Assimilating transient groundwater flow data via a localized ensemble Kalman filter to calibrate a heterogeneous conductivity field

A localized ensemble Kalman filter (EnKF) method is developed to assimilate transient flow data to calibrate a heterogeneous conductivity field. To update conductivity value at a point in a study domain, instead of assimilating all the measurements in the study domain, only limited measurement data in an area around the point are used for the conductivity updating in the localized EnKF method. The localized EnKF is proposed to solve the problems of the filter divergence usually existing in a data assimilation method without localization. The developed method is applied, in a synthetical two dimensional case, to calibrate a heterogeneous conductivity field by assimilating transient hydraulic head data. The simulations by the data assimilation with and without localized EnKF are compared. The study results indicate that the hydraulic conductivity field can be updated efficiently by the localized EnKF, while it cannot be by the EnKF. The covariance inflation and localization are found to solve the problem of the filter divergence efficiently. In comparison with the EnKF method without localization, the localized EnKF method needs smaller ensemble size to achieve stabilized results. The simulation results by the localized EnKF method are much more sensitive to conductivity correlation length than to the localization radius. The developed localized EnKF method provides an approach to improve EnKF method in conductivity calibration.     

Modification of the Bouwer and Rice Method to a Cutoff Wall with a Filter Cake

The Bouwer and Rice method is a line-fitting method used to estimate the hydraulic conductivity of an aquifer by means of a slug test. When considering a relatively impermeable layer, called a filter cake, which may form at the interface between a cutoff wall and the natural soil formation, the assumptions of the Bouwer and Rice method are violated. A modification of the Bouwer and Rice method is proposed that incorporates the concept of a flow net, whereby the geometry of the cutoff wall and filter cake is effectively considered in estimating the hydraulic conductivity of a vertical cutoff wall.     

Synthesis of a Tsunami Spectrum in a Semi-Enclosed Basin Using Its Background Spectrum

We explained spectra of distant tsunamis observed in enclosed basins by applying the synthesis method based on joint analysis of tsunami and background spectra from a number of stations. This method is the generalization of the method proposed by Rabinovich (J. Geopys. Res. 102, 12663-12676, 1997) to separate source and topography effects in recorded tsunami waves. The source function is extracted by inversion of the tsunami/background spectra averaged from many observational sites. The method is applied to the 2009 Papua tsunami observed at the Owase tide station in southwest Japan, a region with complicated topography and numerous bays and inlets. The synthesized spectrum explains the observed spectral amplitudes for each frequency component. It is shown that averaging of tsunami and background from various tide gauge stations in semi-enclosed basins is an efficient approach to extract the source function.     

Dynamic response of a piecewise circular tunnel embedded in a poroelastic medium

Recently, considerable efforts have been devoted to evaluation of seismic dynamic response of a circular tunnel. Conventional approaches have considered integral liners embedded in an elastic medium. In this study, we re-examine the problem with piecewise liners embedded in a porous medium. Surrounding saturated porous medium of tunnels is described by Biot's poroelastic theory, while the liner pieces and the connecting joints are treated as curved beams and characterized by curved beam theories. The scattered wave field in the porous medium is obtained by the wave function expansion method. The differential equations governing the vibration of a curved beam is discretized by the General Differential Quadrature (GDQ) method. The domain decomposition method is used to establish the global discrete dynamic equations for the piecewise tunnel. The surrounding soil and the tunnel are coupled together via the stress and the displacement continuation conditions which are implemented by the boundary collocation method. Numerical results demonstrate that the stiffness difference between the liner piece and the connecting joints has a considerable influence on the internal forces of the liner piece.     

Three-dimensional response of a layered cylindrical valley embedded in a layered half-space

An indirect boundary integral method to obtain the three-dimensional response of an infinitely long, layered, viscoelastic valley of arbitrary cross-section embedded in a layered viscoelastic half-space is presented. The valley is excited by homogeneous plane waves impinging at an oblique angle with respect to the axis of the valley. The method and associated computer programs are tested by comparison with available results in the limiting two-dimensional case of incidence normal to the axis of the valley. Additional comparisons with previous three-dimensional results obtained by a hybrid finite element-boundary integral method for cylindrical valleys subjected to obliquely incident waves show large differences. However, the results obtained here for an infinitely long valley appear to be in some agreement with earlier results for an elongated prolate semi-ellipsoidal valley and with results obtained by a discrete wavenumber boundary element approach. An extensive bibliography on the dynamic response of valleys is also presented.     

