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1.
The scaled boundary finite‐element method has been developed for the dynamic analysis of unbounded domains. In this method only the boundary is discretized resulting in a reduction of the spatial dimension by one. Like the finite‐element method no fundamental solution is required. This paper extends the scaled boundary finite‐element method to simulate the transient response of non‐homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates. To reduce the number of degrees of freedom and the computational cost, the technique of reduced set of base functions is applied. The scaled boundary finite‐element equation for an unbounded domain is reformulated in generalized coordinates. The resulting acceleration unit‐impulse response matrix is obtained and assembled with the equation of motion of standard finite elements. Numerical examples of non‐homogeneous isotropic and transversely isotropic unbounded domains demonstrate the accuracy of the scaled boundary finite‐element method. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
2.
The scaled boundary finite‐element method is extended to simulate time‐harmonic responses of non‐homogeneous unbounded domains with the elasticity modulus and mass density varying as power functions of spatial coordinates. The unbounded domains and the elasticity matrices are transformed to the scaled boundary coordinates. The scaled boundary finite‐element equation in displacement amplitudes are derived directly from the governing equations of elastodynamics. To enforce the radiation condition at infinity, an asymptotic expansion of the dynamic‐stiffness matrix for high frequency is developed. The dynamic‐stiffness matrix at lower frequency is obtained by numerical integration of ordinary differential equations. Only the boundary is discretized yielding a reduction of the spatial dimension by one. No fundamental solution is required. Material anisotropy is modelled without additional efforts. Examples of two‐ and three‐dimensional non‐homogeneous isotropic and transversely isotropic unbounded domains are presented. The results demonstrate the accuracy and simplicity of the scaled boundary finite‐element method. Copyright © 2005 John Wiley & Sons, Ltd. 相似文献
3.
Ho Seuk Bae Sukjoon Pyun Wookeen Chung Seung‐Goo Kang Changsoo Shin 《Geophysical Prospecting》2012,60(3):413-432
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. 相似文献
4.
为解决传统有限元截断边界所引起的问题,本文提出了一种新的三维直流电阻率有限元-无限元耦合数值模拟方法.首先推导了无限元三维单元映射函数,然后提出了一种全新的最优的无限元形函数并与多种其他形函数进行了对比,随后将其与非结构化四面体有限元相结合,取代了传统的混合边界条件,使得电位在无限域内连续并在无限远处衰减为零,最终形成的左端矩阵稀疏对称并与场源位置无关.数值计算表明,该方法可以在近似测区大小的计算范围内得到与混合边界条件相当的计算精度,优于相同计算范围下齐次边界条件的解,有利于减少计算节点数;由于左端矩阵不随场源位置改变,有利于加速反演计算. 相似文献
5.
复电阻率法二维有限元数值模拟 总被引：9，自引：2，他引：9
伴随着复电阻率法的广泛应用，发展精确和快速的正演和反演算法成为复电阻率法研究的重点.本文采用基于三角单元剖分的有限单元法进行了复电阻率二维数值模拟研究.为了提高计算速度，对无穷远边界进行了近似处理.整个正演计算过程分为两步，首先采用有限单元法计算四个不同频率的视复电阻率数据，然后对前一步得到的视复电阻率数据采用递推算法计算视Cole-Cole参数.采用这种正演算法与一维正演的结果进行了对比，验证了本文方法的正确性.设计了两个二维极化模型，数值模拟结果表明视复电阻率和Cole-Cole视参数等值线断面图对于异常目标体都有比较明显的反映. 相似文献
6.
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
7.
