共查询到20条相似文献，搜索用时 15 毫秒
1.
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
2.
Modeling large multicomponent reactive transport systems in porous media is particularly challenging when the governing partial differential algebraic equations (PDAEs) are highly nonlinear and tightly coupled due to complex nonlinear reactions and strong solution-media interactions. Here we present a preconditioned Jacobian-Free Newton-Krylov (JFNK) solution approach to solve the governing PDAEs in a fully coupled and fully implicit manner. A well-known advantage of the JFNK method is that it does not require explicitly computing and storing the Jacobian matrix during Newton nonlinear iterations. Our approach further enhances the JFNK method by utilizing physics-based, block preconditioning and a multigrid algorithm for efficient inversion of the preconditioner. This preconditioning strategy accounts for self- and optionally, cross-coupling between primary variables using diagonal and off-diagonal blocks of an approximate Jacobian, respectively. Numerical results are presented demonstrating the efficiency and massive scalability of the solution strategy for reactive transport problems involving strong solution-mineral interactions and fast kinetics. We found that the physics-based, block preconditioner significantly decreases the number of linear iterations, directly reducing computational cost; and the strongly scalable algebraic multigrid algorithm for approximate inversion of the preconditioner leads to excellent parallel scaling performance. 相似文献
3.
A terrain-following grid formulation (TFG) is presented for simulation of coupled variably-saturated subsurface and surface water flow. The TFG is introduced into the integrated hydrologic model, ParFlow, which uses an implicit, Newton Krylov solution technique. The analytical Jacobian is also formulated and presented and both the diagonal and non-symmetric terms are used to precondition the Krylov linear system. The new formulation is verified against an orthogonal stencil and is shown to provide increased accuracy at lower lateral spatial discretization for hillslope simulations. Using TFG, efficient scaling to a large number of processors (16,384) and a large domain size (8.1 Billion unknowns) is shown. This demonstrates the applicability of this formulation to high-resolution, large-spatial extent hydrology applications where topographic effects are important. Furthermore, cases where the analytical Jacobian is used for the Newton iteration and as a non-symmetric preconditioner for the linear system are shown to have faster computation times and better scaling. This demonstrates the importance of solver efficiency in parallel scaling through the use of an appropriate preconditioner. 相似文献
4.
不同类别参数间的相互耦合使多参数地震全波形反演的非线性程度显著增加,地震波速度与各向异性参数取值数量级的巨大差异也会使反演问题的性态变差.合理使用Hessian逆算子可以减弱这两类问题对反演的影响,提高多参数反演的精度,而截断牛顿法是一种可以比较准确地估计Hessian逆算子的优化方法.本文采用截断牛顿法在时间域进行了VTI介质的声波双参数同时反演的研究.不同模型的反演试验表明,在VTI介质声波双参数同时反演中,截断牛顿法比有限内存BFGS(Limited-memory Broyden-Fletcher-Goldfarb-Shanno,L-BFGS)法能更准确地估计Hessian逆算子,进而较好地平衡两类不同参数的同时更新,得到了比较精确的反演结果. 相似文献
5.
Due to complex dynamics inherent in the physical models, numerical formulation of subsurface and overland flow coupling can be challenging to solve. ParFlow is a subsurface flow code that utilizes a structured grid discretization in order to benefit from fast and efficient structured solvers. Implicit coupling between subsurface and overland flow modes in ParFlow is obtained by prescribing an overland boundary condition at the top surface of the computational domain. This form of implicit coupling leads to the activation and deactivation of the overland boundary condition during simulations where ponding or drying events occur. This results in a discontinuity in the discrete system that can be challenging to resolve. Furthermore, the coupling relies on unstructured connectivities between the subsurface and surface components of the discrete system, which makes it challenging to use structured solvers to effectively capture the dynamics of the coupled flow. We present a formulation of the discretized algebraic system that enables the use of an analytic form of the Jacobian for the Newton–Krylov solver, while preserving the structured properties of the discretization. An effective multigrid preconditioner is extracted from the analytic Jacobian and used to precondition the Jacobian linear system solver. We compare the performance of the new solver against one that uses a finite difference approximation to the Jacobian within the Newton–Krylov approach, previously used in the literature. Numerical results explores the effectiveness of using the analytic Jacobian for the Newton–Krylov solver, and highlights the performance of the new preconditioner and its cost. The results indicate that the new solver is robust and generally outperforms the solver that is based on the finite difference approximation to the Jacobian, for problems where the overland boundary condition is activated and deactivated during the simulation. A parallel weak scaling study highlights the efficiency of the new solver. 相似文献
6.
