射线追踪的微变网格方法

本文给出一种适用于叠前数据速度分析和叠前深度偏移的快速射线追踪方法──微变网格法；该方法不仅精度高，而且计算速度极快，可适用于当前计算条件下的地球介质速度反演和叠前深度偏移成像的要求．     

An efficient numerical model for hydrodynamic parameterization in 2D fractured dual-porosity media

This paper presents a robust and efficient numerical model for the parameterization of the hydrodynamic in fractured porous media. The developed model is based upon the refinement indicators algorithm for adaptive multi-scale parameterization. For each level of refinement, the Levenberg–Marquardt method is used to minimize the difference between the measured and predicted data that are obtained by solving the direct problem with the mixed finite element method. Sensitivities of state variables with respect to the parameters are calculated by the sensitivity method. The adjoint-state method is used to calculate the local gradients of the objective function necessary for the computation of the refinement indicators. Validity and efficiency of the proposed model are demonstrated by means of several numerical experiments. The developed numerical model provides encouraging results, even for noisy data and/or with a reduced number of measured heads.     

面向目标自适应海洋可控源电磁三维矢量有限元正演

本文实现了一种面向目标自适应海洋可控源电磁三维矢量有限元方法.为满足三维复杂电性结构模拟的需求,网格剖分采用非结构化六面体.在组装刚度矩阵之后,形成的大型复数线性方程组分解为等价的实数形式,利用带预条件的广义最小残差法进行求解.在获得微分方程的解之后,为提高解的准确性,通过面向目标的自适应误差估计来指示网格细化,重点加密能使观测点数值模拟精度提高的网格.对于大规模三维数据,为了使模型空间的并行计算达到均衡负载的效果,我们使用METIS函数库来进行网格计算任务量的划分.最后,通过对比一维解析解与三维自适应矢量有限元计算结果,验证了程序的正确性;通过自适应过程中误差指示子的分布,验证了面向目标自适应的有效性;通过对三维复杂模型进行均衡负载下的并行计算,测试了程序的可扩展性.     

A response spectrum method for random vibration analysis of mdf systems

A response spectrum method for stationary random vibration analysis of linear, multi-degree-of-freedom systems is developed. The method is based on the assumption that the input excitation is a wide-band, stationary Gaussian process and the response is stationary. However, it can also be used as a good approximation for the response to a transient stationary Gaussian input with a duration several times longer than the fundamental period of the system. Various response quantities, including the mean-squares of the response and its time derivative, the response mean frequency, and the cumulative distribution and the mean and variance of the peak response are obtained in terms of the ordinates of the mean response spectrum of the input excitation and the modal properties of the system. The formulation includes the cross-correlation between modal responses, which is shown to be significant for modes with closely spaced natural frequencies. The proposed procedure is demonstrated for an example structure that is subjected to an ensemble of earthquake-induced base excitations. Computed results based on the response spectrum method are in close agreement with simulation results obtained from time-history dynamic analysis. The significance of closely spaced modes and the error associated with a conventional method that neglects the modal correlations are also demonstrated.     

Suppressing multiples using an adaptive multichannel filter based on L1-norm

Adaptive subtraction is an important link for removing surface-related multiples in the wave equation-based method. In this paper, we propose an adaptive multichannel subtraction method based on the L1-norm. We achieve enhanced compensation for the mismatch between the input seismogram and the predicted multiples in terms of the amplitude, phase, frequency band, and travel time. Unlike the conventional L2-norm, the proposed method does not rely on the assumption that the primary and the multiples are orthogonal, and also takes advantage of the fact that the L1-norm is more robust when dealing with outliers. In addition, we propose a frequency band extension via modulation to reconstruct the high frequencies to compensate for the frequency misalignment. We present a parallel computing scheme to accelerate the subtraction algorithm on graphic processing units (GPUs), which significantly reduces the computational cost. The synthetic and field seismic data tests show that the proposed method effectively suppresses the multiples.     

