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1.
Toeplitz方程组的近似计算 总被引：2，自引：0，他引：2
从通常所使用的求解Toeplitx方程组的Fourier变换方法出发，结合预条件共乾梯度法(Preconditioned Conjugate Gradient Method,记为PCGM)，在对Toeplitz矩阵系统中的系数矩阵作ω循环延拓后再对其进行求解。理论和实际数值计算表明，该方法化于传统的采用简单循环的普通Fourier变换方法，所得结果具有较好的精度。 相似文献
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初至波走时层析是获取近地表速度结构的一种常用方法.随着采集技术的不断发展,可使用的数据量迅速增多,传统的基于射线追踪和解方程组的地震走时层析成像方法面临着内存占用大、方程求解不稳定等问题.为了解决这些问题,本文基于前人在波形反演研究中提出的一种改进的散射积分算法,提出了一种预条件最速下降法初至波走时层析.该方法无需存储核函数矩阵与Hessian矩阵即可方便地实现目标函数梯度的计算与预条件,且该方法计算效率高、求解稳定、易于并行.数值实验结果表明,该方法可以获得与传统方法精度相当的反演结果,但所占用的内存大幅减小. 相似文献
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基于最小平方的Fourier地震数据重建方法最终转化为求解一个线性方程组, 其系数矩阵是Toeplitz矩阵,可以用共轭梯度法求解该线性方程组.共轭梯度法的迭代次数受系数矩阵病态程度的影响,地震数据的非规则采样程度越高,所形成的系数矩阵病态程度越高,就越难收敛和得到合理的计算结果.本文研究了基于Toeplitz矩阵的不同预条件的构造方法,以及对共轭梯度法收敛性的影响.通过预条件的使用,加快了共轭梯度法的迭代速度, 改进了共轭梯度算法的收敛性,提高了计算的效率.数值算例和实际地震数据重建试验证明了预条件共轭梯度法对计算效率有很大的提高. 相似文献
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采用递推矩阵方法计算径向成层介质的Green函数并将其作为电磁波电阻率仪器的基本理论.根据圆柱形层界面处电场和磁场的连续性条件得到确定待定系数的矩阵方程组并通过递推方法快速求解.只需改变方程组中源项元素的位置,就可以方便地得到当源点和场点在任意层时的Green函数,形式简洁、易于编程.采用将变型Bessel函数的指数项单独列出的方式有效地解决了Green函数计算中的上溢问题.用上述Green函数对随钻电磁波电阻率测量仪器进行数值模拟,分析了钻铤的影响规律、井眼校正方法、仪器的径向探测特性和垂向分辨率.所得到的结论可为随钻电磁波电阻率测量仪器的研制和使用提供理论指导. 相似文献
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高精度及高效频率域声波数值模拟的关键在于高效求解声波方程经离散化后得到的大型稀疏线性方程组.该方程组系数矩阵具有很强的稀疏性,非对称性和非正定性等特征,常用的迭代算法难以准确、高效地求解.为了改善数值模拟迭代算法的收敛性与稳定性,在算法基础上添加预条件算子是求解该类方程的常用方案.本文基于以上思路,引入正则化技术来构造合适的预条件算子,提出正则化预条件迭代算法,以加速求解方程组.通过包含有均匀介质和高非均匀度介质(Marmousi)模型的数值模拟实验结果表明:与单独使用迭代算法相比,本文提出的正则化预条件迭代算法在计算量方面仅多了一次矩阵-矢量相乘,内存消耗未增加;同时,基于该算法的数值模拟结果能够满足精度要求,较单独使用迭代法能够有效改善收敛性质,加快收敛速度;而且,在二维模型算例下,与LU分解算法相比,基于该算法的内存消耗大幅下降. 相似文献
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本文利用世界数字化台网(GDSN)的记录资料,分析计算了1981年1月23日道孚、1985年8月23日新疆以及1981年1月18日日本本州等七个发生在不同构造区的大地震在1—10秒周期下的源谱(ω);汇集了本文作者用相同方法计算得到的发生在消减带、活动板块边界及板块内部不同地区大震的另外31个矩震级M_W≥6.4的源谱(ω)及由P波最大振幅求出的体波震级。将新疆及道孚地震与消减带相同矩震级地震的平均源谱相比,其M(ω)值在10秒周期下与其差别不大,而在1—2秒周期下前二者的(ω)值则高出2—3倍。这一结果相当于应力降高3—5倍。 本文计算出了上述消减带和板内地震在0.1到1Hz的频率范围内的log(ω)-longω的斜率平均值分别为-1.69和-1.26。由此值及10秒周期下的(ω)平均值,可估算出消减带及板内地震在上述频率内不同矩震级M_W下的源谱振幅值(ω)。 通过对25个倾滑型地震在周期T=1.43秒下的源谱振幅和体波震级进行最小二乘回归计算得出:log=0.91m_b+11.60,式中的单位为N·m。对走滑型地震m_b的修订后,得出中国板内走滑型地震的经验公式为log=0.91+11.87。 相似文献
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将瞬变电磁满足的扩散方程转变为波动方程,然后利用地震类成像方法实现瞬变电磁虚拟波场成像,是实现瞬变电磁三维反演的有效手段之一.为了实现由扩散场到虚拟波场的转换,文中采用预条件正则化共轭梯度法求解波场反变换问题.首先,对几种离散方式进行比较,采用条件数最小的离散方式进行离散;然后选择最优的正则化参数,并利用超松弛预条件技术对系数矩阵进行预条件处理;最后,利用共轭梯度法进行迭代求解.超松弛预条件有效降低了系数矩阵的条件数,正则化方法使得反变换得到的波场稳定、可靠,共轭梯度法能够保证计算快速收敛.将反变换结果与已知虚拟波场函数对比,证明算法稳定、可信.将文中算法结果与前人研究结果进行对比,说明方法效果.通过实测数据的波场变换处理给出了文中方法的实际应用效果.结合反变换算法,对不同参数模型进行分析,总结了虚拟波场在色散介质中的传播规律. 相似文献
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本文提出了一种基于非结构化网格的海洋电磁有限单元正演算法.为了回避场源奇异性,文中选用二次场算法,将背景电阻率设置为水平层状且各向异性,场源在水平层状各向异性介质中所激发的一次场通过汉克尔积分得到.基于Coulomb规范得到二次矢量位和标量位所满足的Maxwell方程组,通过Galerkin加权余量法形成大型稀疏有限元方程,采用不完全LU分解(ILU)预条件因子的quasi-minimum residual(QMR)迭代解法对有限元方程进行求解得到二次矢量位和标量位;进而,利用滑动平均方法得到二次矢量位和标量位在空间的导数,由此得到二次电磁场;通过一维模型对算法的可靠性进行验证,与此同时,针对实际复杂海洋电磁模型,比较有限元模拟结果与积分方程模拟结果,进一步验证算法精度.若干计算结果均表明,文中算法具有良好的通用性,适用于井中电磁、航空电磁,环境地球物理等非均匀且各向异性介质中的电磁感应基础研究. 相似文献
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本文采用数值分析的方法探讨Toeplitz矩阵延拓成ω循环矩阵时特征值的逼近程度.对于对称共轭型Toeplitz矩阵,采用ω=±i时对应的循环矩阵特征值的逼近程度较好;对于其它Toeplitz矩阵,采用共轭转置将其转化为对称共轭型矩阵后,才有利于特征值的逼近.可将本文方法广泛应用于地球物理中的数值计算(如位场计算、信号处理中的反褶积、地震资料的偏移处理等). 相似文献
