Statistical analysis of extreme events in a non-stationary context via a Bayesian framework: case study with peak-over-threshold data

Statistical analysis of extremes currently assumes that data arise from a stationary process, although such an hypothesis is not easily assessable and should therefore be considered as an uncertainty. The aim of this paper is to describe a Bayesian framework for this purpose, considering several probabilistic models (stationary, step-change and linear trend models) and four extreme values distributions (exponential, generalized Pareto, Gumbel and GEV). Prior distributions are specified by using regional prior knowledge about quantiles. Posterior distributions are used to estimate parameters, quantify the probability of models and derive a realistic frequency analysis, which takes into account estimation, distribution and stationarity uncertainties. MCMC methods are needed for this purpose, and are described in the article. Finally, an application to a POT discharge series is presented, with an analysis of both occurrence process and peak distribution.     

青藏高原大气热源及其估算的不确定性因素

基于1980—2016年的4套再分析资料(NCEP/DOE资料、MERRA2资料、ERA-Interim资料和JRA-55资料),采用计算大气热源的正算法和倒算法,研究青藏高原大气热源及其计算的不确定性因素,得到以下结论：(1)计算方法和资料均会导致结果的不确定性,正算法只能得到整层热源,而倒算法可得到热源垂直结构,但其结果准确性依赖于再分析资料精度;(2)对比4套再分析资料计算结果发现,正算法结果较倒算法结果普遍偏高,采用ERA-Interim资料,基于两种方法计算的大气热源年代际变化趋势一致。基于4套资料,采用倒算法计算的热源在1980—2016年呈现明显的年代际变化特征;(3)夏半年(3—8月)强热源区主要分布在青藏高原中东部,热源自下而上呈源-汇-源分布;(4)基于正算法和ERA-Interim资料估算的夏半年的降水潜热在喜马拉雅山南坡显著偏小,高原西部地区和南部冈底斯山一带则明显偏大。     

Lisbon earthquake scenarios: A review on uncertainties, from earthquake source to vulnerability modelling

This paper briefly reviews the main topics developed in the last 15 years dealing with advances on predicting earthquake scenarios for the Lisbon Region. These developments, which have been reverted into seismic scenario simulators, include the entire earthquake process, as different modules, from the seismic source to vulnerability modelling. Recent achievements in several modules are presented, describing the level of uncertainties associated with the source, attenuation, soil effect, typology classification and inventory of the building stock, and vulnerability assessment of each typology. One simplified model is shown, and results of other models are compared for two selected occurrence scenarios. The paper ends with a brief appointment on the selection of scenario types, a key point in the application of simulators, and highlights the issues where more research and development should be made to optimize the gains in knowledge and to reduce overall uncertainties.     

Look-ahead vertical seismic profiling inversion approach for density and compressional wave velocity in Bayesian framework

To reduce drilling uncertainties, zero-offset vertical seismic profiles can be inverted to quantify acoustic properties ahead of the bit. In this work, we propose an approach to invert vertical seismic profile corridor stacks in Bayesian framework for look-ahead prediction. The implemented approach helps to successfully predict density and compressional wave velocity using prior knowledge from drilled interval. Hence, this information can be used to monitor reservoir depth as well as quantifying high-pressure zones, which enables taking the correct decision during drilling. The inversion algorithm uses Gauss–Newton as an optimization tool, which requires the calculation of the sensitivity matrix of trace samples with respect to model parameters. Gauss–Newton has quadratic rate of convergence, which can speed up the inversion process. Moreover, geo-statistical analysis has been used to efficiently utilize prior information supplied to the inversion process. The algorithm has been tested on synthetic and field cases. For the field case, a zero-offset vertical seismic profile data taken from an offshore well were used as input to the inversion algorithm. Well logs acquired after drilling the prediction section was used to validate the inversion results. The results from the synthetic case applications were encouraging to accurately predict compressional wave velocity and density from just a constant prior model. The field case application shows the strength of our proposed approach in inverting vertical seismic profile data to obtain density and compressional wave velocity ahead of a bit with reasonable accuracy. Unlike the commonly used vertical seismic profile inversion approach for acoustic impedance using simple error to represent the prior covariance matrix, this work shows the importance of inverting for both density and compressional wave velocity using geo-statistical knowledge of density and compressional wave velocity from the drilled section to quantify the prior covariance matrix required during Bayesian inversion.     

