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1.
《地球物理学进展》2015,(5)
交错网格有限差分方法已经被广泛应用到数值模拟和地震波传播的研究中.传统交错网格有限差分方法中,一阶空间导数的高阶差分系数是通过Taylor级数展开求取的,这种表示空间导数的方法会导致数值频散的产生.本文针对时间二阶空间十阶交错网格有限差分算法,采用最小二乘法通过改变积分区间求取一系列一阶空间导数的差分系数,分析该差分系数和传统方法求取的差分系数的频散关系.选取效果最佳的最小二乘法进行数值模拟,并与传统方法相比较.数值频散分析和弹性波场模拟分析表明:介质弹性参数和离散参数相同的情况下,采用最佳积分区间的最小二乘法更能有效地压制数值频散,比Taylor级数展开法具有更高的数值模拟精度. 相似文献
2.
基于离散控制理论,结合CR法和RST法提出一种无条件稳定的动力学显式新算法。以算法精度和稳定性为条件,通过离散传递函数推导参数表达式和极点,使得新算法可满足零振幅衰减率和零周期延长率。算法参数α和γ作为传递格式选择参数,当α和γ分别取1时,新算法对应CR法和RST法的位移速度表达式。对新算法的精度和稳定性理论分析表明:新算法可满足无振幅衰减和周期延长,且对于线性系统和非线性刚度软化系统为无条件稳定,对非线性刚度硬化系统为条件稳定,并给出了非线性刚度硬化系统的稳定性范围。算例分析验证了新算法的精度和稳定性,证明提出的新算法是可靠有效的。 相似文献
3.
在Newmark精细直接积分法的基础上,应用高斯积分与精细指数运算,提出该方法的两种逐步积分格式。文中对两种积分格式的稳定性和精度进行了分析。经过分析比较,第1种逐步积分格式计算精度较高,其稳定性明显地满足算法稳定性分析的条件;而第2种积分格式计算精度相对较差,且是不稳定的。因此本文将第1种积分格式应用于结构的地震反应分析中。算例表明,该逐步积分格式对地震作用有很好的适应性。 相似文献
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5.
复杂地形条件下地震波走时算法对于研究复杂地形地区的成像问题有着重要的意义.为了得到精度高且适应于复杂地形的走时算法,首先提出阶梯网格迎风差分法.然后将该方法与不等距网格有限差分法和混合网格线性插值法进行对比研究,得出如下结论:混合网格线性插值法的计算精度最高,但其计算效率最低;阶梯网格迎风差分法的计算精度最低,但其计算效率最高;不等距网格有限差分法的计算精度和计算效率均居中;而究竟选取哪种算法作为给定复杂地形模型的地震波走时算法,应该综合考虑地形的特点、所研究问题对计算精度及计算效率的要求等因素.最后通过一个计算实例验证了三种算法在面对复杂地形、近地表及地下复杂介质等复杂地质条件时均有很好的适应性和稳定性. 相似文献
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详细介绍了二级近似加速度法的推导思路,从理论上可以看出它有三阶精度。通过在MATLAB上运行编制的程序,实现了二级近似加速度法在结构动力时程分析中的应用。在单自由度体系和多自由度体系中输入十条地震波后发现:在步长取相同值的情况下,本文方法绝大部分的平均相对误差要小于Wilson-θ法。也就是说要达到相同的精度,二级近似加速度法需要迭代的次数更少,因此收敛速度更快。另外,理论上精度高的算法不一定在任何情况下都比精度较低的算法表现好,算法的精度与步长大小、荷载复杂程度、振幅衰减率和周期延长率都有关系。以上研究为在实际工程应用中选取高精度的逐步积分算法提供参考。 相似文献
7.
