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.

Atomic Decompositions of Weak Hardy Spaces of B-Valued Martingales

The atomic decompositions of weak Hardy spaces of Banach-space-valued martingales are given. With the help of the atomic decompositions, some inequalities for B-valued martingales are established in the case 0〈r≤1. Here the results are connected closely with the p-uniform smoothness and q-uniform convexity of Banach spaces which the martingales take values in.

Spatial Variations of b-Values in the Coastal Area of Guangdong

We used earthquake catalogs recorded by Guangdong Seismological Network from 2008 to 2014 to resolve the spatial variations of b-values in the coastal area of Guangdong, particularly in three key research areas(Yangjiang, Heyuan, and offshore Nanao Island) with strong seismicity. Our results revealed that b-values exhibited significant spatial variations, and zones with low b-values could indicate the most likely seismogenic area of large earthquakes. We observed three clear low b-value patches in the offshore Nanao Island. We found a distinct high b-value peak at the depth of 11 km and two minimum peaks at about 14 and 7–8 km in the Yangjiang area. The overall b-values generally decrease with depth in the Heyuan area. The spatial variations of b-values reflect tectonic anomalies; that is, the ‘low-high-low' distribution of b-values in the offshore Nanao Island and the Yangjiang area may indicate the anomaly of the crustal structure with a weak layer. The b-values of reservoir-induced seismicity are obviously lower than that induced by tectonism. This finding indicates that the reservoir area is generally at high stress state under the condition of high pore pressure. We inferred that large earthquakes might be prone to occur at 10–12 km depth in the offshore Nanao Island, at 12–15 km depth in the Yangjiang area, and at the lower part of the seismic activity zone in the Heyuan area. Moreover, the upstream area of the Xinfengjiang reservoir is the most likely area of future large earthquakes in the Heyuan area.

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.

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 Dcorr. using correlation integral method. The estimated b-value and Dcorr. of this region before 1993 are found to be in good agreement with previously reported studies. In the sub- sequent 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 Dcorr. shows decrease, implying that earth- quake activity gets clustered. This seismic clustering could be helpful for earthquake forecasting.

b-value and fractal dimension variations in Iran

Iran sits on a region with a high intrinsic level of seismic activity due to its tectonic setting.Through statistical examination of the earthquakes listed in the catalogue from International Institute of Earthquake Engineering and Seismology(IIEES),this research attempted to calculate some seismicity factors and find correlation between them.A preliminary analysis indicated changes in theb-value of the Gutenberg-Richter relationship over the study region.Thus,the study area was divided into five zones(Alborz,Zagros,Azerbaijan,Central and East)andb-value was computed for each zone.Considering faulting mechanism styles and theb-values in the region,it was found that the lowestb-values belong to the thrust events and strike-slip faulting earthquakes have intermediate values.These findings support previous studies.Furthermore,results ofb-value calculation were used for the estimation of accumulated differential stresses(σ1–σ2)over each zone.Overall,theb-value for Iran is averagely low which signifies the high stress tectonic regime in this region.Also,by having calculated fractal dimension(D)in each zone,a correlation obtained showing that in Iran region,theb-value correlates to fractal dimension byD=4.2b–2 relation which does not support Aki's(1981)speculation ofD=3b/c.

Correcting the Gutenberg–Richter b-value for effects of rounding and noise

The effects of magnitude rounding and of the presence of noise in the rounded magnitudes on the estimation of the Gutenberg-Richter b-value are explored, and the ways to correct for these effects are proposed. For typical values, b = 1 and rounding interval △M = 0.1, the rounding error is approximately -10^-3 and it can be corrected to a negligible approximately -10^-5. For the same typical values, the effect of noise can be larger, depending on the characteristics of the noise distribution; for normally distributed noise with standard deviation σ = 0.1, the correct b-value may be underestimated by a factor - 0.97.

BOUNDEDNESS OF DYADIC DERIVATIVE AND CESARO MEAN OPERATOR ON SOME B-VALUED MARTINGALE SPACES

In this article, it is proved that the maximal operator of one-dimensional dyadic derivative of dyadic integral I＊ and Cesàro mean operator σ＊ are bounded from the B-valued martingale Hardy spaces pΣα, Dα, pLα, p H#α, pKr to Lα （0 α ∞）, respectively. The facts show that it depends on the geometrical properties of the Banach space.

