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An efficient source wavefield reconstruction scheme using single boundary layer values for the spectral element method

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Earth and Planetary Physics 2019年第4期3卷 342-357页

作者： YouShan Liu Tao Xu YangHua Wang JiWen Teng José Badal haiqiang lan State Key Laboratory of Lithospheric Evolution Institute of Geology and Geophysics Chinese Academy of Sciences Beijing 100029 China Chinese Academy of Sciences Center for Excellence in Tibetan Plateau Earth Sciences Beijing 100101 China Department of Earth Science and Engineering Imperial College London SW7 2AZ UK Physics of the Earth Sciences-B University of Zaragoza Pedro Cerbuna 12 50009 Zaragoza Spain

In the adjoint-state method, the forward-propagated source wavefield and the backward-propagated receiver wavefield must be available simultaneously either for seismic imaging in migration or for gradient calculation in inversion. A feasible way to avoid the excessive storage demand is to reconstruct the source wavefield backward in time by storing the entire history of the wavefield in perfectly matched layers. In this paper, we make full use of the elementwise global property of the Laplace operator of the spectral element method (SEM) and propose an efficient source wavefield reconstruction method at the cost of storing the wavefield history only at single boundary layer nodes. Numerical experiments indicate that the accuracy of the proposed method is identical to that of the conventional method and is independent of the order of the Lagrange polynomials, the element type, and the temporal discretization method. In contrast, the memory-saving ratios of the conventional method versus our method is at least N when using either quadrilateral or hexahedron elements, respectively, where N is the order of the Lagrange polynomials used in the SEM. A higher memorysaving ratio is achieved with triangular elements versus quadrilaterals. The new method is applied to reverse time migration by considering the Marmousi model as a benchmark. Numerical results demonstrate that the method is able to provide the same result as the conventional method but with about 1/25 times lower storage demand. With the proposed wavefield reconstruction method, the storage demand is dramatically reduced;therefore, in-core memory storage is feasible even for large-scale three-dimensional adjoint inversion problems.

关键词： spectral element method source wavefield reconstruction single boundary layer memory-saving ratio adjoint method reverse time migration

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A High-Order Fast-Sweeping Scheme for Calculating First-Arrival Travel Times with an Irregular Surface

A High-Order Fast-Sweeping Scheme for Calculating First-Arri...

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中国科学院地质与地球物理研究所2013年度（第13届）学术年会

作者： haiqiang lan Zhongjie Zhang State Key Laboratory of Lithosphefic Evolution Institute of Geology and Geophysics Chinese Academy of Sciences

Topography-dependent eikonal equation(TDEE)formulated in a curvilinear coordinate system has been recently established and is effective for calculating first-arrival travel times in an Earth model with an irregular *** previous work, the Lax-Friedrichs sweeping scheme used to approximate the TDEE viscosity solutions was only first-order *** present a high-order fast-sweeping scheme to solve the TDEE with the aim of achieving high-order accuracy in the travel-time calculation. The scheme takes advantage of high-order weighted essentially nonoscillatory (WENO)derivative approximations,monotone numerical Hamiltonians,and Gauss Seidel iterations with alternating-direction *** incorporates high-order approximations of the derivatives into the numerical representation of the Hamiltonian such that the resulting numerical scheme is formally high-order accurate and inherits fast convergence from the alternating sweeping *** numerical examples are presented to verify its efficiency,convergence,and high-order accuracy.

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Topography-dependent eikonal equation and its solver for calculating first-arrival traveltimes with an irregular surface

Topography-dependent eikonal equation and its solver for cal...

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中国科学院地质与地球物理研究所2013年度（第13届）学术年会

作者： haiqiang lan Zhongjie Zhang State Key Laboratory of Lithospheric Evolution Institute of Geology and GeophysicsChinese Academy of Sciences

