Uncertainties in probability of occurrence of strong earthquakes for fault sources in the Central Apennines,Italy

Using the characteristic earthquake model, we calculate the probability of occurrence of earthquakes M _w > 5.5 for individual fault sources in the Central Apennines for the 30-year period (2007–2037). We show the effect of time-dependent and time-independent occurrence (Brownian passage time (BPT) and Poisson) models together with uncertain slip rates and uncertain maximum magnitudes and, hence, uncertain recurrence times. In order to reduce the large prior geological slip rate uncertainty distribution for most faults, we obtain a posterior slip rate uncertainty distribution using a likelihood function obtained from regional historical seismicity. We assess the uncertainty of maximum magnitude by assuming that the uncertainty in fault width and length are described by a normal distribution with standard deviation equal to ±20% of the mean values. We then estimate the uncertainties of the 30-year probability of occurrence of a characteristic event using a Monte Carlo procedure. Uncertainty on each parameter is represented by the 16th and the 84th percentiles of simulated values. These percentiles bound the range that has a 68% probability of including the real value of the parameter. We do these both for the Poisson case and for the BPT case by varying the aperiodicity parameter (α value) using the values 0.3, 0.5, and 0.7. The Bayesian posterior slip rate uncertainties typically differ by a factor of about 2 from the 16th to the 84th percentile. Occurrence probabilities for the next 30 years at the 84th percentile typically range from 1% to 2% for faults where the Poisson model dominates and from 2% to 21% where one of the BPT models dominates. The uncertainty in occurrence probability under the time-dependent hypothesis is very large, when measured by the ratio of the 84th to the 16th percentile, frequently being as much as two orders of magnitude. On the other hand, when measured by standard deviation, these standard deviations range from 2% to 6% for those faults whose elapsed time since previous event is large, but always 2% or less for faults with relatively recent previous occurrence, because the probability of occurrence is always small.     

Earthquake hazard in Marmara Region, Turkey

Earthquake hazard in the Marmara Region, Turkey has been investigated using time-independent probabilistic (simple Poissonian) and time-dependent probabilistic (renewal) models. The study culminated in hazard maps of the Marmara Region depicting peak ground acceleration (PGA) and spectral accelerations (SA)'s at 0.2 and 1 s periods corresponding to 10 and 2% probabilities of exceedance in 50 yrs. The historical seismicity, the tectonic models and the known slip rates along the faults constitute the main data used in the assignment. Based on recent findings it has been possible to provide a fault segmentation model for the Marmara Sea. For the main Marmara Fault this model essentially identifies fault segments for different structural, tectonic and geometrical features and historical earthquake occurrences. The damage distribution and pattern of the historical earthquakes have been carefully correlated with this fault segmentation model. The inter-event time period between characteristic earthquakes in these segments is consistently estimated by dividing the seismic slip estimated from the earthquake catalog by the GPS-derived slip rate of 22±3 mm/yr. The remaining segments in the eastern and southern Marmara region are also identified using recent geological, geophysical studies and historical earthquakes. The model assumes that seismic energy along the segments is released by characteristic earthquakes. For the probabilistic studies characteristic earthquake based recurrence relationships are used. Assuming normal distribution of inter-arrival times of characteristic earthquakes, the ‘mean recurrence time’, ‘covariance’ and the ‘time since last earthquake’ are developed for each segment. For the renewal model, the conditional probability for each fault segment is calculated from the mean recurrence interval of the characteristic earthquake, the elapsed time since the last major earthquake and the exposure period. The probabilities are conditional since they change as a function of the time elapsed since the last earthquake. For the background earthquake activity, a spatially smoothed seismicity is determined for each cell of a grid composed of cells of size 0.005°×0.005°. The ground motions are determined for soft rock (NEHRP B/C boundary) conditions. Western US-based attenuation relationships are utilized, since they show a good correlation with the attenuation characteristics of ground motion in the Marmara region. The possibility, that an event ruptures several fault segments (i.e. cascading), is also taken into account and investigated by two possible models of cascading. Differences between Poissonian and renewal models, and also the effect of cascading have been discussed with the help of PGA ratio maps.     

