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 Mw ≥ 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.

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.

Depth and region dependence of b-value for micro-aftershocks of the May 12th,2008 Wenchuan earthquake and its tectonic implications

Micro-aftershocks with magnitude range of 1.5--4 around the Wenchuan earthquake epicenter, the southern part of the Longmenshan fault zone, exhibit good frequency-magnitude linear relationships, thus enabling b-value analysis. The average b-value for micro-aflershocks of M1.5-4 from July to December of 2008 in our local study region is about 0.88, similar to the b-value for all aftershocks ofM3.0-5.5 from May, 2008 to May, 2009 along the whole Longmenshan fault zone. The similarity between the local and regional b-values possibly indicates that the southern part of the Longmenshan fault zone has similar seismogenic environment to the whole Longmenshan fault zone. Alternatively, it may also imply that b-values derived from all events without consideration of structural variation can not discriminate local-scale tectonic information. The present study shows that the b-value for the Wenchuan earthquake micro-aftershocks varies with different regions. The b-value in southwest of the Yingxiu town is higher than that in the northeast of the Yingxiu town. The high b-value in the southwest part where the Wenchuan earthquake main shock hypocenter located indicates that the current stress around the hypocenter region is much lower than its surrounding area. The b-values are also dependent on depth. At shallow depths of 〈5 km, the b-values are very small （-0.4）, possibly being related to strong wave attenuation or strong heterogeneity in shallow layers with high content of porosity and fractures. At depths of-5-11 km, where most aftershocks concentrated, the b-values become as high as -0.9-1.0. At the depth below -11 km, the b-values decrease with the depth increasing, being consistent with increasing tectonic homogeneity and increasing stress with depth.

On the spatio-temporal variation in b-value after 25 April 2015 Gorkha,Nepal earthquake

In the present study,the spatial-temporal distribution of b-value along the five faults area(the Judi fault,Thaple fault,Kathmandu fault,Motihari-Gauri Shanker fault,and Motihari-Everest fault)was investigated after the Gorkha earthquake(M7.8).The earthquake catalog of 10,500 events was prepared by compiling the published catalogs.The study area is bounded in the central Himalaya from 26.5°to 29°in latitude direction and 84°to 87°in longitude direction.The frequency magnitude distribution shows the variation of the b-value along with fault areas from 0.45 to 0.69,indicating a common characteristic of aftershock sequences.In particular,the Judi fault area,Thaple fault area,and Motihari-Everest fault area are characterized by the low b-values of 0.45±0.02,0.48±0.02,and 0.55±0.04,respectively.These regions could be the source region for future earthquakes.The low b-value observed for fault areas are also consistent with the thrust faulting pattern in the region as indicated by the focal mechanism of mainshock and major aftershocks.The temporal variation of b-value shows inevitable fluctuations during25 April to 12 May 2015.Among the area selected,the Motihari-Everest fault area is in critical strain(mechanically locked)conditions,as indicated by the stepwise energy release pattern.

Uncertainties in estimation of extrapolated annual occurence rate of earthquakes using logical tree

he logical tree methods are used for evaluate quantitatively relationship between frequency and magnitude, and deduce uncertainties of annual occurrence rate of earthquakes in the periods of lower magnitude earthquake. The uncertainties include deviations from the self-similarity of frequency-magnitude relations, different fitting methods, different methods obtained the annual occurrence rate, magnitude step used in fitting, start magnitude, error of magnitude and so on. Taking Xianshuihe River source zone as an example, we analyze uncertainties of occurrence rate of earthquakes M4, which is needed in risk evaluation extrapolating from frequency-magnitude relations of stronger earthquakes. The annual occurrence rate of M4 is usually required for seismic hazard assessment.The sensitivity analysis and examinations indicate that, in the same frequencymagnitude relations fitting method, the most sensitive factor is annual occurrence rate, the second is magnitude step and the following is start magnitude. Effect of magnitude error is rather small.Procedure of estimating the uncertainties is as follows:①Establishing a logical tree described uncertainties in frequencymagnitude relations by available data and knowledge about studied region.② Calculating frequencymagnitude relations for each end branches. ③ Examining sensitivities of each uncertainty factors, amending structure of logical tree and adjusting original weights. ④ Recalculating frequencymagnitude relations of end branches and complementary cumulative distribution function (CCDF) in each magnitude intervals.⑤ Obtaining an annual occurrence rate of M4 earthquakes under given fractiles.Taking fractiles as 20% and 80%, annual occurrence rate of M 4 events in Xianshuihe seismic zone is 0.643 0. The annual occurrence rate is 0.631 8 under fractiles of 50%, which is very close to that under fractiles 20% and 80%.

Emergence of non-extensive seismic magnitude-frequency distribution from a Bayesian framework

Non-extensive statistical mechanics has been used in recent years as a framework in order to build some seismic frequency-magnitude models. Following a Bayesian procedure through a process of marginalization, it is shown that some of these models can arise from the result shown here, which reinforces the relevance of the non-extensive distributions to explain the data (earthquake’s magnitude) observed during the seismic manifestation. In addition, it makes possible to extend the non-extensive family of distributions, which could explain cases that, eventually, could not be covered by the currently known distributions within this framework. The model obtained was applied to six data samples, corresponding to the frequency-magnitude distributions observed before and after the three strongest earthquakes registered in Chile during the late millennium. In all cases, fit parameters show a strong trend to a particular non-extensive model widely known in literature.

The December 26, 2004, off the west coast of northern Sumatra, Indonesia, M_W=9.0, earthquake and the critical-point-like model of earthquake preparation

Long-term seismic activity prior to the December 26, 2004, off the west coast of northern Sumatra, Indonesia, MW=9.0 earthquake was investigated using the Harvard CMT catalogue. It is observed that before this great earth-quake, there exists an accelerating moment release (AMR) process with the temporal scale of a quarter century and the spatial scale of 1 500 km. Within this spatial range, the MW=9.0 event falls into the piece-wise power-law-like frequency-magnitude distribution. Therefore, in the perspective of the critical-point-like model of earthquake preparation, the failure to forecast/predict the approaching and/or the size of this earthquake is not due to the physically intrinsic unpredictability of earthquakes.

Seismic Risk Assessment and Maximum Magnitudes of Potential Earthquakes on Active Faults near Lanzhou City

The Zhuanglang river and Baiyin Baiyangshu river faults are late Quaternary faults near Lanzhou city, which pose a threat to the safety of the city. However, the cause of medium- strong earthquakes along the fault is rather complicated and even uncertain. It is important for us how to assess the magnitudes of maximum potential earthquakes and the seismic risk of the faults. The authors make reference to the method that Wen Xueze, et ai. （2007） developed to assess the magnitudes of maximum potential earthquakes in sub-areas of moderately and weakly active faults in the eastern Chinese Mainland, and brought forward an empirical relationship between the maximum magnitudes Mmax and the at/b values of the sub-areas＇ frequency- magnitude relationships in the Lanzhou area. By using this empirical relationship, the authors have estimated the upper-limits Mu of the Zhuanglang river and Baiyin Baiyangshu river active faults near Lanzhou city as Ms6.9 and 6.3, respectively. In addition, they have assessed the average interval recurrence time and the probabilities of destructive earthquakes on the faults.