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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.     

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.     

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。     

Probability of earthquake occurrence and magnitude estimation in the post shut-in phase of geothermal projects

Induced seismicity in geothermal projects is observed to continue after shut-in of the fluid injection. Recent experiments show that the largest events tend to occur after the termination of injection. We use a probabilistic approach based on Omori??s law and the Gutenberg?CRichter magnitude?Cfrequency distribution to demonstrate that the probability of exceeding a certain maximum magnitude still increases after shut-in. This increase is governed by the exponent of Omori??s law q and the Gutenberg?CRichter b value. For a reduced b value in the post-injection phase, the probability of occurrence directly after shut-in can be even higher than the corresponding probability for an ongoing injection. For the reference case of q?=?2 and a 10% probability at shut-in time t _S to exceed a given maximum magnitude, we obtain an increase to 14.6% for t?=?2t _S at a constant Gutenberg?CRichter b value after shut-in. A reduction of the b value by one quarter leads to a probability of 20.5%. If we consider a constant probability level of occurrence for an event larger than a given magnitude at shut-in time, this maximum magnitude increases by 0.12?units for t?=?2t _S (0.26?units for a reduced b value). For the Soultz-sous-Forêts (France) injection experiment in 2000, recent studies reveal q?=?9.5 and a b value reduction by 14%. A magnitude 2.3 event 9?h after shut-in falls in the phase with a probability higher than for the continued injection. The probability of exceeding the magnitude of this post-injection event is determined to 97.1%.     

鄱阳湖流域蚌类环境DNA宏条形码引物的筛选验证

环境DNA技术是一种非侵入、高灵敏、高效率且对环境无破坏性,对生物体无损伤的调查工具.为了筛选适合于蚌类环境DNA生物多样性研究的宏条形码引物,本研究通过对鄱阳湖流域24种常见蚌的基因组DNA进行普通扩增和高通量测序筛选了11对引物(设计了9对通用引物及从相关文献中引用了2对引物),结果显示引物cytb和16S rRN...     

Space-time correlations ofb values with stress release

A total of 1503 events for a 2-month period associated with am _N 2.6 rockburst is investigated for possible space-time correlations between low magnitude (–1.1 to –0.4)b values and several estimates of stress (static stress drop, apparent stress, and dynamic stress). Spatial variations of decreasingb values were found to be well correlated with increasing stress release estimates for time intervals prior to the rockburst and following the aftershock sequence. The strongest correlation tob value was with the dynamic stress drop, having correlation coefficients of 0.87 and 0.79 for the two intervals, respectively. The rockburst was found to actually occur at the intersection of the spatial coordinates corresponding to the largest gradient inb value. Based on these correlations, we conclude that the low magnitude seismicity is an indicator of the stress state within the rock mass, and can be used to study and forecast stress patterns in the vicinity of an impending major event. Time variations, however, did not show the same clear correlations and these are discussed in terms of departure from steady state conditions. Regardless, our results favour the use ofb values in a spatial, context rather than in a time analysis approach, and we consider thatb values provide valuable information regarding the changing stress conditions within the seismogenic volume.     

An advanced process for evaluating a linear dielectric constant–bulk electrical conductivity model using a capacitance sensor in field conditions

Abstract

The Hilhorst model was used to convert bulk electrical conductivity (σ_b) to pore water electrical conductivity (σ_p) under laboratory conditions by using the linear relationship between the soil dielectric constant (ε_b) and σ_b. In the present study, applying the linear relationship ε_b–σ_b to data obtained from field capacitance sensors resulted in strong positive autocorrelations between the residuals of that regression. We were able to derive an accurate offset of the relationship ε_b–σ_b and to estimate the evolution of σ_p over time by including a stochastic component to the linear model, rearranging it to a time-varying dynamic linear model (DLM), and using Kalman filtering and smoothing. The offset proved to vary for each depth in the same soil profile. A reason for this might be the changes in soil temperature along the soil profile.

Editor D. Koutsoyiannis; Associate editor M.D. Fidelibus     

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.     

Properties of the Aftershock Sequences of the 2003 Bingöl, M D = 6.4, (Turkey) Earthquake

Aftershock sequences of the magnitude M _{W =}6.4 Bingöl earthquake of 1 May, 2003 (Turkey) are studied to analyze the spatial and temporal variability of seismicity parameters of the b value of the frequency-magnitude distribution and the p value describing the temporal decay rate of aftershocks. The catalog taken from the KOERI contains 516 events and one month’s time interval. The b value is found as 1.49 ± 0.07 with Mc =3.2. Considering the error limits, b value is very close to the maximum b value stated in the literature. This larger value may be caused by the paucity of the larger aftershocks with magnitude M _D ≥ 5.0. Also, the aftershock area is divided into four parts in order to detect the differences in b value and the changes illustrate the heterogeneity of the aftershock region. The p value is calculated as 0.86 ± 0.11, relatively small. This small p value may be a result of the slow decay rate of the aftershock activity and the small number of aftershocks. For the fitting of a suitable model and estimation of correct values of decay parameters, the sequence is also modeled as a background seismicty rate model. Constant background activity does not appear to be important during the first month of the Bingöl aftershock sequences and this result is coherent with an average estimation of pre-existing seismicity. The results show that usage of simple modified Omori law is reasonable for the analysis. The spatial variability in b value is between 1.2 and 1.8 and p value varies from 0.6 to 1.2. Although the physical interpretation of the spatial variability of these seismicity parameters is not straightforward, the variation of b and p values can be related to the stress and slip distribution after the mainshock, respectively. The lower b values are observed in the high stress regions and to a certain extent, the largest b values are related to Holocene alluvium. The larger p values are found in some part of the aftershock area although no slip occurred after the main shock and it is interpreted that this situation may be caused by the alluvium structure of the region. These results indicate that the spatial distribution in b and p values are generally related to the rupture mechanism and material properties of an aftershock area.     

Increased flexibility in base flow modelling using a power law transmissivity profile

The hydrological catchment model known as TOPMODEL, in its original and most widely‐used form, assumed that subsurface transmissivity decreases exponentially as subsurface water storage decreases. It has been shown that this leads to recession curves of discharge Q that take the form ? dQ/dt = aQ^b, where a is a constant and b = 2. In order to reproduce a wider range of recession, or base flow, behaviour, a power function for transmissivity was subsequently incorporated into TOPMODEL as an alternative to the exponential function. This was claimed to extend the realistic values of b to range from 1 to 2, inclusive. We show here that the power transmissivity function can also generate values of b > 2 without making unrealistic assumptions (beyond those arguably made in the original TOPMODEL), thus generating recession curves consistent with catchments showing prolonged base flow. Furthermore, the power transmissivity function can generate recession curves that steepen with time (b < 1). Copyright © 2007 John Wiley & Sons, Ltd.