The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, e...The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element （SE） method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell＇s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.展开更多
We apply the spectral-element method（SEM）,a high-order finite-element method（FEM） to simulate seismic wave propagation in complex media for exploration and geotechnical problems. The SEM accurately treats geometri...We apply the spectral-element method（SEM）,a high-order finite-element method（FEM） to simulate seismic wave propagation in complex media for exploration and geotechnical problems. The SEM accurately treats geometrical complexities through its flexible FEM mesh and accurately interpolates wavefields through high-order Lagrange polynomials. It has been a numerical solver used extensively in earthquake seismology. We demonstrate the applicability of SEM for selected 2D exploration and geotechnical velocity models with an open-source SEM software package SPECFEM2D. The first scenario involves a marine survey for a salt dome with the presence of major internal discontinuities,and the second example simulates seismic wave propagation for an open-pit mine with complex surface topography. Wavefield snapshots,synthetic seismograms,and peak particle velocity maps are presented to illustrate the promising use of SEM for industrial problems.展开更多
We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations ...We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.展开更多
The strong motion of a small long and narrow basin caused by a moderate scenario earthquake is simulated by using the spectral-element method and the parallel computing technique.A total of five different geometrical ...The strong motion of a small long and narrow basin caused by a moderate scenario earthquake is simulated by using the spectral-element method and the parallel computing technique.A total of five different geometrical profiles within the basin are used to analyze the generation and propagation of surface waves and their relation to the basin structures in both the time and frequency domain.The amplification effects are analyzed by the distribution of peak ground velocity(PGV)and cumulative kinetic energy(Ek) in the basin.The results show that in the 3D basin,the excitation of the fundamental and higher surface wave modes are similar to that of the 2D model.Small bowls in the basin have great influence on the amplification and distribution of strong ground motion,due to their lateral resonances when the wavelengths of the lateral surface waves are comparable to the size of the bowls.Obvious basin edge effects can be seen at the basin edge closer to the source for constructive interference between direct body waves and the basin-induced surface waves.The Ek distribution maps show very large values in small bowls and some corners in the basin due to the interference of waves propagating in different directions.A high impedance contrast model can excite more surface wave modes,resulting in longer shaking durations as well as more complex seismograms and PGV and Ek distributions.展开更多
We provide an introduction to the use of the spectral-elementmethod (SEM)in seismology. Following a brief review of the basic equations that govern seismicwave propagation, we discuss in some detail how these equation...We provide an introduction to the use of the spectral-elementmethod (SEM)in seismology. Following a brief review of the basic equations that govern seismicwave propagation, we discuss in some detail how these equations may be solved numericallybased upon the SEM to address the forward problem in seismology. Examplesof synthetic seismograms calculated based upon the SEM are compared to datarecorded by the Global Seismographic Network. Finally, we discuss the challenge ofusing the remaining differences between the data and the synthetic seismograms toconstrain better Earth models and source descriptions. This leads naturally to adjointmethods, which provide a practical approach to this formidable computational challengeand enables seismologists to tackle the inverse problem.展开更多
为研究层合圆锥壳及其组合壳结构的振动特性,本文基于层合薄壳理论,采用谱元法推导了复合材料层合圆锥壳的基本动刚度矩阵,并利用单个圆锥壳的边界条件和锥顶角变化拼接构建了组合壳体结构的动力学模型。通过与有限元计算(finite elemen...为研究层合圆锥壳及其组合壳结构的振动特性,本文基于层合薄壳理论,采用谱元法推导了复合材料层合圆锥壳的基本动刚度矩阵,并利用单个圆锥壳的边界条件和锥顶角变化拼接构建了组合壳体结构的动力学模型。通过与有限元计算(finite element method,FEM)的固有频率与振动响应对比,验证了本文计算方法和层合圆锥壳动力学模型的正确性。本文分析了圆锥壳两端任意弹性刚度边界、层合铺设角度、铺设层数以及圆锥壳锥顶角等参数对层合圆锥壳振动特性的影响。研究发现铺设角度与弹性边界对固有频率存在影响;随着锥顶角增大,共振峰向低频移动。本文的研究结果可为层合圆锥壳及其组合壳结构的参数化设计和振动计算提供有效的分析工具。展开更多
基金financially supported by the Key Program of National Natural Science Foundation of China(No.41530320)China Natural Science Foundation for Young Scientists(No.41404093)+1 种基金Key National Research Project of China(Nos2016YFC0303100 and 2017YFC0601900)China Natural Science Foundation(No.41774125)
文摘The airborne electromagnetic （AEM） method has a high sampling rate and survey flexibility. However, traditional numerical modeling approaches must use high-resolution physical grids to guarantee modeling accuracy, especially for complex geological structures such as anisotropic earth. This can lead to huge computational costs. To solve this problem, we propose a spectral-element （SE） method for 3D AEM anisotropic modeling, which combines the advantages of spectral and finite-element methods. Thus, the SE method has accuracy as high as that of the spectral method and the ability to model complex geology inherited from the finite-element method. The SE method can improve the modeling accuracy within discrete grids and reduce the dependence of modeling results on the grids. This helps achieve high-accuracy anisotropic AEM modeling. We first introduced a rotating tensor of anisotropic conductivity to Maxwell＇s equations and described the electrical field via SE basis functions based on GLL interpolation polynomials. We used the Galerkin weighted residual method to establish the linear equation system for the SE method, and we took a vertical magnetic dipole as the transmission source for our AEM modeling. We then applied fourth-order SE calculations with coarse physical grids to check the accuracy of our modeling results against a 1D semi-analytical solution for an anisotropic half-space model and verified the high accuracy of the SE. Moreover, we conducted AEM modeling for different anisotropic 3D abnormal bodies using two physical grid scales and three orders of SE to obtain the convergence conditions for different anisotropic abnormal bodies. Finally, we studied the identification of anisotropy for single anisotropic abnormal bodies, anisotropic surrounding rock, and single anisotropic abnormal body embedded in an anisotropic surrounding rock. This approach will play a key role in the inversion and interpretation of AEM data collected in regions with anisotropic geology.