面向目标自适应三维大地电磁正演模拟

本文将面向目标的自适应算法应用于三维大地电磁数值模拟.使用基于非结构网格的矢量有限单元法对起伏地表大地电磁正演模拟问题进行求解.使用利用垂向电流密度在物性界面上的连续性对后验误差进行估算的算法指导网格优化.由于全局自适应算法针对观测点优化网格的能力较差,本文通过求解正演问题的对偶问题计算后验误差的加权系数,并对相关加权系数进行改进,从而实现了面向目标的自适应算法.与传统基于结构化网格的电磁正演算法相比,采用非结构网格能够更好地拟合起伏地表和地下不规则异常体.由于使用了面向目标的自适应算法,本文能够使用更少的网格达到较高的计算精度.通过对比本文模拟结果与半空间响应和全局自适应算法计算结果,并通过对比使用改进前和改进后加权系数得到的网格剖分结果验证了本文算法的有效性.     

An envelope for Mohr's circle in seismically excited three‐dimensional structures

A previously developed response‐spectrum‐based procedure for computing the envelope that bounds the time‐varying realizations of Mohr's circle at any prescribed location within a two‐dimensional structure is extended for use with three‐dimensional structures subjected to as many as three translational components of ground acceleration. The proposed envelope, which is completely defined by quantities that are routinely used and calculated in conventional response spectrum analyses, is developed for the general case in which the principal directions of the earthquake, along which the ground accelerations are uncorrelated, are unknown. The accuracy of the proposed envelope is evaluated by comparing it to the results of an ensemble of time‐history analyses performed on a concrete arch dam using simulated accelerograms. It is found that the proposed envelope has a level of accuracy that is suitable for structural design and analysis. The largest observed difference between the simulated and predicted mean envelopes is less than 5%. Copyright © 2004 John Wiley & Sons, Ltd.     

自适应Kalman滤波反褶积的快速实现方法

提出了以二进小波变换为基础的自适应Kalman滤波反褶积(AKFD)新方法，针对该方法的计算复杂程度，提出了一种快速实现方法.二进小波变换的AKFD抛弃了传统预测反褶积对信号平稳性的假设，克服了提高分辨率而信噪比明显降低的问题，具有很好的抗噪性能.在小波域进行的AKFD在压制假反射以及提高分辨率方面比时间域的AKFD好，克服了在时域内进行AKFD抬升低频成分的缺陷.利用二维地震数据的局部平稳性的假设提出了快速实现方法，通过分段求取自适应预测算子，分别于横向及纵向采用样条插值的方法进行插值，来减少求取自适应预测算子的计算量，达到快速实现的目的.经过大量实验表明计算速度提高数百倍，仍能保持原来的计算效果.     

逆散射级数法预测层间多次波的算法改进及其策略

波动方程预测层间多次波有两类算法.一是由Berkhout和Verschuur（1998）提出的基于CFP（共聚焦点）延拓的算法,另一是由Weglein（1997）等人提出的基于逆散射级数法的算法.ISS（逆散射级数）算法具有不依赖速度模型的优点,但是其计算成本很高.本文改进了Weglein提出的1-D预测公式,提高了计算效率.从理论方面,改进算法的计算速度提高了大约12倍.实际结果表明其计算速度更快,提高近80倍左右,主要原因在于后者的空间复杂度小.此外,由于时间-空间域比伪深度-波数域的层间多次波预测有更多的优点,本文推导了1.5-D时间-空间域ISS层间多次波预测算法,该算法有计算速度快、预测噪音小、适应观测系统能力强和不依赖地震子波等优点.在实际应用中,计算成本高是ISS预测层间多次波算法的主要障碍.因此,本文还讨论了预测层间多次波的策略.结合本文提出的改进算法和应用策略,能够在实际地震资料处理中较好地应用ISS预测层间多次波.     

