Divergence of solutions to perturbation-based advection-dispersion moment equations

Moment equation methods are popular and powerful tools for modeling transport processes in randomly heterogeneous porous media, but the application of these methods to advection-dispersion equations often leads to erroneous oscillations. Perturbative methods, required to close systems of moment equations, become inaccurate for large perturbations; however, little quantitative theory exists for determining when this occurs for advection-dispersion equations. We consider three different methods (asymptotic approximation, Eulerian truncation, and iterative solution) for closing and solving advection-dispersion moment equations describing transport in stratified porous media with random permeability. We obtain approximate analytical expressions for time above which the asymptotic approximation to the mean diverges, in particular quantifying the impact that dispersion has on delaying—but not eliminating—divergence. We demonstrate that Eulerian truncation and iterative solution methods do not eliminate divergent behavior either. Our divergence criteria provide a priori estimates that signal a warning to the practitioner of stochastic advection-dispersion equations to carefully consider whether to apply perturbative approaches.     

基于尺度变换随机共振的瞬变电磁弱信号检测

晚期瞬变电磁信号是大参数、多频率、且各频率分量未知的电磁信号,特别在晚期还是强噪声背景下的微弱信号.随机共振系统可以在极限信噪比的情况下提取微弱信号,但仅适用于小参数、单一频率或频率已知的高频信号的情况,为此,本文提出一种基于尺度变换的随机共振算法用于检测晚期瞬变电磁信号,该方法充分利用了随机共振检测弱信号的优势,通过...     

On the criteria for the initiation of motion in tidal inlets,deterministic and stochastic approaches

Details are given herein of the refinement and application of a three-dimensional layer integrated numerical model to predict morphological changes in tidal basins. The solution of governing differential equations, which consist of the conservation of mass and momentum for the hydrodynamics, the transport equation for the suspended sediment fluxes and the sediment mass conservation equation for the bed level changes are carried out by the use of Alternating Direction Implicit (ADI) Finite Difference Method (FDM). The model includes different criteria for the initiation of motion namely Shields (1936, Application of Similarity Principles and Turbulence Research to Bed load Movement, Hydrodynamics Laboratory, California Institute of Technology, Pub. No. 167), Kolahdoozan (1999, Numerical Modelling of Geomorphological Processes in Estuarine Waters, PhD Thesis, Department of Civil and Environmental Engineering, University of Bradford, Bradford, UK, 288) and Zanke (2003, On the Influence of Turbulence on the Initiation of Sediment Motion, International Journal of Sediment Research, 18(1), 17–31), to compare different aspects of flow conditions. As the flow is highly turbulent with the random nature of its components, many researchers have tried to express sediment transport processes by using stochastic approaches. In the current study both deterministic and stochastic methods are included in the numerical model to evaluate their accuracy and efficiency. To validate the numerical model results, laboratory measurements are used, with these being obtained from an earlier experimental program undertaken by the authors. Results of a short term bed level changes in a laboratory model harbor are included for the model verification purposes. Comparisons are undertaken using different criteria for the initiation of motion, with the results highlighting that the unsteadiness in the flow parameters included in the numerical model has a major effect on the bed level changes inside the harbor, in compare with the turbulence structure of the flow. The model is then applied to a real case study of the Humber Estuary, located in the UK, with comparisons being undertaken for different criteria for the initiation of motion, using both deterministic and stochastic approaches for the long term bed level predictions.     

Kappa (k) derived from accelerograms recorded in the 2008 Wenchuan mainshock,Sichuan, China

High-frequency spectral decay factor, kappa (k), in the accelerograms of the Wenchuan mainshock was measured using strong motion data from 52 stations within 311 km of the epicenter. The derived k range from 0.0034 s to 0.0468 s. The correlation of k versus fault distance was given, which is k = 0.01288 + 5.9068 × 10^–5 R for the N-S component, k = 0.01881 + 1.4219 × 10^–5 R for the E-W component, and k = 0.00855 + 5.6086 × 10^–5 R for the U-D component. The analysis on the spatial variation of k demonstrates that k relates to source effect and propagation effect besides local site effect. Ground motions for the 52 stations were simulated using derived k and compared to actual recordings in terms of waveforms, amplitude spectra and response spectra. The results show agreement at shorter periods (<1 s), but a slight overestimation at longer periods (1–7 s).     

Restoring capability of bilinear hysteretic seismic isolation systems

The restoring capability (or re‐centering capability) is identified by the current design codes as a fundamental feature of seismic isolation systems. In this paper, the restoring capability of bilinear hysteretic or frictional seismic isolation systems is investigated in some detail. Certain energy considerations are examined first in order to provide insight into and reveal governing parameters on individual aspects of the problem. The restoring capability is then investigated through an extensive parametric study of smooth bilinear single‐degree‐of‐freedom hysteretic systems, with parameters covering a range of typical seismic isolation systems, subjected to a large group of recorded earthquakes. The results of the parametric analyses are processed statistically and regression analysis relations are derived that show the dependence of the residual displacement after the earthquake and the cumulative build up of displacements after a series of successive earthquakes on the governing parameters. Based on the analysis results, the features of the bilinear system that ensure sufficient restoring capability are identified. Copyright © 2007 John Wiley & Sons, Ltd.     