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At the mean annual scale, water availability of a basin is substantially determined by how much precipitation will be partitioned into evapotranspiration and run-off. The Budyko framework provides a simple but efficient tool to estimate precipitation partitioning at the basin scale. As one form of the Budyko framework, Fu's equation has been widely used to model long-term basin-scale water balance. The major difficulty in applications of Fu's equation is determining how to estimate the curve shape parameter ω efficiently. Previous studies have suggested that the parameter ω is closely related to the long-term vegetation coverage on large river basins globally. However, on small basins, the parameter ω is difficult to estimate due to the diversity of controlling factors. Here, we focused on the estimation of ω for small basins in China. We identified the major factors controlling the basin-specific (calibrated) ω from nine catchment attributes based on a dataset from 206 small basins (≤50,000 km2) across China. Next, we related the calibrated ω to the major factors controlling ω using two statistical models, that is, the multiple linear regression (MLR) model and artificial neural network (ANN) model. We compared and validated the two statistical models using an independent dataset of 80 small basins. The results indicated that in addition to vegetation, other landscape factors (e.g., topography and human activity) need to be considered to capture the variability of ω on small basins better. Contrary to previous findings reached on large basins worldwide, the basin-specific ω and remote sensing-based vegetation greenness index exhibit a significant negative correlation. Compared with the default ω value of 2.6 used in the Budyko curve method, the two statistical models significantly improved the mean annual ET simulations on validation basins by reducing the root mean square error from 114 mm/year to 74.5 mm/year for the MLR model and 70 mm/year for the ANN model. In comparison, the ANN model can provide a better ω estimation than the MLR model. 相似文献
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Data from flume studies are used to develop a model for predicting bed‐load transport rates in rough turbulent two‐dimensional open‐channel flows moving well sorted non‐cohesive sediments over plane mobile beds. The object is not to predict transport rates in natural channel flows but rather to provide a standard against which measured bed‐load transport rates influenced by factors such as bed forms, bed armouring, or limited sediment availability may be compared in order to assess the impact of these factors on bed‐load transport rates. The model is based on a revised version of Bagnold's basic energy equation ibsb = ebω, where ib is the immersed bed‐load transport rate, ω is flow power per unit area, eb is the efficiency coefficient, and sb is the stress coefficient defined as the ratio of the tangential bed shear stress caused by grain collisions and fluid drag to the immersed weight of the bed load. Expressions are developed for sb and eb in terms of G, a normalized measure of sediment transport stage, and these expressions are substituted into the revised energy equation to obtain the bed‐load transport equation ib = ω G 3·4. This equation applies regardless of the mode of bed‐load transport (i.e. saltation or sheet flow) and reduces to ib = ω where G approaches 1 in the sheet‐flow regime. That ib = ω does not mean that all the available power is dissipated in transporting the bed load. Rather, it reflects the fact that ib is a transport rate that must be multiplied by sb to become a work rate before it can be compared with ω. It follows that the proportion of ω that is dissipated in the transport of bed load is ibsb/ω, which is approximately 0·6 when ib = ω. It is suggested that this remarkably high transport efficiency is achieved in sheet flow (1) because the ratio of grain‐to‐grain to grain‐to‐bed collisions increases with bed shear stress, and (2) because on average much more momentum is lost in a grain‐to‐bed collision than in a grain‐to‐grain one. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
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《Advances in water resources》2005,28(6):643-660
