任志明^1,,
戴雪¹,
包乾宗¹,
蔡晓慧²,
刘洋³
1. 长安大学地质工程与测绘学院, 西安 710064
2. 南京工业大学岩土工程研究所, 南京 210009
3. 西安邮电大学自动化学院, 西安 710121

基金项目: 国家自然科学基金（41804117，41704122）和陕西省自然科学基金（2021JQ-702）联合资助


详细信息

作者简介: 任志明, 男, 1987年生, 长安大学副教授, 主要从事地震波传播、偏移成像与全波形反演等方面的研究工作.E-mail: rzm-213@163.com

中图分类号: P631

收稿日期:2021-01-14
修回日期:2021-08-27
上线日期:2021-11-10

Time and space dispersion in finite difference and its influence on reverse time migration and full-waveform inversion

REN ZhiMing^1,,
DAI Xue¹,
BAO QianZong¹,
CAI XiaoHui²,
LIU Yang³
1. College of Geological Engineering and Geomatics, Chang'an University, Xi'an 710064, China
2. Institute of Geotechnical Engineering, Nanjing University of Technology, Nanjing 210009, China
3. College of Automation, Xi'an University of Posts and Telecommunications, Xi'an 710121, China


MSC: P631

--> Received Date: 14 January 2021
Revised Date: 27 August 2021
Available Online: 10 November 2021


摘要
摘要:有限差分是最常用的地震波方程数值模拟方法，但时间和空间离散会产生数值频散.正演是逆时偏移和全波形反演的基本单元，成像和反演的精度很大程度依赖于所采用的数值模拟算法.本文研究了有限差分的时间和空间频散特性及其对逆时偏移和全波形反演的影响.通过时间有限差分+伪谱法、时间频散校正+空间有限差分、时间频散校正+伪谱法获取时间频散、空间频散和无频散数据；发展了抗时间频散、抗空间频散、抗时间+空间频散的逆时偏移和全波形反演方法；采用理论模型和实际资料对提出的方法进行了测试.数值结果表明：逆时偏移同时受时间和空间频散影响，时间频散导致同相轴不聚焦、成像位置偏离，空间频散会产生高频噪声和虚假反射界面；全波形反演在低频大尺度反演中几乎不受时间和空间频散影响，高频精细反演中时间频散引起波形相移、降低反演精度，空间频散增加多解性、导致反演不收敛；抗频散方法可以有效缓解时间和空间频散影响，获得高质量的偏移剖面和反演结果.
关键词: 有限差分/
正演模拟/
数值频散/
逆时偏移/
全波形反演

Abstract:The Finite Difference (FD) is the most commonly used method in modeling of seismic wave equations. The time and space discretizations in this method, however, can cause numerical dispersion. Forward modeling is a basic unit of Reverse Time Migration (RTM) and Full-Waveform Inversion (FWI). The accuracy of imaging and inversion largely depends on the numerical algorithm used. This paper studies the time and space dispersion of FD and its effect on RTM and FWI. We obtain the time dispersion, space dispersion and dispersion-free data through the temporal FD and pseudospectral method, time dispersion correction and spatial FD, time dispersion correction and pseudospectral method, respectively. Additionally, we develop the anti-time-dispersion, anti-space-dispersion and anti-time+space-dispersion RTM and FWI methods. Tests on synthetic and real seismic data are conducted to verify the proposed methods. Numerical results show that the RTM results are affected by both time and space dispersion. The time dispersion causes defocused images and incorrect imaging positions, whereas the space dispersion produces high-frequency noise and false reflection interfaces. FWI is almost immune to the time and space dispersion in the low-frequency large-scale inversion. The time dispersion in the high-frequency fine inversion brings in phase shift and reduces inversion accuracy. The space dispersion increases the nonlinearity, leading to the non-convergence of FWI. By contrast, the anti-dispersion method can alleviate the effect of time and space dispersion and produce high-quality migration profiles and inversion results.
Key words:Finite difference/
Forward modeling/
Numerical dispersion/
Reverse time migration/
Full-waveform inversion



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