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.     

The b-value and fractal dimension of local seismicity around Koyna Dam (India)

Earthquakes began to occur in Koyna region (India) soon after the filling of Koyna Dam in 1962. In the present study, three datasets 1964–1993, 1993–1995, and 1996–1997 are analyzed to study the b-value and fractal dimension. The b-value is calculated using the Gutenberg–Richter relationship and fractal dimension D _corr. using correlation integral method. The estimated b-value and D _corr. of this region before 1993 are found to be in good agreement with previously reported studies. In the subsequent years after 1995, the b-value shows an increase. The estimated b-values of this region are found within the limits of global average. Also, the pattern of spatial clustering of earthquakes show increase in clustering and migration along the three zones called North-East Zone, South-East Zone (SEZ), and Warna Seismic Zone. The earthquake events having depth ≤5 km are largely confined to SEZ. After 1993, the D _corr. shows decrease, implying that earthquake activity gets clustered. This seismic clustering could be helpful for earthquake forecasting.     

The spatiotemporal variation of the b-value and its tectonic implications in North China

In this study, we adopt an improved Bayesian approach based on free-knot B-spline bases to study the spatial and temporal distribution of the b-value. Synthetic tests show that the improved Bayesian approach has a superior performance compared to the Bayesian approach as well as the widely used maximum likelihood estimation (MLE) method in fitting the real variation of b-values. We then apply the improved Bayesian approach to North China and find that the b-value has a clear relevance to seismicity. Temporal changes of b-values are also investigated in two specific areas of North China. We interpret sharp decreases in the b-values as useful messages in earthquake hazard analysis.     

Evaluation of seismicity and seismic hazard parameters in Turkey and surrounding area using a new approach to the Gutenberg–Richter relation

In this study, the spatial distributions of seismicity and seismic hazard were assessed for Turkey and its surrounding area. For this purpose, earthquakes that occurred between 1964 and 2004 with magnitudes of M ≥ 4 were used in the region (30–42°N and 20–45°E). For the estimation of seismicity parameters and its mapping, Turkey and surrounding area are divided into 1,275 circular subregions. The b-value from the Gutenberg–Richter frequency–magnitude distributions is calculated by the classic way and the new alternative method both using the least-squares approach. The a-value in the Gutenberg–Richter frequency–magnitude distributions is taken as a constant value in the new alternative method. The b-values calculated by the new method were mapped. These results obtained from both methods are compared. The b-value shows different distributions along Turkey for both techniques. The b-values map prepared with new technique presents a better consistency with regional tectonics, earthquake activities, and epicenter distributions. Finally, the return period and occurrence hazard probability of M ≥ 6.5 earthquakes in 75 years were calculated by using the Poisson model for both techniques. The return period and occurrence hazard probability maps determined from both techniques showed a better consistency with each other. Moreover, maps of the occurrence hazard probability and return period showed better consistency with the b-parameter seismicity maps calculated from the new method. The occurrence hazard probability and return period of M ≥ 6.5 earthquakes were calculated as 90–99% and 5–10 years, respectively, from the Poisson model in the western part of the studying region.     

A Probabilistic Assessment of Earthquake Hazard Parameters in NW Himalaya and the Adjoining Regions