Iteratively re‐weighted and refined least squares algorithm for robust inversion of geophysical data

A robust metric of data misfit such as the ?₁‐norm is required for geophysical parameter estimation when the data are contaminated by erratic noise. Recently, the iteratively re‐weighted and refined least‐squares algorithm was introduced for efficient solution of geophysical inverse problems in the presence of additive Gaussian noise in the data. We extend the algorithm in two practically important directions to make it applicable to data with non‐Gaussian noise and to make its regularisation parameter tuning more efficient and automatic. The regularisation parameter in iteratively reweighted and refined least‐squares algorithm varies with iteration, allowing the efficient solution of constrained problems. A technique is proposed based on the secant method for root finding to concentrate on finding a solution that satisfies the constraint, either fitting to a target misfit (if a bound on the noise is available) or having a target size (if a bound on the solution is available). This technique leads to an automatic update of the regularisation parameter at each and every iteration. We further propose a simple and efficient scheme that tunes the regularisation parameter without requiring target bounds. This is of great importance for the field data inversion where there is no information about the size of the noise and the solution. Numerical examples from non‐stationary seismic deconvolution and velocity‐stack inversion show that the proposed algorithm is efficient, stable, and robust and outperforms the conventional and state‐of‐the‐art methods.     

自适应时间步长法及三维堤坝地震液化数值模拟

三维大模型数值计算因巨大的单元和结点数目而非常耗时,在地震响应分析中受计算时间步长的限值则更加耗时。在饱和砂土动力液化计算平台上开发时域离散误差评估方法和时间步长自适应调整的计算程序,并成功应用于三维堤坝地震液化响应分析。时域离散误差包括土骨架的位移误差和单元孔压误差,通过定义孔压误差影响系数计算出混合误差,根据混合误差和设定的误差允许值进行计算步长的自适应调整。在三维堤坝地震液化数值模拟中,采用自适应时间步长法有效避免小步长精确但耗时、大步长省时而不精确的缺点。在大模型和超大模型计算中,最优调整每一步的计算时间步长,完美实现既节省时间又不失精度的时域离散策略。     

Global SH-wavefield calculation for a two-dimensional whole-Earth model with the parallel hybrid PSM/FDM algorithm

We present a parallel hybrid algorithm based on pseudospectral method (PSM) and finite difference method (FDM) for two-dimensional (2-D) global SH-wavefield simulation. The whole-Earth model is taken as a cross section of spherical Earth, and corresponding wave equations are defined in 2-D cylindrical coordinates. Spatial derivatives in the wave equations are approximated with efficient and high accuracy PSM in the lateral and high-order FDM in the radial direction on staggered grids. This algorithm allows us to divide the whole-Earth into sub-domains in radial direction and implement efficient parallel computing on PC cluster, while retains high accuracy and efficiency of PSM in lateral direction. A transformation of moment tensor between 3-D spherical Earth and our 2-D model was proposed to give corresponding moment tensor components used in 2-D modeling. Comparison of modeling results with those obtained by direct solution method shows very good accuracy of our algorithm. We also demonstrate its feasibility with a lateral heterogeneous whole-Earth model with localized velocity perturbation.     

Robust salt-dome detection using the ranking of texture-based attributes

The accurate interpretation and analysis of seismic data heavily depends on the robustness of the algorithms used. We focus on the robust detection of salt domes from seismic surveys. We discuss a novel feature-ranking classification model for saltdome detection for seismic images using an optimal set of texture attributes. The proposed algorithm overcomes the limitations of existing texture attribute-based techniques, which heavily depend on the relevance of the attributes to the geological nature of salt domes and the number of attributes used for accurate detection. The algorithm combines the attributes from the Gray-Level Co-occurrence Matrix (GLCM), the Gabor filters, and the eigenstructure of the covariance matrix with feature ranking using the information content. The top-ranked attributes are combined to form the optimal feature set, which ensures that the algorithm works well even in the absence of strong reflectors along the salt-dome boundaries. Contrary to existing salt-dome detection techniques, the proposed algorithm is robust and computationally efficient, and works with small-sized feature sets. I used the Netherlands F3 block to evaluate the performance of the proposed algorithm. The experimental results suggest that the proposed workflow based on information theory can detect salt domes with accuracy superior to existing salt-dome detection techniques.     