通常工业界实现逆时偏移算法时采用有限差分数值方法模拟地震波场,波场模拟常常受稳定性条件限制,且易产生数值频散,成像精度降低.本文引入了一步法波场延拓方法,首先构建声波传播算子,借助Chebyshev多项式和Jacobi-Anger展开式近似传播算子中的e指数项,进而实现波场递推,该方法时间步长的选取不受稳定性条件限制而且不存在空间频散现象.本文将一步法波场延拓方法用于逆时偏移成像的波场模拟,并提出双缓冲区存储策略,在不增加计算量的前提下,大幅降低了逆时偏移方法的波场存储量.波场模拟和逆时偏移成像测试表明,本文提出的一步法波场延拓方法模拟地震波场精度高,消除了频散影响,可在较大时间步长的情况下实现高精度波场模拟;提出的基于一步法波场延拓的逆时偏移方法成像质量好;基于双缓冲区存储策略的逆时偏移成像方法存储成本低. 相似文献
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从分形几何的新视角出发,分析近断层地震动的不规则性和复杂性.利用盒维数法计算了来自台湾集集地震和美国北岭地震的30条近断层地震动加速度时程的分形维数.计算结果表明,这些地震动加速度时程具有统计分形特征.近断层地震动运动特征对其分维数影响明显,滑冲效应脉冲地震动的分维数平均值最小,向前方向性效应脉冲地震动的分维数平均值居中,无脉冲地震动的分维数平均值最大,其波形不规则程度也最高.而且,地震动时程的分维数反映了其频谱特性,可作为频谱周期的表征参数.地震动的分维数D与特征周期Tc具有较强的负相关关系.最后,对于近断层地震动作用下单自由度(SDOF)体系的弹性和非弹性动力反应时程,应用盒维数法计算了其分形维数,考察了其分形性质. 相似文献
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采用与传统频域法相反的思路,提出一种内蕴基线漂移校正且匹配目标反应谱的人工地震波直接拟合新方法。该方法首先构造非平稳位移时程表达式,进而求导得到速度、加速度时程表达式,由各表达式满足的归零条件确定相关的包络函数;其次,结合单自由度系统谐波响应的解析式,将匹配目标反应谱的拟合问题转化为关于待求幅值谱的非线性方程组;最后,结合高效的非线性方程迭代算法给出自然满足归零条件的加速度、速度及位移时程。分别以Rg1.60标准谱、某核岛楼层谱和《建筑抗震设计规范》中的设计谱为拟合算例验证所提方法的效率和精度。所提方法可成为人工地震波快速拟合的新途径。 相似文献
10.
《地震工程与工程振动》2021,41(2)
粒子群优化算法是模拟群体智能所建立起来的一种全局优化算法,在解决多参数非线性函数的优化问题上具有良好的性能,为了有更好的收敛精度和更快的收敛速度,本文构建了带有压缩因子的粒子群算法,可用于设计反应谱的标定。利用这一方法可给出第一拐点周期、特征周期、平台值和衰减指数等刻画设计反应谱特征的参数值。本文以埃尔森特罗台(El Centro)加速度时程的反应谱标定为例,采用本文提出的改进粒子群算法、Newmark三参数法、双参数法和差分进化算法对其进行标定。对比分析了4种标定方法给出的特征参数及计算精度,实例证明,改进粒子群算法具有较高的精度,给出的设计反应谱较好地反映了地震反应谱的特征。 相似文献
11.
Taking the anisotropy of velocity and attenuation into account, we investigate the wavefield simulation of viscoacoustic waves in 3D vertical transversely isotropic attenuating media. The viscoacoustic wave equations with the decoupled amplitude attenuation and phase dispersion are derived from the fractional Laplacian operator and using the acoustic approximation. With respect to the spatially variable fractional Laplacian operator in the formulation, we develop an effective algorithm to realize the viscoacoustic wavefield extrapolation by using the arbitrary-order Taylor series expansion. Based on the approximation, the mixed-domain fractional Laplacian operators are decoupled from the wavenumbers and fractional orders. Thus, the viscoacoustic wave propagation can be conveniently implemented by using a generalized pseudospectral method. In addition, we perform the accuracy and efficiency analyses among first-, second- and third-order Taylor series expansion pseudospectral methods with different quality factors. Considering both the accuracy and computational cost, the second-order Taylor series expansion pseudospectral method can generally satisfy the requirements for most attenuating media. Numerical modelling examples not only illustrate that our decoupled viscoacoustic wave equations can effectively describe the attenuating property of the medium, but also demonstrate the accuracy and the high robustness of our proposed schemes. 相似文献
12.