First-arrival traveltime is commonly used in problems that involve static correction,prestack migration,earthquake location,seismic tomography,*** classical eikonal equation discretized with regular rectilinear grids is effective for calculating the first-arrival traveltimes in a rectangular domain,but is less efficient for an Earth model that has an irregular surface. Here,we present a topography-dependent eikonal equation in 2-D that makes use of the wave equation in a curvilinear coordinate system,and is equivalent to a direct derivation of the classical eikonal equation together with a transformation from Cartesian to curvilinear *** topography-dependent eikonal equation is reduced to the classical version when the surface is *** topography-dependent equation(in the curvilinear coordinate system)displays the mathematical form of an anisotropic eikonal equation(even though the medium is isotropic in the Cartesian coordinate system).Then,we use a Lax-Friedrichs sweeping scheme,which has been developed as an iterative method for Hamilton-Jacobi equations,to approximate the viscosity solutions(first-arrival traveltimes)of the topographydependent eikonal equation formulated in the curvilinear coordinate *** numerical experiments performed with different models illustrate that the method is stable and accurate in calculating seismic traveltimes with an irregular(non-flat)surface.

关键词： Numerical solutions Computational seismology Theoretical seismology

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模型扩展和地形平化起伏地形处理方案在地震走时层析成像中的对比研究

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地球物理学报 2019年第5期62卷 1704-1715页

作者：郭高山兰海强陈凌中国科学院地质与地球物理研究所岩石圈演化国家重点实验室北京100029 中国科学院大学北京100049 中国科学院青藏高原地球科学卓越创新中心北京100101

中国大陆中西部普遍具有强烈的地形起伏,起伏地形会对地震资料的处理分析产生严重干扰.精细处理起伏地形成为高精度地震成像的必然要求.传统方法通过填充低速介质将不规则模型扩展为规则模型来处理起伏地形.近年来,借助坐标变换将物理... 详细信息

中国大陆中西部普遍具有强烈的地形起伏,起伏地形会对地震资料的处理分析产生严重干扰.精细处理起伏地形成为高精度地震成像的必然要求.传统方法通过填充低速介质将不规则模型扩展为规则模型来处理起伏地形.近年来,借助坐标变换将物理空间不规则模型转换为计算空间规则模型的地形平化方法,为解决起伏地形问题提供了新思路.本文基于经典的模型扩展和新发展的地形平化方法分别处理起伏地形,从走时正演、射线追踪和反演成像三个方面,全面细致地评判了两种地形处理方法在起伏地形层析成像中的适用性和有效性.结果表明,模型扩展中阶梯状近似和填充介质速度参与计算,会造成起伏地形走时计算精度损失,出现虚假射线路径和错误出射角,导致反演分辨率降低,成像结果模糊甚至失真;地形平化中采用贴体网格参数化,能够保证离散模型完全匹配起伏地形,并且保持起伏地形在物理空间和计算空间中均为自由表面.在此基础上发展的层析成像技术具有高度的保真性,有效地处理了地形起伏效应,为起伏地形区域精细速度成像提供了有力的技术保障.

关键词：模型扩展地形平化起伏地形层析成像

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Reverse time migration from irregular surface by flattening surface topography

Reverse time migration from irregular surface by flattening ...

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中国科学院地质与地球物理研究所2014年度（第14届）学术年会

作者： haiqiang lan Zhongjie Zhang Jingyi Chen Youshan Liu State Key Laboratory of Lithospheric Evolution Institute of Geology and GeophysicsChinese Academy of Sciences Department of Geosciences The University of Tulsa

Prestack reverse time migration(RTM)is a powerful tool to provide high resolution structure images of crust and upper mantle in wide-angle seismic *** a standard migration algorithm assumes that data are recorded on a flat surface,RTM meets severe challenge on the issue of complicated topography where many seismic surveys are carried *** till now,there are two popular techniques for handling elevation changes,i.e.,elevation-static correction(or time shift)and wave equation *** studies demonstrate that the elevation-static correction is inaccurate for non-vertically traveling energy and subsequently may migrate reflectors to incorrect *** equation datuming is more accurate but more sophisticated and too computationally demanding for routine ***,we present an alternative scheme to deal with topography in prestack RTM that can migrate seismic data acquired in areas with irregular topography to the reflector positions directly without datuming or elevation static *** this scheme,surface topography is flattened by a transformation of coordinates from Cartesian to *** a transformation is equivalent to map a rectangular grid onto a curved one,and is implemented by the introduction of boundary conforming *** we use an explicit finite-difference scheme with second-order accuracy to discretize the elastic wave equations and perform the RTM in the curvilinear coordinate ***,a flux-corrected transport(FCT)algorithm,adapted from hydrodynamics,is incorporated in the RTM implementation,which can not only overcome problems of numerical dispersion that arise in finite difference algorithms,but also offer the opportunity to use a coarse grid to obtain the same accuracy as conventional finite difference methods on a dense *** FCTRTM method presented here has no limitations on surface irregularity,complexity of the subsurface structure,or velocity *** numerical examples demonstrate