Abstract An approach is presented to solve the inverse problem for simultaneous identification of different aquifer parameters under steady-state conditions. The proposed methodology is formulated as a maximum likelihood parameter estimation problem. Gauss-Newton and full Newton algorithms are used for optimization with an adjoint-state method for calculating the complete Hessian matrix. The methodology is applied to a realistic groundwater model and Monte-Carlo analysis is used to check the results. 相似文献
7.
Nuree Han Myung Jin Nam Hee Joon Kim Tae Jong Lee Yoonho Song Jung Hee Suh 《Journal of Applied Geophysics》2009,68(4):533-545
Magnetotelluric (MT) surveys were conducted in Pohang, Korea, for low-temperature geothermal exploration in 2002 and 2003. Pohang is located in the southeastern part of the Korean Peninsula and close to the East Sea. In the interpretation of MT data from a coastal environment, sea effects must be correctly included because seawater is a strong conductor. We first constructed a five-layered earth model with a realistic coastline and bathymetry to investigate sea effects on MT data measured in Pohang. This model clearly shows that the Pohang data are significantly influenced by sea water at frequencies blow 1 Hz at the whole measurement sites. Next, we utilized a three-dimensional inversion algorithm based on the Gauss–Newton approach to produce a reliable resistivity model. Seawater is excluded from the inversion domain to fix the resistivity, while included in the modeling domain to simulate sea effects on MT responses. Blocks for the sub-seafloor are included in unknown parameters since they are sufficiently close to the survey area to affect MT responses in Pohang. Static shifts are also considered in inversion for more accurate interpretation. The rms data misfit is smoothly reduced from 11.2 to 1.87 after 7 iterations. The resulting resistivity model shows a pattern of low–high–low resistivity with depth. The model is compatible with resistivity logs obtained from four boreholes in the survey area, and can explain major geological features in Pohang. 相似文献
8.
应用交错网格有限差分法计算三维复杂环境中的感应测井响应. 其中，利用Krylov子空间不变性求解离散得到的大型稀疏复对称线性方程组. 在构造Krylov子空间时使用其系数矩阵的伪逆以改善迭代的收敛性. 迭代中，使用不完全Cholesky分解共轭梯度法求解4个三维Poisson方程以得到新的Lanczos向量. 通常迭代不超过20次可得到理想结果. 另外，提出一种新的物质平均公式以计算电导率平均值，可保证电流守恒. 相似文献
9.
10.
Modelling of 2D resistivity imaging was done in order to understand the principle resolution of the technique in different geological situations, and for assessing the behaviour of the interpretation methods under controlled circumstances. The Wenner array was used throughout. The results show that the 1D approximation only provides reasonable results in environments with very gradual lateral resistivity changes, otherwise the result may be strongly misleading. Inversion using the 2D quasi-Newton technique results in adequate resolution of the structures in moderately complex environments, but the Gauss–Newton method holds a significant advantage in some complicated cases. The data density can also be of crucial importance for the resolution capability, notably of narrow structures. 相似文献
11.
Lagrangian approaches are well suited to transport in contrasted media but have been considered irrelevant when inversion is envisioned. The randomness of results for the same transport scenario adds to the rough evaluation by perturbation of the sensitivities, yielding an inaccurate search of parameters. It is shown here how a Time Domain Random Walk (TDRW) method can be inverted by deriving the sensitivities analytically. The calculations are very rapid and provide a precise evaluation of the descent directions followed by a Gauss–Newton optimizer. The method handles advection–dispersion + retention by matrix diffusion or sorption with first-order kinetics and proves its worth in all cases. Since analytical sensitivities are available, calculations are rigorous and allow discussing the inversion feasibility, the accuracy of the sought parameters, according to the predominant mechanism involved in the transport scenario. 相似文献
12.