Calibration of the specific barrier model to Iranian plateau earthquakes and development of physically based attenuation relationships for Iran

Earthquake ground-motion relationships for soil and rock sites in Iran have been developed based on the specific barrier model (SBM) used within the context of the stochastic modeling and calibrated against up-to-date Iranian strong-motion data. A total of 171 strong-motion accelerograms recorded at distances of up to 200 km from 24 earthquakes with moment magnitudes ranging from Mw 5.2 to 7.4 are used to determine the region-specific source parameters of this model. Regression analysis was conducted using the “random effects” methodology that considers both earthquake-to-earthquake (inter-event) variability and within-earthquake (intra-event) variability to effectively handle the problem of weighting observations from different earthquakes. The minimization of the error function in each iteration of the “random effects” procedure was performed using the genetic algorithm method. The residuals are examined against available Iranian strong-motion data to confirm that the model predictions are unbiased and that there are no significant residual trends with distance and magnitude. No evidence of self-similarity breakdown is observed between the source radius and its seismic moment. To verify the robustness of the results, tests were performed to confirm that the results are unchanged if the number of observations is changed by removing different randomly selected datasets from the original database. Stochastic simulations, using the derived SBM, are then performed to predict peak ground-motion and response spectra parameters for a wide range of magnitudes and distances. The stochastic SBM predictions agree well with the new empirical regression equations proposed for Iran, Europe and Middle East in the magnitude–distance ranges well represented by the data. It has been shown that the SBM of this study provides unbiased ground-motion estimates over the entire frequency range of most engineering interests (1–10 Hz) for the Iranian earthquakes. Our results are also important for the assessment of hazards in other seismically active environments in the Middle East and Mediterranean regions.     

Issues in characterizing heterogeneity and connectivity in non-multiGaussian media

The performances of kriging, stochastic simulations and sequential self-calibration inversion are assessed when characterizing a non-multiGaussian synthetic 2D braided channel aquifer. The comparison is based on a series of criteria such as the reproduction of the original reference transmissivity or head fields, but also in terms of accuracy of flow and transport (capture zone) forecasts when the flow conditions are modified. We observe that the errors remain large even for a dense data network. In addition some unexpected behaviours are observed when large transmissivity datasets are used. In particular, we observe an increase of the bias with the number of transmissivity data and an increasing uncertainty with the number of head data. This is interpreted as a consequence of the use of an inadequate multiGaussian stochastic model that is not able to reproduce the connectivity of the original field.     

On the cumulant expansion up scaling of ground water contaminant transport equation with nonequilibrium sorption

The laboratory-scale ground water transport equation with nonequilibrium sorption reaction subjected to unsteady, nondivergence-free, and nonstationary velocity fields is up-scaled to the field-scale by using the ensemble-averaged equations obtained from the cumulant expansion ensemble-averaging method. It is found that existing ensemble-averaged equations obtained with the help of the cumulant expansion method for the system of linear partial differential equations are not second-order exact. Although the cumulant expansion methodology is designed for noncommuting operators, it is found that there are still commudativity requirements that need to be satisfied by the functions and constants exist in the coefficient matrix of the system of ordinary/partial differential equations. A reversibility requirement, which covers the commudativity requirements, is also proposed when applying the cumulant expansion method to a system of partial differential equations/a partial differential equation. The significance of the new velocity correction obtained in this study due to the applied second-order exact cumulant expansion is investigated on a numerical example with a linear trend in the distribution coefficient. It is found that the effect of the new velocity correction can be significant enough to affect the maximum concentration values and the plume center of mass in the case of a trending distribution coefficient in a physically heterogeneous environment.     

经验格林函数法与随机有限断层法在合成近场强地震动中的联合运用

本文采取将经验格林函数法与随机有限断层法相结合的方式,突出体现了各自方法的优点,通过经验格林函数法确定地震震源参数,用随机有限断层法计算参数、检验其合理性。利用1998年新疆阿图什M6．9级地震的肘L4．7级余震记录,合成了这次地震的最大余震Ms6．0级地震的加速度记录,并将合成的结果与实际记录在频域和时域做了对比,分析研究了地震动特征和这次最大余震的可能破裂特征。同时对经验格林函数法需进一步改进的方向进行了探讨。     

A new multiscale scheme for computing statistical moments in single phase flow in heterogeneous porous media

In this work we develop a new multiscale procedure to compute numerically the statistical moments of the stochastic variables which govern single phase flow in heterogeneous porous media. The technique explores the properties of the log-normally distributed hydraulic conductivity, characterized by power-law or exponential covariances, which shows invariance in its statistical structure upon a simultaneous change of the scale of observation and strength of heterogeneity. We construct a family of equivalent stochastic hydrodynamic variables satisfying the same flow equations at different scales and strengths of heterogeneity or correlation lengths. Within the new procedure the governing equations are solved in a scaled geology and the numerical results are mapped onto the original medium at coarser scales by a straightforward rescaling. The new procedure is implemented numerically within the Monte Carlo algorithm and also in conjunction with the discretization of the low-order effective equations derived from perturbation analysis. Numerical results obtained by the finite element method show the accuracy of the new procedure to approximated the two first moments of the pressure and velocity along with its potential in reducing drastically the computational cost involved in the numerical modeling of both power-law and exponential covariance functions.