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Perfectly matched layer-absorbing boundary condition for finite-element time-domain modeling of elastic wave equations 被引量:3
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作者 赵建国 史瑞其 《Applied Geophysics》 SCIE CSCD 2013年第3期323-336,359,共15页
The perfectly matched layer (PML) is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-eleme... The perfectly matched layer (PML) is a highly efficient absorbing boundary condition used for the numerical modeling of seismic wave equation. The article focuses on the application of this technique to finite-element time-domain numerical modeling of elastic wave equation. However, the finite-element time-domain scheme is based on the second- order wave equation in displacement formulation. Thus, the first-order PML in velocity-stress formulation cannot be directly applied to this scheme. In this article, we derive the finite- element matrix equations of second-order PML in displacement formulation, and accomplish the implementation of PML in finite-element time-domain modeling of elastic wave equation. The PML has an approximate zero reflection coefficients for bulk and surface waves in the finite-element modeling of P-SV and SH wave propagation in the 2D homogeneous elastic media. The numerical experiments using a two-layer model with irregular topography validate the efficiency of PML in the modeling of seismic wave propagation in geological models with complex structures and heterogeneous media. 展开更多
关键词 Absorbing boundary condition elastic wave equation perfectly matched layer finite-element modeling
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Borehole-GPR numerical simulation of full wave field based on convolutional perfect matched layer boundary 被引量:7
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作者 朱自强 彭凌星 +1 位作者 鲁光银 密士文 《Journal of Central South University》 SCIE EI CAS 2013年第3期764-769,共6页
The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) appr... The absorbing boundary is the key in numerical simulation of borehole radar.Perfect match layer(PML) was chosen as the absorbing boundary in numerical simulation of GPR.But CPML(convolutional perfect match layer) approach that we have chosen has the advantage of being media independent.Beginning with the Maxwell equations in a two-dimensional structure,numerical formulas of finite-difference time-domain(FDTD) method with CPML boundary condition for transverse electric(TE) or transverse magnetic(TM) wave are presented in details.Also,there are three models for borehole-GPR simulation.By analyzing the simulation results,the features of targets in GPR are obtained,which can provide a better interpretation of real radar data.The results show that CPML is well suited for the simulation of borehole-GPR. 展开更多
关键词 borehole-GPR numerical simulation convolutional perfect match layer finite-difference time-domain method
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An improved convolution perfectly matched layer for elastic second-order wave equation 被引量:2
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作者 Yang Ling-Yun Wu Guo-Chen +1 位作者 Li Qing-Yang Liang Zhan-Yuan 《Applied Geophysics》 SCIE CSCD 2021年第3期317-330,432,共15页
