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胡勇, 韩立国, 于江龙, 陈瑞鼎. 2018. 基于自适应非稳态相位校正的时频域多尺度全波形反演. 地球物理学报, 61(7): 2969-2988, doi: 10.6038/cjg2018L0421
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| Citation: |
HU Yong, HAN LiGuo, YU JiangLong, CHEN RuiDing. 2018. Time-frequency domain multi-scale full waveform inversion based on adaptive non-stationary phase correction. Chinese Journal of Geophysics (in Chinese), 61(7): 2969-2988, doi: 10.6038/cjg2018L0421
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Time-frequency domain multi-scale full waveform inversion based on adaptive non-stationary phase correction
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摘要:
本文提出非稳态相位校正时频域目标函数，通过缩小观测数据与模拟数据在波形相位上的差异来缓解全波形反演过程中对应波形匹配错位的问题（周波跳跃）.同时引入自适应相位校正因子，可以根据观测数据与模拟数据的差异来调整相位校正量的大小.在构建非稳态相位校正时频域全波形反演目标函数的基础上，利用链式法则详细推导了对应的伴随震源，并从理论上证明了该方法的可行性与优越性.数值测试过程中结合了低通滤波多尺度反演策略，进一步缓解全波形反演过程中的强非线性问题.缺失低频分量测试结果表明，利用自适应非稳态相位校正时频域多尺度全波形反演方法结合常规全波形反演方法在缺失7 Hz以下低频分量的地震数据中仍然能够得到高精度的反演结果.震源不准确测试结果表明，即使震源子波相位差异较大，利用非稳态相位校正方法仍然能够一定程度上缓解周波跳跃现象.测试结果综合证明了本文提出的方法在构建初始速度建模，缓解周波跳跃等方面具有一定的优势.
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关键词:
- 全波形反演 /
- 多尺度策略 /
- 伴随状态法 /
- 自适应非稳态相位校正 /
- 时频域
Abstract:In this paper, we propose a non-stationary phase correction objective function to mitigate the waveform mismatch problem for the time-frequency domain Full-Waveform Inversion (FWI). At the same time, according to the difference between recorded data and synthetic data, we introduce an adaptive correction factor to adjust the size of the phase correction. Based on the objective function of time frequency domain FWI, we use the chain rule to deduce the corresponding adjoint source and theoretically prove the feasibility and superiority of the Adaptive Non-stationary Phase correction Time-frequency multi-scale Full Waveform Inversion (ANPTFWI). In the process of numerical testing, we combine the advantages of low-pass filtering and multi-scale inversion strategy to alleviate the non-linearity of FWI. The numerical tests without low frequency information show that when the seismic data lack low frequency information below 7 Hz, the ANPTFWI method combined with the conventional FWI method still can obtain high accuracy inversion results. The numerical tests with an inaccurate wavelet show that even if there is a large phase difference between the two wavelets, we still can use the non-stationary phase correction method to mitigate the cycle skipping problem. The numerical test proves that the ANPTFWI has a strong ability for building good initial velocity models and mitigating the cycle skipping problem.
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图 4
常规FWI目标函数与非稳态相位校正目标函数
Figure 4.
Conventional FWI objective function and non-stationary phase correction objective function
图 5
基于自适应非稳态相位校正的时频域多尺度FWI流程图
Figure 5.
Time-frequency multi-scale FWI based on adaptive non-stationary phase correction flow chart
图 8
低频段反演结果+常规FWI结果
Figure 8.
Inversion results with low frequency band + Conventional FWI
图 9
自适应非稳态相位校正时频域FWI低频段结果(不同的自适应相位校正因子，缺失7 Hz以下低频信息)
Figure 9.
Adaptive non-stationary phase correction time frequency domain FWI result with low frequency band (With different adaptive phase correction factors, lack low frequency information below 7 Hz)
图 10
自适应非稳态相位校正时频域FWI低频段结果+常规FWI结果(不同的自适应相位校正因子，缺失7 Hz以下低频信息)
Figure 10.
Adaptive non-stationary phase correction time frequency domain FWI result with low frequency band + Conventional FWI (With different adaptive phase correction factors, lack low frequency information below 7 Hz)
图 11
FWI单道对比图(不同的自适应相位校正因子，距离为0.75 km处)
Figure 11.
One trace of FWI inversion results (With different adaptive phase correction factors, at the distance of 0.75 km)
图 12
FWI单道对比图(不同的自适应相位校正因子，距离为1.75 km处)
Figure 12.
One trace of FWI inversion results (With different adaptive phase correction factors, at the distance of 1.75 km)
图 15
自适应非稳态相位校正的时频域多尺度FWI伴随震源(不同自适应相位校正因子和不同震源子波，真实速度模型上正演得到)
Figure 15.
Adjoint source of adaptive non-stationary phase correction Time-frequency domain FWI (With different adaptive phase correction factors and wavelet, forward modeling from the true velocity model)
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Figure 1.
Waveform phase correction
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Figure 2.
Single trace seismic waveform
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Figure 3.
Waveform phase correction results with different frequency band (From red rectangular of Fig. 2a)
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Figure 4.
Conventional FWI objective function and non-stationary phase correction objective function
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Figure 5.
Time-frequency multi-scale FWI based on adaptive non-stationary phase correction flow chart
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Figure 6.
Velocity models
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Figure 7.
Inversion results with low frequency band
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Figure 8.
Inversion results with low frequency band + Conventional FWI
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Figure 9.
Adaptive non-stationary phase correction time frequency domain FWI result with low frequency band (With different adaptive phase correction factors, lack low frequency information below 7 Hz)
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Figure 10.
Adaptive non-stationary phase correction time frequency domain FWI result with low frequency band + Conventional FWI (With different adaptive phase correction factors, lack low frequency information below 7 Hz)
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Figure 11.
One trace of FWI inversion results (With different adaptive phase correction factors, at the distance of 0.75 km)
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Figure 12.
One trace of FWI inversion results (With different adaptive phase correction factors, at the distance of 1.75 km)
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Figure 13.
The difference between synthetic data and recorded data (With different adaptive phase correction factors, forward modeling from Fig. 10, with source location: 0.75 km)
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Figure 14.
True wavelet and Modeling wavelet
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Figure 15.
Adjoint source of adaptive non-stationary phase correction Time-frequency domain FWI (With different adaptive phase correction factors and wavelet, forward modeling from the true velocity model)
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Figure 16.
Adaptive non-stationary phase correction time frequency domain FWI result with low frequency band (With different adaptive phase correction factors, lack low frequency information below 7 Hz, inaccurate wavelet)