共查询到20条相似文献，搜索用时 31 毫秒
1.
Xinya Li Bill X. Hu 《Stochastic Environmental Research and Risk Assessment (SERRA)》2013,27(5):1181-1191
Numerical models with fine discretization normally demand large computational time and space, which lead to computational burden for state estimations or model parameter inversion calculation. This article presented a reduced implicit finite difference scheme that based on proper orthogonal decomposition (POD) for two-dimensional transient mass transport in heterogeneous media. The reduction of the original full model was achieved by projecting the high-dimension full model to a low-dimension space created by POD bases, and the bases are derived from the snapshots generated from the model solutions of the forward simulations. The POD bases were extracted from the ensemble of snapshots by singular value decomposition. The dimension of the Jacobian matrix was then reduced after Galerkin projection. Thus, the reduced model can accurately reproduce and predict the original model’s transport process with significantly decreased computational time. This scheme is practicable with easy implementation of the partial differential equations. The POD method is illustrated and validated through synthetic cases with various heterogeneous permeability field scenarios. The accuracy and efficiency of the reduced model are determined by the optimal selection of the snapshots and POD bases. 相似文献
2.
Nonlinear groundwater flow models have the propensity to be overly complex leading to burdensome computational demands. Reduced modeling techniques are used to develop an approximation of the original model that has smaller dimensionality and faster run times. The reduced model proposed is a combination of proper orthogonal decomposition (POD) and the discrete empirical interpolation method (DEIM). Solutions of the full model (snapshots) are collected to represent the physical dynamics of the system and Galerkin projection allows the formulation of a reduced model that lies in a subspace of the full model. Interpolation points are added through DEIM to eliminate the reduced model's dependence on the dimension of the full model. POD is shown to effectively reduce the dimension of the full model and DEIM is shown to speed up the solution by further reducing the dimension of the nonlinear calculations. To show the concept can work for unconfined groundwater flow model, with added nonlinear forcings, one-dimensional and two-dimensional test cases are constructed in MODFLOW-OWHM. POD and DEIM are added to MODFLOW as a modular package. Comparing the POD and the POD-DEIM reduced models, the experimental results indicate similar reduction in dimension size with additional computation speed up for the added interpolation. The hyper-reduction method presented is effective for models that have fine discretization in space and/or time as well as nonlinearities with respect to the state variable. The dual reduction approach ensures that, once constructed, the reduced model can be solved in an equation system that depends only on reduced dimensions. 相似文献
3.
Full-wavefield inversion for distributions of acoustic velocity, density and Q on a vertical slice through a25D model is implemented for common-source gathers in a cross-hole geometry. The wavefield extrapolation used is 3D, so all geometrical spreading, scattering, reflection, and transmission effects are correctly and automatically compensated for. In order to keep the number of unknowns tractable, application was limited to 2.5D models of known geometry; the latter assurnes a prior step, such as tomography, to fix the layer geometries. With the model geometry fixed, reliable solutions are obtained using synthetic data from only two independent source locations. Solutions from data with noisy and missing traces are comparable to those from noise-free data, but with higher residuals. When the source locations are spatially widely separated, conunon-source gathers may be summed and treated as a single wavefield to yield the same model estimates as when the individual source wavefields are treated separately, at substantially reduced cost. Inversions for full 3D parameter distributions can be handled with the same software, requiring only solution for more unknowns. 相似文献
4.
A new model order reduction strategy adapted to nonlinear problems in earthquake engineering 
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下载免费PDF全文 Earthquake dynamic response analysis of large complex structures, especially in the presence of nonlinearities, usually turns out to be computationally expensive. In this paper, the methodical developments of a new model order reduction strategy (MOR) based on the proper orthogonal decomposition (POD) method as well as its practical applicability to a realistic building structure are presented. The seismic performance of the building structure, a medical complex, is to be improved by means of base isolation realized by frictional pendulum bearings. According to the new introduced MOR strategy, a set of deterministic POD modes (transformation matrix) is assembled, which is derived based on the information of parts of the response history, so‐called snapshots, of the structure under a representative earthquake excitation. Subsequently, this transformation matrix is utilized to create reduced‐order models of the structure subjected to different earthquake excitations. These sets of nonlinear low‐order representations are now solved in a fractional amount of time in comparison with the computations of the full (non‐reduced) systems. The results demonstrate accurate approximations of the physical (full) responses by means of this new MOR strategy if the probable behavior of the structure has already been captured in the POD snapshots. Copyright © 2016 The Authors. Earthquake Engineering & Structural Dynamics Published by John Wiley & Sons Ltd. 相似文献
5.