A convolution perfectly matched layer(CPML)can efficiently absorb boundary reflection in numerical simulation.However,the CPML is suitable for the first-order elastic wave equation and is difficult to apply directly t... A convolution perfectly matched layer(CPML)can efficiently absorb boundary reflection in numerical simulation.However,the CPML is suitable for the first-order elastic wave equation and is difficult to apply directly to the second-order elastic wave equation.In view of this,based on the first-order CPML absorbing boundary condition,we propose a new CPML(NCPML)boundary which can be directly applied to the second-order wave equation.We first systematically extend the first-order CPML technique into second-order wave equations,neglecting the space-varying characteristics of the partial damping coefficient in the complex-frequency domain,avoiding the generation of convolution in the time domain.We then transform the technique back to the time domain through the inverse Fourier transform.Numerical simulation indicates that the space-varying characteristics of the attenuation factor have little influence on the absorption effect and increase the memory at the same time.A number of numerical examples show that the NCPML proposed in this study is effective in simulating elastic wave propagation,and this algorithm is more efficient and requires less memory allocation than the conventional PML absorbing boundary. 展开更多
关键词 convolutional perfectly matched layer absorbing boundary conditions second-order elastic wave equation numerical simulation
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DISCRETE SINGULAR CONVOLUTION METHOD WITH PERFECTLY MATCHED ABSORBING LAYERS FOR THE WAVE SCATTERING BY PERIODIC STRUCTURES
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作者 Feng Lixin Jia Niannian 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2007年第2期138-152,共15页
A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is uti... A new computational algorithm is introduced for solving scattering problem in periodic structure. The PML technique is used to deal with the difficulty on truncating the unbounded domain while the DSC algorithm is utilized for the spatial discretization. The present study reveals that the method is efficient for solving the problem. 展开更多
关键词 Maxwell's equations periodic structures perfect matched layer (PMI) discrete singular convolution (DSC)
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Comparison of perfectly matched layer and multi-transmitting formula artificial boundary condition based on hybrid finite element formulation
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作者 李宁 谢礼立 翟长海 《Acta Seismologica Sinica(English Edition)》 CSCD 2007年第6期684-695,共12页
The theory of perfectly matched layer (PML) artificial boundary condition (ABC), which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The co... The theory of perfectly matched layer (PML) artificial boundary condition (ABC), which is characterized by absorption any wave motions with arbitrary frequency and arbitrarily incident angle, is introduced. The construction process of PML boundary based on elastodynamic partial differential equation (PDE) system is developed. Combining with velocity-stress hybrid finite element formulation, the applicability of PML boundary is investigated and the numerical reflection of PML boundary is estimated. The reflectivity of PML and multi-transmitting formula (MTF) boundary is then compared based on body wave and surface wave simulations. The results show that although PML boundary yields some reflection, its absorption performance is superior to MTF boundary in the numerical simulations of near-fault wave propagation, especially in comer and large angle grazing incidence situations. The PML boundary does not arise any unstable phenomenon and the stability of PML boundary is better than MTF boundary in hybrid finite element method. For a specified problem and analysis tolerance, the computational efficiency of PML boundary is only a little lower than MTF boundary. 展开更多