Joint analysis of b-value and apparent stress before the 2011 M_(W)9.0 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 MW9.0 TohokuOki,Japan earthquake.Earthquakes that occurred between January 1,2000 and March 8,2011 were used to estimate bvalues,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.

ATOMIC DECOMPOSITION FOR B-VALUED R.V. SEQUENCE SPACES

In this article,atomic decompositions and the duals of some B-valued r.v.se- quence spaces are investigated.The results show that it closely depends on the geometrical properties of the sequence that take values in.

Self-Organized Fractal Seismicity and b-Value of Aftershocks of the 2015 Gorkha Earthquake, Nepal

The Gorkha Earthquake that occurred on 25th April 2015 was a long anticipated, low angle thrust-faulting shallow event in Central Nepal that devastated the mountainous southern rim of the High Himalayan range. The earthquake was felt throughout central and eastern Nepal, much of the Ganges River plain in northern India, and northwestern Bangladesh, as well as in the southern parts of the Plateau of Tibet and western Bhutan. Two large aftershocks, with magnitudes 6.6 and 6.7, occurred in the region within one day of the main event, and several dozen smaller aftershocks occurred in the region during the succeeding days. In this study, we have analyzed the 350 aftershocks of the 2015 Gorkha Earthquake of Mw 7.8 to understand the spatial and temporal distribution of b-value and the fractal correlation dimension. The b-value is found to be 0.833 ± 0.035 from the Gutenberg-Richter relation by the least squares method and 0.95 ± 0.05 by the maximum likelihood method, indicating high stress bearing source zone. The spatial and temporal correlation dimension is estimated to be 1.07 ± 0.028 and 0.395 ± 0.0027 respectively. Spatial correlation dimension suggests a heterogeneous distribution of earthquake epicenters over a linear structure in space, while the temporal correlation dimension suggests clustering of aftershock activity in the time domain. The spatial variation of the b-value reveals that the b-value is high in the vicinity of the mainshock which is due to the sudden release of stress energy in the form of seismic waves. The spatial distribution of correlation dimension further confirms a linear source in the source zone as it varies from 0.8-1.0 in most of the region. We have also studied the temporal variation of b-value and correlation dimension that shows positive correlation for about first 15 days, then a negative correlation for next 45 days and after that, a positive correlation. The positive correlation suggests that the probability of large magnitude earthquakes decreases in response to increased fragmentation of the fault zone. The negative correlation means that there is a considerable probability of occurrences of large magnitude earthquakes, indicating stress release along the faults of a larger surface area [1]. The correlation coefficient between b-value and the correlation dimension is estimated to be 0.26, which shows that there is no significant relation between them.

Analysis of the b-value and Seismic Deformation in the North of China

The accuracy of b-value is limited by the uncertainty of the magnitude.In order to improvethe accuracy of the b-value,a statistic methodology was used to estimate the number of eventsbased on that there are several magnitude values for one historical event by several methods toestimate the magnitude.The b-value and seismic strain rates were calculated for the threeregions in the North of China.The method proved to be valid for all the regions,especiallyfor the data with large fluctuation.In order to study the stress state,the strain rate tensorand the principal axes of tension and compression were calculated for each of three regions bythe data of the focal mechanism,finally the stress state in each region was discussed.

A Moment Characterization of B-Valued Generalized Functionals of White Noise

Kernel theorems are established for Bananch space-valued multilinear mappings, A moment characterization theorem for Banach space-valued generalized functionals of white noise is proved by using the above kernel theorems. A necessary and sufficient condition in terms of moments is given for sequences of Banach space-valued generalized functionals of white noise to converge strongly. The integration is also discussed of functions valued in the space of Banach space-valued generalized functionals.

Duals of Hardy Spaces of B-valued Martingales for 0

The dual of B-valued martingale Hardy space Hr^s（p） （B） with small index 0 〈 r ≤ 1, which is associated with the conditional p-variation of B-valued martingale, is characterized. In order to obtain the results, a new type of Campanato spaces for B-valued martingales is introduced and the classical technique of atomic decompositions is improved. Some results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of the underlying Banach space.

A Characterization Theorem of the Differential of Functions Valued in B-Valued Generalized Functionals

Banach space-valued generalized functionals of white noise form an important part of vector-valued generalized functionals of white noise. In this paper, we discuss the differential of abstract function valued in B-valued generalized functional space. A characterized theorem is obtained by using their S-transform.