Adapting to climate change: a comparison of two strategies for dike heightening

In the Netherlands the current dike design policy is to design flood defence structures corresponding to an agreed flooding probability with an extra safety board of at least 0.5 m. For river dikes a return period of 1,250 years is used to determine the design water levels. A problem with this strategy is that it builds on assumptions with regard to the intrinsically uncertain probability distributions for the peak discharges. The uncertainty is considerable and due to (1) the measuring records that are limited to about 100 years and (2) the changing natural variability as a result of climate change. Although the probability distributions are regularly updated based on new discharge data the nature of the statistics is such that a change in the natural variability of the peak discharge affects the probability distribution only long after the actual change has happened. Here we compare the performance of the probabilistic dike design strategy with the older strategy, referred to as the ‘self-learning dike’. The basic principle of the latter strategy is that the dike height is kept at a level equal to the highest recorded water level plus a certain safety margin. The two flood prevention strategies are compared on the basis of the flooding safety over a 100-year period. The Rhine gauge station at Lobith serves as case study. The results indicate that the self-learning dike performs better than the probabilistic design in terms of safety and costs, both under current and climate change conditions.     

Conditioned Simulations of Random Velocity Fields

In petroleum exploration and production, it is essential to have good estimations of the uncertainties on the reserves. Uncertainties on the velocity model used during the data processing are of major importance in this estimation. The generation of several velocity fields gives access to a quantified estimation of the uncertainties due to the velocity model inversion. The use of statistical methods helps in generating several important, equiprobable velocity fields, matching all the available velocity information. This paper presents an efficient simulation algorithm to generate instantaneous velocity fields, constrained by the distribution of values measured at the wells, and calibrated by the stacking velocities, taken as root-mean-square velocities. The simulations also match the covariance model given for the instantaneous velocity fields. The method is developed in a simple one-layer case with constant velocity, and then extended to more realistic situations. Finally, a real data application is shown, using data provided by ENI–Agip Division, and the efficiency of the proposed simulation method is discussed.     

The first post‐injection seismic monitor survey at the Ketzin pilot CO2 storage site: results from time‐lapse analysis

The injection of CO₂ at the Ketzin pilot CO₂ storage site started in June 2008 and ended in August 2013. During the 62 months of injection, a total amount of about 67 kt of CO₂ was injected into a saline aquifer. A third repeat three‐dimensional seismic survey, serving as the first post‐injection survey, was acquired in 2015, aiming to investigate the recent movement of the injected CO₂. Consistent with the previous two time‐lapse surveys, a predominantly west–northwest migration of the gaseous CO₂ plume in the up‐dip direction within the reservoir is inferred in this first post‐injection survey. No systematic anomalies are detected through the reservoir overburden. The extent of the CO₂ plume west of the injection site is almost identical to that found in the 2012 second repeat survey (after injection of 61 kt); however, there is a significant decrease in its size east of the injection site. Assessment of the CO₂ plume distribution suggests that the decrease in the size of the anomaly may be due to multiple factors, such as limited vertical resolution, CO₂ dissolution, and CO₂ migration into thin layers, in addition to the effects of ambient noise. Four‐dimensional seismic modelling based on dynamic flow simulations indicates that a dynamic balance between the newly injected CO₂ after the second repeat survey and the CO₂ migrating into thin layers and being dissolved was reached by the time of the first post‐injection survey. In view of the significant uncertainties in CO₂ mass estimation, both patchy and non‐patchy saturation models for the Ketzin site were taken into consideration.