Modelling Positional Uncertainty of Line Features by Accounting for Stochastic Deviations from Straight Line Segments

The assessment of positional uncertainty in line and area features is often based on uncertainty in the coordinates of their elementary vertices which are assumed to be connected by straight lines. Such an approach disregards uncertainty caused by sampling and approximation of a curvilinear feature by a sequence of straight line segments. In this article, a method is proposed that also allows for the latter type of uncertainty by modelling random rectangular deviations from the conventional straight line segments. Using the model on a dense network of sub‐vertices, the contribution of uncertainty due to approximation is emphasised; the sampling effect can be assessed by applying it on a small set of randomly inserted sub‐vertices. A case study demonstrates a feasible way of parameterisation based on assumptions of joint normal distributions for positional errors of the vertices and the rectangular deviations and a uniform distribution of missed sub‐vertices along line segments. Depending on the magnitudes of the different sources of uncertainty, not accounting for potential deviations from straight line segments may drastically underestimate the positional uncertainty of line features.     

肋柱式锚杆支挡结构的徐变次内力分析

采用老化徐变理论和等效弹性模量法,对肋柱式锚杆支挡结构的徐变影响提出了具体计算方法,并通过实例计算了支挡结构的徐变次内力。计算结果表明,在逆作法条件下,随着开挖深度的加大,岩土侧向压力也增大,使后期施工的混凝土构件产生的徐变次内力也随之增大;考虑徐变后使结构设计更加安全可靠,尤其坡脚处后期浇筑的混凝土构件,更要关注徐变的影响。     

鲁23井“动水位”观测的分析

本文介绍了鲁23井“动水位”观测情况。提出了一个分析有泄流的“动水位”的新方法,即把流量换算成水位,以等效静水位来表示“动水位”与流量。由于把“动水位”与流量用一个量来计算,从而为“动水位”观测定量的、统一的分析研究提供了新的方法。这对提高“动水位”井的监测预报地震能力起一定的作用。 本文还以鲁23井“动水位”观测资料为例,利用新方法进行处理的观测分析结果与理论研究结果是一致的。     

Reservoir description using dynamic parameterisation selection with a combined stochastic and gradient search

There is a correspondence between flow in a reservoir and large scale permeability trends. This correspondence can be derived by constraining reservoir models using observed production data. One of the challenges in deriving the permeability distribution of a field using production data involves determination of the scale of resolution of the permeability. The Adaptive Multiscale Estimation (AME) seeks to overcome the problems related to choosing the resolution of the permeability field by a dynamic parameterisation selection. The standard AME uses a gradient algorithm in solving several optimisation problems with increasing permeability resolution. This paper presents a hybrid algorithm which combines a gradient search and a stochastic algorithm to improve the robustness of the dynamic parameterisation selection. At low dimension, we use the stochastic algorithm to generate several optimised models. We use information from all these produced models to find new optimal refinements, and start out new optimisations with several unequally suggested parameterisations. At higher dimensions we change to a gradient-type optimiser, where the initial solution is chosen from the ensemble of models suggested by the stochastic algorithm. The selection is based on a predefined criterion. We demonstrate the robustness of the hybrid algorithm on sample synthetic cases, which most of them were considered insolvable using the standard AME algorithm.     

Optimization of nonconventional wells under uncertainty using statistical proxies

The determination of the optimal type and placement of a nonconventional well in a heterogeneous reservoir represents a challenging optimization problem. This determination is significantly more complicated if uncertainty in the reservoir geology is included in the optimization. In this study, a genetic algorithm is applied to optimize the deployment of nonconventional wells. Geological uncertainty is accounted for by optimizing over multiple reservoir models (realizations) subject to a prescribed risk attitude. To reduce the excessive computational requirements of the base method, a new statistical proxy (which provides fast estimates of the objective function) based on cluster analysis is introduced into the optimization process. This proxy provides an estimate of the cumulative distribution function (CDF) of the scenario performance, which enables the quantification of proxy uncertainty. Knowledge of the proxy-based performance estimate in conjunction with the proxy CDF enables the systematic selection of the most appropriate scenarios for full simulation. Application of the overall method for the optimization of monobore and dual-lateral well placement demonstrates the performance of the hybrid optimization procedure. Specifically, it is shown that by simulating only 10% or 20% of the scenarios (as determined by application of the proxy), optimization results very close to those achieved by simulating all cases are obtained.     