Dynamic response of a pair of walls retaining a viscoelastic solid

Making use of a previously reported, simple, approximate method of analysis, a critical evaluation is made of the dynamic pressures and forces induced by horizontal ground shaking on a pair of infinitely long, parallel walls retaining a uniform viscoelastic solid. The walls are presumed to be rigid but elastically constrained against rotation at their base. The effects of both harmonic and earthquake-induced excitations are examined. The accuracy of the method is assessed by comparing its predictions for the special case of fixed-based walls with those obtained by an exact method, and comprehensive numerical data are presented which elucidate the underlying response mechanisms, and the effects and relative importance of the parameters involved. The parameters examined include the characteristics of the ground motion, the ratio of the distance between walls to the height of the contained material, and the flexibility of the rotational wall constraints. In addition to valuable insights into the responses of the systems investigated, the results presented provide a convenient framework for the analysis of more complex systems as well.     

Response of a randomly inhomogeneous layer overlying a homogeneous half-space to surface harmonic excitation

The paper is concerned with the study of the effect of the randomness of material parameters on mean wave propagation in a semi-infinite viscoelastic medium. The medium considered in this paper is a configuration of a randomly non-homogeneous layer overlying a homogeneous half-space and is loaded harmonically on the top surface. The method used is that of Karal and Keller and is based on the idea of fundamental matrix and Bourret approximation. The integro-differential equation obtained in this paper is solved by the Laplace transform method. By using boundary and continuity conditions the mean wave solution is obtained. Numerical results show that the correlation functions, which introduce long-range interactions, can be the source of the wave amplification.     

Excitation of a half-space by a radial current sheet source

Some advantages and problems of the new geoelectrical prospecting method, i.e., vertical electric current soundings (VECS) are discussed. This method is based on using a new source, namely a circular electric dipole (CED). The source is installed by one of the transmitter poles grounded in the central point and the other pole uniformly grounded around with a radius determined by the depth of investigation desired. It can be defined as a noninductive source. The previous research was based on the diffusion approach. In this paper the author uses the solution with due regards for displacement currents in the frequency and time domain. A major disadvantage of the CED scheme is the need to provide a symmetrical grounding of the outer ring electrode. A possible way to avoid this requirement is to adopt an ungrounded CED array.     

Stochastic study of solute transport in a nonstationary medium

A Lagrangian stochastic approach is applied to develop a method of moment for solute transport in a physically and chemically nonstationary medium. Stochastic governing equations for mean solute flux and solute covariance are analytically obtained in the first-order accuracy of log conductivity and/or chemical sorption variances and solved numerically using the finite-difference method. The developed method, the numerical method of moments (NMM), is used to predict radionuclide solute transport processes in the saturated zone below the Yucca Mountain project area. The mean, variance, and upper bound of the radionuclide mass flux through a control plane 5 km downstream of the footprint of the repository are calculated. According to their chemical sorption capacities, the various radionuclear chemicals are grouped as nonreactive, weakly sorbing, and strongly sorbing chemicals. The NMM method is used to study their transport processes and influence factors. To verify the method of moments, a Monte Carlo simulation is conducted for nonreactive chemical transport. Results indicate the results from the two methods are consistent, but the NMM method is computationally more efficient than the Monte Carlo method. This study adds to the ongoing debate in the literature on the effect of heterogeneity on solute transport prediction, especially on prediction uncertainty, by showing that the standard derivation of solute flux is larger than the mean solute flux even when the hydraulic conductivity within each geological layer is mild. This study provides a method that may become an efficient calculation tool for many environmental projects.     

Dynamic initialization for barotropic flow crossing a barrier

Summary A method to obtain balanced initial state in the presence of mountains is presented. Using a prescribed initial state the primitive equations are iterated forward and backward about the initial time, using an Euler-backward time integration scheme. During this iteration the mountains are built-up steadily.The method is tested against a steady-state analytical solution of the non-linear equations of the homogeneous atmosphere. The results of this test demonstrate that the method is capable of generating the theoretical steady-state numerical solution with a good degree of accuracy.     

Boundary element method for analyzing flow through a random semiconfined aquifer

With the aid of perturbation technique a boundary element procedure is developed for solution of two-dimensional Helmholtz equation with a random parameter of small variability. The perturbation boundary element method does not require specification of probability density function of the parameter but only its mean and standard deviation. The method is used to analyze steady-state groundwater flows in a horizontal shallow semiconfined aquifer (homogeneous and isotropic) of probabilistic properties. To illustrate the applicability of the method, a simple numerical example is presented. As the nature of perturbation method suggests, the developed method is valid only when the perturbed value of the parameter is of a small order.     