This work presents a highly efficient numerical scheme for solving immiscible, advection-dominated two-phase flow in heterogeneous porous media. The pressure equation is decoupled from the saturation equation using an IMPES approach, while the advective terms are decoupled from the capillary diffusive terms in the saturation equation through sequential operator splitting. The parabolic and hyperbolic equations are approximated in time by implicit and explicit schemes, respectively. Damped Newton linearization is applied to the implicit non-linear diffusive step. Mixed hybrid finite elements are applied to the global pressure equation and to the regularized capillary diffusion term. For both linear systems arising from the approximation procedure, an AMG preconditioned conjugate gradient solver is used. A finite volume scheme with slope limiter is applied to the advective step. Numerical comparison with standard preconditioners demonstrates the reliability of the proposed AMG-preconditioner. Benchmark examples illustrate the robustness of the method. 相似文献
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The boundary-volume integral equation numerical technique can be a powerful tool for piecewise heterogeneous media, but it is limited to small problems or low frequencies because of great computational cost. Therefore, a restarted GMRES method is applied to solve large-scale boundary-volume scattering problems in this paper to overcome the computational barrier. The iterative method is firstly applied to responses of dimensionless frequency to a semicircular alluvial valley filled with sediments, compared with the standard Gaussian elimination method. Then the method is tested by a heterogeneous multilayered model to show its applicability. Numerical experiments indicate that the preconditioned GMRES method can significantly improve computational efficiency especially for large Earth models and high frequencies, but with a faster convergence for the left diagonal preconditioning. 相似文献
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系统地论述了用有限单元法研究复杂地形条件下三维直流电阻率的正演计算技术.首先给出了三维构造中点源电场的边值问题以及相应的变分问题;然后利用有限单元法求解变分问题,采用四面体单元对研究区域进行剖分,在单元中进行三线性函数插值,将变分方程化为线性代数方程组;最后,考虑到节约计算时间,利用对称超松弛顸条件共轭梯度迭代算法求解大型线性方程组,得到了各节点的电位值,进而计算出地表的视电阻率.通过理论模型的计算检验了算法的可行性之后,给出了几种常见纯地形异常的数值模拟结果和一个组合模型的计算结果,其研究工作为研究三维直流电阻率反演奠定了基础. 相似文献
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In this paper we propose a 3D acoustic full waveform inversion algorithm in the Laplace domain. The partial differential equation for the 3D acoustic wave equation in the Laplace domain is reformulated as a linear system of algebraic equations using the finite element method and the resulting linear system is solved by a preconditioned conjugate gradient method. The numerical solutions obtained by our modelling algorithm are verified through a comparison with the corresponding analytical solutions and the appropriate dispersion analysis. In the Laplace‐domain waveform inversion, the logarithm of the Laplace transformed wavefields mainly contains long‐wavelength information about the underlying velocity model. As a result, the algorithm smoothes a small‐scale structure but roughly identifies large‐scale features within a certain depth determined by the range of offsets and Laplace damping constants employed. Our algorithm thus provides a useful complementary process to time‐ or frequency‐domain waveform inversion, which cannot recover a large‐scale structure when low‐frequency signals are weak or absent. The algorithm is demonstrated on a synthetic example: the SEG/EAGE 3D salt‐dome model. The numerical test is limited to a Laplace‐domain synthetic data set for the inversion. In order to verify the usefulness of the inverted velocity model, we perform the 3D reverse time migration. The migration results show that our inversion results can be used as an initial model for the subsequent high‐resolution waveform inversion. Further studies are needed to perform the inversion using time‐domain synthetic data with noise or real data, thereby investigating robustness to noise. 相似文献