关键词： Reverse time migration Irregular surface Boundary conforming grid Finite difference Flux corrected transport

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A comparative study of finite element and spectral element methods in seismic wavefield modeling

A comparative study of finite element and spectral element m...

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中国科学院地质与地球物理研究所2014年度（第14届）学术年会

作者： Youshan Liu Jiwen Teng haiqiang lan Xiang Si Xueying Ma Chinese Academy of Sciences Institute of Geology and GeophysicsBeijingChina University of Chinese Academy of Sciences Chinese Academy of Sciences Institute of Geology and Geophysics

The computational accuracy and efficiency of finite element method and spectral element method(SEM) are investigated thoroughly in time-domain elastic wavefield modeling. The diagonal mass matrices of the FEM and SEM free from matrix inversion are compared comprehensively by making full use of the mass-lumped technique and quadrature rules. We investigate the FEM and SEM based, respectively, on quadrilateral with the polynomials of degrees one and two, and on triangular grids with the polynomials of degrees one and three. Generally, the numerical solutions based on quadrilateral grids have a higher precision than those computed on triangular grids when the same order of polynomials is used. The FEM has a comparable accuracy to the SEM with the same number of interpolant points. In view of the triangular and quadrilateral SEMs, the former suffers from larger computational costs and relatively lower accuracy compared with the latter. Furthermore, the convergence study proves that the triangular SEM produces consistently larger errors than the quadrilateral SEM for any order and element sizes. However, the triangular SEM can adapt to arbitrary complex geometries effectively. In terms of efficiency,the FEM has an efficiency comparable with the SEM on condition that the order of interpolation polynomials is identical. In addition, a perfectly matched layer(PML) boundary condition in variational form is deduced. By introducing four intermediate variables in frequency domain, the PML avoids convolution calculation and obtains an exact solution through inverse Fourier transform in time domain. The numerical examples verify the validity and effectiveness of the PML.

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曲线坐标系因式分解程函方程及其走时计算

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地球物理学报 2020年第2期63卷 638-651页

作者：周小乐兰海强陈凌郭高山中国科学院地质与地球物理研究所岩石圈演化国家重点实验室北京100029 中国科学院大学北京100049 中国科学院青藏高原地球科学卓越创新中心北京100101

地震波走时广泛应用于静校正、层析成像、Kirchhoff偏移成像、地震定位等研究.复杂地表条件是影响走时计算精度的重要因素.近年来,发展的曲线坐标系程函方程为精细刻画起伏地表条件下的地震波走时场特征提供了新的思路.然而,基于有限差... 详细信息

地震波走时广泛应用于静校正、层析成像、Kirchhoff偏移成像、地震定位等研究.复杂地表条件是影响走时计算精度的重要因素.近年来,发展的曲线坐标系程函方程为精细刻画起伏地表条件下的地震波走时场特征提供了新的思路.然而,基于有限差分程函方程的求解方法不可避免地受到震源奇异性的影响,即震源附近波前的曲率较大,此时使用平面波近似假设的差分格式会导致较大误差.而震源误差会随着波前的传播到达整个计算区域,从而影响整个区域的求解精度.针对该问题,本文借鉴因式分解的思想,推导建立了曲线坐标系因式分解程函方程,并针对性地发展了其数值求解方法,从根源上解决了复杂模型走时计算中的震源奇异性问题.数值实例表明因式分解法能够有效降低震源误差,显著提高起伏地表走时计算的精度和效率,为起伏地表地震波走时计算提供更佳的选择,在复杂模型的地震资料处理中展现出广泛的应用前景.

关键词：曲线坐标系因式分解程函方程震源奇异性

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Three-Dimensional Wave-Field Simulation in Heterogeneous Transversely Isotropic Medium with Irregular Free Surface

Three-Dimensional Wave-Field Simulation in Heterogeneous Tra...