基金supported by the Natural Sciences and Engineering Research Council of Canada (NSERC)Center for Excellence in Mining Innovations (CEMI,through SUMIT project)+2 种基金Computations for this study were performed on hardwares purchased through the combined funding of Canada Foundation for Innovation (CFI)Ontario Research Fund (ORF)University of Toronto Startup Fund
文摘We apply the spectral-element method（SEM）,a high-order finite-element method（FEM） to simulate seismic wave propagation in complex media for exploration and geotechnical problems. The SEM accurately treats geometrical complexities through its flexible FEM mesh and accurately interpolates wavefields through high-order Lagrange polynomials. It has been a numerical solver used extensively in earthquake seismology. We demonstrate the applicability of SEM for selected 2D exploration and geotechnical velocity models with an open-source SEM software package SPECFEM2D. The first scenario involves a marine survey for a salt dome with the presence of major internal discontinuities,and the second example simulates seismic wave propagation for an open-pit mine with complex surface topography. Wavefield snapshots,synthetic seismograms,and peak particle velocity maps are presented to illustrate the promising use of SEM for industrial problems.
文摘We extend the monolithic convex limiting(MCL)methodology to nodal discontinuous Galerkin spectral-element methods(DGSEMS).The use of Legendre-Gauss-Lobatto(LGL)quadrature endows collocated DGSEM space discretizations of nonlinear hyperbolic problems with properties that greatly simplify the design of invariant domain-preserving high-resolution schemes.Compared to many other continuous and discontinuous Galerkin method variants,a particular advantage of the LGL spectral operator is the availability of a natural decomposition into a compatible subcellflux discretization.Representing a highorder spatial semi-discretization in terms of intermediate states,we performflux limiting in a manner that keeps these states and the results of Runge-Kutta stages in convex invariant domains.In addition,local bounds may be imposed on scalar quantities of interest.In contrast to limiting approaches based on predictor-corrector algorithms,our MCL procedure for LGL-DGSEM yields nonlinearflux approximations that are independent of the time-step size and can be further modified to enforce entropy stability.To demonstrate the robustness of MCL/DGSEM schemes for the compressible Euler equations,we run simulations for challenging setups featuring strong shocks,steep density gradients,and vortex dominatedflows.
基金National Natural Science Foundation of China under Grant No.51078337,No.51108431 and No.91315301
文摘The strong motion of a small long and narrow basin caused by a moderate scenario earthquake is simulated by using the spectral-element method and the parallel computing technique.A total of five different geometrical profiles within the basin are used to analyze the generation and propagation of surface waves and their relation to the basin structures in both the time and frequency domain.The amplification effects are analyzed by the distribution of peak ground velocity(PGV)and cumulative kinetic energy(Ek) in the basin.The results show that in the 3D basin,the excitation of the fundamental and higher surface wave modes are similar to that of the 2D model.Small bowls in the basin have great influence on the amplification and distribution of strong ground motion,due to their lateral resonances when the wavelengths of the lateral surface waves are comparable to the size of the bowls.Obvious basin edge effects can be seen at the basin edge closer to the source for constructive interference between direct body waves and the basin-induced surface waves.The Ek distribution maps show very large values in small bowls and some corners in the basin due to the interference of waves propagating in different directions.A high impedance contrast model can excite more surface wave modes,resulting in longer shaking durations as well as more complex seismograms and PGV and Ek distributions.
基金Broadband data were obtained from the IRIS Data Management Center.
文摘We provide an introduction to the use of the spectral-elementmethod (SEM)in seismology. Following a brief review of the basic equations that govern seismicwave propagation, we discuss in some detail how these equations may be solved numericallybased upon the SEM to address the forward problem in seismology. Examplesof synthetic seismograms calculated based upon the SEM are compared to datarecorded by the Global Seismographic Network. Finally, we discuss the challenge ofusing the remaining differences between the data and the synthetic seismograms toconstrain better Earth models and source descriptions. This leads naturally to adjointmethods, which provide a practical approach to this formidable computational challengeand enables seismologists to tackle the inverse problem.
文摘为研究层合圆锥壳及其组合壳结构的振动特性,本文基于层合薄壳理论,采用谱元法推导了复合材料层合圆锥壳的基本动刚度矩阵,并利用单个圆锥壳的边界条件和锥顶角变化拼接构建了组合壳体结构的动力学模型。通过与有限元计算(finite element method,FEM)的固有频率与振动响应对比,验证了本文计算方法和层合圆锥壳动力学模型的正确性。本文分析了圆锥壳两端任意弹性刚度边界、层合铺设角度、铺设层数以及圆锥壳锥顶角等参数对层合圆锥壳振动特性的影响。研究发现铺设角度与弹性边界对固有频率存在影响;随着锥顶角增大,共振峰向低频移动。本文的研究结果可为层合圆锥壳及其组合壳结构的参数化设计和振动计算提供有效的分析工具。
