快速精确的二维频率空间域弹性波数值模拟

二维频率空间域的数值模拟方法具有以下的优势:多炮模拟时,计算成本比时间域方法低;无累计误差;在地震反演中处理多震源模拟时,只需要有限的几个频率就可以得到好的反演结果.差分离散化形成的稀疏系数矩阵,需要求解一个巨大规模的线性方程组,最大瓶颈是需要海量的计算机内存,导致计算量庞大.本文在前人研究的基础上,采用嵌套剖分网格排序法,极大限度减少对计算机内存的需求,从而减少了计算量.针对弹性波数值模拟的特征,提出二维频率空间域弹性波多炮模拟的快速计算流程.数值模拟试验证明使用嵌套剖分排序法的弹性波多炮数值模拟比压缩存储法具有节省存储量、计算效率高等优势,为后续的二维频率空间域弹性波全波形反演奠定了很好的基础.     

频率域航空电磁法一维正演与探测深度

计算了偶极一偶极方式均匀半空间的频率域航空电磁响应及层状模型的相对异常响应,阐明了大地电导率、磁化系数,以及飞机飞行高度、探测装置、收发距对电磁响应的影响,计算结果说明了频率域航空电磁法的探测能力和探测条件．分析了三层模型的相对异常响应,给出了基于层状模型确定探测深度的方法．在水平共面方式下,收发距8m,飞行高度30m时,在3～4ppm噪声水平条件下,100Ωm大地探测深度为120m．     

A hybrid analysis method for linear dynamic soil-structure interaction in time and frequency domain

IntroductionThe analysis of dynamic soil-structure interaction for important engineering project is still based on linear model (including equivalent linear model) with complex damping, and traditional frequency domain method (Lysmer, et al, 1975, 1981; DING, et al, 1999). Namely, first calculating frequency domain solution by Fourier transform, and then calculating time domain solution by Fourier inverse transform. The motion equation of a system in frequency domain is usually written as (…     

Evaluation of the half‐power bandwidth method to estimate damping in systems without real modes

The objective of this work was to assess the significance of the values of damping obtained applying the half‐power bandwidth method to the frequency response records of the steady‐state response of a system that does not possess real modes either because the damping matrix does not satisfy the orthogonality condition or because its parameters are functions of frequency. A multi‐degree of freedom system with real modes and different types of damping is considered first. A two degree of freedom system with an arbitrary damping matrix, a rigid mass on an elastic foundation subjected to vertical and coupled horizontal/rocking vibrations, and a single degree of freedom model of a building accounting for inertial soil structure interaction effects are considered next in more detail. The results show that the predictions of the method, when applicable compare very well with those provided by approximate formulae and procedures used in practice. Copyright © 2010 John Wiley & Sons, Ltd.     

Stability of the time‐domain analysis method including a frequency‐dependent soil–foundation system

A number of methods have been proposed that utilize the time‐domain transformations of frequency‐dependent dynamic impedance functions to perform a time‐history analysis. Though these methods have been available in literature for a number of years, the methods exhibit stability issues depending on how the model parameters are calibrated. In this study, a novel method is proposed with which the stability of a numerical integration scheme combined with time‐domain representation of a frequency‐dependent dynamic impedance function can be evaluated. The method is verified with three independent recursive parameter models. The proposed method is expected to be a useful tool in evaluating the potential stability issue of a time‐domain analysis before running a full‐fledged nonlinear time‐domain analysis of a soil–structure system in which the dynamic impedance of a soil–foundation system is represented with a recursive parameter model. Copyright © 2015 John Wiley & Sons, Ltd.     

线圈中心近区频率域电磁测深数值模拟研究

论述了一种在线圈中心测量磁场垂直分量的近区频率域电磁测深方法的原理及一维正演数值模拟研究结果.推导出线圈中心近区频域电磁法的视电阻率表达式,提出了在线圈中心测量磁场垂直分量频域电磁法的基本思路,利用MATLAB编程进行一维正演模拟,先后正演模拟了7种有代表性的地电模型.结果表明:此方法对层状地电构造的电性参数和厚度变化比较敏感,分辨力较高,对二层断面的上层厚度和基底电性分辨,对三层断面的中间层的电性和厚度变化分辨比较清楚,是一种有前景的近区频率域电磁测深方法.     

