Optimized Seismic Threshold Monitoring – Part 2: Teleseismic Processing

v--vThis second paper (Part 2) pertaining to optimized site-specific threshold monitoring addresses the application of the method to regions covered by a teleseismic or a combined regional-teleseismic network. In the first paper (Part 1) we developed the method for the general case, and demonstrated its application to an area well-covered by a regional network (the Novaya Zemlya nuclear test site). In the present paper, we apply the method to the Indian and Pakistani nuclear test sites, and show results during the periods of nuclear testing by these two countries in May 1998. Since the coverage by regional stations in these areas is poor, an optimized approach requires the use of selected, high-quality stations at teleseismic distances.¶To optimize the threshold monitoring of these test sites, we use as calibration events either one of the nuclear explosions or a nearby earthquake. From analysis of the calibration events we derive values for array beamforming steering delays, filter bands, short-term averages (STA) lengths, phase travel times (P waves), and amplitude-magnitude relationships for each station. By applying these parameters, we obtain a monitoring capability of both test sites ranging from m_b 2.8-3.0 using teleseismic stations only. When including the nearby Nilore station to monitor the Indian tests, we show that the threshold can be reduced by about 0.4 magnitude units. In particular, we demonstrate that the Indian tests on 13 May, 1998, which were not detected by any known seismic station, must have corresponded to a magnitude (m_b) of less than 2.4.¶We also discuss the effect of a nearby aftershock sequence on the monitoring capability for the Pakistani test sites. Such an aftershock sequence occurred in fact on the day of the last Pakistani test (30 May, 1998), following a large (m_b 5.5) earthquake in Afghanistan located about 1100 km from the test site. We show that the threshold monitoring technique has sufficient resolution to suppress the signals from these interfering aftershocks without significantly affecting the true peak of the nuclear explosion on the threshold trace.     

A Bayesian method for missing rainfall estimation using a conceptual rainfall–runoff model

The estimation of missing rainfall data is an important problem for data analysis and modelling studies in hydrology. This paper develops a Bayesian method to address missing rainfall estimation from runoff measurements based on a pre-calibrated conceptual rainfall–runoff model. The Bayesian method assigns posterior probability of rainfall estimates proportional to the likelihood function of measured runoff flows and prior rainfall information, which is presented by uniform distributions in the absence of rainfall data. The likelihood function of measured runoff can be determined via the test of different residual error models in the calibration phase. The application of this method to a French urban catchment indicates that the proposed Bayesian method is able to assess missing rainfall and its uncertainty based only on runoff measurements, which provides an alternative to the reverse model for missing rainfall estimates.     

利用相对静力学强度测定1998年5月11日印度核爆的当量

核爆当量是核试验的重要参数之一. 许多地震学家对1998年5月11日在印度Pokhran地区的核试验(POK2)进行研究,给出了(12～60)kt的当量估计,近5倍的估计偏差引起了较为广泛的关注. 基于全球数字地震台网宽频带体波资料,我们通过波形反演计算等效震源模型参数,包括静力学强度ψ∞、特征频率k、以及震源深度h和P波在自由表面的反射系数rpp,并利用相对的静力学强度估算了POK2事件的当量. 我们发现Lay［1］在美国Nevada试验场(NTS)获得的相对静力学强度与当量的经验公式更适合印度核试验当量估计,并据此计算了这次试验的当量约36kt. 这一结果支持1998年5月11日印度核试验的总当量低于60kt的观点.     

Stochastic inversion of pressure and saturation changes from time-lapse multi component data