Optimal implicit staggered‐grid finite‐difference schemes based on the sampling approximation method for seismic modelling 
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下载免费PDF全文 We propose new implicit staggered‐grid finite‐difference schemes with optimal coefficients based on the sampling approximation method to improve the numerical solution accuracy for seismic modelling. We first derive the optimized implicit staggered‐grid finite‐difference coefficients of arbitrary even‐order accuracy for the first‐order spatial derivatives using the plane‐wave theory and the direct sampling approximation method. Then, the implicit staggered‐grid finite‐difference coefficients based on sampling approximation, which can widen the range of wavenumber with great accuracy, are used to solve the first‐order spatial derivatives. By comparing the numerical dispersion of the implicit staggered‐grid finite‐difference schemes based on sampling approximation, Taylor series expansion, and least squares, we find that the optimal implicit staggered‐grid finite‐difference scheme based on sampling approximation achieves greater precision than that based on Taylor series expansion over a wider range of wavenumbers, although it has similar accuracy to that based on least squares. Finally, we apply the implicit staggered‐grid finite difference based on sampling approximation to numerical modelling. The modelling results demonstrate that the new optimal method can efficiently suppress numerical dispersion and lead to greater accuracy compared with the implicit staggered‐grid finite difference based on Taylor series expansion. In addition, the results also indicate the computational cost of the implicit staggered‐grid finite difference based on sampling approximation is almost the same as the implicit staggered‐grid finite difference based on Taylor series expansion. 相似文献
13.
L. Jones 《Stochastic Environmental Research and Risk Assessment (SERRA)》1989,3(3):179-190
The expected head and standard deviation of the head from the first order Taylor series approximation is compared to Monte Carlo simulation, for steady flow in a confined aquifer with transmissivity as a random variable. Emphasis is on the effect of changes in the covariance structure of the transmissivity, and pumping rates, on the errors in the first order Taylor series approximation. The accuracy of the first order Taylor series approximation is found to be particularly sensitive to pumping rates. With significant pumping the approximation is found to under estimate both the expected drawdown and head variance, and the error increases as the pumping rate increases. This can lead to large errors in probability constraints based on moments from the first order Taylor series approximation. 相似文献
14.
双相各向异性介质中偶数阶精度有限差分数值模拟 总被引：1，自引：1，他引：0
To improve the accuracy of the conventional finite-difference method, finitedifference numerical modeling methods of any even-order accuracy are recommended. We introduce any even-order accuracy difference schemes of any-order derivatives derived from Taylor series expansion. Then, a finite-difference numerical modeling method with any evenorder accuracy is utilized to simulate seismic wave propagation in two-phase anisotropic media. Results indicate that modeling accuracy improves with the increase of difference accuracy order number. It is essential to find the optimal order number, grid size, and time step to balance modeling precision and computational complexity. Four kinds of waves, static mode in the source point, SV wave cusps, reflection and transmission waves are observed in two-phase anisotropic media through modeling. 相似文献
15.
The magnetic interface forward and inversion method is realized using the Taylor series expansion to linearize the Fourier transform of the exponential function. With a large expansion step and unbounded neighborhood, the Taylor series is not convergent, and therefore, this paper presents the magnetic interface forward and inversion method based on Padé approximation instead of the Taylor series expansion. Compared with the Taylor series, Padé’s expansion’s convergence is more stable and its approximation more accurate. Model tests show the validity of the magnetic forward modeling and inversion of Padé approximation proposed in the paper, and when this inversion method is applied to the measured data of the Matagami area in Canada, a stable and reasonable distribution of underground interface is obtained. 相似文献
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A new approach is presented for improving the computational efficiency of regional-scale ground water models based on the analytic element method (AEM). The algorithm is an extension of the existing "superblock" algorithm, which combines the effects of multiple analytic elements into Laurent series and Taylor series (superblock expansions). With the new "nested superblock" formulation, Laurent series are nested in a hierarchical (quad-tree) data structure with direct mathematical relationships between parent and child superblock coefficients. Nested superblocks significantly accelerate the evaluation of the complex potential and discharge function in models that contain a large number of analytic elements at multiple scales. This evaluation process, the primary computational cost of AEM models, is required to determine the element coefficients, generate contour plots, and trace pathlines. The performance of the nested superblocks is demonstrated with a simplified model based on the Lake Ontario watershed geometry comprising thousands of hydrogeologic features at multiple geographic scales. 相似文献
17.