The maximum likelihood estimation method is applied to study the geographical distribution of earthquake hazard parameters and seismicity in 28 seismogenic source zones of NW Himalaya and the adjoining regions. For this purpose, we have prepared a reliable, homogeneous and complete earthquake catalogue during the period 1500–2010. The technique used here allows the data to contain either historical or instrumental era or even a combination of the both. In this study, the earthquake hazard parameters, which include maximum regional magnitude (M _max), mean seismic activity rate (λ), the parameter b (or β?=?b/log e) of Gutenberg–Richter (G–R) frequency-magnitude relationship, the return periods of earthquakes with a certain threshold magnitude along with their probabilities of occurrences have been calculated using only instrumental earthquake data during the period 1900–2010. The uncertainties in magnitude have been also taken into consideration during the calculation of hazard parameters. The earthquake hazard in the whole NW Himalaya region has been calculated in 28 seismogenic source zones delineated on the basis of seismicity level, tectonics and focal mechanism. The annual probability of exceedance of earthquake (activity rate) of certain magnitude is also calculated for all seismogenic source zones. The obtained earthquake hazard parameters were geographically distributed in all 28 seismogenic source zones to analyze the spatial variation of localized seismicity parameters. It is observed that seismic hazard level is high in Quetta-Kirthar-Sulaiman region in Pakistan, Hindukush-Pamir Himalaya region and Uttarkashi-Chamoli region in Himalayan Frontal Thrust belt. The source zones that are expected to have maximum regional magnitude (M _max) of more than 8.0 are Quetta, southern Pamir, Caucasus and Kashmir-Himanchal Pradesh which have experienced such magnitude of earthquakes in the past. It is observed that seismic hazard level varies spatially from one zone to another which suggests that the examined regions have high crustal heterogeneity and seismotectonic complexity.     

古登堡-里希特定律中的b值统计样本量研究

b值是研究地震活动的重要指标,其广泛应用于地震危险性分析和地震预测研究之中,与实际资料的完整性、样本量的大小、计算方法等因素有着重要的关系。常见的b值计算方法有最小二乘法和最大似然法,样本量的大小对这2种方法影响很大。本文利用蒙特卡罗模拟地震目录和汾渭地震带实际目录作为样本,从中抽取不同大小的样本量进行计算,研究不同样本量下这2种方法计算得到的b值与设定值或真实值之间的差别。结果表明,最小二乘法需要的最低样本量为1000,最大似然法为200;当样本量达不到要求时,计算出的b值是不可靠的;由于对样本量的要求不同,前者适用于计算区域的整体b值,而后者在研究某区域b值在时间轴上的变化方面更有优势。本研究为确定2种b值计算方法对样本量的最低要求提供了参考依据。     

Joint analysis of b-value and apparent stress before the 2011 MW9.0 Tohoku-Oki,Japan earthquake

Detecting tempo-spatial changes of crust stress associated with major earthquakes has implications for understanding earthquake seismogenic processes. We conducted a joint analysis of b-value and apparent stress in the source region before the March 11, 2011 M_W9.0 Tohoku-Oki, Japan earthquake. Earthquakes that occurred between January 1, 2000 and March 8, 2011 were used to estimate b-values, while source parameters of events with magnitudes of Ms5.0–6.9 between January 1, 1997 and March 8, 2011 were used to calculate the apparent stresses. Our results show that the average b-value decreased steadily from 1.26 in 2003 to 0.99 before the Tohoku-Oki mainshock. This b-value decrease coincided with an increase in the apparent stress from 0.65 MPa to 1.64 MPa. Our results reveal a clear negative correlation between the decrease in b-value and increase in apparent stress, which lasted for approximately eight years prior to the 2011 mainshock. Additionally, spatial pattern results of the relative change in b-value show that the area associated with drastic b-value decreases (25% or greater) was concentrated near the 2011 mainshock epicenter. The joint analysis of b-value and apparent stress provides a promising method for detecting anomalies that could serve as potential indicators of large earthquakes.     