Knowledge about saturation and pressure distributions in a reservoir can help in determining an optimal drainage pattern, and in deciding on optimal well designs to reduce risks of blow‐outs and damage to production equipment. By analyzing time‐lapse PP AVO or time‐lapse multicomponent seismic data, it is possible to separate the effects of production related saturation and pressure changes on seismic data. To be able to utilize information about saturation and pressure distributions in reservoir model building and simulation, information about uncertainty in the estimates is useful. In this paper we present a method to estimate changes in saturation and pressure from time‐lapse multicomponent seismic data using a Bayesian estimation technique. Results of the estimations will be probability density functions (pdfs), giving immediate information about both parameter values and uncertainties. Linearized rock physical models are linked to the changes in saturation and pressure in the prior probability distribution. The relationship between the elastic parameters and the measured seismic data is described in the likelihood model. By assuming Gaussian distributed prior uncertainties the posterior distribution of the saturation and pressure changes can be calculated analytically. Results from tests on synthetic seismic data show that this method produces more precise estimates of changes in effective pressure than a similar methodology based on only PP AVO time‐lapse seismic data. This indicates that additional information about S‐waves obtained from converted‐wave seismic data is useful for obtaining reliable information about the pressure change distribution.     

Fracture Density Distributions and Well Yields in Coastal Maine

Understanding the distribution of water-bearing fractures in crystalline rock is an important component in evaluating the availability and vulnerability of water resources throughout the northeastern U.S. The State of Maine requests well drillers to report estimates of fracture depths and fracture yields for all bedrock wells drilled in the state. Using these data we analyze fracture-depth and fracture-yield data from 227 bedrock wells in coastal Maine in order to understand how fracture locations and yields are distributed with depth. Numerical simulations and statistical tests show that it is not possible to infer how fractures are distributed with depth: fracture depths are consistent with several distributions, including uniform fracture density with depth. In order to understand how fracture yield varies with depth, we group yield data into 50 foot depth intervals and compare distributions in each interval using nonparametric statistical tests. These tests show that the distribution of fracture yield in different depth intervals are statistically equivalent. These results imply that there is no empirical justification for limiting well depth when drilling for water resources in fractured bedrock in coastal Maine.     

纵向和横向同时约束AVO反演

为了提高AVO(amplitude versus offset)反演结果的精度和横向连续性,本文提出了一种新的AVO反演约束方法,该方法结合贝叶斯原理和卡尔曼滤波算法实现了对反演参数纵向和横向的同时约束.文章首先结合反演参数的纵向贝叶斯先验概率约束和反演参数的横向连续性假设建立了与卡尔曼滤波算法对应的AVO反演系统的数学模型,然后将该数学模型代入卡尔曼滤波算法框架,利用卡尔曼滤波算法实现了双向约束AVO反演.二维模型测试和实际数据测试结果表明,相对于单纯的纵向贝叶斯先验概率约束,双向约束能更准确地刻画参数的横向变化,得到更准确、横向连续性更好的反演结果.     

含噪声数据反演的概率描述

根据贝叶斯理论给出了对含噪声地球物理数据处理的具体流程和方法,主要包括似然函数估计和后验概率计算.我们将数据向量的概念扩展为数据向量的集合,通过引入数据空间内的信赖度,把数据噪声转移到模型空间的概率密度函数上,即获得了反映数据本身的不确定性的似然函数.该方法由于避免了处理阶段数据空间内的人工干预,因而可以保证模型空间中的概率密度单纯反映数据噪声,具有信息保真度高、保留可行解的优点.为了得到加入先验信息的后验分布,本文提出了使用加权矩阵的概率分析法,该方法在模型空间直接引入地质信息,对噪声引起的反演多解性有很强的约束效果.整个处理流程均以大地电磁反演为例进行了展示.     

A Study of Small Magnitude Seismic Events During 1961–1989 on and near the Semipalatinsk Test Site, Kazakhstan