Modeling Full Seismogram Envelopes Using Radiative Transfer Theory with Born Scattering Coefficients
The equation of radiative transfer is used to model the transport of seismic energy in 2-D and 3-D acoustic random media.
Monte-Carlo solutions of this equation using non-isotropic Born scattering coefficients are compared to three analytical solutions:
Markov approximation, radiative transfer theory with isotropic scattering coefficients, and diffusion approximation. Additionally,
we compare to finite differences solutions of the full wave equation in 2-D. We find a good correspondence of radiative transfer
theory to Markov approximation for the case of multiple forward scattering. The comparison to radiative transfer theory with
isotropic scattering coefficients, a model frequently used in data analysis, demonstrates that in the case of forward scattering
the isotropic scattering model is not better than a diffusion approach. To compare radiative transfer theory with non-isotropic
scattering coefficients to finite differences solutions of the full wave equation, the finite source duration and the bandpass
filter process as well as the normalization of absolute amplitudes are explicitely taken into account. We find a good coincidence
of both theories for scattering parameters, which are realistic for usual Earth crust. The theory correctly describes the
unscattered direct wavefront, the envelope broadening caused by multiple forward scattering, as well as the late coda caused
by multiple wide angle scattering. For strong scattering, which can be expected for very heterogeneous media such as strato
volcanoes, the solutions of radiative transfer differ from the more complete solutions of the full wave equation. 相似文献
6.
Accurate Location of Synthetic Acoustic Emissions and Location Sensitivity to Relocation Methods, Velocity Perturbations, and Seismic Anisotropy 总被引：1，自引：0，他引：1
G. A. Jones S. E. J. Nippress A. Rietbrock J. M. Reyes-Montes 《Pure and Applied Geophysics》2008,165(2):235-254
Acoustic emission (AE) monitoring is a non-invasive method of monitoring fracturing both in situ, and in experimental rock deformation studies. Until recently, the major impediment for imaging brittle failure within a
rock mass is the accuracy at which the hypocenters may be located. However, recent advances in the location of regional scale
earthquakes have successfully reduced hypocentral uncertainties by an order of magnitude. The least-squares Geiger, master
event relocation, and double difference methods have been considered in a series of synthetic experiments which investigate
their ability to resolve AE hypocentral locations. The effect of AE hypocenter location accuracy due to seismic velocity perturbations,
uncertainty in the first arrival pick, array geometry and the inversion of a seismically anisotropic structure with an isotropic
velocity model were tested. Hypocenters determined using the Geiger procedure for a homogeneous, isotropic sample with a known
velocity model gave a RMS error for the hypocenter locations of 2.6 mm; in contrast the double difference method is capable
of reducing the location error of these hypocenters by an order of magnitude. We test uncertainties in velocity model of up
to ±10% and show that the double difference method can attain the same RMS error as using the standard Geiger procedure with
a known velocity model. The double difference method is also capable of precise locations even in a 40% anisotropic velocity
structure using an isotropic model for location and attains a RMS mislocation error of 2.6 mm that is comparable to a RMS
mislocation error produced with an isotropic known velocity model using the Geiger approach. We test the effect of sensor
geometry on location accuracy and find that, even when sensors are missing, the double difference method is capable of a 1.43
mm total RMS mislocation compared to 4.58 mm for the Geiger method. The accuracy of automatic picking algorithms used for
AE studies is ±0.5 μs (1 time sample when the sampling rate is 0.2 μs). We investigate how AE locations are effected by the
accuracy of first arrival picking by randomly delaying the actual first arrival by up to 5 time samples. We find that even
when noise levels are set to 5 time samples the double difference method successfully relocates the synthetic AE. 相似文献
7.
Full moment tensor inversion constrained by double-couple focal mechanism for induced seismicity* 下载免费PDF全文
下载免费PDF全文 In this study, we propose a new method to determine full moment tensor solution for induced seismicity. This method generalizes the full waveform matching algorithm we have developed to determine the double-couple (DC) focal mechanism based on the neighbourhood algorithm. One major difference between the new method and the former one is that we adopt a new misfit function to constrain the candidate moment tensor solutions with respect to a reference DC solution in addition to other misfit terms characterizing the waveform matching. Through synthetic tests using a real passive seismic survey geometry, the results show the new constraint can help better recover the DC components of inverted moment tensors. We further investigate how errors in the velocity model and source location affect the moment tensor solution. The synthetic test results indicate that the constrained inversion is robust in recovering both the DC and non-DC components. We also test the proposed method on several real induced events in an oil/gas field in Oman using the same observation system as synthetic tests. While it is found that the full moment tensor solutions without using the DC constraints have much larger non-DC components than solutions with the DC constraints, both solutions are able to fit the observed waveforms at similar levels. The synthetic and real test results suggest the proposed DC constrained inversion method can reliably retrieve full moment tensor solutions for the induced seismicity. 相似文献
8.