Rupture segmentation and assessment of probabilities of seismic potential on the Xiaojiang fault zone

Spatial distribution of sources of strong and large earthquakes on the Xiaojiang fault zone in eastern Yunnan is studied according to historical earthquake data. 7 segments of relatively independent sources or basic units of rupture along the fault zone have been identified preliminarily. On every segment, time intervals between main historical earthquakes are generally characterized by “time-predictable” recurrence behavior with indetermination. A statistic model for the time intervals between earthquakes of the fault zone has been preliminarily established. And a mathematical method has been introduced into this paper to reckon average recurrence interval between earthquakes under the condition of having known the size of the last event at a specific segment. Based on these, ranges of the average recurrence intervals given confidence have been estimated for events of various sizes on the fault zone. Further, the author puts forward a real-time probabilistic model that is suitable to analyze seismic potential for individual segments along a fault zone on which earthquake recurrence intervals have been characterized by quasi-time-predictable behavior, and applies this model to calculate conditional probabilities and probability gains of earthquake recurring on the individual segments of the Xiaojiang fault zone during the period from 1991 to 2005. As a consequence, it has shown that two parts of this fault zone, from south of Dongchuan to Songming and from Chengjiang to Huaning, have relatively high likelihoods for strong or large earthquake recurring in the future. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 322–330, 1993.     

Changes in earthquake energy class as a factor affecting the parameters of the recurrence relation: The Baikal region

The numerical modeling of actually observed events contained in the Baikal earthquake catalog allowed the production of synthetic catalogs. These catalogs reflect real situations that can give rise to heterogeneities in earthquake catalogs acquired by seismological monitoring. For each of the resulting 65 catalogs we calculated the slope γ and seismic activity (so-called in Russian; it is the seismicity rate or the constant term in the frequency-size relation) A ₁₀ in the recurrence relation. We also investigated the effects of changes in estimates of earthquake energy class on the parameters of the recurrence relation. It was shown that the slope γ is not very sensitive, but that the seismic activity A ₁₀ is sensitive, to changes in earthquake energy class and can be used to test an earthquake catalog for heterogeneity. Formulas were derived to relate the parameters of recurrence relations and the scaling factors of two energy scales, which can yield recurrence parameters for one of the scales, provided we know the ratio of the respective scaling factors and the recurrence parameters based on the other scale.     

基于特征地震模型含时间的概率地震危险性分析方法及其应用研究

本文介绍了特征地震的对数正态分布模型、 正态分布模型和布朗过程时间模型, 提出了使用地震破裂面源模型的特征地震含时间的概率地震危险性分析理论和方法. 通过具体算例对不同的特征地震模型进行了比较, 并对特征地震危险性分析方法进行了系统探索. 研究结果表明, 特征地震含时间模型在复发周期早期的地震危险性低于不含时间模型, 而在后期其地震危险性则高于不含时间模型. 特征地震复发周期的对数正态分布模型与布朗过程时间模型计算得出的地震危险性差别不大. 在未到期望复发时间时, 正态分布模型与前两种模型计算的地震危险性差别不大; 而接近期望复发时间及之后时段, 正态分布模型计算的地震危险性则迅速增大.      

A GIS-based time-dependent seismic source modeling of Northern Iran

The first step in any seismic hazard study is the definition of seismogenic sources and the estimation of magnitude-frequency relationships for each source. There is as yet no standard methodology for source modeling and many researchers have worked on this topic. This study is an effort to define linear and area seismic sources for Northern Iran. The linear or fault sources are developed based on tectonic features and characteristic earthquakes while the area sources are developed based on spatial distribution of small to moderate earthquakes. Time-dependent recurrence relationships are developed for fault sources using renewal approach while time-independent frequency-magnitude relationships are proposed for area sources based on Poisson process. GIS functionalities are used in this study to introduce and incorporate spatial-temporal and geostatistical indices in delineating area seismic sources. The proposed methodology is used to model seismic sources for an area of about 500 by 400 square kilometers around Tehran. Previous researches and reports are studied to compile an earthquake/fault catalog that is as complete as possible. All events are transformed to uniform magnitude scale; duplicate events and dependent shocks are removed. Completeness and time distribution of the compiled catalog is taken into account. The proposed area and linear seismic sources in conjunction with defined recurrence relationships can be used to develop time-dependent probabilistic seismic hazard analysis of Northern Iran.     