Gorkha earthquake (MW7.8) and aftershock sequence: A fractal approach

On April 25, 2015, Nepal was struck by the M_W7.8 Gorkha earthquake followed by an intense aftershock sequence. It was one of the most destructive earthquakes in the Himalayan arc, causing more than 8900 fatalities. In this study, we analyzed the dataset (429 events, magnitude of completeness (M_c) ≥ 4.2 local magnitude) of the first 45 days after the Gorkha earthquake to estimate the seismicity parameters b-value, D-value, and p-value. We used the maximum likelihood method to estimate the b-value and Omori-Utsu parameters, whereas the correlation integral method was applied to estimate the fractal dimension (D-value). The analysis was carried out using running and sliding window techniques. The lowest b-value (0.57 ± 0.04) and the highest D-value (1.65 ± 0.02) were computed at the time of the Gorkha earthquake, after which the b-value significantly increased to a maximum of 1.57. It again dropped to 0.93 at the time of the major aftershock on May 12, 2015. The D-value showed an initial quick drop and then decreased in a wavy pattern until the end of the study period, indicating the clustering and scattering of earthquakes in a fault region. The b-value contour map identified the eastern part of the study area as a high stress region (b = ～0.8), implying that the stress shifted to that region. The D-value contour map reveals that the seismogenic structure shifted from linear to planar in the region. The rate of aftershock decay (p = 0.86 ± 0.04) for a short period reflects that the level of stress decreased rapidly. This study helps to understand the level of stress and seismicity pattern of a region, which could be useful for aftershock studies.     

Seismic Hazard Estimate at the Iberian Peninsula

—?Seismic hazard at the Iberian Peninsula has been evaluated by using a methodology which combines both zonified and non-zonified probabilistic methods. Seismic sources are used when considering zones where certain calculation parameters may be considered homogeneous, as in zonified methods, while, on the other hand, earthquakes are considered wherever it has taken place, as in non-zonified methods. The methodology which is applied in this paper has been originally used to calculate the seismic hazard maps in the United States. In our case, it has been necessary to adapt the method to the specific features of the seismicity in the Iberian Peninsula and its geographical surroundings, not only with respect to its distribution and characteristics, but also with respect to the properties of the seismic catalog used.¶Geographically, the main feature of the result is the fact that it reflects both historical seismicity and current seismic clusters of the region. Despite the smoothing, maps show marked differences between several seismic zones; these differences becoming more noticeable as exposure time increases. Maximum seismic hazard is found to be in the southwestern region of the Peninsula, especially in the area of the Cape St. Vicent, and around Lisbon. The uncertainty of the results, without considering that due to the attenuation laws, as deduced from the other evaluation parameters, is quite stable, being more sensitive to the parameters b and m _max of the Gutenberg-Richter relation.     

Detailed Study of Time Variations in the Gutenberg–Richter <Emphasis Type="Italic">b</Emphasis>-value Based on Highly Accurate Seismic Observations at the Garm Prognostic Site,Tajikistan

The time variations in the Gutenberg–Richter b-value are minutely studied based on the data of highly accurate seismological observations at the Garm prognostic site, Tajikistan, where a stationary network of seismic stations of the Complex Seismological Expedition (CSE) of Schmidt Institute of Physics of the Earth (IPE) of the USSR (Russian) Academy of Sciences was in operation from 1955 to 1992. A total of 93035 local earthquakes ranging from 0.0 to 6.3 in the Ml magnitudes are considered. The spatiotemporal fluctuations in the minimal magnitude of completeness of the earthquakes, Mc, are analyzed. The study considers a 25-year interval of the observations at the center of the observation system within which Mc = 0.9. It is shown that in most cases, the b-value and log₁₀E^2/3 experience characteristic time variations before the earthquakes with magnitudes higher than the minimal magnitude of the predicted earthquake (MPE). The 6-year anomaly in the parameters’ b-value, log₁₀E^2/3, and log₁₀N associated with the single strongest earthquake with M = 6.3 that occurred in the observation region on October 26, 1984 is revealed. The inversely proportional relationship is established between the time variations in the b-value and the time variations in the velocities of seismic waves Vp and Vp/Vs. It is shown that the exponent p in the power function which links the time variations of the b-value and log₁₀E^2/3 is higher in the zones of crustal compression than in the zones of extension. It is simultaneously confirmed that the average b-value in the zones of compression is lower than in the zones of extension. It is established that in the case of earthquakes with M ≥ 2.6, the time series of seismic activity log₁₀N_i and the time series of the b-value are highly cross correlated with a coefficient of r ≈ 0.75, whereas in the case of earthquakes with M ≥ 0.9, the coefficient of cross correlation between these time series is close to zero (r ≈ 0.06). The law of variations in the slope of the lines approximating the relationship between the log₁₀N_i time series in the different magnitude ranges (M ≥ Mc_i) and b-value time series is obtained. It is hypothesized that the seismic activity of the earthquakes with high magnitudes can be estimated provided that the parameters of the time series of the b-value and time series of the number of earthquakes logN(ΔM_i) in the range of low magnitudes are known. It is concluded that using the parameter log₁₀N for prognostic estimates of the strong earthquakes only makes sense for earthquakes having moderate and large magnitudes. It is inferred that the time variations in the b-value are predominantly contributed by the time variations of the earthquakes with relatively large magnitudes.     