Accelerating the T‐matrix approach to seismic full‐waveform inversion by domain decomposition 
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下载免费PDF全文 A seismic variant of the distorted Born iterative inversion method, which is commonly used in electromagnetic and acoustic (medical) imaging, has been recently developed on the basis of the T‐matrix approach of multiple scattering theory. The distorted Born iterative method is consistent with the Gauss–Newton method, but its implementation is different, and there are potentially significant computational advantages of using the T‐matrix approach in this context. It has been shown that the computational cost associated with the updating of the background medium Green functions after each iteration can be reduced via the use of various linearisation or quasi‐linearisation techniques. However, these techniques for reducing the computational cost may not work well in the presence of strong contrasts. To deal with this, we have now developed a domain decomposition method, which allows one to decompose the seismic velocity model into an arbitrary number of heterogeneous domains that can be treated separately and in parallel. The new domain decomposition method is based on the concept of a scattering‐path matrix, which is well known in solid‐state physics. If the seismic model consists of different domains that are well separated (e.g., different reservoirs within a sedimentary basin), then the scattering‐path matrix formulation can be used to derive approximations that are sufficiently accurate but far more speedy and much less memory demanding because they ignore the interaction between different domains. However, we show here that one can also use the scattering‐path matrix formulation to calculate the overall T‐matrix for a large model exactly without any approximations at a computational cost that is significantly smaller than the cost associated with an exact formal matrix inversion solution. This is because we have derived exact analytical results for the special case of two interacting domains and combined them with Strassen's formulas for fast recursive matrix inversion. To illustrate the fact that we have accelerated the T‐matrix approach to full‐waveform inversion by domain decomposition, we perform a series of numerical experiments based on synthetic data associated with a complex salt model and a simpler two‐dimensional model that can be naturally decomposed into separate upper and lower domains. If the domain decomposition method is combined with an additional layer of multi‐scale regularisation (based on spatial smoothing of the sensitivity matrix and the data residual vector along the receiver line) beyond standard sequential frequency inversion, then one apparently can also obtain stable inversion results in the absence of ultra‐low frequencies and reduced computation times. 相似文献
8.
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
9.
在多源直流电阻率法有限元三维数值模拟中,传统混合边界条件由于刚度矩阵与源点位置相关,无法实现线性方程组的快速回代求解,目前常用齐次边界条件或无限元边界进行替代,虽然实现了快速回代求解,但同时也降低了数值模拟的精度.为了实现快速回代求解,并确保数值模拟的计算精度,本文提出了一种近似边界条件方法.其核心思想是将与场源位置相关的边界系数矩阵从刚度矩阵中分离出来,使得分离后的刚度矩阵与场源位置无关.并将边界系数矩阵与边界处一次电场向量的乘积移到线性方程组右端源项中,当场源位置发生改变时,只需要重新计算右端源项就可以实现快速回代求解.理论模型数值计算表明,在水平地形条件下,本文边界条件数值精度优于混合边界条件;在起伏地形条件下,与齐次边界条件相比,本文边界条件数值结果与混合边界条件吻合度更高. 相似文献
10.
Application of Large‐Scale Inversion Algorithms to Hydraulic Tomography in an Alluvial Aquifer 下载免费PDF全文
下载免费PDF全文 P. Fischer A. Jardani A. Soueid Ahmed M. Abbas X. Wang H. Jourde N. Lecoq 《Ground water》2017,55(2):208-218
Large‐scale inversion methods have been recently developed and permitted now to considerably reduce the computation time and memory needed for inversions of models with a large amount of parameters and data. In this work, we have applied a deterministic geostatistical inversion algorithm to a hydraulic tomography investigation conducted in an experimental field site situated within an alluvial aquifer in Southern France. This application aims to achieve a 2‐D large‐scale modeling of the spatial transmissivity distribution of the site. The inversion algorithm uses a quasi‐Newton iterative process based on a Bayesian approach. We compared the results obtained by using three different methodologies for sensitivity analysis: an adjoint‐state method, a finite‐difference method, and a principal component geostatistical approach (PCGA). The PCGA is a large‐scale adapted method which was developed for inversions with a large number of parameters by using an approximation of the covariance matrix, and by avoiding the calculation of the full Jacobian sensitivity matrix. We reconstructed high‐resolution transmissivity fields (composed of up to 25,600 cells) which generated good correlations between the measured and computed hydraulic heads. In particular, we show that, by combining the PCGA inversion method and the hydraulic tomography method, we are able to substantially reduce the computation time of the inversions, while still producing high‐quality inversion results as those obtained from the other sensitivity analysis methodologies. 相似文献
11.