考虑发射波形的瞬变电磁三维模型降阶快速正演算法

瞬变电磁响应受到发射波形的影响,正演计算中需考虑发射波形.基于位移逆Krylov子空间投影的模型降阶算法能够精确模拟三维全波形瞬变电磁正演响应,但该算法计算精确的on-time响应非常耗时.目前实际工作中多数情况下都是对off-time时间段的数据进行处理解释,因此可以将正演问题简化为精确模拟考虑发射波形的off-ti...     

Efficient analysis of dynamic response of linear systems

After reviewing briefly a recently proposed procedure for evaluating the dynamic transient response of a classically damped linear system from its corresponding steady-state response, a modified procedure is presented which also appears to be highly efficient for non-classically damped systems of the type encountered in studies of soil-structure interaction. The concepts involved are developed by reference to viscously damped single-degree-of-freedom systems, and numerical solutions are included to illustrate the accuracy and efficiency of the proposed procedure and its superiority over the classical Discrete Fourier Transform approach.     

On the predictivity of pore-scale simulations: Estimating uncertainties with multilevel Monte Carlo

A fast method with tunable accuracy is proposed to estimate errors and uncertainties in pore-scale and Digital Rock Physics (DRP) problems. The overall predictivity of these studies can be, in fact, hindered by many factors including sample heterogeneity, computational and imaging limitations, model inadequacy and not perfectly known physical parameters. The typical objective of pore-scale studies is the estimation of macroscopic effective parameters such as permeability, effective diffusivity and hydrodynamic dispersion. However, these are often non-deterministic quantities (i.e., results obtained for specific pore-scale sample and setup are not totally reproducible by another “equivalent” sample and setup). The stochastic nature can arise due to the multi-scale heterogeneity, the computational and experimental limitations in considering large samples, and the complexity of the physical models. These approximations, in fact, introduce an error that, being dependent on a large number of complex factors, can be modeled as random. We propose a general simulation tool, based on multilevel Monte Carlo, that can reduce drastically the computational cost needed for computing accurate statistics of effective parameters and other quantities of interest, under any of these random errors. This is, to our knowledge, the first attempt to include Uncertainty Quantification (UQ) in pore-scale physics and simulation. The method can also provide estimates of the discretization error and it is tested on three-dimensional transport problems in heterogeneous materials, where the sampling procedure is done by generation algorithms able to reproduce realistic consolidated and unconsolidated random sphere and ellipsoid packings and arrangements. A totally automatic workflow is developed in an open-source code [1], that include rigid body physics and random packing algorithms, unstructured mesh discretization, finite volume solvers, extrapolation and post-processing techniques. The proposed method can be efficiently used in many porous media applications for problems such as stochastic homogenization/upscaling, propagation of uncertainty from microscopic fluid and rock properties to macro-scale parameters, robust estimation of Representative Elementary Volume size for arbitrary physics.     

Performance‐based optimum seismic design of reinforced concrete structures

A fully automated design methodology based on nonlinear response history analysis is proposed for the optimum seismic design of reinforced concrete (RC) structures. The conventional trial‐and‐error process is replaced by a structural optimization algorithm that serves as a search engine capable of locating the most efficient design in terms of cost and performance. Two variations of the proposed design methodology are introduced. The first approach treats the optimum design problem in a deterministic manner, while in the second variation the optimum design is sought in the framework of a reliability‐based optimization problem. The reliability‐based approach seems to be a more rational procedure since more meaningful design criteria that correlate better with the performance‐based design concept can be adopted. Thus, the practice of using the mean annual frequency of a limit‐state being exceeded to assess the candidate designs is compared with the use of deterministic criteria. Both formulations take into consideration the structural response for a number of limit‐states, from serviceability to collapse prevention. The proposed design procedure is specifically tailored to the design of RC structures, where a preliminary design step of generating tables of concrete sections is introduced. In order to handle the large size of the tables, the concept of multi‐database cascade optimization is implemented. The final design has to comply with the provisions of European design codes. The proposed methodology allows for a significant reduction of the direct construction cost combined with improved control of the seismic performance under earthquake loading. Copyright © 2008 John Wiley & Sons, Ltd.     