2D acoustic‐elastic coupled waveform inversion in the Laplace domain

Although waveform inversion has been intensively studied in an effort to properly delineate the Earth's structures since the early 1980s, most of the time‐ and frequency‐domain waveform inversion algorithms still have critical limitations in their applications to field data. This may be attributed to the highly non‐linear objective function and the unreliable low‐frequency components. To overcome the weaknesses of conventional waveform inversion algorithms, the acoustic Laplace‐domain waveform inversion has been proposed. The Laplace‐domain waveform inversion has been known to provide a long‐wavelength velocity model even for field data, which may be because it employs the zero‐frequency component of the damped wavefield and a well‐behaved logarithmic objective function. However, its applications have been confined to 2D acoustic media. We extend the Laplace‐domain waveform inversion algorithm to a 2D acoustic‐elastic coupled medium, which is encountered in marine exploration environments. In 2D acoustic‐elastic coupled media, the Laplace‐domain pressures behave differently from those of 2D acoustic media, although the overall features are similar to each other. The main differences are that the pressure wavefields for acoustic‐elastic coupled media show negative values even for simple geological structures unlike in acoustic media, when the Laplace damping constant is small and the water depth is shallow. The negative values may result from more complicated wave propagation in elastic media and at fluid‐solid interfaces. Our Laplace‐domain waveform inversion algorithm is also based on the finite‐element method and logarithmic wavefields. To compute gradient direction, we apply the back‐propagation technique. Under the assumption that density is fixed, P‐ and S‐wave velocity models are inverted from the pressure data. We applied our inversion algorithm to the SEG/EAGE salt model and the numerical results showed that the Laplace‐domain waveform inversion successfully recovers the long‐wavelength structures of the P‐ and S‐wave velocity models from the noise‐free data. The models inverted by the Laplace‐domain waveform inversion were able to be successfully used as initial models in the subsequent frequency‐domain waveform inversion, which is performed to describe the short‐wavelength structures of the true models.     

结构地震反应的频域精细传递矩阵法

传统的传递矩阵法需要对控制微分方程进行求解,获得相应的传递矩阵。公式繁琐、复杂。文中提出将传递矩阵法与精细积分法中的指数矩阵运算技巧结合起来,在频域内对结构进行动力分析。与传统的传递矩阵法相比,无需对微分方程进行求解,只需按照迭代公式进行计算,就可以得到所需要的传递矩阵。这种方法公式简单,理论上可实现任意精度,而且计算效率较高,能够快速、高精度的进行结构的地震反应分析。算例显示了精细传递矩阵法的有效性。     

Assessment of the frequency domain decomposition technique by forced‐vibration tests of a full‐scale structure

Dynamic characteristics of buildings are of utmost importance in earthquake engineering. The vibration periods are required to determine design loads, and damping is necessary in time‐history analysis. These parameters are generally obtained through forced‐vibration tests (FVTs) or after a seismic event in the case of permanently instrumented structures. However, for large civil engineering structures, FVTs are often too costly or practically difficult, and ambient or output‐only methods are used. This paper describes a comparison between ambient and FVTs carried out on a two‐story building. Results from both testing methods are compared and discussed in order to assess the vibration properties estimates obtained with the frequency domain decomposition technique. Copyright © 2007 John Wiley & Sons, Ltd.     

Visco‐acoustic prestack reverse‐time migration based on the time‐space domain adaptive high‐order finite‐difference method

It is important to include the viscous effect in seismic numerical modelling and seismic migration due to the ubiquitous viscosity in an actual subsurface medium. Prestack reverse‐time migration (RTM) is currently one of the most accurate methods for seismic imaging. One of the key steps of RTM is wavefield forward and backward extrapolation and how to solve the wave equation fast and accurately is the essence of this process. In this paper, we apply the time‐space domain dispersion‐relation‐based finite‐difference (FD) method for visco‐acoustic wave numerical modelling. Dispersion analysis and numerical modelling results demonstrate that the time‐space domain FD method has great accuracy and can effectively suppress numerical dispersion. Also, we use the time‐space domain FD method to solve the visco‐acoustic wave equation in wavefield extrapolation of RTM and apply the source‐normalized cross‐correlation imaging condition in migration. Improved imaging has been obtained in both synthetic and real data tests. The migration result of the visco‐acoustic wave RTM is clearer and more accurate than that of acoustic wave RTM. In addition, in the process of wavefield forward and backward extrapolation, we adopt adaptive variable‐length spatial operators to compute spatial derivatives to significantly decrease computing costs without reducing the accuracy of the numerical solution.     