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We present preconditioned non‐linear conjugate gradient algorithms as alternatives to the Gauss‐Newton method for frequency domain full‐waveform seismic inversion. We designed two preconditioning operators. For the first preconditioner, we introduce the inverse of an approximate sparse Hessian matrix. The approximate Hessian matrix, which is highly sparse, is constructed by judiciously truncating the Gauss‐Newton Hessian matrix based on examining the auto‐correlation and cross‐correlation of the Jacobian matrix. As the second preconditioner, we employ the approximation of the inverse of the Gauss‐Newton Hessian matrix. This preconditioner is constructed by terminating the iteration process of the conjugate gradient least‐squares method, which is used for inverting the Hessian matrix before it converges. In our preconditioned non‐linear conjugate gradient algorithms, the step‐length along the search direction, which is a crucial factor for the convergence, is carefully chosen to maximize the reduction of the cost function after each iteration. The numerical simulation results show that by including a very limited number of non‐zero elements in the approximate Hessian, the first preconditioned non‐linear conjugate gradient algorithm is able to yield comparable inversion results to the Gauss‐Newton method while maintaining the efficiency of the un‐preconditioned non‐linear conjugate gradient method. The only extra cost is the computation of the inverse of the approximate sparse Hessian matrix, which is less expensive than the computation of a forward simulation of one source at one frequency of operation. The second preconditioned non‐linear conjugate gradient algorithm also significantly saves the computational expense in comparison with the Gauss‐Newton method while maintaining the Gauss‐Newton reconstruction quality. However, this second preconditioned non‐linear conjugate gradient algorithm is more expensive than the first one. 相似文献
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《Advances in water resources》2002,25(2):147-157
The contaminant transport equation is solved in three dimensions using the Eulerian–Lagrangian Localized Adjoint Method (ELLAM). Trilinear and finite volume test functions defined by the characteristics of the governing equation are employed and compared. Integrations are simplified by forward tracking of integration points along the characteristics. The resulting equations are solved using a preconditioned conjugate gradient method. The algorithm is coupled to a block-centered finite difference approximation of the groundwater flow equation similar to that used in the popular MODFLOW code. The ELLAM is tested by comparison with 1D and 3D analytic solutions. The method is then applied with random, spatially correlated hydraulic conductivities in a simulation of a tracer experiment performed on Cape Cod, Massachusetts. The linear test function ELLAM was found to perform better than the finite volume ELLAM. Both ELLAM formulations were found to be robust, computationally efficient and relatively straightforward to implement. When compared to traditional particle tracking and characteristics codes commonly used with MODFLOW, the ELLAM retains the computational advantages of traditional characteristic methods with the added advantage of good mass conservation. 相似文献
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多道瞬变电磁法(MTEM)是近年来发展起来的一种新的地球物理勘查技术,其数据采集方式与地震法类似,因此,采用瞬变电磁拟地震解释方法对MTEM数据进行处理解释具有一定的优越性.研究MTEM虚拟波场有效提取方法具有重要意义.在以往奇异值分解法、预条件正则化共轭梯度法两种不同的常规提取方法研究基础上,本文提出采用相关叠加法提取MTEM虚拟波场信息.首先采用预条件正则化共轭梯度法对全时段MTEM数据进行虚拟波场提取,然后采用同种方法对划分的各时间段数据进行虚拟波场提取,最后对全时段提取结果与各个时间段提取结果进行相关性叠加,叠加结果作为最终的提取结果.实测MTEM数据虚拟波场提取结果表明,采用相关叠加法可以得到稳定、光滑的虚拟波场波形曲线,且抗干扰能力强. 相似文献