非线性抛物型方程反问题的一种新算法

利用反问题新算法—时间域正演反演法研究非线性抛物型方程的逆时反问题。该方法处理反问题的主要思路是先求解相对应的正问题,获得解在特定时间网格处的近似值;然后构造一个合适的全纯映射,在象空间中获得解在时间网格对应点处的近似值;最后利用解析函数的唯一延拓性质实现反问题的逆时间反演。数值模拟例子说明了方法的有效性。     

非线性水驱曲线

本文以Ａ油田的开发动态数据为基础，依据冯文光教授提出的非线性水驱曲线模型，首次将混沌动力学非线性反演理论引入水驱曲线研究之中，用非线性理论求取Ａ油田非线性水驱曲线参数，建立非线性水驱曲线方程     

一类抛物型方程反问题的数值解法

讨论了一类二阶抛物型方程反问题的数值解法。应用拟解法的思想,把原问题分解为一系列适定的正问题和一个不适定的线性代数方程组。对于相应的正问题,证明了解连续依赖于初始分布,由此得到了在时刻的稳定性估计。使用古典欧拉差分格式求解正问题和用截断奇异值分解法求解病态方程组。数值结果显示数值解与理论解吻合很好。     

用非线性遗传反演方法进行自动静校正

静校正处理是消除近地层影响的一个重要地震资料数字处理方法,在近地表层纵,横向变化复杂,静校正量变化较大的地区,常规静校正方法和线性反演方法均不能解决问题,遗传算法是近年发展起来的一种模拟生物生化过程的较先进的非线性反演方法,对用遗传算法进行静校正的若干问题进行了讨论,说明它是可以解决表层情况复杂地区静校正问题的一个有效方法。     

Identification of the diffusion coefficient for a semi-linear hyperbolic-parabolic problem with discontinuous nonlinear terms

Numerical computations concerning geochemical processes in porous media require a knowledge of the values of the macroscopic parameters. In the context of the interpretation of leaching tests one such parameter is the apparent macroscopic diffusivity. In this paper, a mathematical model for dissolution in the presence of diffusion is considered. It is shown that the constant diffusion coefficient can be identifiable when the time integral of the flux is known. Moreover, a practical algorithm for computing the diffusion coefficient is proposed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Mean Traveltime Curves Analysis: A Method to Improve Understanding of Data Behaviour in 2-D Transmission Tomography at the Pre-Inversion Stage

Transmission tomography methods show a great sensibility to data variability, which eventually includes data errors, often present in field experiments. Local optimization methods, traditionally used to solve this inverse problem, are very sensitive to these difficulties, failing to converge properly in the presence of spurious data. Regularization methods partially cope with these weaknesses, damping the instabilities.A complementary approach, adopted here, is to perform a structured analysis of data variability before the inversion, oriented to discriminate the contribution of errors from that of true geological heterogeneities. The key concept of mean traveltime curves ( and ) is introduced and described. Their analytical equations are deduced for isotropic homogeneous media and any recording geometry. Empirical mean traveltime curves can be inferred based solely on traveltime data, using the corresponding discrete estimators. The methodology proposed here proceeds through a user-defined subdivision of the domain of interest into isotropic homogeneous areas. Least squares velocity estimations and associated data misfits are used to scrutinize the behaviour of the implied source-receiver sets and of the ray-swept part of the geologic medium. Data are considered suspicious if zonal estimated velocities are non-consistent with a priori information. Also, independent fitting of both empirical curves helps to classify the genesis of the residuals: some situations are illustrated.Finally, we show the application of this technique to a data set from the Grimsel test site in Switzerland. Using this methodology, we detect some anomalous gathers, which may be responsible for the large range of velocities found in the initial imaging with this data set. Also, we give some indications of the possible sources of these anomalies. This approach offers a quick data variability analysis in the pre-processing stage, which, even if no data editing algorithms are finally used, always improves the understanding of the data structure.     

A GCV based method for nonlinear ill-posed problems

This paper discusses the inversion of nonlinear ill-posed problems. Such problems are solved through regularization and iteration and a major computational problem arises because the regularization parameter is not known a priori. In this paper we show that the regularization should be made up of two parts. A global regularization parameter is required to deal with the measurement noise, and a local regularization is needed to deal with the nonlinearity. We suggest the generalized cross validation (GCV) as a method to estimate the global regularization parameter and the damped Gauss-Newton to impose local regularization. Our algorithm is tested on the magnetotelluric problem. In the second part of this paper we develop a methodology to implement our algorithm on large-scale problems. We show that hybrid regularization methods can successfully estimate the global regularization parameter. Our algorithm is tested on a large gravimetric problem. This revised version was published online in July 2006 with corrections to the Cover Date.     