Probabilistic Assessment of Earthquake Recurrence in Northeast India and Adjoining Regions

Northeast India and adjoining regions (20°–32° N and 87°–100° E) are highly vulnerable to earthquake hazard in the Indian sub-continent, which fall under seismic zones V, IV and III in the seismic zoning map of India with magnitudes M exceeding 8, 7 and 6, respectively. It has experienced two devastating earthquakes, namely, the Shillong Plateau earthquake of June 12, 1897 (M _w 8.1) and the Assam earthquake of August 15, 1950 (M _w 8.5) that caused huge loss of lives and property in the Indian sub-continent. In the present study, the probabilities of the occurrences of earthquakes with magnitude M ≥ 7.0 during a specified interval of time has been estimated on the basis of three probabilistic models, namely, Weibull, Gamma and Lognormal, with the help of the earthquake catalogue spanning the period 1846 to 1995. The method of maximum likelihood has been used to estimate the earthquake hazard parameters. The logarithmic probability of likelihood function (ln L) is estimated and used to compare the suitability of models and it was found that the Gamma model fits best with the actual data. The sample mean interval of occurrence of such earthquakes is estimated as 7.82 years in the northeast India region and the expected mean values for Weibull, Gamma and Lognormal distributions are estimated as 7.837, 7.820 and 8.269 years, respectively. The estimated cumulative probability for an earthquake M ≥ 7.0 reaches 0.8 after about 15–16 (2010–2011) years and 0.9 after about 18–20 (2013–2015) years from the occurrence of the last earthquake (1995) in the region. The estimated conditional probability also reaches 0.8 to 0.9 after about 13–17 (2008–2012) years in the considered region for an earthquake M ≥ 7.0 when the elapsed time is zero years. However, the conditional probability reaches 0.8 to 0.9 after about 9–13 (2018–2022) years for earthquake M ≥ 7.0 when the elapsed time is 14 years (i.e. 2009).     

中国大陆基于BPT模型的时间相依地震危险性分析

概率地震危险性分析是地震区划图编制、重大工程场地地震安全性评估以及地震风险管理等领域的重要依据,地震时间活动性模型则是概率地震危险性分析的主要理论基础.本研究中基于布朗过程时间（Brownian passage time（BPT））模型,计算了不同情况下中国大陆特征地震震源区时间相依的地震发生率,采用概率地震危险性计算方法,选择合适的地震动模型,评估了中国大陆地区时间相依的地震危险性,并与基于泊松模型的地震危险性做了比较.结果表明,时间相依的地震活动特征对概率地震危险性具有显著影响,在那些地震离逝时间相对较长,离逝率较大（大于1）的震源区,时间相依的地震危险性结果相较于基于泊松模型的地震危险性结果显著增大,增大幅度最大可达50%以上.相反,在那些刚发生地震不久,地震离逝时间较短的震源区,时间相依的地震危险性结果相较于泊松模型显著减小,减小幅度最大可达50%左右.地震复发间隔的变异系数对地震危险性结果也有显著影响,选择合适的变异系数对时间相依地震危险性分析十分重要,后续应该加强对地震复发间隔不确定性的研究.研究结果还表明,时间相依的地震活动特征对不同超越概率下的地震危险性结果的影响是一致的,不随超越概率水平的变化而变化.本文研究结果对地震风险管理、地震保险以及相关防震减灾政策的制定等方面具有重要的应用价值.

     

Perturbation of earthquake probability for interacting faults by static Coulomb stress changes

This work aims at the assessment of the occurrence probability of future earthquakes on the Italian territory, conditional to the time elapsed since the last characteristic earthquake on a fault and to the history of the following events on the neighbouring active sources. We start from the estimate of the probability of occurrence in the period 2007–2036 for a characteristic earthquake on geological sources, based on a time-dependent renewal model, released in the frame of Project DPC-INGV S2 (2004–2007) “Assessing the seismogenic potential and the probability of strong earthquakes in Italy”. The occurrence rate of a characteristic earthquake is calculated, taking into account both permanent (clock advance) and temporary (rate-and-state) perturbations. The analysis has been carried out on a wide area of Central and Southern Italy, containing 32 seismogenetic sources reported in the DISS 3.0.2 database. The results show that the estimated effect of earthquake interaction in this region is small if compared with the uncertainties affecting the statistical model used for the basic time-dependent hazard assessment.     