Complete Conyergence and Strong Laws of Large Numbers-for Weighted Sums of Sequences of Independent B-Valued Random Elements

In this paper, we obtain theorems of complete convergence and strong laws of large numbers for weighted sums of sequences of independent random elements in a Banach space of type p （1 ≤ p ≤ 2）. The results improve and extend the corresponding results on real random variables obtained by [1] and [2].

SOME DISCUSSION ON THE CONDITIONS OF COMPLETE CONVERGENCE FOR SUMS OF B-VALUED RANDOM ELEMENTS

In this paper, we discuss the conditions of complete convergence for partial sums and randomly indexed partial sums of independent but not necessarily identically distributed random elements in type p space, and obtain the characterization of Banach space of type p. Yu. H.’s some results(1989) on the case of real value are extended.

Some Statistical Aspects for Algerian Earthquake Catalogue

The scope of this study is to analyze some aspects of the Algerian earthquake catalogue between 1980 and 2009.Seismicity analysis is based on reliable compilation of earthquake catalogs obtained from different agencies.All intensities and magnitudes were converted to Ms magnitude using appropriate relationships.Dependent events were removed using adapted time and space windows.In addition,the completeness of the catalogue as a function of magnitude was determined from the standard deviation of occurrence rate plots,using the Stepp’s methodology.The remaining 2,016 independent earthquakes with Ms 2.2 were used to obtain various parameters(b-value,z-value)to characterize the temporal and spatial seismic activity for the entire northern part of Algeria.Finally,the obtained results are discussed to explain parameters variability.

Machine learning-based automatic construction of earthquake catalog for reservoir areas in multiple river basins of Guizhou province,China

Large reservoirs have the risk of reservoir induced seismicity.Accurately detecting and locating microseismic events are crucial when studying reservoir earthquakes.Automatic earthquake monitoring in reservoir areas is one of the effective measures for earthquake disaster prevention and mitigation.In this study,we first applied the automatic location workflow(named LOCFLOW)to process 14-day continuous waveform data from several reservoir areas in different river basins of Guizhou province.Compared with the manual seismic catalog,the recall rate of seismic event detection using the workflow was 83.9%.Of the detected earthquakes,88.9%had an onset time difference below 1 s,81.8%has a deviation in epicenter location within 5 km,and 77.8%had a focal depth difference of less than 5 km,indicating that the workflow has good generalization capacity in reservoir areas.We further applied the workflow to retrospectively process continuous waveform data recorded from 2020 to the first half of 2021 in reservoir areas in multiple river basins of western Guizhou province and identified five times the number of seismic events obtained through manual processing.Compared with manual processing of seismic catalog,the completeness magnitude had decreased from 1.3 to 0.8,and a b-value of 1.25 was calculated for seismicity in western Guizhou province,consistent with the b-values obtained for the reservoir area in previous studies.Our results show that seismicity levels were relatively low around large reservoirs that were impounded over 15 years ago,and there is no significant correlation between the seismicity in these areas and reservoir impoundment.Seismicity patterns were notably different around two large reservoirs that were only impounded about 12 years ago,which may be explained by differences in reservoir storage capacity,the geologic and tectonic settings,hydrogeological characteristics,and active fault the reservoir areas.Prominent seismicity persisted around two large reservoirs that have been impounded for less than 10 years.These events were clustered and had relatively shallow focal depths.The impoundment of the Jiayan Reservoir had not officially begun during this study period,but earthquake location results suggested a high seismicity level in this reservoir area.Therefore,any seismicity in this reservoir area after the official impoundment deserves special attention.

Trade space for time for inspecting an earthquake cycle by modern seismological observation: The central-southern part of the Sichuan-Yunnan rhombic block

The central-southern part of the eastern border of the Sichuan-Yunnan rhombic block provides the research strategy of ‘trade space for time' with an interesting fault system, where the segments have similar focal mechanisms and cover almost continuous spectra of elapse rates. We experiment to study the seismological characteristics of different segments with different elapse rates. We employed the de-clustered earthquake catalog for the calculation of b values for each segment. The analysis revealed that different segments have similar b values,which implies that, although different segments have different periods of earthquake recurrence, the 'natural time' for the whole fault system elapses with a homogeneous pace. We extended the earthquake potential score(EPS)for nowcasting earthquakes to a quasi-EPS(q EPS). It is found that q EPS increases with the increase of elapse rates,albeit for those fault segments whose elapse rates have exceeded 1, q EPS may better reflect the seismic hazard.