与地面地震资料相比,VSP资料具有分辨率高、环境噪声小及能更好地反映井旁信息等优点.常规VSP偏移主要对上行反射波进行成像,存在照明度低、成像范围受限等问题.为了增加照明度、拓宽成像范围、提高成像精度,本文采用直达波除外的所有声波波场数据(全波),包括一次反射波、多次反射波等进行叠前逆时偏移成像.针对逆时偏移中的四个关键问题,即波场延拓、吸收边界条件、成像条件及低频噪声的压制,本文分别采用自适应变空间差分算子长度的优化有限差分方法(自适应优化有限差分方法)求解二维声波波动方程以实现高精度、高效率的波场延拓,采用混合吸收边界条件压制因计算区域有限所引起的人工边界反射,采用震源归一化零延迟互相关成像条件进行成像,采用拉普拉斯滤波方法压制逆时偏移中产生的低频噪声.本文对VSP模型数据的逆时偏移成像进行了分析,结果表明:自适应优化有限差分方法比传统有限差分方法具有更高的模拟精度与计算效率,适用于VSP逆时偏移成像;全波场VSP逆时偏移成像比上行波VSP逆时偏移的成像范围大、成像效果好;相对于反褶积成像条件,震源归一化零延迟互相关成像条件具有稳定性好、计算效率高等优点.将本文方法应用于某实际VSP资料的逆时偏移成像,进一步验证了本文方法的正确性和有效性. 相似文献
18.
The traditional conservation of mass equation is derived using a first-order Taylor series to represent flux change in a control volume, which is valid strictly for cases of linear changes in flux through the control volume. We show that using higher-order Taylor series approximations for the mass flux results in mass conservation equations that are intractable. We then show that a fractional Taylor series has the advantage of being able to exactly represent non-linear flux in a control volume with only two terms, analogous to using a first-order traditional Taylor series. We replace the integer-order Taylor series approximation for flux with the fractional-order Taylor series approximation, and remove the restriction that the flux has to be linear, or piece-wise linear, and remove the restriction that the control volume must be infinitesimal. As long as the flux can be approximated by a power-law function, the fractional-order conservation of mass equation will be exact when the fractional order of differentiation matches the flux power-law. There are two important distinctions between the traditional mass conservation, and its fractional equivalent. The first is that the divergence term in the fractional mass conservation equation is the fractional divergence, and the second is the appearance of a scaling term in the fractional conservation of mass equation that may eliminate scale effects in parameters (e.g., hydraulic conductivity) that should be scale-invariant. 相似文献
19.
Expanding the magnetic field intensity measured at a constant altitude in a Taylor series allows the efficient continuation of such fields onto any given arbitrary surface. This is particularly useful for draping of constant altitude surveys in areas of rugged topography. The Taylor series approach allows the continuation to points below the level of the shallowest magnetic source present. Low-pass filtering is necessary to ensure the convergence of the series. The filtering parameters can be estimated from the power spectrum of the observed field and the maximum continuation distance. A synthetic data example shows that convergence of the series is slowest in areas of high vertical gradients, usually associated with body edges, and large (downward) continuation distances. The Taylor series method is used to drape data from a constant barometric altitude survey from central British Columbia (Canada) onto a surface with a constant terrain clearance. This survey is then joined to an adjacent survey flown in the draped mode. The resolution and amplitudes of the two surveys is seen to be comparable and results in a more coherent combined data set than that where no computational draping is done. 相似文献
20.
The dynamic element method has been shown previously to provide a computational advantage over the ordinary finite element method for various beam elements. The Taylor expansions are computed here for the dynamic shape functions (two terms) and dynamic stiffness matrix (four terms) for the axisymmetric vibrations of an annular plate element. The complicated matrices which result are made more tractable by expressing them as power series in powers of the aspect ratio. The percentage error in the natural frequencies is then calculated using both the two- and the three-term dynamic stiffness matrix, demonstrating the increased accuracy for a given number of elements. 相似文献