Updating seismic hazard at Parkfield

The occurrence of the September 28, 2004 M _w = 6.0 mainshock at Parkfield, California, has significantly increased the mean and aperiodicity of the series of time intervals between mainshocks in this segment of the San Andreas fault. We use five different statistical distributions as renewal models to fit this new series and to estimate the time-dependent probability of the next Parkfield mainshock. Three of these distributions (lognormal, gamma and Weibull) are frequently used in reliability and time-to-failure problems. The other two come from physically-based models of earthquake recurrence (the Brownian Passage Time Model and the Minimalist Model). The differences resulting from these five renewal models are emphasized.     

Preliminary analysis of earthquake probability based on the synthetic seismic catalog

The analysis of seismic hazards relies on the statistical analysis of historical seismic data and the instrumental seismic catalog to obtain the regional earthquake recurrence interval and earthquake probability. The accuracy of analysis thus depends strongly on the completeness of the seismic data used. However, available seismic catalogs are too short or incomplete for the reliable analysis of the statistical characteristics of earthquakes. If a long-term synthetic seismic catalog can be generated using a physics-based numerical simulation, and the simulation results match the crustal deformation, seismicity, and other observations,then such a synthetic catalog helps us to further understand the characteristics of seismic activity and analyze the regional seismic hazard. In this paper, taking the northeastern Tibetan Plateau as a case study, we establish a three-dimensional visco-elastoplastic finite-element model to simulate earthquake cycles and the spatiotemporal evolution of earthquakes on the model fault system and obtain a seismic catalog on a time scale of tens of thousands of years. On the basis that the model satisfies the regional geodynamics of the northeastern Tibetan Plateau, we analyze seismicity on the northeastern Tibetan Plateau using the simulated synthetic earthquake catalog. The characteristics of earthquake recurrence at different locations and different magnitudes, and the long-term average probability of earthquake occurrence within the fault system on the northeastern Tibetan plateau are studied. The results are a reference for regional seismic hazard assessment and provide a basis for the physics-based numerical prediction of earthquakes.     

Probabilistic Seismic Hazard Assessment for Japan

A probabilistic seismic hazard assessment was performed for the Japanese islands and surrounding areas. Seismic hazard parameters characteristic of the seismic history of the regions were obtained. The probability of occurrence of a large M ≥ 7 earthquake within a 10- and 50-year period was also calculated. Regions of very high levels of hazard occur where the Pacific, Phillipine and Eurasian Plates meet. High probabilities of occurrence of a large M ≥ 7 earthquake within a 10- and 50-year period occur within the region where the Pacific Plate subducts with the Eurasian Plate.     

Earthquake recurrence models and occurrence probabilities of strong earthquakes in the North Aegean Trough (Greece)

The determination of strong earthquakes’ recurrence time above a predefined magnitude, associated with specific fault segments, is an important component of seismic hazard assessment. The occurrence of these earthquakes is neither periodic nor completely random but often clustered in time. This fact in connection with their limited number, due to shortage of the available catalogs, inhibits a deterministic approach for recurrence time calculation, and for this reason, application of stochastic processes is required. In this study, recurrence time determination in the area of North Aegean Trough (NAT) is developed by the application of time-dependent stochastic models, introducing an elastic rebound motivated concept for individual fault segments located in the study area. For this purpose, all the available information on strong earthquakes (historical and instrumental) with M_w ≥ 6.5 is compiled and examined for magnitude completeness. Two possible starting dates of the catalog are assumed with the same magnitude threshold, M_w ≥ 6.5 and divided into five data sets, according to a new segmentation model for the study area. Three Brownian Passage Time (BPT) models with different levels of aperiodicity are applied and evaluated with the Anderson–Darling test for each segment in both catalog data where possible. The preferable models are then used in order to estimate the occurrence probabilities of M_w ≥ 6.5 shocks on each segment of NAT for the next 10, 20, and 30 years since 01/01/2016. Uncertainties in probability calculations are also estimated using a Monte Carlo procedure. It must be mentioned that the provided results should be treated carefully because of their dependence to the initial assumptions. Such assumptions exhibit large variability and alternative means of these may return different final results.     