—?Official Russian sources in 1996 and 1997 have stated that 340 underground nuclear tests (UNTs) were conducted during 1961–1989 at the Semipalatinsk Test Site (STS) in Eastern Kazakhstan. Only 271 of these nuclear tests appear to have been described with well-determined origin time, coordinates and magnitudes in the openly available technical literature. Thus, good open documentation has been lacking for 69 UNTs at STS.¶The main goal of our study was to provide detections, estimates of origin time and location, and magnitudes, for as many of these previously undocumented events as possible. We used data from temporary and permanent seismographic stations in the former USSR at distances from 500?km to about 1500?km from STS. As a result, we have been able to assign magnitude for eight previously located UNTs whose magnitude was not previously known. For 31 UNTs, we have estimated origin time an d assigned magnitude — and for 19 of these 31 we have obtained locations based on seismic signals. Of the remaining 30 poorly documented UNTs, 15 had announced yields that were less than one ton, and 13 occurred simultaneously with another test which was detected. There are only two UNTs, for which the announced yield exceeds one ton and we have been unable to find seismic signals.¶Most of the newly detected and located events were sub-kiloton. Their magnitudes range from 2.7 up to 5.1 (a multi-kiloton event on 1965 Feb. 4 that was often obscured at teleseismic stations by signals from an earthquake swarm in the Aleutians).¶For 17 small UNTs at STS, we compare the locations (with their uncertainties) that we had earlier determined in 1994 from analysis of regional seismic waves, with ground-truth information obtained in 1998. The average error of the seismically-determined locations is only about 5?km. The ground-truth location is almost alw ays within the predicted small uncertainty of the seismically-determined location.¶Seismically-determined yield estimates are in good agreement with the announced total annual yield of nuclear tests, for each year from 1964 to 1989 at Semipalatinsk.¶We also report the origin time, location, and seismic magnitude of 29 chemical explosions and a few earthquakes on or near STS during the years 1961–1989.¶Our new documentation of STS explosions is important for evaluating the detection, location, and identification capabilities of teleseismic and regional arrays and stations; and how these capabilities have changed with time.     

Estimation of a non-stationary prior covariance from seismic data

Non-stationarity in statistical properties of the subsurface is often ignored. In a classical linear Bayesian inversion setting of seismic data, the prior distribution of physical parameters is often assumed to be stationary. Here we propose a new method of handling non-stationarity in the variance of physical parameters in seismic data. We propose to infer the model variance prior to inversion using maximum likelihood estimators in a sliding window approach. A traditional, and a localized shrinkage estimator is defined for inferring the prior model variance. The estimators are assessed in a synthetic base case with heterogeneous variance of the acoustic impedance in a zero-offset seismic cross section. Subsequently, this data is inverted for acoustic impedance using a non-stationary model set up with the inferred variances. Results indicate that prediction as well as posterior resolution is greatly improved using the non-stationary model compared with a common prior model with stationary variance. The localized shrinkage predictor is shown to be slightly more robust than the traditional estimator in terms of amplitude differences in the variance of acoustic impedance and size of local neighbourhood. Finally, we apply the methodology to a real data set from the North Sea basin. Inversion results show a more realistic posterior model than using a conventional approach with stationary variance.     

朝鲜地下核试验的地震学观测

自2006年至2017年,朝鲜民主主义人民共和国在中朝边界地区的试验场进行了6次地下核试验.本文综合报道根据东北亚地区的宽频带数字地震资料利用地震学方法对这六次地下核爆炸的研究.结果表明,朝鲜地下核试验在区域台网产生的地震记录具有典型浅源爆炸的特征.针对上述资料发展了处理核爆数据的方法并据此得出各次朝鲜核爆的地震学参数,包括事件识别、当量测定、以及震中相对定位等.对6次核爆和4次天然地震P/S类型谱振幅比的统计分析表明,2 Hz以上台网平均谱振幅比可以正确地将朝鲜核爆从天然地震中识别出来,从而有效监测在朝鲜半岛进行的当量大于0.5 kt的地下核试验.同时也发现,建立在体波-面波震级比之上的识别方法不适用于朝鲜核试验场.通过建立中朝边界地区基于Lg波的体波震级系统,计算了各次朝鲜核试验的体波震级m_b（Lg）,并由此估计了它们的地震学当量,其值介于0.5 kt至60 kt之间.由于缺少爆炸埋藏深度的数据,上述当量有可能被低估,因而有必要对深度影响做进一步研究.以第一次爆炸的位置为参考震中,利用Pn波相对走时数据和高精度相对定位方法获得了各次核爆在试验场中的精确定位.     