本文从总电位法和异常电位法两个方面,分别就直流电法有限元中所采用的三类边界条件对计算结果的影响进行了分析,为采用合适的边界条件及选取最佳边界距离来提高正演精度提供了基础.结果表明,混合边界条件精度最高,可大大缩小求解区域而不影响计算精度,其次是Dirichlet边界条件精度较高,但测点越靠边界误差会越大,必须取足够大的边界区域,齐次边界条件的误差比较大,但如果采用非二极装置,通过电位差计算得到的视电阻率,由于无穷远边界对电位差的影响基本消除,视电阻率计算误差与混合边界条件下的接近,在反演中,为了节省计算时间,经常使用齐次边界条件进行有限元正演. 相似文献
12.
A three‐dimensional transmitting boundary is formulated in the Cartesian co‐ordinate system. It is developed for the dynamic soil–structure interaction problems of arbitrary shape foundations in laterally heterogeneous strata overlying rigid bedrock. Dynamics of a rectangular rigid surface foundation on a homogeneous stratum is analysed by a hybrid approach in which the finite region including foundation is modelled by the conventional finite element method and the surrounding infinite region by the newly developed transmitting boundary. To demonstrate its strength, the present method is applied to a rectangular foundation in a horizontally heterogeneous ground consisting of two distinct regions divided by and welded along a vertical plane. Copyright © 2000 John Wiley & Sons, Ltd. 相似文献
13.
Ho Seuk Bae Changsoo Shin Young Ho Cha Yunseok Choi Dong‐Joo Min 《Geophysical Prospecting》2010,58(6):997-1010
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. 相似文献
14.
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
15.
模拟地震波传播的三维逐元并行谱元法 总被引：2，自引：0，他引：2
高效地震波场正演模拟对于复杂模型中地震波传播与成像研究至关重要.本文在谱元法原理框架内,对已有逐元谱元法改进,提出一种新的逐元并行谱元法求解三维地震波运动方程,并得到地震波场.逐元并行谱元法的核心思想在于在单元上进行质量矩阵与解向量的乘积运算,并将此运算平均分配至每一个CPU计算核心,此处理有利提升谱元法的并行计算效率.同时,根据Gauss-Lobatto-Legendre(GLL)数值积分点与插值点重合的特点,将稠密单元刚度矩阵的存储转化成单元雅克比矩阵行列式的值及其逆的存储,大幅减少谱元法计算内存开销.此外,在模型边界上利用逐元并行谱元法求解二阶位移形式完美匹配层(PML)吸收边界条件,消除边界截断而引入的虚假反射.通过逐元并行谱元法得到的数值解与解析解对比,以及实际地震波场模拟,数值结果证实了逐元并行谱元法用于地震波场模拟的高效性. 相似文献
16.
Passive seismic has recently attracted a great deal of attention because non‐artificial source is used in subsurface imaging. The utilization of passive source is low cost compared with artificial‐source exploration. In general, constructing virtual shot gathers by using cross‐correlation is a preliminary step in passive seismic data processing, which provides the basis for applying conventional seismic processing methods. However, the subsurface structure is not uniformly illuminated by passive sources, which leads to that the ray path of passive seismic does not fit the hyperbolic hypothesis. Thereby, travel time is incorrect in the virtual shot gathers. Besides, the cross‐correlation results are contaminated by incoherent noise since the passive sources are always natural. Such noise is kinematically similar to seismic events and challenging to be attenuated, which will inevitably reduce the accuracy in the subsequent process. Although primary estimation for transient‐source seismic data has already been proposed, it is not feasible to noise‐source seismic data due to the incoherent noise. To overcome the above problems, we proposed to combine focal transform and local similarity into a highly integrated operator and then added it into the closed‐loop surface‐related multiple elimination based on the 3D L1‐norm sparse inversion framework. Results proved that the method was capable of reliably estimating noise‐free primaries and correcting travel time at far offsets for a foresaid virtual shot gathers in a simultaneous closed‐loop inversion manner. 相似文献
17.