关键词 perfectly matched layer multi-transmitting formula elastodynamic wave artificial boundary hybrid finite element
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The Application of the Nonsplitting Perfectly Matched Layer in Numerical Modeling of Wave Propagation in Poroelastic Media 被引量:4
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作者 宋若龙 马俊 王克协 《Applied Geophysics》 SCIE CSCD 2005年第4期216-222,共7页
The nonsplitting perfectly matched layer (NPML) absorbing boundary condition (ABC) was first provided by Wang and Tang (2003) for the finite-difference simulation of elastic wave propagation in solids. In this p... The nonsplitting perfectly matched layer (NPML) absorbing boundary condition (ABC) was first provided by Wang and Tang (2003) for the finite-difference simulation of elastic wave propagation in solids. In this paper, the method is developed to extend the NPML to simulating elastic wave propagation in poroelastic media. Biot's equations are discretized and approximated to a staggered-grid by applying a fourth-order accurate central difference in space and a second-order accurate central difference in time. A cylindrical twolayer seismic model and a borehole model are chosen to validate the effectiveness of the NPML. The results show that the numerical solutions agree well with the solutions of the discrete wavenumber (DW) method. 展开更多
关键词 FINITE-DIFFERENCE numerical simulation absorbing boundary condition and perfectly matched layer.
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A study of perfectly matched layers for joint multicomponent reverse-time migration 被引量:3
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作者 杜启振 秦童 +1 位作者 朱钇同 毕丽飞 《Applied Geophysics》 SCIE CSCD 2010年第2期166-173,194,195,共10页
Reverse-time migration in finite space requires effective boundary processing technology to eliminate the artificial truncation boundary effect in the migration result.On the basis of the elastic velocity-stress equat... Reverse-time migration in finite space requires effective boundary processing technology to eliminate the artificial truncation boundary effect in the migration result.On the basis of the elastic velocity-stress equations in vertical transversely isotropic media and the idea of the conventional split perfectly matched layer(PML),the PML wave equations in reverse-time migration are derived in this paper and then the high order staggered grid discrete schemes are subsequently given.Aiming at the"reflections"from the boundary to the computational domain,as well as the effect of seismic event's abrupt changes at the two ends of the seismic array,the PML arrangement in reverse-time migration is given.The synthetic and real elastic,prestack,multi-component,reverse-time depth migration results demonstrate that this method has much better absorbing effects than other methods and the joint migration produces good imaging results. 展开更多
关键词 perfectly matched layer(PML) absorbing boundary reverse-time migration velocity-stress equation MULTI-COMPONENT
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发展方程的完美匹配边界层模型
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作者 余涛 邹诗影 《井冈山大学学报(自然科学版)》 2024年第3期8-12,共5页
在有界区域上使用数值方法模拟无界区域上的偏微分方程时,要求在有界区域边界上添加人工边界条件。构造的人工边界条件必须能消除边界上不必要的反射,完美匹配边界层是非常有效的人工吸收边界条件之一。本研究采用复值坐标拉伸的方法,... 在有界区域上使用数值方法模拟无界区域上的偏微分方程时,要求在有界区域边界上添加人工边界条件。构造的人工边界条件必须能消除边界上不必要的反射,完美匹配边界层是非常有效的人工吸收边界条件之一。本研究采用复值坐标拉伸的方法,在不分离变量的前提下对发展方程推导出了完美匹配边界层模型。通过平面波分析可知,波在初始求解区域边界上无反射,且在有界的完美匹配边界层上振幅是指数衰减的。 展开更多