用变分玻恩迭代方法重建二维非均匀介质结构 总被引：8，自引：1，他引：7
提出了用于二维轴对称非均匀介质结构的反演和成像的一种新的反演迭代方法──变分玻恩迭代方法（ＶＢＩＭ）．首先利用玻恩近似将非线性积分方程线性化,然后应用变分方法导出用于反演的电场积分方程．正演数据则利用高效的数值模式匹配方法获得．数值结果表明,ＶＢＩＭ与ＢＩＭ相比,其收敛速度、成像质量等均得到较大的改善。 相似文献
13.
Zhaohai Meng 《Geophysical Prospecting》2018,66(3):626-646
The quantitative explanation of the potential field data of three‐dimensional geological structures remains one of the most challenging issues in modern geophysical inversion. Obtaining a stable solution that can simultaneously resolve complicated geological structures is a critical inverse problem in the geophysics field. I have developed a new method for determining a three‐dimensional petrophysical property distribution, which produces a corresponding potential field anomaly. In contrast with the tradition inverse algorithm, my inversion method proposes a new model norm, which incorporates two important weighting functions. One is the L0 quasi norm (enforcing sparse constraints), and the other is depth‐weighting that counteracts the influence of source depth on the resulting potential field data of the solution. Sparseness constraints are imposed by using the L0 quasinorm on model parameters. To solve the representation problem, an L0 quasinorm minimisation model with different smooth approximations is proposed. Hence, the data space (N) method, which is much smaller than model space (M), combined with the gradient‐projected method, and the model space, combined with the modified Newton method for L0 quasinorm sparse constraints, leads to a computationally efficient method by using an N × N system versus an M × M one because N ? M. Tests on synthetic data and real datasets demonstrate the stability and validity of the L0 quasinorm spare norms inversion method. With the aim of obtaining the blocky results, the inversion method with the L0 quasinorm sparse constraints method performs better than the traditional L2 norm (standard Tikhonov regularisation). It can obtain the focus and sparse results easily. Then, the Bouguer anomaly survey data of the salt dome, offshore Louisiana, is considered as a real case study. The real inversion result shows that the inclusion the L0 quasinorm sparse constraints leads to a simpler and better resolved solution, and the density distribution is obtained in this area to reveal its geological structure. These results confirm the validity of the L0 quasinorm sparse constraints method and indicate its application for other potential field data inversions and the exploration of geological structures. 相似文献
14.
15.
A brief history of the development of the inverse problem in resistivity sounding is presented with the development of the equations governing the least-squares inverse. Five algorithms for finding the minimum of the least-square problem are described and their speed of convergence is compared on data from two planar earth models. Of the five algorithms studied, the ridge-regression algorithm required the fewest numbers of forward problem evaluations to reach a desired minimum. Solution space statistics, including (1) parameter-standard errors, (2) parameter correlation coefficients, (3) model parameter eigenvectors, and (4) data eigenvectors are discussed. The type of weighting applied to the data affects these statistical parameters. Weighting the data by taking log10 of the observed and calculated values is comparable to weighting by the inverse of a constant data error. The most reliable parameter standard errors are obtained by weighting by the inverse of observed data errors. All other solution statistics, such as dataparameter eigenvector pairs, have more physical significance when inverse data error weighting is used. 相似文献
16.
Two-dimensional direct current (DC) resistivity inversion: Data space Occam's approach 总被引：1，自引：0，他引：1
Songkhun Boonchaisuk Chatchai Vachiratienchai Weerachai Siripunvaraporn 《Physics of the Earth and Planetary Interiors》2008,168(3-4):204-211
A data space Occam's inversion algorithm for 2D DC resistivity data has been developed to seek the smoothest structure subject to an appropriate fit to the data. For traditional model space Gauss–Newton (GN) type inversion, the system of equations has the dimensions of M × M, where M is the number of model parameter, resulting in extensive computing time and memory storage. However, the system of equations can be mathematically transformed to the data space, resulting in a dramatic drop in its dimensions to N × N, where N is the number of data parameter, which is usually less than M. The transformation has helped to significantly reduce both computing time and memory storage. Numerical experiments with synthetic data and field data show that applying the data space technique to 2D DC resistivity data for various configurations is robust and accurate when compared with the results from the model space method and the commercial software RES2DINV. 相似文献
17.