Bayesian probabilistic damage detection of a reinforced‐concrete bridge column

A Bayesian probabilistic approach for damage detection has been proposed for the continuous monitoring of civil structures (Sohn H, Law KH. Bayesian probabilistic approach for structure damage detection. Earthquake Engineering and Structural Dynamics 1997; 26 :1259–1281). This paper describes the application of the Bayesian approach to predict the location of plastic hinge deformation using the experimental data obtained from the vibration tests of a reinforced‐concrete bridge column. The column was statically pushed incrementally with lateral displacements until a plastic hinge is fully formed at the bottom portion of the column. Vibration tests were performed at different damage stages. The proposed damage detection method was able to locate the damaged region using a simplified analytical model and the modal parameters estimated from the vibration tests, although (1) only the first bending and first torsional modes were estimated from the experimental test data, (2) the locations where the accelerations were measured did not coincide with the degrees of freedom of the analytical model, and (3) there existed discrepancies between the undamaged test structure and the analytical model. The Bayesian framework was able to systematically update the damage probabilities when new test data became available. Better diagnosis was obtained by employing multiple data sets than just by using each test data set separately. Copyright © 2000 John Wiley & Sons, Ltd.     

Single Well Tracer Tests in Aquifer Characterization

When the purpose of aquifer testing is to yield data for modeling aqueous mass transport, pumping tests and gradient measurement can only partially satisfy characterization requirements. Effective porosity, ground water flow velocity, and the vertical distribution of hydraulic conductivity within the aquifer are left as unknowns. Single well tracer methods, when added to the testing program, can be used to estimate these parameters. A drift, and pumpback test yields porosity and velocity, and point-dilution testing yields depth-discrete hydraulic information, A single emplacement of tracer into a test well is sufficient to conduct both tests. The tracer tests are facilitated by a simple method for injecting and evenly distributing the tracer solution into a wellbore, and by new ion-selective electrode instrumentation, specifically designed for submersible service, for monitoring the concentration of tracers such as bromide.     

Updating of snow depletion curve with remote sensing data

A method for using remotely sensed snow cover information in updating a hydrological model is developed, based on Bayes' theorem. A snow cover mass balance model structure adapted to such use of satellite data is specified, using a parametric snow depletion curve in each spatial unit to describe the subunit variability in snow storage. The snow depletion curve relates the accumulated melt depth to snow‐covered area, accumulated snowmelt runoff volume, and remaining snow water equivalent. The parametric formulation enables updating of the complete snow depletion curve, including mass balance, by satellite data on snow coverage. Each spatial unit (i.e. grid cell) in the model maintains a specific depletion curve state that is updated independently. The uncertainty associated with the variables involved is formulated in terms of a joint distribution, from which the joint expectancy (mean value) represents the model state. The Bayesian updating modifies the prior (pre‐update) joint distribution into a posterior, and the posterior joint expectancy replaces the prior as the current model state. Three updating experiments are run in a 2400 km² mountainous region in Jotunheimen, central Norway (61°N, 9°E) using two Landsat 7 ETM+ images separately and together. At 1 km grid scale in this alpine terrain, three parameters are needed in the snow depletion curve. Despite the small amount of measured information compared with the dimensionality of the updated parameter vector, updating reduces uncertainty substantially for some state variables and parameters. Parameter adjustments resulting from using each image separately differ, but are positively correlated. For all variables, uncertainty reduction is larger with two images used in conjunction than with any single image. Where the observation is in strong conflict with the prior estimate, increased uncertainty may occur, indicating that prior uncertainty may have been underestimated. Copyright © 2006 John Wiley & Sons, Ltd.     

