Space- and Time-Dependent Probabilities for Earthquake Fault Systems from Numerical Simulations: Feasibility Study and First Results

In weather forecasting, current and past observational data are routinely assimilated into numerical simulations to produce ensemble forecasts of future events in a process termed “model steering”. Here we describe a similar approach that is motivated by analyses of previous forecasts of the Working Group on California Earthquake Probabilities (WGCEP). Our approach is adapted to the problem of earthquake forecasting using topologically realistic numerical simulations for the strike-slip fault system in California. By systematically comparing simulation data to observed paleoseismic data, a series of spatial probability density functions (PDFs) can be computed that describe the probable locations of future large earthquakes. We develop this approach and show examples of PDFs associated with magnitude M > 6.5 and M > 7.0 earthquakes in California.     

Prediction of magnitude of the largest potentially induced seismic event

We propose a method for determining the possible magnitude of a potentially largest induced seismic event derived from the Gutenberg–Richter law and an estimate of total released seismic moment. We emphasize that the presented relationship is valid for induced (not triggered) seismicity, as the total seismic moment of triggered seismicity is not bound by the injection. The ratio of the moment released by the largest event and weaker events is determined by the constants a and b of the Gutenberg–Richter law. We show that for a total released seismic moment, it is possible to estimate number of events greater than a given magnitude. We determine the formula for the moment magnitude of a probable largest seismic event with one occurrence within the recurrence interval (given by one volumetric change caused by mining or injecting). Finally, we compare theoretical and measured values of the moment magnitudes of the largest induced seismic events for selected geothermal and hydraulic fracturing projects.     

Magnitudes of large shallow earthquakes from 1904 to 1980

In order to obtain a uniform magnitude catalogue, surface-wave magnitudes M_s and broad-band body-wave magnitudes m_B have been determined for large shallow earthquakes from 1904 to 1980. In making the catalogue homogeneous, the author consistently adheres to the original definitions of M_s and m_B given by Gutenberg (1945) and Gutenberg and Richter (1956). The determinations of M_s and m_B are all based on the amplitude and period data listed in Gutenberg and Richter's unpublished notes, bulletins from stations worldwide, and other basic information. m_B is measured on broad-band instruments in periods of ～8 s. Consistency of the magnitude determinations from these different sources is carefully checked in detail. More than 900 shallow shocks of magnitude 7 and over are catalogued. The meaning of the magnitude scales in various catalogues is examined in terms of M_s and m_B. Most of the magnitudes listed by Gutenberg and Richter (1954) in their “Seismicity of the Earth” are basically M_s for large shocks shallower than 40 km, but are basically m_B for large shocks at depths of 40–60 km. The surface-wave magnitudes given by “Earthquake Data Reports” are higher than M_s by 0.2 unit whether the combined horizontal amplitude or the vertical amplitude is used. m_B and the currently used 1 s body-wave magnitude are measured at different periods and should not be directly compared.     

Unified Scaling Law for Earthquakes as Applied to Assessment of Seismic Hazard and Associate Risks

Izvestiya, Physics of the Solid Earth - The distribution of the number of seismic events by magnitudes—the Gutenberg–Richter frequency–magnitude relation—is of paramount...     

An investigation of seismicity for the Central Anatolia region,Turkey

The aim of this study is to investigate the seismicity of Central Anatolia, within the area restricted to coordinates 30–35° longitude and 38–41° latitude, by determining the “a” and “b” parameters in a Gutenberg–Richter magnitude–frequency relationship using data from earthquakes of moment magnitude (Mw)?≥?4.0 that occurred between 1900 and 2010. Based on these parameters and a Poisson model, we aim to predict the probability of other earthquakes of different magnitudes and return periods (recurrence intervals). To achieve this, the study area is divided into six seismogenic zones, using spatial distributions of earthquakes greater than Mw?≥?4.0 with active faults. For each seismogenic zone, the a and b parameters in the Gutenberg–Richter magnitude–frequency relationship were calculated by the least squares method. The probability of occurrence and return periods of various magnitude earthquakes were calculated from these statistics using the Poisson method.     