This paper presents a method for inverting ground penetrating radargrams in terms of one-dimensional profiles. We resort to a special type of linearization of the damped E-field wave equation to solve the inverse problem. The numerical algorithm for the inversion is iterative and requires the solution of several forward problems, which we evaluate using the matrix propagation approach. Analytical expressions for the derivatives with respect to physical properties are obtained using the self-adjoint Green's function method. We consider three physical properties of materials; namely dielectrical permittivity, magnetic permeability and electrical conductivity. The inverse problem is solved minimizing the quadratic norm of the residuals using quadratic programming optimization. In the iterative process to speed up convergence we use the Levenberg–Mardquardt method. The special type of linearization is based on an integral equation that involves derivatives of the electric field with respect to magnetic permeability, electrical conductivity and dielectric permittivity; this equation is the result of analyzing the implication of the scaling properties of the electromagnetic field. The ground is modeled using thin horizontal layers to approximate general variations of the physical properties. We show that standard synthetic radargrams due to dielectric permittivity contrasts can be matched using electrical conductivity or magnetic permeability variations. The results indicate that it is impossible to differentiate one property from the other using GPR data. 相似文献
18.
Andrea Zanini Peter K. Kitanidis 《Stochastic Environmental Research and Risk Assessment (SERRA)》2009,23(5):565-577
The estimation of field parameters, such as transmissivity, is an important part of groundwater modeling. This work deals
with the quasilinear geostatistical inverse approach to the estimation of the transmissivity fields from hydraulic head measurements.
The standard quasilinear approach is an iterative method consisting of successive linearizations. We examine a synthetic case
to evaluate the basic methodology and some modifications and extensions. The first objective is to evaluate the performance
of the quasilinear approach when applied to strongly heterogeneous (or “high-contrast”) transmissivity fields and, when needed,
to propose improvements that allow the solution of such problems. For large-contrast cases, the standard quasilinear method
often fails to converge. However, by introducing a derivative-free line search as a polishing step after each Gauss–Newton
iteration, we have found that convergence can be practically assured. Another issue is that the quasilinear procedure, which
uses linearization about the best estimate to evaluate estimation variances, may lead to inaccurate estimation of the variance
of the estimated variable. Our numerical results suggest that this may not be a particularly serious problem, though it is
hard to say whether this conclusion will apply to other cases. Nevertheless, since the quasilinear approach is an approximation,
we propose a potentially more accurate but computer-intensive Markov Chain Monte Carlo (MCMC) procedure based on conditional
realizations generated through the quasilinear approach and accepted or rejected according to the Metropolis–Hastings algorithm.
Six transmissivity fields with increasing contrast were generated and one thousand conditional realizations were computed
for each studied case. The MCMC procedure proposed in this work gives an overall more accurate picture than the quasilinear
approach but at a considerably higher computational cost. 相似文献
19.
对于时间域航空电磁法二维和三维反演来说,最大的困难在于有效的算法和大的计算量需求.本文利用非线性共轭梯度法实现了时间域航空电磁法2.5维反演方法,着重解决了迭代反演过程中灵敏度矩阵计算、最佳迭代步长计算、初始模型选取等问题.在正演计算中,我们采用有限元法求解拉式傅氏域中的电磁场偏微分方程,再通过逆拉氏和逆傅氏变换高精度数值算法得到时间域电磁响应.在灵敏度矩阵计算中,采用了基于拉式傅氏双变换的伴随方程法,时间消耗只需计算两次正演,从而节约了大量计算时间.对于最佳步长计算,二次插值向后追踪法能够保证反演迭代的稳定性.设计两个理论模型,检验反演算法的有效性,并讨论了选择不同初始模型对反演结果的影响.模型算例表明:非线性共轭梯度方法应用于时间域航空电磁2.5维反演中稳定可靠,反演结果能够有效地反映地下真实电性结构.当选择的初始模型电阻率值与真实背景电阻率值接近时,能得到较好的反演结果,当初始模型电阻率远大于或远小于真实背景电阻率值时反演效果就会变差. 相似文献
20.
Benjamin Ross 《Ground water》1984,22(5):569-572
In using least-squares parameter estimation techniques to solve for hydrogeologic parameters, one may use a weighting function to reflect differing reliabilities of head measurements. In studies published to date, the weighting function has been used in an ad boc manner or not at all. The inverse square of the observed hydraulic gradient, adjusted to reflect the modeler's perception of geologic heterogeneity and data reliability, is typically an appropriate weighting function. 相似文献