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中国科学院地质与地球物理研究所第11届（2011年度）学术年会

作者： haiqiang lan and Zhongjie Zhang State Key Laboratory of Lithosphere Evolution Institute of Geology and Geophysics Chinese Academy of Sciences Beijing,100029,PR China

Modeling of seismic-wave propagation in anisotropic medium with irregular topography is beneficial to interpret seismic data acquired by active and passive source seismology conducted in areas of interest such as mountain ranges and *** major challenge in this context is the difficulty in tackling the irregular free-surface boundary condition in a Cartesian coordinate *** implement surface topography,we use the boundary-conforming grid and map a rectangular grid onto a curved *** use a stable and explicit second-order accurate finite-difference scheme to discretize the elastic wave equations(in a curvilinear coordinate system) in a 3D heterogeneous transversely isotropic *** free-surface boundary conditions are accurately applied by introducing a discretization that uses boundary-modified difference operators for the mixed derivatives in the governing equations. The accuracy of the proposed method is checked by comparing the numerical results obtained by the trial algorithm with the analytical solutions of the Lamb’s problem,for an isotropic medium and a transversely isotropic medium with a vertical symmetry axis, *** tests performed by different numerical experiments illustrate clearly the influence of an irregular(nonflat) free surface on seismic-wave propagation.

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基于物理信息约束的神经网络复杂模型高精度走时计算

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地球物理学进展 2022年第5期37卷 1840-1853页

作者：邵帅雷一鸣兰海强中国科学院地质与地球物理研究所岩石圈演化国家重点实验室北京100029 中国科学院大学地球与行星科学学院北京100049

走时计算广泛应用于地震数据处理中,其中对复杂地表地形的处理一直是走时计算的关键和难点.相比于传统的规则网格,贴体网格的建模方式可以完美地刻画地表的起伏形态.然而,目前常用的方法在利用贴体网格变换解决复杂地形问题的同时,需要... 详细信息

走时计算广泛应用于地震数据处理中,其中对复杂地表地形的处理一直是走时计算的关键和难点.相比于传统的规则网格,贴体网格的建模方式可以完美地刻画地表的起伏形态.然而,目前常用的方法在利用贴体网格变换解决复杂地形问题的同时,需要针对性地发展适应贴体网格的特殊求解方法,这导致算法复杂且在网格扭曲较大的地方易造成精度损失.基于物理信息约束的神经网络是一种无网格方法,它对程函方程的求解不受具体网格形态的限制.为此,本文中我们将基于物理信息约束的神经网络和贴体网格结合,提出一种有效计算复杂模型中地震波走时的方法;用贴体网格构建任意复杂地质体,然后用基于物理信息约束的神经网络求解该复杂地质体上的地震波传播的走时.另外,我们使用残差神经网络替换了原有的神经网络架构,这在一定程度上提高了神经网络的学习能力.我们利用三组模型的数值模拟结果来验证方法的有效性和高精度;同时讨论了训练替代模型和迁移学习等神经网络技术在复杂模型中计算走时的应用,这极大地加速了实际问题的求解过程,有望在具体问题的求解中得到广泛应用.

关键词：基于物理信息约束的神经网络残差学习程函方程走时复杂模型

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航空发动机换热器强度试验标准分析解读

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压力容器 2019年第10期36卷 45-48页

作者：兰海强曹航柏汉松沈阳发动机研究所

由于航空发动机换热器特殊的工作环境(高温、高压、振动环境恶劣),因此要求在研制阶段进行充分的强度试验考核,以保证可靠性。目前对航空发动机换热器还没有统一明确的强度试验要求,为此对多个换热器强度试验相关标准进行研究、对比、解... 详细信息

由于航空发动机换热器特殊的工作环境(高温、高压、振动环境恶劣),因此要求在研制阶段进行充分的强度试验考核,以保证可靠性。目前对航空发动机换热器还没有统一明确的强度试验要求,为此对多个换热器强度试验相关标准进行研究、对比、解读,对耐压试验中关键的试验载荷值、试验时间等进行确认,确定了对航空发动机换热器需要开展的强度试验的项目及顺序。

关键词：航空发动机换热器强度试验标准

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