环境水力学反问题研究进展

反问题广泛存在于环境水力学的各个研究领域,通过环境水力学反问题研究可以实现对水流及伴随水流系统的污染物质迁移、输运过程的识别和控制,促进水资源的可持续利用。近年来,环境水力学反问题研究内容逐渐丰富,其重要性日渐突出。基于反问题理念阐述了环境水力学反问题的内涵,从不同的角度对环境水力学反问题进行了分类,强调了环境水力学反问题研究的重要意义。从参数反问题、源项反问题、边界条件反问题、初始条件反问题和形状反问题5个方面分析评述了环境水力学反问题的研究现状和研究成果。在此基础上,讨论了研究现状存在的问题并对该领域未来研究方向进行了展望。     

感潮河道区间入流反分析

区间入流是影响水动力模型精度的重要因素,实际的区间径流情况复杂难以量化。从反问题的角度出发,由基本方程导出区间入流校正量的解析表达式,应用数值离散方法,得到节点水位与区间入流的响应函数,根据实测的潮位资料建立区间入流的迭代求解方法。数值实验验证了方法的可行性,反问题的计算值与真值非常接近,模拟的确定性系数达到0.996。该方法应用于长江下游大通至镇江河段的水动力模型实例计算,得出了概化的区间入流过程,提高了模拟精度,验证了方法的有效性。     

Unbiased identification of nonlinear sorption characteristics by soil column breakthrough experiments

Accurate identification of interactions of reactive solutes with porous media constituents is necessary for reliable risk assessment studies and the development of efficient sanitation strategies. Standard parameter estimation procedures bear a number of unsolved problems with respect to uniqueness and identifiability. This paper presents a new approach for the identification of nonlinear interaction parameters of column outflow experiments. The procedure requires no a priori assumptions on the shape of the underlying interaction process functions. Employing experimental data sets on cadmium and anthracene breakthrough as case studies, possible applications of the new approach will be shown, and its features will be discussed. Error analysis based on singular value decomposition of the sensitivity matrix quantifies the identification error. Identification procedures without a priori shape information are superior to fixed parametrizations in diagnostic investigations, especially in cases without reliable a priori knowledge on the sorptive interactions.     

A level-set corrector to an adaptive multiscale permeability prediction

We consider the inverse problem of permeability estimation for two-phase porous-media flow. The novel approach is based on regularization by zonation, where the geometry and size of the regions are chosen adaptively during the optimization procedure. To achieve this, we have utilized level-set functions to represent the permeability. The available data are sparsely distributed in space; hence, it is reasonable to confine the estimation to coarse-scale structures. The level-set approach is able to alter the boundaries between regions of different permeability without strict restrictions on their shape; however, when the data are sparse, a reasonable initial guess for the permeability is required. For this task, we use adaptive multiscale permeability estimation, which has the potential of identifying main permeability variations. These are described by a piecewise constant function, where the constant values are attained on rectangular zones. In the current work, we develop a level-set corrector strategy, assuming adaptive multiscale permeability estimation as a predictor.     

Numerical Reliability for Mixed Methods Applied to Flow Problems in Porous Media

This paper is devoted to the numerical reliability and time requirements of the Mixed Finite Element (MFE) and Mixed-Hybrid Finite Element (MHFE) methods. The behavior of these methods is investigated under the influence of two factors: the mesh discretization and the medium heterogeneity. We show that, unlike the MFE, the MHFE suffers with the presence of badly shaped discretized elements. Thereat, a numerical reliability analyzing software (Aquarels) is used to detect the instability of a matrix-inversion code generated automatically by a symbolic manipulator. We also show that the spectral condition number of the algebraic systems furnished by both methods in heterogeneous media grows up linearly according to the smoothness of the hydraulic conductivity. Furthermore, it is found that the MHFE could accumulate numerical errors if large jumps in the tensor of conductivity take place. Finally, we compare running-times for both algorithms by giving various numerical experiments.     

Parameter identification for a suction‐dependent plasticity model

In this paper, the deterministic parameter identification procedure proposed in a companion paper is applied to suction‐dependent elasto‐plasticity problems. A mathematical model for such type of problems is firstly presented, then it is applied to the parameter identification using laboratory data. The identification procedure is applied in a second example to exploitation of a gas reservoir. The effects of the extraction of underground fluids appear during and after quite long periods of time and strongly condition the decision to profit or not of the natural resources. Identification procedures can be very useful tools for reliable long‐term predictions. Copyright © 2001 John Wiley & Sons, Ltd.     

抛物型方程和Poisson方程参数控制反问题的求解及其应用

提出用脉冲谱技术(PST)求解抛物型方程参数控制反问题和边界元-优化法求解Poisson方程参数控制反问题;推导了算式,给出了计算程式,并分别用这两种方法反演了非均质矩形土坝的渗透系数和新安江大坝坝基帷幕区补强前后的渗透系数.计算结果表明,用脉冲谱法和边界元-优化法求解参数控制反问题是行之有效的,应用于坝工渗流计算,可基本解决坝体和地基渗透系数的反演问题,其优点是,所需附加信息量少,无需大面积的钻孔取样工作,可节省大量投资.     

重磁勘探正反演理论方法研究的新进展

首先概略地介绍了国内外具有较高理论价值的重磁勘探正反演理论前沿性研究成果 ,并给予了适当的对比评述。然后 ,延续复杂条件下局部重磁场源全方位成像正反演理论体系 ,较详细地阐述了作者最近独立完成的关于任意单值边界和磁化强度连续变化的二维、三维局部磁性场源正反演这一前沿性课题的研究成果 ,并简要指出了这些研究成果的理论价值和应用前景。     

低渗透油藏注采井间压力分布与流态响应研究

利用非线性数学模型,能够全程描述低渗透油藏的非线性流动规律,从理论上给出了低渗透油藏中流态分布的计算方法,分析了注采压差、注采井距和地层渗透率对流态分布的影响,指出了流体在低渗透油藏中以特低速度流动时压力分布的特点,纠正了前人在这个问题上的认识失误。实际岩芯的渗流试验检验了理论的正确性。