关键词 发展方程 完美匹配边界层 吸收边界条件 反射系数
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基于ADI-FDTD法的探地雷达正演数值模拟及验证
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作者 曾良生 迟耀丹 +1 位作者 周庆才 衣淼 《吉林建筑大学学报》 CAS 2024年第1期48-55,共8页
探地雷达(GPR)是一种应用前景广泛、用于探测和定位地下物体的浅层地球物理方法。通过开展探地雷达正演模拟研究,可以获得复杂地下结构的探地雷达图像回波特征。时域有限差分(FDTD)法受到稳定性和收敛性条件的限制,导致效率和精度低。... 探地雷达(GPR)是一种应用前景广泛、用于探测和定位地下物体的浅层地球物理方法。通过开展探地雷达正演模拟研究,可以获得复杂地下结构的探地雷达图像回波特征。时域有限差分(FDTD)法受到稳定性和收敛性条件的限制,导致效率和精度低。交替方向隐式-时域有限差分(ADI-FDTD)法克服FDTD法的稳定性限制,可以选择更大的时间步长来提高计算效率。从原理出发,对ADI-FDTD法进行公式推导,在基于ADI-FDTD法的基础上进行卷积完全匹配层(CPML)的结合。通过进行ADI-FDTD法的时间稳定性仿真和不同材质、不同填充介质的双管,沙槽正演模拟实验,结果表明,ADI-FDTD法可以保证时间无条件稳定性,相同情况下可采用更大的时间步长进行正演模拟,提高正演效率。对不同管线、不同材质情况下的正演剖面曲线特征进行解译分析,最后与沙槽实测进行对比,证明得到的探测解译结果与实际状况达到较好的吻合。 展开更多
关键词 探地雷达(GPR) 正演模拟 无条件稳定 卷积完全匹配层(CPML) 交替方向隐式-时域有限差分(ADI-FDTD)法
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APPLICATION OF THE PML ABSORBING BOUNDARY CONDITION TO FD-TD SIMULATION
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作者 Guo Ziqin Lin Deyun(Dept. of Electronic Engineering, Tsinghua University, Beijing 100084) 《Journal of Electronics(China)》 1998年第2期168-173,共6页
The key problem of finite-difference time-domain (FD-TD) method is the skillful application of special conditions on the boundaries of the computational domain. A new technique named Perfectly Matched Layer(PML) yield... The key problem of finite-difference time-domain (FD-TD) method is the skillful application of special conditions on the boundaries of the computational domain. A new technique named Perfectly Matched Layer(PML) yields a robust Absorbing Boundary Condition(ABC) independent of the angle of incidence and the frequency of outgoing waves. In this paper, the principle of the PML technique is briefly presented. Then some problems in the application and their settlements are discussed emphatically. Finally three numerical tests and a measured result are devoted to examine the accuracy and effectiveness of this approach. 展开更多
关键词 FINITE-DIFFERENCE TIME-DOMAIN Absorbing boundary CONDITION perfectly matched layer REFLECTION COEFFICIENT
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Fast division-free parallel structure for convolution perfectly matched layer in finite difference time domain method
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作者 Bai Bing Niu Zhongqi +2 位作者 Niu Yi Wei Bing Zhao Gang 《The Journal of China Universities of Posts and Telecommunications》 EI CSCD 2015年第1期72-76,82,共6页
Parallel acceleration of convolution perfectly matched layer (CPML) algorithm suffers from massive division operation which is widely accepted as one of the most expensive operations for the equipment such as graphi... Parallel acceleration of convolution perfectly matched layer (CPML) algorithm suffers from massive division operation which is widely accepted as one of the most expensive operations for the equipment such as graphic processing unit (GPU), field programmable gate array (FPGA) etc. In pursuit of higher efficiency and lower power consumption, this article revisited the CPML theory and proposed a new fast division-free parallel CPML structure. By optimally rearranging the CPML inner iteration process, all the division operators can be eliminated and replaced by recalculating the related field updating coefficients offline. Experiments show that the proposed division-free structure can save more than 50% arithmetic instructions and 25% execution time of the traditional parallel CPML structure without any accuracy loss. 展开更多