青藏高原北部地区小震目录完整性分析

将青藏高原北部地区划分为祁连山地震带、甘东南地区、库玛地震带和柴达木一共和地块4个研究区域,基于古登堡一里希科特的震级一频度关系和震级一序号图像法对每个区域1970年以来的小震目录进行完整性分析,分别确定不同区域、不同时段的完整小震目录的震级下限,其结论可供青藏高原北部地区地震活动性分析和地震危险性评价研究时参考。     

震级离散下的震级频度关系

运用最大熵原理,研究震级离散条件下震级频度关系,得到震级离散条件下震级概率分布函数,结果表明:(1)震级大于等于某一震级的地震次数应通过离散求和的方式得到,而不应通过积分的方式得到;(2)震级上限取为∞的情况下,古登堡意义和里克特意义两种震级频度关系式的b值相等;震级上限有限的情况下,里克特意义震级频度关系式可能不是直...     

关于地震震级-频度关系式及其非线性项的讨论

研究了震级频度关系式中非线性项产生的原因,指出由于地震孕育过程是非线性的,很多地震现象都服从分形和混沌规律,因此传统的震级频度关系式中应含有非线性项,才能全面描述地震过程的非线性规律．得出了新的含有非线性项的震级频度关系式．讨论了该公式中非线性项的含义．     

Assessment of Creep Events as Potential Earthquake Precursors: Application to the Creeping Section of the San Andreas Fault, California

—We report the analysis of over 16 years of fault creep and seismicity data from part of the creeping section of the San Andreas fault to examine and assess the temporal association between creep events and subsequent earthquakes. The goal is to make a long-term evaluation of creep events as a potential earthquake precursor. We constructed a catalog of creep events from available digital creepmeter data and compared it to a declustered seismicity catalog for the area between San Juan Bautista and San Benito, California, for 1980 to 1996. For magnitude thresholds of 3.8 and above and time windows of 5 to 10 days, we find relatively high success rates (40% to 55% 'hits') but also very high false alarm rates (generally above 90%). These success rates are statistically significant (0.0007 < P < 0.04). We also tested the actual creep event catalog against two different types of synthetic seismicity catalogs, and found that creep events are followed closely in time by earthquakes from the real catalog far more frequently than the average for the synthetic catalogs, generally by more than two standard deviations. We find no identifiable spatial pattern between the creep events and earthquakes that are hit or missed. We conclude that there is a significant temporal correlation between creep events and subsequent small to moderate earthquakes, however that additional information (such as from other potential precursory phenomena) is required to reduce the false alarm rate to an acceptable level.     

Coal Mining Induced Seismicity in the Ruhr Area, Germany

Over the last 25 years mining-induced seismicity in the Ruhr area has continuously been monitored by the Ruhr-University Bochum. About 1,000 seismic events with local magnitudes between 0.7 ≤ M _L ≤ 3.3 are located every year. For example, 1,336 events were located in 2006. General characteristics of induced seismicity in the entire Ruhr area are spatial and temporal correlation with mining activity and a nearly constant energy release per unit time. This suggests that induced stresses are released rapidly by many small events. The magnitude–frequency distribution follows a Gutenberg–Richter relation which is a result from combining distributions of single longwalls that themselves show large variability. A high b-value of about 2 was found indicating a lack of large magnitude events. Local analyses of single longwalls indicate that various factors such as local geology and mine layout lead to significant differences in seismicity. Stress redistribution acts very locally since differences on a small scale of some hundreds of meters are observed. A regional relation between seismic moment M ₀ and local magnitude M _L was derived. The magnitude–frequency distribution of a single longwall in Hamm was studied in detail and shows a maximum at M _L = 1.4 corresponding to an estimated characteristic source area of about 2,200 m². Sandstone layers in the hanging or foot wall of the active longwall might fail in these characteristic events. Source mechanisms can mostly be explained by shear failure of two different types above and below the longwall. Fault plane solutions of typical events are consistent with steeply dipping fracture planes parallel to the longwall face and nearly vertical dislocation in direction towards the goaf. We also derive an empirical relation for the decay of ground velocity with epicenter distance and compare maximum observed ground velocity to local magnitude. This is of considerable public interest because about 30 events larger than M _L ≥ 1.2 are felt each month by people living in the mining regions. Our relations, for example, indicate that an event in Hamm with a peak ground velocity of 6 mm/s which corresponds to a local magnitude M _L between 1.7 and 2.3 is likely to be felt within about 2.3 km radius from the event.     