Evaluation of the Reduction in Uncertainty Obtained by Conditioning a 3D Stochastic Channel to Multiwell Pressure Data

A stochastic channel embedded in a background facies is conditioned to data observed at wells. The background facies is a fixed rectangular box. The model parameters consist of geometric parameters that describe the shape, size, and location of the channel, and permeability and porosity in the channel and nonchannel facies. We extend methodology previously developed to condition a stochastic channel to well-test pressure data, and well observations of the channel thickness and the depth of the top of the channel. The main objective of this work is to characterize the reduction in uncertainty in channel model parameters and predicted reservoir performance that can be achieved by conditioning to well-test pressure data at one or more wells. Multiple conditional realizations of the geometric parameters and rock properties are generated to evaluate the uncertainty in model parameters. The ensemble of predictions of reservoir performance generated from the suite of realizations provides a Monte Carlo estimate of the uncertainty in future performance predictions. In addition, we provide some insight on how prior variances, data measurement errors, and sensitivity coefficients interact to determine the reduction in model parameters obtained by conditioning to pressure data and examine the value of active and observation well data in resolving model parameters.     

Propriétés fractales de la fragmentation et processus stochastiques de fracturation : approche géométrique 3D à l'aide du modèle ObsifracFractal properties of fragmentation and stochastic fracturing processes: geometrical 3D approach by OBSIFRAC model

A numerical rock fragmentation model was elaborated, producing a 3D puzzle of convex polyhedra, geometrically described in a database. In the first scenario, a constant proportion of blocks are fragmented at each step of the process and leads to fractal distribution. In the second scenario, division affects one random block at each stage of the process, and produces a Weibull volume distribution law. Imposing a minimal distance between the fractures, the third scenario reveals a power law. The inhibition of new fractures in the neighbourhood of existing discontinuities could be responsible for fractal properties in rock mass fragmentation. To cite this article: L. Empereur-Mot, T. Villemin, C. R. Geoscience 334 (2002) 127–133.     

Spatial variation of seismic motion induced by propagation of body waves

Spatial variation of earthquake ground motion is an important phenomenon that cannot be ignored in the design and safety of strategic structures. Several models have been developed to describe this variation using statistical, mathematical or physical approaches. The latter approach is not specific to an event. A recent contribution, which uses such an approach and called complete stochastic deamplification approach (CSDA), was developed [1]. The aim of this paper is to analyze the spatial variation of earthquake motion induced by the propagation of body waves using the CSDA. Coherency functions are evaluated for the cases of SH–SV–P waves propagating through stratified soil. Results obtained show that the variation of the coherency function is not the same for vertical and horizontal components and that the motion is more coherent at depth than at the free surface. In fact, we found that the rate of decrease with frequency and distance is not the same if P–SV waves propagate through stratified soil.     

Optimal placement of dampers and actuators based on stochastic approach

A general method is developed for optimal application of dampers and actuators by installing them at optimal location on seismic-resistant structures. The study includes development of a statistical criterion, formulation of a general optimization problem and establishment of a solution procedure. Numerical analysis of the seismic response in time-history of controlled structures is used to verify the proposed method for optimal device application and to demonstrate the effectiveness of seismic response control with optimal device location. This study shows that the proposed method for the optimal device application is simple and general, and that the optimally applied dampers and actuators are very efficient for seismic response reduction.     

河流水质风险评价的灰色-随机风险率方法

提出了量化影响河流水质的随机不确定性与灰色不确定性的水质超标灰色－随机风险率概念，建立了水质超标灰色－随机风险率评价模型。在水质单项参数评价模型中，将河流污染物浓度变量的分布处理成灰色概率分布，将污染物浓度超过水质类别标准值的风险率处理成灰色概率，即水质超标灰色－随机风险率。在水质综合评价模型中，河流水环境系统被考虑为担任某一使用可能的可靠性系统，而任意一种水质参数超标意味着河流水体使用功能不能得到应有的保证，也即表明水体综合评价超标，最后借鉴系统可靠性分析的理论和方法计算水质综合超标率。该方法应用于黄河花园口断面重金属污染风险评价。