Three‐dimensional controlled‐source electromagnetic modelling with a well casing as a grounded source: a hybrid method of moments and finite element scheme 下载免费PDF全文
下载免费PDF全文 Steel well casings in or near a hydrocarbon reservoir can be used as source electrodes in time‐lapse monitoring using grounded line electromagnetic methods. A requisite component of carrying out such monitoring is the capability to numerically model the electromagnetic response of a set of source electrodes of finite length. We present a modelling algorithm using the finite‐element method for calculating the electromagnetic response of a three‐dimensional conductivity model excited using a vertical steel‐cased borehole as a source. The method is based on a combination of the method of moments and the Coulomb‐gauged primary–secondary potential formulation. Using the method of moments, we obtain the primary field in a half‐space due to an energized vertical steel casing by dividing the casing into a set of segments, each assumed to carry a piecewise constant alternating current density. The primary field is then substituted into the primary–secondary potential finite‐element formulation of the three‐dimensional problem to obtain the secondary field. To validate the algorithm, we compare our numerical results with: (i) the analytical solution for an infinite length casing in a whole space, excited by a line source, and (ii) a three‐layered Earth model without a casing. The agreement between the numerical and analytical solutions demonstrates the effectiveness of our algorithm. As an illustration, we also present the time‐lapse electromagnetic response of a synthetic model representing a gas reservoir undergoing water flooding. 相似文献
18.
本用震源力学理论和方法研究了徐淮地区从１９７０年以来构造应力场的方向和强度的时空变化过程。结果表明：以唐山地震为分界线，本区的应力场Ｐ轴取向由震前平均６１．８°变为震后平均７７．７°。如果将本区以宿北断裂为界分为南区和北区两个部分，则北区的Ｐ轴取向从６８．１°变７１．２°，而南区的Ｐ轴取向由６２．５°变到８３．６°，南区的变化明显于北区。 相似文献
19.
Linear geophysical inversion via the discrete cosine pseudo‐inverse: application to potential fields 下载免费PDF全文
下载免费PDF全文 J.L. Fernández‐Martínez Z. Fernández‐Muñiz J.L.G. Pallero S. Bonvalot 《Geophysical Prospecting》2017,65(Z1):94-111
In this paper, we present a methodology to perform geophysical inversion of large‐scale linear systems via a covariance‐free orthogonal transformation: the discrete cosine transform. The methodology consists of compressing the matrix of the linear system as a digital image and using the interesting properties of orthogonal transformations to define an approximation of the Moore–Penrose pseudo‐inverse. This methodology is also highly scalable since the model reduction achieved by these techniques increases with the number of parameters of the linear system involved due to the high correlation needed for these parameters to accomplish very detailed forward predictions and allows for a very fast computation of the inverse problem solution. We show the application of this methodology to a simple synthetic two‐dimensional gravimetric problem for different dimensionalities and different levels of white Gaussian noise and to a synthetic linear system whose system matrix has been generated via geostatistical simulation to produce a random field with a given spatial correlation. The numerical results show that the discrete cosine transform pseudo‐inverse outperforms the classical least‐squares techniques, mainly in the presence of noise, since the solutions that are obtained are more stable and fit the observed data with the lowest root‐mean‐square error. Besides, we show that model reduction is a very effective way of parameter regularisation when the conditioning of the reduced discrete cosine transform matrix is taken into account. We finally show its application to the inversion of a real gravity profile in the Atacama Desert (north Chile) obtaining very successful results in this non‐linear inverse problem. The methodology presented here has a general character and can be applied to solve any linear and non‐linear inverse problems (through linearisation) arising in technology and, particularly, in geophysics, independently of the geophysical model discretisation and dimensionality. Nevertheless, the results shown in this paper are better in the case of ill‐conditioned inverse problems for which the matrix compression is more efficient. In that sense, a natural extension of this methodology would be its application to the set of normal equations. 相似文献
20.
In order to account for the effects of elastic wave propagation in marine seismic data, we develop a waveform inversion algorithm for acoustic‐elastic media based on a frequency‐domain finite‐element modelling technique. In our algorithm we minimize residuals using the conjugate gradient method, which back‐propagates the errors using reverse time migration without directly computing the partial derivative wavefields. Unlike a purely acoustic or purely elastic inversion algorithm, the Green's function matrix for our acoustic‐elastic algorithm is asymmetric. We are nonetheless able to achieve computational efficiency using modern numerical methods. Numerical examples show that our coupled inversion algorithm produces better velocity models than a purely acoustic inversion algorithm in a wide variety of cases, including both single‐ and multi‐component data and low‐cut filtered data. We also show that our algorithm performs at least equally well on real field data gathered in the Korean continental shelf. 相似文献