Frequency‐domain acoustic‐elastic coupled waveform inversion using the Gauss‐Newton conjugate gradient method

We developed a frequency‐domain acoustic‐elastic coupled waveform inversion based on the Gauss‐Newton conjugate gradient method. Despite the use of a high‐performance computer system and a state‐of‐the‐art parallel computation algorithm, it remained computationally prohibitive to calculate the approximate Hessian explicitly for a large‐scale inverse problem. Therefore, we adopted the conjugate gradient least‐squares algorithm, which is frequently used for geophysical inverse problems, to implement the Gauss‐Newton method so that the approximate Hessian is calculated implicitly. Thus, there was no need to store the Hessian matrix. By simultaneously back‐propagating multi‐components consisting of the pressure and displacements, we could efficiently extract information on the subsurface structures. To verify our algorithm, we applied it to synthetic data sets generated from the Marmousi‐2 model and the modified SEG/EAGE salt model. We also extended our algorithm to the ocean‐bottom cable environment and verified it using ocean‐bottom cable data generated from the Marmousi‐2 model. With the assumption of a hard seafloor, we recovered both the P‐wave velocity of complicated subsurface structures as well as the S‐wave velocity. Although the inversion of the S‐wave velocity is not feasible for the high Poisson's ratios used to simulate a soft seafloor, several strategies exist to treat this problem. Our example using multi‐component data showed some promise in mitigating the soft seafloor effect. However, this issue still remains open.     

Data‐driven time–frequency analysis of seismic data using non‐stationary Prony method

Empirical mode decomposition aims to decompose the input signal into a small number of components named intrinsic mode functions with slowly varying amplitudes and frequencies. In spite of its simplicity and usefulness, however, empirical mode decomposition lacks solid mathematical foundation. In this paper, we describe a method to extract the intrinsic mode functions of the input signal using non‐stationary Prony method. The proposed method captures the philosophy of the empirical mode decomposition but uses a different method to compute the intrinsic mode functions. Having the intrinsic mode functions obtained, we then compute the spectrum of the input signal using Hilbert transform. Synthetic and field data validate that the proposed method can correctly compute the spectrum of the input signal and could be used in seismic data analysis to facilitate interpretation.     

Regional extreme‐dry‐spell frequency analysis using the L‐moments method in the middle reaches of the Yellow River Basin,China

In this research, the regional extreme‐dry‐spell frequency in the middle reaches of the Yellow River Basin (YRB) is studied by the L‐moments method. The research area has been divided into three subregions (regions 1, 2 and 3), which have been identified as homogenous regions. The results of a goodness‐of‐fit test indicate that a generalized normal distribution is the optimal regional model for regions 1 and 2 whereas a generalized Pareto distribution is the optimal regional model for region 3. The return period analysis figures out that the maximum length‐of‐dry‐spell (MxDS) values increase from south to north in the southern part and increase from northeast to southwest in the northern part of the middle reaches of the YRB under different return periods. The increments of quantiles of dry spell under different return levels indicate that drought risk in region 1 is higher than that in regions 2 and 3. The analysis of the occurrence day of MxDS shows that MxDS mostly occurred during winter of 1998 and spring of 1999 in most stations during the considered period. By comparing summer MxDS events, it can be found that mean MxDS values have slightly increased in regions 1 and 2 during the last five decades. The maximum mean MxDS values appeared in the 2000s for regions 1 and 2 and in the 1990s for region 3. The atmospheric circulation shows that the positive anomaly centre in the west of North China, negative anomaly centre in the east of North China and the strong western Pacific subtropical high led to the decrease of precipitation in North China during the summer of 1997. Copyright © 2013 John Wiley & Sons, Ltd.     