关键词 division elimination convolution perfectly matched layer finit difference time domain parallel computing graphic processing unit
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Perfectly Matched Layer Method for Acoustic Scattering Problem by a Locally Perturbed Line with Impedance Boundary Condition
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作者 Xue Jiang Xujing Li 《Advances in Applied Mathematics and Mechanics》 SCIE 2020年第1期101-140,共40页
In this paper,we study the two-dimensional Helmholtz scattering problem by a locally perturbed line with impedance boundary condition.Different from the problem with Dirichlet boundary condition,the Green function of ... In this paper,we study the two-dimensional Helmholtz scattering problem by a locally perturbed line with impedance boundary condition.Different from the problem with Dirichlet boundary condition,the Green function of the Helmholtz equation with impedance boundary condition becomes very complicated and comprises surface waves along the locally perturbed line.A uniaxial perfectly matched layer(UPML)method is proposed to truncate the half plane into a bounded computational domain.The main contribution of this paper is to prove the well-posedness of the PML problem and the exponential convergence of the approximate solution to the exact solution as either the thickness or the medium parameter of PML increases. 展开更多
关键词 Uniaxial perfectly matched layer Helmholtz equation locally perturbed half-plane impedance condition
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Layer-oriented Element Integration Algorithm of Conformal Perfectly Matched Layer
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作者 张永杰 孙秦 《Chinese Journal of Aeronautics》 SCIE EI CAS CSCD 2009年第3期268-272,共5页
As an efficient artificial truncating boundary condition, conformal perfectly matched layer (CPML) is a kind of multilayer anisotropic absorbing media. To reduce computing effort of CPML, this article proposes a layer... As an efficient artificial truncating boundary condition, conformal perfectly matched layer (CPML) is a kind of multilayer anisotropic absorbing media. To reduce computing effort of CPML, this article proposes a layer-oriented element integration algorithm. In this algorithm, the relative dielectric constant and permeability are considered as constants for each the very thin monolayer of CPML, and the element integration of multilayer along the normal direction is substituted by the element integration of m... 展开更多
关键词 conformal perfectly matched layer layer-oriented element integration algorithm boundary conditions
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基于非均匀介质的城市隧道渗水检测地质雷达数值模拟
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作者 陈熙国 《中国高新科技》 2023年第3期78-80,共3页
随着城市建设的日新月异,因隧道相比桥梁而言能够更好地利用地下空间,导致城市交通出现越来越多的隧道。我国较多城市都建立在河流附近,以至于过江隧道在城市交通中的应用越来越广泛,如长沙的营盘路隧道、南湖路隧道。过江隧道由于位于... 随着城市建设的日新月异,因隧道相比桥梁而言能够更好地利用地下空间,导致城市交通出现越来越多的隧道。我国较多城市都建立在河流附近,以至于过江隧道在城市交通中的应用越来越广泛,如长沙的营盘路隧道、南湖路隧道。过江隧道由于位于江底,隧道渗水会带来一系列的隧道病害,因此对过江隧道的渗水检测尤为重要。文章从非均匀介质的地质雷达探测正演出发,总结富水区域在雷达扫描中的特征,说明该正演方法的有效性,这为隧道渗水病害检测的实际雷达扫描图中富水体的判定提供了一个更为可靠的依据。 展开更多
关键词 非均匀介质 地质雷达 数值模拟 CPML 渗水检测
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完全匹配层吸收边界在孔隙介质弹性波模拟中的应用 被引量:49
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作者 赵海波 王秀明 +1 位作者 王东 陈浩 《地球物理学报》 SCIE EI CAS CSCD 北大核心 2007年第2期581-591,共11页
