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物探与化探  2022, Vol. 46 Issue (3): 693-703    DOI: 10.11720/wtyht.2022.1180
  方法研究·信息处理·仪器研制 本期目录 | 过刊浏览 | 高级检索 |
多源并发下Mur二阶吸收边界和非分裂递归卷积完全匹配层对比研究
崔凡1,2(), 陈毅1(), 薛晗鹏1, 彭苏萍1,2, 杜云飞1
1.中国矿业大学(北京) 地球科学与测绘工程学院,北京 100083
2.中国矿业大学(北京) 煤炭资源与安全开采国家重点实验室,北京 100083
A comparative study of Mur second-order absorbing boundary condition and unsplit recursive convolutional perfectly matched layer method under multi-source concurrency
CUI Fan1,2(), CHEN Yi1(), XUE Han-Peng1, PENG Su-Ping1,2, DU Yun-Fei1
1. School of Geosciences and Surveying Engineering,China University of Mining and Technology(Beijing),Beijing 100083,China
2. State Key Laboratory of Coal Resources and Safe Mining,China University of Mining and Technology(Beijing),Beijing 100083,China
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摘要 

多个激励源无延时发射(多源并发)相同中心频率脉冲会形成平面波束信号,增强数据记录质量。本文通过数值模拟对比分析在多源并发情况下,非分裂递归卷积完全匹配层作为吸收边界条件和Mur二阶吸收边界条件对电磁波的吸收效果。其研究结果表明,传统的Mur二阶吸收边界条件对多源并发、多角度掠射情况下电磁波的吸收效果不佳,在大偏移距下会造成波形畸变和形成虚假反射。而在多源并发情况下采用非分裂递归卷积完全匹配层作为吸收边界条件,将坐标伸缩因子引进时域有限差分算法中。通过傅里叶逆变换将频率域坐标伸缩变换PML方程转换到时域,对电场和磁场值在离散状态下进行递归卷积运算求解。从而避免了直接对卷积进行数值求解的复杂计算,在保证计算准确性的同时,节约了内存空间,提高了计算效率。在不分裂波场情况下,改善了网格截断位置对电磁波的吸收效果。

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崔凡
陈毅
薛晗鹏
彭苏萍
杜云飞
关键词 多源并发坐标伸缩因子递归卷积完全匹配层时域有限差分傅里叶逆变换    
Abstract

Plane beam signals form when multiple excitation sources simultaneously emit pulses with the same center frequency (multiple-source concurrency),thus enhancing the quality of data records.This paper compares and analyzes the electromagnetic wave absorption effects of unsplit recursive convolutional perfectly matched layer (PML) as the absorbing boundary condition and Mur second-order absorbing boundary condition under multi-source concurrency through numerical simulation.According to study results,the traditional Mur second-order absorbing boundary condition did not perform well in absorbing electromagnetic waves under the conditions of multi-source concurrency and multi-angle grazing,and it will cause waveform distortion and spurious reflections in the case of large offsets.For the unsplit recursive convolutional perfectly matched layer as the absorbing boundary condition under multi-source concurrency,coordinate scale factors were introduced into the finite-difference time-domain (FDTD) algorithm.Then,the PML equation for coordinate stretching was transformed from frequency domain into time domain through the inverse Fourier transform.Finally,the electric and magnetic field values were solved using the recursive convolution method in the discrete state,thus avoiding the complicated calculation involved in directly determining the numerical solution of convolution.This allows less memory space and high calculation efficiency while ensuring accuracy.Therefore,the unsplit recursive convolutional perfectly matched layer method improves the electromagnetic wave absorption effect at the positions where the grid terminate without inducing wave-field splitting.

Key wordsmulti-source concurrency    coordinate stretch factor    recursive convolution    perfect matched layer(PML)    finite difference time-domain    inverse Fourier transform
收稿日期: 2021-04-12      修回日期: 2022-01-14      出版日期: 2022-06-20
ZTFLH:  P631.4  
基金资助:国家自然科学基金项目(52074306);国家能源投资集团科技创新项目(GJNY2030XDXM-19-03.2);陕煤化集团重大项目(2018SMHKJ-A-J-03)
通讯作者: 陈毅
作者简介: 崔凡(1984-),男,汉族,安徽淮南人,博士,副教授,从事探地雷达理论与方法研究工作。Email:cuifan_cumtb@126.com
引用本文:   
崔凡, 陈毅, 薛晗鹏, 彭苏萍, 杜云飞. 多源并发下Mur二阶吸收边界和非分裂递归卷积完全匹配层对比研究[J]. 物探与化探, 2022, 46(3): 693-703.
CUI Fan, CHEN Yi, XUE Han-Peng, PENG Su-Ping, DU Yun-Fei. A comparative study of Mur second-order absorbing boundary condition and unsplit recursive convolutional perfectly matched layer method under multi-source concurrency. Geophysical and Geochemical Exploration, 2022, 46(3): 693-703.
链接本文:  
https://www.wutanyuhuatan.com/CN/10.11720/wtyht.2022.1180      或      https://www.wutanyuhuatan.com/CN/Y2022/V46/I3/693
Fig.1  函数f(t)阶梯表示法
Fig.2  未修正角点不同时间步的Ez波场
Fig.3  TM波左下角点修正示意
Fig.4  均匀介质递归卷积完全匹配层不同时间步Ez波场快照
Fig.5  均匀介质Mur二阶吸收边界不同时间步Ez波场快照
Fig.6  低洼模型结构示意
Fig.7  低洼模型不同时间步Ez波场快照
Fig.8  低洼模型700时间步Ez波场快照
a—递归卷积完全匹配层波场快照;b—Mur二阶吸收边界波场快照
Fig.9  多源并发雷达数据记录
a—递归卷积完全匹配层数据记录;b—Mur二阶吸收边界数据记录
Fig.10  单个激励源雷达数据记录
a—递归卷积完全匹配层数据记录;b—Mur二阶吸收边界数据记录
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