Evidence of non extensivity in the evolution of seismicity along the San Andreas Fault,California, USA: An approach based on Tsallis statistical physics

We examine the nature of the seismogenetic system along the San Andreas Fault (SAF), California, USA, by searching for evidence of complexity and non-extensivity in the earthquake record. We use accurate, complete and homogeneous earthquake catalogues in which aftershocks are included (raw catalogues), or have been removed by a stochastic declustering procedure (declustered catalogues). On the basis of Non-Extensive Statistical Physics (NESP), which generalizes the Boltzmann–Gibbs formalism to non-equilibrating (complex) systems, we investigate whether earthquakes are generated by an extensive self-excited Poisson process or by a non-extensive complex process. We examine bivariate cumulative frequency distributions of earthquake magnitudes and interevent times and determine the size and time dependence of the respective magnitude and temporal entropic indices, which indicate the level on non-equilibrium (correlation). It is shown that the magnitude entropic index is very stable and corresponds to proxy b-values that are remarkably consistent with the b-values computed by conventional means. The temporal entropic index computed from the raw catalogues indicate moderately to highly correlated states during the aftershock sequences of large earthquakes, progressing to quasi-uncorrelated states as these die out and before the next large event. Conversely, the analysis of the declustered catalogues shows that background seismicity exhibits moderate to high correlation that varies significantly albeit smoothly with time. This indicates a persistent sub-extensive seismogenetic system. The degree of correlation is generally higher in the southern SAF segment, which is consistent with the observation of shorter return periods for large earthquakes. A plausible explanation is that because aftershock sequences are localized in space and time, their efficient removal unveils long-range background interactions which are obscured by their presence! Our results indicate complexity in the expression of background seismicity along the San Andreas Fault, with criticality being a very likely mechanism as a consequence of the persistent non-equilibrium inferred from the temporal entropic index. However, definite conclusions cannot be drawn until the earthquake record is exhaustively studied in all its forms.     

Site-specific Seismic Hazard Estimation in the Main Seismogenic Zones of North Algeria

—?The procedure developed by Kijko and Sellevoll (1989, 1992) and Kijko and Graham (1998, 1999) is used to estimate seismic hazard parameters in north Algeria. The area-specific seismic hazard parameters that were calculated consist of the b value of the Gutenberg–Richter frequency–magnitude relation, the activity rate λ(M) for events above the magnitude M, and the maximum regional magnitude M _max. These parameters were calculated for each of the six seismogenic zones of north Algeria. The site-specific seismic hazard was calculated in terms of the maximum possible PGA at hypothetical engineering structures (HES), situated in each of the six seismogenic zones with coordinates corresponding with those of the six most industrial and populated cities in Algeria.     