Gutenberg-Richter <Emphasis Type="Italic">b</Emphasis>-value maximum likelihood estimation and sample size

The Aki-Utsu maximum likelihood method is widely used for estimation of the Gutenberg-Richter b-value, but not all authors are conscious of the method’s limitations and implicit requirements. The Aki/Utsu method requires a representative estimate of the population mean magnitude; a requirement seldom satisfied in b-value studies, particularly in those that use data from small geographic and/or time windows, such as b-mapping and b-vs-time studies. Monte Carlo simulation methods are used to determine how large a sample is necessary to achieve representativity, particularly for rounded magnitudes. The size of a representative sample weakly depends on the actual b-value. It is shown that, for commonly used precisions, small samples give meaningless estimations of b. Our results give estimates on the probabilities of getting correct estimates of b for a given desired precision for samples of different sizes. We submit that all published studies reporting b-value estimations should include information about the size of the samples used.     

The depth variations in the b-value of frequency-magnitude distribution of the earthquakes in the Garm region of Tajikistan

The depth changes in the b-value and density of the number of earthquakes in different magnitude bins (M ≥ 1.8, M ≥ 3.0, M ≥ 3.5) are analyzed using highly accurate seismological observations carried out in 1955–1991 at the Garm prognostic area in Tadjikistan. It is found that the observed b-values are controlled by the variations in the proportion between weak and strong earthquakes. Two horizons with different patterns of the b-value are identified in the Earth’s crust above and below a depth of 15–16 km. The b-value in the upper and lower horizons is close to 0.8 and 1.2, respectively. The lower horizon is marked by almost complete absence of relatively strong earthquakes with M ≥ 3.0. The observed changes in the b-value with increasing depth could probably be due to the increase in the strength of crustal material caused by the growth in temperature and confining pressure in the depth interval from 0 to 15 km. The transitional interval between the upper and lower crustal horizons (～13–18 km), which is characterized by a sharp drop in seismic activity, can probably be associated with the zone of the phase transition of crustal material from an elastic brittle state to a plastic state, as suggested by some authors. Typically, the top of this zone hosts the hypocenters of the strongest earthquakes in a given territory. The correlation is established between the crustal areas with low b-values and the locations of the strongest earthquakes in the region. It is suggested that the three-dimensional mapping of the b-value can be helpful for estimating the location, depth, and maximal magnitude of the probable strong earthquakes in seismically active regions and can be used to assess seismic risks.     

An estimation of the maximum b-value in the Gutenberg-Richter relation

An estimation of the maximum b-value in the Gutenberg-Richter relation is achieved from empirical laws of earthquake occurrence and from dimensional considerations of power law distributions of earthquake size. The deduced maximum b-value, 1.5 (or with error limits 1.30⩽b_max⩽1.64) agrees very well with maximum b-values computed from earthquake catalogues or published elsewhere in the literature. © 1999 Elsevier Science Ltd. All rights reserved.     

