Time interval of earthquake recurrence for strike - slip fault

On the basis of fault’s dynamic model of Knopoffet al. (1973), this paper has finally obtained a simple approximate formula to be able to estimate the recurrence time intervalT _R of earthquake on strike-slip fault. Preliminary result holds thatμ andδ _s — δ _f have not much effect onT _R . Leta is the ratio of the coseismic displacementD _s to the total displacementD _t in whole event course, i.e.,a =D _s /D _t , thena = 1/3 may represent the standard theoretical state in whichT _R is independent onμ andδ _s — δ _f . At this time,T _R is the arithmetic average ofs ₀/v andkd/β, wheres ₀ is the long-term preseismic accumulated slippage,v is fault’s average displacement rate,d is the fracture length on the fault of seismic focal region andβ is shear wave velocity. In addition,k =υ ₀/aυ, whereυ ₀ is the initial fracture velocity of actual structure at the coseismic instant. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,14, 187–194, 1992. This paper is a part of contracted item of State Seismological Bureau — Tectonic Physical Study of Earthquake Recurrence Period and Characteristic Magnitude.     

强震复发间隔变异系数的一种计算方法

确定强震复发间隔变异系数在强震发生概率的计算中具有重要意义. 考虑到由小样本量地震序列计算得到变异系数的估计值与实际值可能存在一定的偏差, 本文提出了一种计算强震复发间隔变异系数的新方法. 该方法首先利用最大似然估计法计算出大量小样本地震序列的变异系数估计值; 然后先对这些变异系数的估计值进行标准化处理, 再对这些标准化的变异系数估计值进行统计分析; 最后在广泛搜集的39个地震序列的基础上, 利用该方法计算得到一个通用的变异系数值(α=0.34), 并讨论了该值的物理意义及其应用.      

New magnitude scaling relations for earthquake early warning in the Alborz region,Iran

Rapid magnitude estimation relations for earthquake early warning systems in the Alborz region have been developed based on the initial first seconds of the P-wave arrival. For this purpose, a total of 717 accelerograms recorded by the Building and Housing Research Center in the Alborz region with the magnitude (M_w) range of 4.8–6.5 in the period between 1995 and 2013 were employed. Average ground motion period (\( \tau_{\text{c}} \)) and peak displacement (\( P_{\text{d}} \)) in different time windows from the P-wave arrival were calculated, and their relation with magnitude was examined. Four earthquakes that were excluded from the analysis process were used to validate the results, and the estimated magnitudes were found to be in good agreement with the observed ones. The results show that using the proposed relations for the Alborz region, earthquake magnitude could be estimated with acceptable accuracy even after 1 s of the P-wave arrival.     

On the lower energy bound of the recurrence law

The energy of the initiation of incipient cracks by groups of dislocations in crystalline substance is considered. The distribution of such cracks over energy obtained in the paper has the same form as the recurrence law, supporting the hypothesis that the latter is bounded from below by incipient cracks initiated by groups of dislocations.     

中国大陆中强地震复发间隔的概率分布研究

地震复发间隔的概率分布是计算地震发生概率的基础。利用我国历史地震目录资料,统计分析中国大陆中强地震归一化区域复发间隔,分析发现中国大陆中强地震活动兼具周期性和丛集性特点。采用对数正态分布与指数分布构建混合概率分布模型,通过最小二乘法拟合混合概率分布函数的最优参数。拟合结果的误差分析表明,混合概率分布模型更加符合中国大陆中强地震的活动特点。     

中国大陆活动地块边界带强震震级分布特征研究

本文利用基于广义帕累托分布的超阈值分布模型,对中国大陆活动地块边界带强震震级分布特征开展研究,给出了各活动地块边界带强震震级的广义帕累托分布参数估计。结果表明,广义帕累托分布较好地拟合了各边界带强震数据,形状参数估计均为负值,说明对应震级应有上限,因此广义帕累托分布为潜在震级上限提供了一种自然的刻画。在此基础上,估计了震级上限,并给出了分布0.99997高分位数估计,通过与历史最大震级比较发现,高分位数估计相对稳健。在地震发生过程为泊松过程假设下,推导了广义帕累托分布与广义极值分布之间的联系,揭示了一种利用强震数据推断最大震级分布的可能途径。     

常熟区域地震活动性规律研究

运用常熟地方震群记录资料，讨论了常熟地方区域地震活动性规律；频次高、震级小，地震活动具有分段连续等特点，进而指出地震危险区及中强地震的先期特征。     

Identifying the occurrence time of an impending major earthquake: a review

The procedure through which the occurrence time of an impending major earthquake can be determined is reviewed in the light of the recent advances. This can be achieved by analyzing in natural time the seismicity in the candidate area. To apply this general procedure, we need two important elements: first, to know when we should start the analysis, i.e., set the natural time equal to zero. This is the time at which the system enters the critical stage. Second a reliable estimation of the candidate epicentral area. If geoelectrical measurements are taken and the VAN method (after the initials of the three researchers Varotsos, Alexopoulos and Nomicos) is applied, both these elements become available upon the recording of a precursory Seismic Electric Signals (SES) activity, because its initiation marks the time when the system enters the critical stage, and in addition the SES data enable the determination of the epicentral area of the impending mainshock. On the other hand, if geoelectrical data are lacking, we make use of the following two recent findings by means of natural time analysis: First, the fluctuations of the order parameter of seismicity in a large area exhibit a minimum a few months before a major earthquake almost simultaneously with the initiation of an SES activity. Second, a spatiotemporal study of this minimum unveils an estimate of the epicentral area of the impending major earthquake. Two examples are given that refer to the strongest earthquakes that occurred in Greece and Japan during the last 3 decades, i.e., the M _W6.9 earthquake in southwestern Greece on 14 February 2008 and the M _W9.0 Tohoku earthquake in Japan on 11 March 2011.     