An extended Bayesian sediment fingerprinting mixing model for the full Bayes treatment of geochemical uncertainties 总被引：2，自引：0，他引：2 下载免费PDF全文
下载免费PDF全文 Recent advances in sediment fingerprinting research have seen Bayesian mixing models being increasingly employed as an effective method to coherently translate component uncertainties into source apportionment results. Here, we advance earlier work by presenting an extended Bayesian mixing model capable of providing a full Bayes treatment of geochemical uncertainties. The performance of the extended full Bayes model was assessed against the equivalent empirical Bayes model and traditional frequentist optimisation. The performance of models coded in different Bayesian software (JAGS and Stan) was also evaluated, alongside an assessment of model sensitivity to reduced source representativeness and nonconservative fingerprint behaviour. Results revealed comparable accuracy and precision for the full and empirical Bayes models across both synthetic and real sediment geochemistry datasets, demonstrating that the empirical treatment of source data here represents a close approximation of the full Bayes treatment. Contrasts in the performance of models coded in JAGS and Stan revealed that the choice of software employed can impact significantly upon source apportionment results. Bayesian models coded in Stan were the least sensitive to both reduced source representativeness and nonconservative fingerprint behaviour, indicating Stan as the preferred software for future Bayesian sediment fingerprinting studies. Whilst the frequentist optimisation generally yielded comparable accuracy to the Bayesian models, uncertainties around apportionment estimates were substantially greater and the frequentist model was less effective at dealing with nonconservative behaviour. Overall, the effective performance of the extended full Bayes mixing model coded in Stan represents a notable advancement in source apportionment modelling relative to previous approaches. Both the mixing model and the software comparisons presented here should provide useful guidelines for future sediment fingerprinting studies. 相似文献
9.
用于控制高柔结构振动的POD技术 总被引：5，自引：0，他引：5
本文通过模型试验和理论分析研究了一种控制高柔结构振动的新方法－－－ＰＯＤ（摆、油阻尼器）减振系统。文中详细分析了其减震原理,并提出了与试验结果相吻合的三角形非缄性滞回模型。试验结果表明,在接近调谐状态下ＰＯＤ法可减振４８％。数据计算的结果也表明,ＰＯＤ不仅减振效果比ＴＭＤ高得多,而且有效频带也宽得多。ＰＯＤ系统具有造价低、易安装、占用空间小、免维护等优点,可用于风可于震等荷载引起的电视塔、悬索桥塔 相似文献
10.
The use of data‐driven modelling techniques to deliver improved suspended sediment rating curves has received considerable interest in recent years. Studies indicate an increased level of performance over traditional approaches when such techniques are adopted. However, closer scrutiny reveals that, unlike their traditional counterparts, data‐driven solutions commonly include lagged sediment data as model inputs, and this seriously limits their operational application. In this paper, we argue the need for a greater degree of operational reasoning underpinning data‐driven rating curve solutions and demonstrate how incorrect conclusions about the performance of a data‐driven modelling technique can be reached when the model solution is based upon operationally invalid input combinations. We exemplify the problem through the re‐analysis and augmentation of a recent and typical published study, which uses gene expression programming to model the rating curve. We compare and contrast the previously published solutions, whose inputs negate their operational application, with a range of newly developed and directly comparable traditional and data‐driven solutions, which do have operational value. Results clearly demonstrate that the performance benefits of the published gene expression programming solutions are dependent on the inclusion of operationally limiting, lagged data inputs. Indeed, when operationally inapplicable input combinations are discounted from the models and the analysis is repeated, gene expression programming fails to perform as well as many simpler, more standard multiple linear regression, piecewise linear regression and neural network counterparts. The potential for overstatement of the benefits of the data‐driven paradigm in rating curve studies is thus highlighted. Copyright © 2011 John Wiley & Sons, Ltd. 相似文献
11.
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
12.