张家口-渤海断裂带西段及中西段b值时空扫描

张家口-渤海断裂带作为华北平原地区重要的活动断裂带,地震活动频繁,是我国地震监测预测重点区域之一。本文选取该断裂带西段及中西段1970-2016年的地震目录,采用最大似然法进行时间扫描,分析显示研究区b值为0.28-1.52,其随时间变化的特点是在大地震发生前降至最低,震后逐渐恢复;研究区空间扫描结果显示,该区b值的平均值为0.93,其中怀安-万全盆地北缘断裂和蓟运河断裂平均b值较低,反映该区域应力水平较高。综合以上结果,本次研究揭示出研究区地震危险性的时间和空间差异,为对研究区地震危险性评价提供基础数据。     

Estimation of site effects using strong motion data of BYTNet array in Turkey

Simultaneous estimation of effects of source, propagation path, and local site amplification was carried out using observed strong motion records in a frequency range from 0.8 to 20 Hz for the purpose of empirical evaluation of the local site effects in different geological conditions in the northwestern part of Turkey. The analyzed data are S-wave portions of 162 accelerograms from 39 shallow events observed at 14 sites of BYTNet array. A spectral separation method was applied to the observed S-wave spectra. The solutions for source spectra, inelasticity factor of propagation path for S-waves (Q _s-value), and factor of site amplification at each site were obtained in a least squares sense. In the analysis, we assumed that the factor of the site amplification at a reference site is the same as that of theoretical amplification of S-waves to the soil model whose bottom layer has an S-wave velocity around 2.15 km/s. The estimated Q _s-value of the propagation path is modeled as Q _s(f)?=?87.4f^0.78. The estimated site amplifications are characterized into three groups. The sites in the first group belong to rock site with no dominant peaks at a frequency range of 2 to 10 Hz. The second group of hard soil sites is characterized with moderately dominant peaks at a frequency of 5 Hz. The last group for soft soil sites has common peaks at a frequency of 4 Hz with larger amplitudes than those in the hard soil group. We, then, compare the amplifications with average S-wave velocity in top 30 m of the shallow S-wave profiles and proposed linear empirical formula between them at each frequency. We, furthermore, inverted the observed amplification factors into S-wave velocity and Q _s-value profiles of the deep soil over the basement.     

Probabilistic seismic hazard assessment of Switzerland: best estimates and uncertainties

We present the results of a new genera tion of probabilistic seismic hazard assessment for Switzerland. This study replaces the previous intensity-based generation of national hazard maps of 1978. Based on a revised moment-magnitude earthquake catalog for Switzerland and the surrounding regions, covering the period 1300–2003, sets of recurrence parameters (a and b values, M _max ) are estimated. Information on active faulting in Switzerland is too sparse to be used as source model. We develop instead two models of areal sources. The first oriented towards capturing historical and instrumental seismicity, the second guided largely by tectonic principles and express ing the alterative view that seismicity is less stationary and thus future activity may occur in previously quiet regions. To estimate three alterna tive a and b value sets and their relative weighting, we introduce a novel approach based on the modified Akaike information criterion, which allows us to decide when the data in a zone deserves to be fitted with a zone-specific b value. From these input parameters, we simulate synthetic earthquake catalogs of one-million-year duration down to magnitude 4.0, which also reflect the difference in depth distribution between the Alpine Foreland and the Alps. Using a specific predictive spectral ground motion model for Switzerland, we estimate expected ground motions in units of the 5% damped acceleration response spectrum at frequencies of 0.5–10 Hz for all of Switzerland, referenced to rock sites with an estimated shear wave velocity of 1,500 m/s² in the upper 30 m. The highest hazard is found in the Wallis, in the Basel region, in Graubünden and along the Alpine front, with maximum spectral accelerations at 5 Hz frequency reaching 150 cm/s² for a return period of 475 years and 720 cm/s² for 10,000 years. Electronic supplementary material The online version of this article (doi: ) contains supplementary material, which is available to authorized users.     