The spatiotemporal analysis of the minimum magnitude of completeness <Emphasis Type="Italic">Mc</Emphasis> and the Gutenberg–Richter law <Emphasis Type="Italic">b</Emphasis>-value parameter using the earthquake catalog of Greece

Spatiotemporal mapping the minimum magnitude of completeness Mc and b-value of the Gutenberg–Richter law is conducted for the earthquake catalog data of Greece. The data were recorded by the seismic network of the Institute of Geodynamics of the National Observatory of Athens (GINOA) in 1970–2010 and by the Hellenic Unified Seismic Network (HUSN) in 2011–2014. It is shown that with the beginning of the measurements at HUSN, the number of the recorded events more than quintupled. The magnitude of completeness Mc of the earthquake catalog for 1970–2010 varies within 2.7 to 3.5, whereas starting from April 2011 it decreases to 1.5–1.8 in the central part of the region and fluctuates around the average of 2.0 in the study region overall. The magnitude of completeness Mc and b-value for the catalogs of the earthquakes recorded by the old (GINOA) and new (HUSN) seismic networks are compared. It is hypothesized that the magnitude of completeness Mc may affect the b-value estimates. The spatial distribution of the b-value determined from the HUSN catalog data generally agrees with the main geotectonic features of the studied territory. It is shown that the b-value is below 1 in the zones of compression and is larger than or equal to 1 in the zones dominated by extension. The established depth dependence of the b-value is pretty much consistent with the hypothesis of a brittle–ductile transition zone existing in the Earth’s crust. It is assumed that the source depth of a strong earthquake can probably be estimated from the depth distribution of the b-value, which can be used for seismic hazard assessment.     

Forecasting aftershock activity: 1. Adaptive estimates based on the Omori and Gutenberg–Richter laws

The method for forecasting the intensity of the aftershock processes after strong earthquakes in different magnitude intervals is considered. The method is based on the joint use of the time model of the aftershock process and the Gutenberg–Richter law. The time model serves for estimating the intensity of the aftershock flow with a magnitude larger than or equal to the magnitude of completeness. The Gutenberg–Richter law is used for magnitude scaling. The suggested approach implements successive refinement of the parameters of both components of the method, which is the main novelty distinguishing it from the previous ones. This approach, to a significant extent, takes into account the variations in the parameters of the frequency–magnitude distribution, which often show themselves by the decreasing fraction of stronger aftershocks with time. Testing the method on eight aftershock sequences in the regions with different patterns of seismicity demonstrates the high probability of successful forecasts. The suggested technique can be employed in seismological monitoring centers for forecasting the aftershock activity of a strong earthquake based on the results of operational processing.     

Multifractality in Seismicity Spatial Distributions: Significance and Possible Precursory Applications as Found for Two Cases in Different Tectonic Environments

We explore fractal properties of two observed seismicity distributions prior to the 2003 M _w 7.4 Colima, Mexico and 1992 M _w 7.3 Landers, USA earthquakes, together with several mathematical fractal distributions and two non-fractal ones, in order to estimate minimum reliable sample sizes, determine whether fractality for observed seismicity is essentially different from random uniform distributions, and explore the possibility of extracting premonitory information from fractal characteristics of seismicity before large earthquakes. Sample sizes above 800 events for whole catalogs appear to be sufficient to maintain ordered multifractality and to yield dimension estimates that vary smoothly and reliably. Fractal estimates appear to be best for whole catalogs that include aftershocks. The fractal characteristics of spatial distributions of seismicity are essentially different from those of the uniform random distribution, which is the null hypothesis of a non-fractal distribution with minimum information. The fractal dimensions and afractality measures of seismicity distributions change with time and show distinctive behaviors associated with foreshocks and main events, although these behaviors are different for each example. Results suggest the possibility of a priori identification of foreshocks to large earthquakes. A combination of fractal dimension and afractality measures over time may be helpful in large earthquake premonitory studies.     