柯西波场及在角度域成像条件中的应用

角度域成像道集是叠前深度偏移的重要输出结果,它是偏移速度分析、各向异性分析和AVA分析等研究工作的基础.目前存在的角度域成像道集的生成方法受计算效率或角度分辨率的影响,仍然满足不了实际生产的要求.角度域成像道集的生成方法可以大致分为直接法和间接法两大类.在直接方法中,波矢量方向计算和局部平面波分解是两个最重要的内容,它们共同决定角度域成像条件的实现效率和角度域成像道集的质量.为了完善现有的角度域成像道集生成方法,本文提出一种新的波矢量计算方法和局部平面波分解方法.本文先用波动方程任意时刻的柯西条件构造一个只含原波场负频率成分的柯西波场,然后根据柯西波场在时间波数域的振幅谱计算波场的波矢量方向.该方法仅在需要计算波矢量方向的时刻合成柯西波场,不需要增加额外的数据读写操作,是一种高效的波矢量计算方法.本文还以柯西波场为基础提出一种高效的局部平面波分解方法,保证角度域成像条件的实现效率.结合柯西波场和局部平面波分解方法,本文最后给出一种新的角度域成像方法.文中最后的数值实验证明该方法得到的角度域成像道集具有理想的角度分辨率,可以反映地下构造的角度照明情况.     

An improved spectral turning-bands algorithm for simulating stationary vector Gaussian random fields

We propose a spectral turning-bands approach for the simulation of second-order stationary vector Gaussian random fields. The approach improves existing spectral methods through coupling with importance sampling techniques. A notable insight is that one can simulate any vector random field whose direct and cross-covariance functions are continuous and absolutely integrable, provided that one knows the analytical expression of their spectral densities, without the need for these spectral densities to have a bounded support. The simulation algorithm is computationally faster than circulant-embedding techniques, lends itself to parallel computing and has a low memory storage requirement. Numerical examples with varied spatial correlation structures are presented to demonstrate the accuracy and versatility of the proposal.     

Gaussian mixture–based equivalent linearization method (GM-ELM) for fragility analysis of structures under nonstationary excitations

Gaussian mixture–based equivalent linearization method (GM-ELM) is a recently developed stochastic dynamic analysis approach which approximates the random response of a nonlinear structure by collective responses of equivalent linear oscillators. The Gaussian mixture model is employed to achieve an equivalence in terms of the probability density function (PDF) through the superposition of the response PDFs of the equivalent linear system. This new concept of linearization helps achieve a high level of estimation accuracy for nonlinear responses, but has revealed some limitations: (1) dependency of the equivalent linear systems on ground motion intensity and (2) requirements for stationary condition. To overcome these technical challenges and promote applications of GM-ELM to earthquake engineering practice, an efficient GM-ELM-based fragility analysis method is proposed for nonstationary excitations. To this end, this paper develops the concept of universal equivalent linear system that can estimate the stochastic responses for a range of seismic intensities through an intensity-augmented version of GM-ELM. Moreover, the GM-ELM framework is extended to identify equivalent linear oscillators that could capture the temporal average behavior of nonstationary responses. The proposed extensions generalize expressions and philosophies of the existing response combination formulations of GM-ELM to facilitate efficient fragility analysis for nonstationary excitations. The proposed methods are demonstrated by numerical examples using realistic ground motions, including design code–conforming nonstationary ground motions.