The model of double bounds of stochastic stress in seismic risk analysis of faults

In this paper, the major idea is: when seismic stress accumulates to a certain extent, a stick slip earthquake will occur on the fault plane. The seismic stress before and after the stick slip earthquake occurrence are both stochastic variables. According to this idea, the model of double bounds of stochastic stress is proposed, and also it is used to analyse the seismic risk of Xian Shui River Fault Zone in the coming 30 years, the result is similar to what the Seismological Bureau of Sichuan Province has predicted. The Chinese version of this paper appeared in the Chinese edition ofActa Seismologica Sinica,15, 477–483, 1993.     

A probabilistic model of seismicity: Kamchatka earthquakes

The catalog of Kamchatka earthquakes is represented as a probability space of three objects {Ω, $ \tilde F $ \tilde F P}. Each earthquake is treated as an outcome ω _i in the space of elementary events Ω whose cardinality for the period under consideration is given by the number of events. In turn, ω _i is characterized by a system of random variables, viz., energy class k_i, latitude φ _i , longitude λ _i , and depth h _i . The time of an outcome has been eliminated from this system in this study. The random variables make up subsets in the set $ \tilde F $ \tilde F and are defined by multivariate distributions, either by the distribution function $ \tilde F $ \tilde F (φ, λ, h, k) or by the probability density f(φ, λ, h, k) based on the earthquake catalog in hand. The probabilities P are treated in the frequency interpretation. Taking the example of a recurrence relation (RR) written down in the form of a power law for probability density f(k), where the initial value of the distribution function f(k ₀) is the basic data [Bogdanov, 2006] rather than the seismic activity A ₀, we proceed to show that for different intervals of coordinates and time the distribution f _elim(k) of an earthquake catalog with the aftershocks eliminated is identical to the distribution f _full(k), which corresponds to the full catalog. It follows from our calculations that f ₀(k) takes on nearly identical numeral values for different initial values of energy class k ₀ (8 ≤ k ₀ ≤ 12) f(k ₀). The difference decreases with an increasing number of events. We put forward the hypothesis that the values of f(k ₀) tend to cluster around the value 2/3 as the number of events increases. The Kolmogorov test is used to test the hypothesis that statistical recurrence laws are consistent with the analytical form of the probabilistic RR based on a distribution function with the initial value f(k ₀) = 2/3. We discuss statistical distributions of earthquake hypocenters over depth and the epicenters over various areas for several periods     

Probability forecast of earthquake magnitude in Chinese mainland before A．D． 2005

ＰｒｏｂａｂｉｌｉｔｙｆｏｒｅｃａｓｔｏｆｅａｒｔｈｑｕａｋｅｍａｇｎｉｔｕｄｅｉｎＣｈｉｎｅｓｅｍａｉｎｌａｎｄｂｅｆｏｒｅＡ．Ｄ．２００５ＸＩＡＯ－ＱＩＮＧＷＡＮＧ（王晓青），ＺＨＥＮＧ－ＸＩＡＮＧＦＵ（傅征祥）ａｎｄＭＩＮＧＪＩＡＮＧ（蒋铭）...     

时间-震级可预报模式在南北地震带分段危险性评估中的应用

为了定量评估南北地震带不同段落的长期地震危险性,引入了时间－震级可预报模式。在详细地震复发行为的基础上,沿南北地震带划分了３９个震源区。利用其中２７个震源的多轮回复发资料初步建立起时间－震级可预报统计模型。计算结果表明,不同震源的地震复发表现出较好的时间可预报行为以及相对较弱的震级可预报行为。以时间可预报模型为基础,对所有震源区未来地震的复发概率进行了估算,同时,用震级可预报模型对未来地震的震级作     

On the seismicity of central Kamchatka before the 1997, M = 7.9 Kronotskii earthquake