川东南长宁地区地震活动及b值演化特征

利用全国统一目录和流动台站目录,研究了四川盆地东南部长宁地区的地震活动特征和b值的空间分布特征.研究结果显示,长宁地区的地震活动在时间上呈现明显的分段特征,地震活动在2015年后明显增强;在空间上,长宁地区的地震活动主要集中在以28.3°N为界限的南、北2个地区,对于这2个区域的b值演化,计算结果显示出不同的分段特征....     

Inferring seismic hazard in Sichuan-Yunnan region of China based on the modern earthquake catalogue (1980-2019)*

Based on the modern earthquake catalogue, the incomplete centroidal voronoi tessellation (ICVT) method was used in this study to estimate the seismic hazard in Sichuan-Yunnan region of China. We calculated spatial distributions of the total seismic hazard and background seismic hazard in this area. The Bayesian delaunay tessellation smoothing method put forward by Ogata was used to calculate the spatial distributions of b-value. The results show that seismic hazards in Sichuan-Yunnan region are high, and areas with relatively high hazard values are distributed along the main faults, while seismic hazards in Sichuan basin are relatively low.     

A new seismic hazard assessment in the region of Andalusia (Southern Spain)

A probabilistic seismic hazard assessment of Andalusia (Southern Spain) in terms of peak ground acceleration, PGA, and spectral accelerations, SA(T), is presented in this paper. In contrast to most of the previous studies in the region, which were performed for PGA, making use of Intensity-to-PGA relationships, hazard was here calculated in terms of magnitude, using published spectral ground-motion models. Moreover, we considered different ground-motion models for the Atlantic sources, since the attenuation of those motions seems to be slower, as evidenced in the case of the extensive macroseismic areas of earthquakes like those occurred in the years 1755, 1969 and 2007. A comprehensive review of the seismic catalogue and of the seismogenic models proposed for the region was carried out, including those for Northern Africa, which is part of the influence area. Hazard calculations were performed following the Probabilistic Seismic Hazard Assessment (PSHA) methodology using a logic tree, which accounts for six different seismic source zonings and five different ground-motion attenuation relationships. Hazard maps in terms of PGA and SA (0.2 s) and SA (1 s) and coefficient of variation (COV) maps, for the 475-year return period were first obtained in rock sites. A geotechnical classification and amplification factors were proposed and new hazard maps including local effects were represented, showing PGA values ranging from 24 to 370 cm/s² for the whole Andalusian territory, with the highest expected values (PGA > 300 cm/s²) in some parts of the Granada Province and in the town of Vélez Málaga. Lowest values (PGA < 50 cm/s²) correspond to some towns of the Huelva and Córdoba provinces. The inclusion of soil effects provides a more detailed picture of the actual hazard the region is subjected to.     

Continuous-cyclic variations in the b-value of the earthquake frequency-magnitude distribution

Seismicity of the Earth (M ≥ 4.5) was compiled from NEIC, IRIS and ISC catalogues and used to compute b-value based on various time windows. It is found that continuous cyclic b-variations occur on both long and short time scales, the latter being of much higher value and sometimes in excess of 0.7 of the absolute b-value. These variations occur not only yearly or monthly, but also daily. Before the occurrence of large earthquakes, b-values start increasing with variable gradients that are affected by foreshocks. In some cases, the gradient is reduced to zero or to a negative value a few days before the earthquake occurrence. In general, calculated b-values attain maxima 1 day before large earthquakes and minima soon after their occurrence. Both linear regression and maximum likelihood methods give correlatable, but variable results. It is found that an expanding time window technique from a fixed starting point is more effective in the study of b-variations. The calculated b-variations for the whole Earth, its hemispheres, quadrants and the epicentral regions of some large earthquakes are of both local and regional character, which may indicate that in such cases, the geodynamic processes acting within a certain region have a much regional effect within the Earth. The b-variations have long been known to vary with a number of local and regional factors including tectonic stresses. The results reported here indicate that geotectonic stress remains the most significant factor that controls b-variations. It is found that for earthquakes with M _w ≥ 7, an increase of about 0.20 in the b-value implies a stress increase that will result in an earthquake with a magnitude one unit higher.