Minimum relative entropy and probabilistic inversion in groundwater hydrology

The similarity between maximum entropy (MaxEnt) and minimum relative entropy (MRE) allows recent advances in probabilistic inversion to obviate some of the shortcomings in the former method. The purpose of this paper is to review and extend the theory and practice of minimum relative entropy. In this regard, we illustrate important philosophies on inversion and the similarly and differences between maximum entropy, minimum relative entropy, classical smallest model (SVD) and Bayesian solutions for inverse problems. MaxEnt is applicable when we are determining a function that can be regarded as a probability distribution. The approach can be extended to the case of the general linear problem and is interpreted as the model which fits all the constraints and is the one model which has the greatest multiplicity or “spreadout” that can be realized in the greatest number of ways. The MRE solution to the inverse problem differs from the maximum entropy viewpoint as noted above. The relative entropy formulation provides the advantage of allowing for non-positive models, a prior bias in the estimated pdf and `hard' bounds if desired. We outline how MRE can be used as a measure of resolution in linear inversion and show that MRE provides us with a method to explore the limits of model space. The Bayesian methodology readily lends itself to the problem of updating prior probabilities based on uncertain field measurements, and whose truth follows from the theorems of total and compound probabilities. In the Bayesian approach information is complete and Bayes' theorem gives a unique posterior pdf. In comparing the results of the classical, MaxEnt, MRE and Bayesian approaches we notice that the approaches produce different results. In␣comparing MaxEnt with MRE for Jayne's die problem we see excellent comparisons between the results. We compare MaxEnt, smallest model and MRE approaches for the density distribution of an equivalent spherically-symmetric earth and for the contaminant plume-source problem. Theoretical comparisons between MRE and Bayesian solutions for the case of the linear model and Gaussian priors may show different results. The Bayesian expected-value solution approaches that of MRE and that of the smallest model as the prior distribution becomes uniform, but the Bayesian maximum aposteriori (MAP) solution may not exist for an underdetermined case with a uniform prior.     

Minimum relative entropy and probabilistic inversion in groundwater hydrology

The similarity between maximum entropy (MaxEnt) and minimum relative entropy (MRE) allows recent advances in probabilistic inversion to obviate some of the shortcomings in the former method. The purpose of this paper is to review and extend the theory and practice of minimum relative entropy. In this regard, we illustrate important philosophies on inversion and the similarly and differences between maximum entropy, minimum relative entropy, classical smallest model (SVD) and Bayesian solutions for inverse problems. MaxEnt is applicable when we are determining a function that can be regarded as a probability distribution. The approach can be extended to the case of the general linear problem and is interpreted as the model which fits all the constraints and is the one model which has the greatest multiplicity or “spreadout” that can be realized in the greatest number of ways. The MRE solution to the inverse problem differs from the maximum entropy viewpoint as noted above. The relative entropy formulation provides the advantage of allowing for non-positive models, a prior bias in the estimated pdf and `hard' bounds if desired. We outline how MRE can be used as a measure of resolution in linear inversion and show that MRE provides us with a method to explore the limits of model space. The Bayesian methodology readily lends itself to the problem of updating prior probabilities based on uncertain field measurements, and whose truth follows from the theorems of total and compound probabilities. In the Bayesian approach information is complete and Bayes' theorem gives a unique posterior pdf. In comparing the results of the classical, MaxEnt, MRE and Bayesian approaches we notice that the approaches produce different results. In␣comparing MaxEnt with MRE for Jayne's die problem we see excellent comparisons between the results. We compare MaxEnt, smallest model and MRE approaches for the density distribution of an equivalent spherically-symmetric earth and for the contaminant plume-source problem. Theoretical comparisons between MRE and Bayesian solutions for the case of the linear model and Gaussian priors may show different results. The Bayesian expected-value solution approaches that of MRE and that of the smallest model as the prior distribution becomes uniform, but the Bayesian maximum aposteriori (MAP) solution may not exist for an underdetermined case with a uniform prior.     

On the performance of a new bivariate pseudo Pareto distribution with application to drought data

A new bivariate pseudo Pareto distribution is proposed, and its distributional characteristics are investigated. The parameters of this distribution are estimated by the moment-, the maximum likelihood- and the Bayesian method. Point estimators of the parameters are presented for different sample sizes. Asymptotic confidence intervals are constructed and the parameter modeling the dependency between two variables is checked. The performance of the different estimation methods is investigated by using the bootstrap method. A Markov Chain Monte Carlo simulation is conducted to estimate the Bayesian posterior distribution for different sample sizes. For illustrative purposes, a real set of drought data is investigated.     