Probabilistic seismic hazard assessment of Eastern Marmara Region

The objective of this study is to evaluate the seismic hazard in Eastern Marmara Region using an improved probabilistic seismic hazard assessment methodology. Two significant improvements over the previous seismic hazard assessment practices are accomplished in this study: advanced seismic source characterization models in terms of source geometry and recurrence relationships are developed, and improved global ground motion models (NGA-W1 models) are employed to represent the ground motion variability. Planar fault segments are defined and a composite magnitude distribution model is used for all seismic sources in the region to properly represent the characteristic behavior of the North Anatolian Fault without the need for an additional background zone. Multi-segment ruptures are considered using the rupture model proposed by the Working Group on California Earthquake Probabilities (2003). Events in the earthquake catalogue are attributed to the fault zones and scenario weights are determined by releasing the accumulated seismic energy. The uniform hazard spectra at 10 % probability of exceedance in 50 years hazard level for different soil conditions (soil and rock) are revealed for specific locations in the region (Adapazar?, Düzce, Gemlik, Izmit, Iznik and Sapanca). Hazard maps of the region for rock site conditions at the selected hazard levels are provided to allow the readers perform site-specific hazard assessment and develop site-specific design spectrum for local site conditions.     

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.     

Analysis of the spatial distribution between successive earthquakes occurred in various regions in the world

The earthquake spatial distribution is being studied, using earthquake catalogs from different seismic regions (California, Canada, Central Asia, Greece, and Japan). The quality of the available catalogs, taking into account the completeness of the magnitude, is examined. Based on the analysis of the catalogs, it was determined that the probability densities of the inter-event distance distribution collapse into single distribution when the data is rescaled. The collapse of the data provides a clear illustration of earthquake-occurrence self-similarity in space.     

Pore Creation due to Fault Slip in a Fluid-permeated Fault Zone and its Effect on Seismicity: Generation Mechanism of Earthquake Swarm

—Spatio-temporal variation of rupture activity is modeled assuming fluid migration in a narrow porous fault zone formed along a vertical strike-slip fault in a semi-infinite elastic medium. Pores are assumed to be created in the fault zone by fault slip. The effective stress principle coupled to the Coulomb failure criterion introduces mechanical coupling between fault slip and pore fluid. The fluid is assumed to flow out of a localized high-pressure fluid compartment in the fault with the onset of earthquake rupture. The duration of the earthquake sequence is assumed to be considerably shorter than the recurrence period of characteristic events on the fault. The rupture process is shown to be significantly dependent on the rate of pore creation. If the rate is large enough, a foreshock–mainshock sequence is never observed. When an inhomogeneity is introduced in the spatial distribution of permeability, high complexity is observed in the spatio-temporal variation of rupture activity. For example, frequency-magnitude statistics of intermediate-size events are shown to obey the Gutenberg–Richter relation. Rupture sequences with features of earthquake swarms can be simulated when the rate of pore creation is relatively large. Such sequences generally start and end gradually with no single event dominating in the sequence. In addition, the b values are shown to be unusually large. These are consistent with seismological observations on earthquake swarms.     

中国大陆及周缘地震目录完整性统计分析

地震目录资料是进行地震预测、地震危险性分析、地震活动性研究等地震学研究的基础资料.对地震目录资料的完整性可靠性分析是地震学研究的基础工作之一.近几十年来我国积累的大量的仪器地震记录,历史地震也在不断更新,为地震活动性研究提供了更为丰富的样本,因此有必要对新的地震目录进行完整性分析.本文采用了新的统计方法对我国仪器记录地震目录和历史破坏性地震目录进行了完整性分析.结果表明,对于仪器记录地震目录（M≥3.0）我国东部地区1975年后基本完整,西部地区1980年后基本完整.对于历史地震目录（M≥5.0）,东部地区1500年后基本完整,西部地区1950年后基本完整.考虑到华北地震区历史破坏性地震（M≥4³/₄）活动的时间非平稳性,我们采用突变点分析法研究了华北地震区历史破坏性地震目录的时间特征,得到了华北地震区地震活动周期性变化的突变点位置,并揭示了华北地震区历史破坏性地震目录完整起始时间约为公元1500年前后.