We report results from a detailed study of seismicity in central Kamchatka for the period from 1960 to 1997 using a modified traditional approach. The basic elements of this approach include (a) segmentation of the seismic region concerned (the Kronotskii and Shipunskii geoblocks, the continental slope and offshore blocks), (b) studying the variation in the rate of M = 4.5–7.0 earthquakes and in the amount of seismic energy release over time, (c) studying the seismicity variations, (d) separate estimates of earthquake recurrence for depths of 0–50 and 50–100 km. As a result, besides corroborating the fact that a quiescence occurred before the December 5, 1997, M = 7.9 Kronotskii earthquake, we also found a relationship between the start of the quiescence and the position of the seismic zone with respect to the rupture initiation. The earliest date of the quiescence (decreasing seismicity rate and seismic energy release) was due to the M = 4.5–7.0 earthquakes at depths of 0–100 km in the Kronotskii geoblock (8–9 years prior to the earthquake). The intermediate start of the quiescence was due to distant seismic zones of the Shipunskii geoblock and the circular zone using the RTL method, combining the Shipunskii and Kronotskii geoblocks (6 years). Based on the low magnitude seismicity (M≥2.6) at depths of 0–70 km in the southwestern part of the epicentral zone (50–100 km from the mainshock epicenter), the quiescence was inferred to have occurred a little over 3 years (40 months) before the mainshock time and a little over 2 years (25 months) in the immediate vicinity of the epicenter (0–50 km). These results enable a more reliable identification of other types of geophysical precursors during seismic quiescences before disastrous earthquakes.     

Evidence for a Tang-Song Dynasty great earthquake along the Longmen Shan Thrust Belt prior to the 2008 <Emphasis Type="Italic">M</Emphasis><Subscript>w</Subscript> 7.9 Wenchuan earthquake,China

The magnitude (M _w) 7.9 Wenchuan earthquake occurred on 12 May 2008 in the Longmen Shan region of China, the transition zone between the Tibetan Plateau and the Sichuan Basin, resulting in widespread damage throughout central and western China. The steep, high-relief eastern margin of the Tibetan Plateau has undergone rapid Cenozoic uplift and denudation accompanied by folding and thrusting, yet no large thrust earthquakes are known prior to the 2008 M _w 7.9 Wenchuan earthquake. Field and excavation investigations reveal that a great historical earthquake occurred in the Sichuan region that ruptured a >200-km-long thrust fault within the Longmen Shan Thrust Belt, China, which also triggered the 2008 M _w 7.9 Wenchuan earthquake. The average co-seismic slip amount produced by this historical earthquake is estimated to be 2–3 m, comparable with that caused by the 2008 Wenchuan earthquake. Paleoseismic and archaeological evidence and radiocarbon dating results show that the penultimate great earthquake occurred in the Sichuan region during the late Tang-Song Dynasty, between AD 800 and 1000, suggesting a recurrence interval of ~1,000–1,200 years for Wenchuan-magnitude (M = ~8) earthquakes in the late Holocene within the Longmen Shan Thrust Belt. This finding is in contrast with previous estimates of 2,000–10,000 years for the recurrence interval of large earthquakes within the Longmen Shan Thrust Belt, as obtained from long-term slip rates based on the Global Positioning System and geological data, thereby necessitating substantial modifications to existing seismic-hazard models for the densely populated region at the eastern marginal zone of the Tibetan Plateau.     

Long-term earthquake triggering in the Southern and Northern Apennines

We argue that the study of long-range interaction between seismic sources in the peri-Adriatic regions may significantly contribute to estimating seismic hazard in Italy. This hypothesis is supported by the reconstruction of the geodynamic and tectonic settings in the Central Mediterranean region, the space–time distribution of major past earthquakes, and the quantification of post-seismic relaxation. The most significant evidence of long-distance interaction is recognized for the Southern Apennines, whose major earthquakes have almost regularly followed within a few years the largest events in the Montenegro-Albania zone since 1850. Statistical analyses of the post-1850 earthquake catalogues give a probability of about 10% that a major event in the Southern Apennines is not preceded by the occurrence of a strong event in the Southern Dinarides–Albanides within 3–5 years. Conversely, the probability of false alarms is relevant (50% within 3 years, 33% within 5 years). Northward, the tectonic setting and some patterns of regularity seen in major events suggest that the seismic activation of the main transtensional decoupling shear zones in the Central Apennines should influence the probability of major earthquakes in the Northern Apennines.