Probabilistic assessment of earthquake recurrence in the January 26, 2001 earthquake region of Gujrat, India

Kutch region of Gujrat is one of the most seismic prone regions of India. Recently, it has been rocked by a large earthquake (M _w = 7.7) on January 26, 2001. The probabilities of occurrence of large earthquake (M≥6.0 and M≥5.0) in a specified interval of time for different elapsed times have been estimated on the basis of observed time-intervals between the large earthquakes (M≥6.0 and M≥5.0) using three probabilistic models, namely, Weibull, Gamma and Lognormal. The earthquakes of magnitude ≥5.0 covering about 180 years have been used for this analysis. However, the method of maximum likelihood estimation (MLE) has been applied for computation of earthquake hazard parameters. The mean interval of occurrence of earthquakes and standard deviation are estimated as 20.18 and 8.40 years for M≥5.0 and 36.32 and 12.49 years, for M≥6.0, respectively, for this region. For the earthquakes M≥5.0, the estimated cumulative probability reaches 0.8 after about 27 years for Lognormal and Gamma models and about 28 years for Weibull model while it reaches 0.9 after about 32 years for all the models. However, for the earthquakes M≥6.0, the estimated cumulative probability reaches 0.8 after about 47 years for all the models while it reaches 0.9 after about 53, 54 and 55 years for Weibull, Gamma and Lognormal model, respectively. The conditional probability also reaches about 0.8 to 0.9 for the time period of 28 to 40 years and 50 to 60 years for M≥5.0 and M≥6.0, respectively, for all the models. The probability of occurrence of an earthquake is very high between 28 to 42 years for the magnitudes ≥5.0 and between 47 to 55 years for the magnitudes ≥6.0, respectively, past from the last earthquake (2001).     

Distance scaling of vertical and horizontal response spectra of the Loma Prieta earthquake

Attenuations of the vertical and horizontal response spectra of the 17 October 1989 Loma Prieta, California, earthquake are developed through analyses of the ground motion at 53 sites within a 100 km radius of the source. The analyses are performed on the spectral ordinates for 16 incremental periods ranging from 0.05 to 2.0 sec. The response spectra are modelled empirically for two different site conditions characterized by rock and stiff-soil geologies. Data analysis is performed by the application of a non-linear multivariate regression procedure allowing for distance and site factor as independent variables. Variation of the vertical-to-horizontal (V/H) spectral ratios with wave frequency and distance shows the same behaviour as observed previously in the widely separated geographic regions of northeastern Taiwan and east-central Iran. The predicted ratios at sites underlain by stiff soil are generally higher than the commonly used value of 2/3 at high frequencies ( > 5 Hz) in the near-source region (R < 30 km), but reduce to 1/2 or less at longer periods and farther distances. This behaviour is also observed at rock sites; however, it is somewhat less pronounced. With a faster attenuation of spectral ordinates at higher frequencies, the shape of the response spectrum is found to change with distance. As expected, the spectral attenuation with distance is generally higher for the vertical spectrum than for the horizontal spectrum. The difference is particularly significant at the higher-frequency end of spectrum. Site amplification factors for stiff soil with respect to rock geology varies between 1.17 and 1.72 for horizontal spectrum and 1.01 and 1.81 for vertical spectrum. Spectral amplifications at four sites underlain by soft soil and artificial fill, are also evaluated. This is done by a comparison of the observed spectra with those predicted for rock geology at corresponding distances. As expected, the resulting amplification factors at soft-soil sites show significant increase relative to those at sites underlain by rock.     

A stochastic methodology for risk assessment of a large earthquake when a long time has elapsed

We propose a stochastic methodology for risk assessment of a large earthquake when a long time has elapsed from the last large seismic event. We state an approximate probability distribution for the occurrence time of the next large earthquake, by knowing that the last large seismic event occurred a long time ago. We prove that, under reasonable conditions, such a distribution is exponential with a rate depending on the asymptotic slope of the cumulative intensity function corresponding to a nonhomogeneous Poisson process. As it is not possible to obtain an empirical cumulative distribution function of the waiting time for the next large earthquake, an estimator of its cumulative distribution function based on existing data is derived. We conduct a simulation study for detecting scenario in which the proposed methodology would perform well. Finally, a real-world data analysis is carried out to illustrate its potential applications, including a homogeneity test for the times between earthquakes.     

识别地震与爆炸的一种时间域新方法

利用地震观测波形直达纵横波能量的差异,在时间域创建标志地震事件震源性质的新参量a,计算182个台站记录的24个地震事件的a值,并用以分析2017年9月3日敏感地区发生的地震事件性质。结果表明,判据a具有良好的震源性质依附效应,从而为地震与爆炸的识别引进了一种新方法。     

Neural network for earthquake selection in structural time history analysis

A neural network is employed to select earthquake waves in a time history approach for structural dynamics. The neural network is a preferable alternative to an expert system because knowledge can easily be renewed. It involves a back propagation model having three layers (one input, one hidden and one output layer) and is used to avoid inappropriate earthquake input prior to practical numerical computations. Knowledge to categorize the earthquake waves is acquired through network training with earthquake response spectra and structural responses. The trained network is tested by categorizing the responses of three types of unknown structures caused by 50 previously recorded earthquakes. Comparisons are made with analogous data from the traditional site dominant period method. Results demonstrate that, unlike the latter method, a neural network is generally more successful as the number of training patterns increases.