Boundary element method for analyzing flow through a random semiconfined aquifer

With the aid of perturbation technique a boundary element procedure is developed for solution of two-dimensional Helmholtz equation with a random parameter of small variability. The perturbation boundary element method does not require specification of probability density function of the parameter but only its mean and standard deviation. The method is used to analyze steady-state groundwater flows in a horizontal shallow semiconfined aquifer (homogeneous and isotropic) of probabilistic properties. To illustrate the applicability of the method, a simple numerical example is presented. As the nature of perturbation method suggests, the developed method is valid only when the perturbed value of the parameter is of a small order.     

Static solution of a crack degenerated from dynamic solution of a propagating crack

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Non-parametric identification of a class of nonlinear multidegree dynamic systems

A non-parametric identification technique is presented for chain-like multidegree-of-freedom non-linear dynamic systems. The method uses information about the state variables of non-linear systems to express the system characteristics in terms of two-dimensional orthogonal functions. The technique is applied to a model of a steel frame that has been extensively investigated both analytically and experimentally. The method can be used with deterministic or random excitation to identify dynamic systems with arbitrary non-linearities, including those with hysteretic characteristics. It is also shown that the method is easy to implement and needs much less computer time and storage requirements compared to the Wiener-kernel approach. The method is shown to have low sensitivity to the effects of additive noise in the experimental data.     

非经典振型分解法求混凝土房屋及其上钢塔的地震响应

钢结构与混凝土结构阻尼比不同,混凝土房屋与其顶上钢塔组成了非比例阻尼结构系统。本文用非经典振型分解法求解该类结构系统的线弹性地震响应,发现只用前几阶振型响应迭加的结果即可逼近直接积分法的精确度。     

Dynamic interaction analysis of a circular cylindrical shell of finite length in a half-space

A study on the transient response of a circular cylindrical shell of finite length embedded in a homogeneous, isotropic and linear elastic half-space is presented. The soil-structure system is subjected to suddenly applied explosion waves. The numerical method employed is a combination of the time domain semi-analytical boundary element method used for the semi-infinite soil medium and the finite strip method used for the circular cylindrical shell. The two methods are combined through equilibrium and compatibility conditions at the soil-structure interface. The dynamic responses at the interface between the soil medium and the structure for every time step are obtained. Numerical examples are presented in detail to demonstrate the use and versatility of the proposed method. The following parameters are found to affect the response: (1) the slenderness ratio of the length over the diameter of the shell, L/D; (2) the relative wall thickness, h/a; (3) the relative stiffness ratio between the shell and the medium, E_s/E_m; and (4) the incidence angle of the explosion wave, α.     

横向不均匀介质中Kirchhoff-Helmholtz积分合成地震图

本文将Kirchhoff-Helmholtz积分方法应用于横向非均匀介质的合成地震图计算.与反射率方法及二维有限差分方法进行了比较.表明KH积分方法能很好的模拟反射波震相,且精度较高.KH 积分方法能够计算复杂界面的反射波,且其计算效率明显大于有限差分.     

Diffraction of a compressional wave by a rigid barrier in a liquid layer — Part II

Summary The problem of diffraction of compressional waves striking obliquely at a rigid barrier fixed in the surface of a liquid layer lying over a solid halfspace has been studied. Exact values for the amplitudes of the waves reflected in the solid halfspace have been obtained. The method of solution is based on the Wiener-Hopf technique.     

A Tool for Forecasting the Arrival Time of a Tracer or a Pollutant at a Karst Spring

Karst aquifers are a groundwater resource of global importance. Protection and contamination of karst water resources are often tackled by means of land-use planning and monitoring of physico-chemical and microbial water properties coupled to early-warning systems. However, these solutions of management do not integrate observational data on karst hydrodynamic, for example, tracer tests. Thus, this technical note aims at introducing a straightforward method for forecasting the arrival time of a tracer or a pollutant at a karst spring. Deliverables from the proposed method can assist professionals in the case of a pollution involving a swallow hole of the karst network. The approach is based on repeated tracer testing, gauging of spring flow rate and mathematical curve fitting. Tracer tests and gauging of spring flow rates are repeated under low, middle, and high flow periods. Arrival times of tracer from a given swallow hole of the network are plotted as a function of measured flow rates at the karst spring. The observational data are finally fitted by a mathematical function. Flow rate monitoring at high-temporal resolution at the karst spring and the mathematical functions allow forecasting the arrival of a tracer or a pollutant at the spring in the case of an accident involving a swallow hole of the network or estimating the duration of a pollution if hydrodynamic conditions do not change abruptly. The applicability of the method is documented by three study sites in Switzerland.