模拟弹性波在孔隙介质中传播,需要稳定有效的吸收边界来消除或尽可能的减小由人工边界引起的虚假反射.本文在前人工作基础上,首次建立了弹性孔隙介质情况下完全匹配层吸收边界的高阶速度-应力交错网格有限差分算法,并详细讨论了完全匹... 模拟弹性波在孔隙介质中传播,需要稳定有效的吸收边界来消除或尽可能的减小由人工边界引起的虚假反射.本文在前人工作基础上,首次建立了弹性孔隙介质情况下完全匹配层吸收边界的高阶速度-应力交错网格有限差分算法,并详细讨论了完全匹配层的构建及其有限差分算法实现.首先,本文通过均匀孔隙模型的数值解与解析解的对比,验证所提出的数值方法的正确性;然后,本文考察了完全匹配层对不同入射角度入射波和自由表面上的瑞利波的吸收性能,将完全匹配层与廖氏和阻尼吸收边界进行了对比,研究了这三种吸收边界在不同吸收厚度情况下对弹性波吸收能力.数值结果表明,在孔隙介质中,完全匹配层作为吸收边界能十分有效地吸收衰减外行波,无论对体波还是面波,是一种高效边界吸收算法. 展开更多
关键词 数值模拟 吸收边界 孔隙介质 完美匹配层 有限差分
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二阶声波方程频域PML边界条件及频域变网格步长并行计算 被引量:9
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作者 韩利 韩立国 +2 位作者 李翔 王德利 崔杰 《吉林大学学报(地球科学版)》 EI CAS CSCD 北大核心 2011年第4期1226-1232,共7页
研究了二阶声波方程频域PML边界条件和频域变网格并行计算技术。PML边界是一种较为理想的吸收边界方法,多用在求解时域应力速度方程中,但对于频域声波正演,二阶位移方程更常用。从一阶声波方程PML吸收边界条件导出频域二阶位移方程PML... 研究了二阶声波方程频域PML边界条件和频域变网格并行计算技术。PML边界是一种较为理想的吸收边界方法,多用在求解时域应力速度方程中,但对于频域声波正演,二阶位移方程更常用。从一阶声波方程PML吸收边界条件导出频域二阶位移方程PML边界条件,模拟算例得到的频率切片、时间切片和地震记录对比都说明该边界条件吸收效果很好。频域单炮正演不同频率间是独立的,据此低频部分采用大网格计算,高频采用小网格,实现变网格步长计算技术,这是较时间域正演的一个优势,在保证模拟质量的同时,减少计算量和内存消耗。 展开更多
关键词 完全匹配层 边界条件 频率域正演 并行计算 变网格
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粒子模拟软件吸收边界的研究 被引量:6
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作者 胡旻 祝大军 +2 位作者 刘大刚 周俊 刘盛纲 《强激光与粒子束》 EI CAS CSCD 北大核心 2006年第8期1315-1318,共4页
实现了时域有限差分法的Gedney完全匹配层吸收边界条件,并进行了数值验证和参数优化。从结果可以看出其有较低的反射,性能优良;对吸收媒质厚度和电导率分布阶数的参数优化结果与Gedney经验值基本一致。将此吸收边界模块加入到国产粒子... 实现了时域有限差分法的Gedney完全匹配层吸收边界条件,并进行了数值验证和参数优化。从结果可以看出其有较低的反射,性能优良;对吸收媒质厚度和电导率分布阶数的参数优化结果与Gedney经验值基本一致。将此吸收边界模块加入到国产粒子模拟软件CHIPIC中,同美国商业粒子模拟软件MAGIC相比有更好的吸收效果。通过对2维极坐标下磁控管的模拟,证明了此吸收边界具有实际应用价值。 展开更多
关键词 吸收边界 完全匹配层(PML) PIC模拟 磁控管
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组合边界条件下二维三分量TTI介质波场数值模拟 被引量:18
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作者 杜启振 孙瑞艳 张强 《石油地球物理勘探》 EI CSCD 北大核心 2011年第2期187-195,156,共9页
从TTI介质一阶应力—速度方程出发,利用旋转交错网格高阶有限差分方法,将非分裂完全匹配层(Non-spliting Perfect Match Layer,简称NPML)边界吸收条件和自由边界条件相结合形成组合边界条件,进行了二维三分量TTI介质弹性波场数值模拟。... 从TTI介质一阶应力—速度方程出发,利用旋转交错网格高阶有限差分方法,将非分裂完全匹配层(Non-spliting Perfect Match Layer,简称NPML)边界吸收条件和自由边界条件相结合形成组合边界条件,进行了二维三分量TTI介质弹性波场数值模拟。波场快照和炮记录表明:①采用非分裂式边界条件能较好地消除近地表大角度入射波和瞬逝波;②组合边界条件与NPML边界吸收条件相比,不仅有效地压制了边界反射,同时实现了对自由地表的模拟,获得了丰富的全波场信息,其中在地表产生的PS转换横波作为一种特殊的横波现象,可为近地表结构调查以及多波波场分析等提供有益信息;③自由地表引起的面波以及多次波对偏移结果有着重要影响,因此在实际地震资料处理中应当充分考虑自由地表条件对波场的影响效应。数值模拟结果证实了组合边界条件下二维三分量TTI介质波场数值模拟方法的可行性和正确性。 展开更多
关键词 有限差分法 旋转交错网格 NPML边界吸收条件 自由地表边界条件 组合边界条件 TTI介质 一阶应力—速度方程 波场 数值模拟
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基于褶积完全匹配吸收边界的声波方程数值模拟 被引量:8
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作者 柯璇 石颖 +1 位作者 宋利伟 李松龄 《石油物探》 EI CSCD 北大核心 2017年第5期637-643,666,共8页
完全匹配层(PML)吸收边界条件已广泛应用于地震波场模拟中,但PML吸收边界条件存在一些问题,如对低频和地震波为掠射波时会产生虚假反射等。褶积完全匹配层(CPML)吸收边界条件能够有效地解决PML吸收边界条件存在的问题。推导了带有CPML... 完全匹配层(PML)吸收边界条件已广泛应用于地震波场模拟中,但PML吸收边界条件存在一些问题,如对低频和地震波为掠射波时会产生虚假反射等。褶积完全匹配层(CPML)吸收边界条件能够有效地解决PML吸收边界条件存在的问题。推导了带有CPML条件的一阶速度-应力波动方程,并且在方程中引入记忆变量代替复杂褶积项的运算,将CPML与交错网格有限差分算法相结合,发挥了该边界条件节省计算存储空间、易于编程实现等优点。数值模拟结果表明,在不增加计算量的情况下,CPML吸收边界条件有效地提高了波场模拟精度。 展开更多
关键词 褶积完全匹配层 交错网格 数值模拟 声波方程 边界条件
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一种改进的二阶弹性波动方程的最佳匹配层吸收边界条件 被引量:16
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作者 刘有山 刘少林 +1 位作者 张美根 马德堂 《地球物理学进展》 CSCD 北大核心 2012年第5期2113-2122,共10页
在分析前人有关二阶波动方程的最佳匹配层(PML)吸收边界条件的构建方式的基础上,讨论了这些PML吸收边界条件在计算效率和计算精度方面的不足,并给出了一种新的改进PML吸收边界条件.本文的核心思想是在频率域引入一个中间变量,避免了褶... 在分析前人有关二阶波动方程的最佳匹配层(PML)吸收边界条件的构建方式的基础上,讨论了这些PML吸收边界条件在计算效率和计算精度方面的不足,并给出了一种新的改进PML吸收边界条件.本文的核心思想是在频率域引入一个中间变量,避免了褶积运算,对该变量做傅里叶逆变换得到时间域的精确解.通过模型试算,把本文的改进算法与前人的算法的计算精度和计算时间进行比较.对比分析表明,本文提出的PML吸收边界条件计算量小且精度较高,并且是一种稳定的算法. 展开更多
关键词 二阶波动方程 最佳匹配层 吸收边界条件
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