由于GRACE卫星数据解算的时变重力场模型中高阶位系数存在误差,这些误差在重力异常图中表现为南北向的条带噪声,在应用GRACE时变重力场数据时必须进行滤波.本文在空间域引入了一种有效消除GRACE时变重力场条带噪声的平滑先验信息方法,并将其与目前常用的高斯滤波和去相关误差等滤波方法分别应用于合成的质量变化趋势数字模型,检测不同滤波方法消除条带噪声的能力及其对真实信号的影响.滤波结果显示,与目前常用的高斯滤波和去相关误差滤波器相比,本文滤波方法在有效移除条带噪声的同时,具有有效信号幅度衰减小、有效信号形变小以及保存了更多的短波长细节信息等优势;此外,统计结果显示,本文滤波结果在信号最大值、最小值以及残差均方根等方面均与模拟真实信号最为接近.相比300km高斯平滑和组合滤波结果,有效信号振幅的极小值和极大值分别提高了约18%和6%,残差均方根分别降低了25%和33%.说明本文滤波方法移除GRACE相关误差的同时,在保留有效信号方面具有明显的优势. 相似文献
13.
A novel numerical model based on solid deformation is presented in this paper. This thermo-mechanical model can simulate the tectonic evolution of crust and (lithospheric and asthenospheric) mantle under different conditions. Our implementation uses the finite element method (FEM) in order to solve the equations. As a Lagrangian approach is employed, remeshing techniques are implemented to avoid distortion problems when a certain deformation threshold is reached. The translation of the state between the old and new mesh is achieved by means of the information stored on Lagrangian particles, which minimizes the diffusion. The model is able to represent elastic, viscous and plastic behaviour inside the studied domain. Three types of creep mechanism (diffusion, dislocation and Peierls) are included. Two different quadrilateral isoparametric elements were implemented and can be employed to perform the calculations. The first one is an element with 4 nodes, selective reduced integration and a stabilization operator to diminish hourglass modes, which reduces the computational time needed. The second one has 8 nodes located in standard positions, uses full integration scheme and has no hourglass modes as it satisfies the Inf-Sup condition. Several test cases with known solutions were run to validate the different aspects of the implementation. 相似文献
14.
A new methodology is proposed for the development of parameter-independent reduced models for transient groundwater flow models. The model reduction technique is based on Galerkin projection of a highly discretized model onto a subspace spanned by a small number of optimally chosen basis functions. We propose two greedy algorithms that iteratively select optimal parameter sets and snapshot times between the parameter space and the time domain in order to generate snapshots. The snapshots are used to build the Galerkin projection matrix, which covers the entire parameter space in the full model. We then apply the reduced subspace model to solve two inverse problems: a deterministic inverse problem and a Bayesian inverse problem with a Markov Chain Monte Carlo (MCMC) method. The proposed methodology is validated with a conceptual one-dimensional groundwater flow model. We then apply the methodology to a basin-scale, conceptual aquifer in the Oristano plain of Sardinia, Italy. Using the methodology, the full model governed by 29,197 ordinary differential equations is reduced by two to three orders of magnitude, resulting in a drastic reduction in computational requirements. 相似文献
15.
16.
Integrating migration velocity analysis and full waveform inversion can help reduce the high non‐linearity of the classic full waveform inversion objective function. The combination of inverting for the long and short wavelength components of the velocity model using a dual objective function that is sensitive to both components is still very expensive and have produced mixed results. We develop an approach that includes both components integrated to complement each other. We specifically utilize the image to generate reflections in our synthetic data only when the velocity model is not capable of producing such reflections. As a result, we get the migration velocity analysis working when we need it, and we mitigate its influence when the velocity model produces accurate reflections (possibly first for the low frequencies). This is achieved using a novel objective function that includes both objectives. Applications to a layered model and the Marmousi model demonstrate the main features of the approach. 相似文献
17.
This paper presents a procedure to develop scalable reduced models for the through-the soil interaction and traveling wave effects of distant sleepers in a long railway track. For development purposes, and, without loss of generality, the geometry of the sleepers is consistent with the UIC-60 track system commonly used in European high speed rail and the vertical vibration mode is considered. The ballast and the effects of soil layering are not considered in the present paper; however, it is the subject of ongoing research. The proposed reduced models are based on B-Spline impulse response functions (BIRF) of the sleepers only as computed through boundary element method (BEM) solutions of the full model, preserve the frequency content of the full models, and they are highly accurate within the assumptions of linear isotropic and homogeneous soil media. They are expressed in a scalable form with respect to soil properties and sleeper spacing. In particular, the BIRFs of distant sleepers can be accurately approximated by appropriate scaling operations of time and amplitude of a reference sleeper BIRF while retaining all dynamic characteristics of the full model. Three main scaling parameters are proposed: (i) the apparent propagation velocity, (ii) the geometric damping coefficient, and (iii) the soil properties of a reference soil (i.e., the shear modulus and shear wave velocity). The models are validated through comparisons with other BEM solutions, and the accuracy and efficiency are established. The proposed models are developed as part of an NSF funded research on vibrations induced by high-speed rail traffic and are consistent with the associated train and rail models and a multi-system interface coupling (MSIC) technique that were developed as a part of the project and presented in companion papers. The proposed procedure forms the framework for developing scaled reduced models for other vibration modes and different sleeper geometries and can be generalized to include any foundation type or layered soil profiles. 相似文献
18.