基于模型降阶的贝叶斯方法在三维重力反演中的实践

三维重力反演是地质工作者了解地球深部构造,认知地下结构的重要手段.按照反演单元划分,三维重力反演有离散多面体(Discrete)反演和网格节点(Voxels)反演两种方式.离散多面体反演由于易于吸收先验地质信息得到的理论场能够很好地拟合观测场,因此,在实际重力反演中更受欢迎.目前离散多面体重力反演中初始模型的建立方法繁杂不一,实际应用受到很大的限制.本文本着充分挖掘利用先验信息和重力观测数据得到丰富可靠的反演结果这一原则,以离散多面体反演技术为基础,改进建模过程.在初始模型的建立中,吸收贝叶斯算法优势,采用隐马尔科夫链改善朴素贝叶斯方法的分类效果,通过最大似然函数算法求解,再采取模型降阶技术,固定所建模型中几何体的形态或密度,达到在几何体形态(x,y,z)、密度(σ)和重力值(g)五个参数中降低维数目的,从而减小高维不确定性和正演的计算量,由此反演计算的地质体密度和分布范围相对更准确,更利于重现重力模型结构.通过单位球体和任意形态几何体模拟实验,以及安徽省泥河矿区三维重力反演实践,得到非常接近实际的密度或重力值,大幅提高了三维重力反演的精度和效率,说明该方法是有效、实用的.     

The segmentation procedure as a tool for discrete modeling of hydrometeorological regimes

A possible cause of nonstationarity in time series is the existence of some abrupt modification of their statistical parameters, and especially of a sudden change of the mean. Series with such a change exhibit a strong temporal persistence, with high values of the Hurst coefficient, but with poor possibilities to fit any autoregressive model. Some classical tests (Pettitt, 1979; Buishand, 1982) enable to find a possible change point of the mean and then to split the original nonstationary series into two stationary sub-series. The Bayesian procedure defined by Lee and Heghinian (1977) supposes the “a-priori” existence of a change of the mean somewhere in the series and yields at each time step an “a-posteriori” probability of mean change. But these classical tests and procedures consider only one change point in the original series. To go further and to explore the theoretical multiple singularity models defined by Klemeš (1974) and Potter (1976), a segmentation procedure of time series has been designed. This procedure yields an optimal partition (from a least squares point of view) of the original series into as many subseries as possible, all differences between two contiguous means remaining simultaneously significant. This last requirement is ensured using the Scheffe test of contrasts. The main problem has been to master the combinatory explosion while exploring the tree of all possible segmentations of a series. Some applications of the procedure to hydrometeorological time series are reviewed and some possible improvements are presented.     

A Bayesian analysis of the Gumbel distribution: an application to extreme rainfall data

With the objective of modelling annual rainfall maximum intensities in different geographical zones of Chile, we have created a Bayesian inference method for the generalized extreme value type I distribution (Gumbel distribution). We considered an uninformative prior distribution for the location parameter, μ, and three different prior distributions for the scale parameter, σ. Under these conditions we obtained the posterior distribution of (μ, σ) and associated summary statistics such as modes, expected values, quantiles and credibility intervals. In order to predict and estimate return periods, we obtained the posterior distribution of future observations, its expected value, quantiles and credibility intervals. To obtain several of these posterior summary measures it was necessary to utilize both numerical and Laplace approximations. Furthermore we estimate return period curves and intensity–duration–frequency curves.     

Permeability estimation conditioned to geophysical downhole log data in sandstones of the northern Galilee Basin,Queensland: Methods and application

This study uses borehole geophysical log data of sonic velocity and electrical resistivity to estimate permeability in sandstones in the northern Galilee Basin, Queensland. The prior estimates of permeability are calculated according to the deterministic log–log linear empirical correlations between electrical resistivity and measured permeability. Both negative and positive relationships are influenced by the clay content. The prior estimates of permeability are updated in a Bayesian framework for three boreholes using both the cokriging (CK) method and a normal linear regression (NLR) approach to infer the likelihood function. The results show that the mean permeability estimated from the CK-based Bayesian method is in better agreement with the measured permeability when a fairly apparent linear relationship exists between the logarithm of permeability and sonic velocity. In contrast, the NLR-based Bayesian approach gives better estimates of permeability for boreholes where no linear relationship exists between logarithm permeability and sonic velocity.