三维地形频率域人工源电磁场的边界元模拟方法

提出了一种用边界元法计算频率域人工源三维地形电磁场的数值模拟方法.首先用矢量积分理论和电磁场边界条件,将上半空间（空气）和下半空间（地下介质）两个区域电磁场边值问题变为仅对地形界面的两个矢量面积分方程.然后将对地形界面的积分剖分为一系列的三角单元积分.在三角单元积分中,假设单元中电磁场为无限大气空间电磁场与地形影响的叠加,并假设地形影响为常项,这样既保证了计算精度又使得计算方法简便.通过分解和计算,每一个矢量面积分方程分解为对应三个坐标方向的三个常量线性方程,这些线性方程组成了对角占优的线性方程组,可用SSOR方法求解.文中给出了垂直磁偶源的垂直磁场地形影响的例子.     

频率域电磁法三维有限元正演线性方程组迭代算法

在三维频率域电磁法的正演模拟方法中,有限元方法具有计算精度高、适应性强的优点,近年来来得到了越来越多的关注.在正演过程中,主要的计算量集中在求解由偏微分方程组离散得到的线性方程组上,因此求解线性方程组关系着正演计算速度以及模拟精度.由于由有限元方法离散得到的复系数线性方程组条件数非常大,使用常规的迭代法和预条件很难收敛.目前大多数的研究工作采用直接解法,需要大量的计算机内存,限制了可求解问题的规模.本文研究了线性方程组的迭代解法,通过将复系数线性方程组转化为其实对称形式,构造分块对角预条件.在应用预条件的过程中,需要求解两个较小的实数方程,通过辅助空间解法求解.本文的算法适用于可控源电磁法和大地电磁法,对一系列的数值算例的模拟结果证明了迭代算法的效率,结果表明迭代算法可以在小于20次迭代内收敛,同时迭代次数与模型电阻率、问题规模和频率无关.

     

多点输入下大跨结构地震反应的频域精细传递矩阵法

地震输入问题一直是工程结构抗震研究所关注的焦点.在对大跨度结构进行抗震设计时,需要考虑多点地震输入的影响已成为国内外学术界和工程界的共识.本文根据傅氏变换,运用精细传递矩阵法推导出了大跨结构在多点地震输入下的频域精细传递矩阵,并在频域内对大跨度结构进行了动力分析.这种方法公式简单,能够快速、高精度地进行结构的地震反应分析.算例显示了本文方法的有效性.     

Soil‐structure system frequency and damping: Estimation from eigenvalues and results for a 2D model in layered half‐space

This paper presents a formulation for estimation of the frequency and damping of a soil‐structure interaction system based on the classical modal analysis and solving the system eigenvalue problem. Without loss of generality, the structure is represented by a single degree of freedom oscillator, while the soil effects are included through impedance functions for in‐plane motion of a 2D rigid foundation. For the results presented in this paper, the impedance functions were computed by the indirect boundary element method for a rectangular foundation embedded in a soil layer over elastic bedrock. The study shows that the classical modal‐analysis approach works well, with the exception of squat, stiff structures, even though the impedance functions are frequency‐dependent and the soil‐structure interaction system does not possess normal modes. The study also shows that system frequency and damping are independent of the wave passage effects, contrary to findings of some previous studies, and that the site conditions, represented by the soil‐layer thickness and stiffness contrast between bedrock and soil layer, have significant influences on both system frequency and system damping. Finally, the paper examines the accuracy of some of the simple methods for estimation of these two system parameters and comments on some conflicting conclusions of previous studies about the effects of foundation embedment.     

求解弹性波动方程的频率域近似解析离散化波场模拟方法

为提高频率域弹性波动方程数值求解的计算效率,本文引入近似解析离散化(NAD)方法将其进行数值离散并得到大型线性代数方程组.在详细分析了相应系数矩阵的稀疏分块结构与数学性质之后,本文提出采用不精确旋转分块三角预处理子加速Krylov子空间迭代方法来快速求解该线性方程组,并利用数值试验证实这种方法在弹性波场模拟方面的数值效...