We present a methodology conducive to the application of a Galerkin model order reduction technique, Proper Orthogonal Decomposition (POD), to solve a groundwater flow problem driven by spatially distributed stochastic forcing terms. Typical applications of POD to reducing time-dependent deterministic partial differential equations (PDEs) involve solving the governing PDE at some observation times (termed snapshots), which are then used in the order reduction of the problem. Here, the application of POD to solve the stochastic flow problem relies on selecting the snapshots in the probability space of the random quantity of interest. This allows casting a standard Monte Carlo (MC) solution of the groundwater flow field into a Reduced Order Monte Carlo (ROMC) framework. We explore the robustness of the ROMC methodology by way of a set of numerical examples involving two-dimensional steady-state groundwater flow taking place within an aquifer of uniform hydraulic properties and subject to a randomly distributed recharge. We analyze the impact of (i) the number of snapshots selected from the hydraulic heads probability space, (ii) the associated number of principal components, and (iii) the key geostatistical parameters describing the heterogeneity of the distributed recharge on the performance of the method. We find that our ROMC scheme can improve significantly the computational efficiency of a standard MC framework while keeping the same degree of accuracy in providing the leading statistical moments (i.e. mean and covariance) as well as the sample probability density of the state variable of interest. 相似文献
19.
《中国科学:地球科学(英文版)》2017,(3)
The Proper Orthogonal Decomposition(POD)-based ensemble four-dimensional variational(4DVar) assimilation method(POD4DEnVar) was proposed to combine the strengths of EnKF(i.e.,the ensemble Kalman filter) and 4DVar assimilation methods.Recently,a POD4DEnVar-based radar data assimilation scheme(PRAS) was built and its effectiveness was demonstrated.POD4 DEnVar is based on the assumption of a linear relationship between the model perturbations(MPs)and the observation perturbations(OPs);however,this assumption is likely to be destroyed by the highly non-linear forecast model or observation operator.To address this issue,using the Gauss-Newton iterative method,the nonlinear least squares enhanced POD4 DEnVar algorithm(referred to as NLS-4DVar) was proposed.Naturally,the PRAS was upgraded to form the NLS-4DVar-based radar data assimilation scheme(NRAS).To evaluate the performance of NRAS against PRAS,observing system simulation experiments(OSSEs) were conducted to assimilate reflectivity and radial velocity individually,with one,two,and three iterations.The results demonstrated that the NRAS outperformed PRAS in improving the initial condition and the forecasting of model variables and rainfall.The NRAS,with a smaller number of iterations,can yield a convergent result.In contrast to the situation when assimilating radial velocity,the advantages of NRAS over PRAS were more obvious when assimilating reflectivity. 相似文献
20.
Discrimination of induced seismicity by full moment tensor inversion and decomposition 总被引：3，自引：1，他引：2
Human activities, including operations related to mining and reservoir exploitation, may induce seismicity and pose a risk for population and infrastructures. While different observations are commonly used to assess the origin of earthquakes, there is a lack of rules and methods for the discrimination between natural and induced seismicity. The inversion and decomposition of the full moment tensor and the observation of relevant deviation from a pure double couple (DC) model may be an indicator for induced seismicity. We establish here a common procedure to analyse a set of natural and induced events of similar magnitude, which occurred in Germany and neighbouring regions. The procedure is based on an inversion method and on a consistent velocity model and recording network. Induced seismicity is recorded during different mining and/or reservoir exploitations. Moment tensors are inverted using a multi-step inversion approach. This method, which was successfully applied in previous studies at regional and teleseismic distances, is further developed here to account for full moment tensor analysis. We first find a best DC solution and then perform a full moment tensor inversion, fitting full waveforms amplitude spectra at regional distances. The moment tensor solution is decomposed into DC, compensated linear vector dipole and isotropic terms. The discrimination problem is then investigated through the evaluation of distributions of non-DC source components for natural and induced data sets. Results illustrate the potential of the inversion and discrimination approach. Additional detailed analyses are carried out for the two most significant induced earthquakes, and rupture models are compared with the full moment tensor solutions. 相似文献