改进的伴随状态法初至波走时层析成像方法

董良国, 张建明, 韩佩恩. 2021. 改进的伴随状态法初至波走时层析成像方法. 地球物理学报, 64(3): 982-992, doi: 10.6038/cjg2021O0368
引用本文: 董良国, 张建明, 韩佩恩. 2021. 改进的伴随状态法初至波走时层析成像方法. 地球物理学报, 64(3): 982-992, doi: 10.6038/cjg2021O0368
DONG LiangGuo, ZHANG JianMing, HAN PeiEn. 2021. The improved first-arrival traveltime tomography based on the adjoint-state method. Chinese Journal of Geophysics (in Chinese), 64(3): 982-992, doi: 10.6038/cjg2021O0368
Citation: DONG LiangGuo, ZHANG JianMing, HAN PeiEn. 2021. The improved first-arrival traveltime tomography based on the adjoint-state method. Chinese Journal of Geophysics (in Chinese), 64(3): 982-992, doi: 10.6038/cjg2021O0368

改进的伴随状态法初至波走时层析成像方法

  • 基金项目:

    国家重点研发计划项目(2019YFC0312004)以及国家自然科学基金项目(41874127)和上海市科技创新行动计划项目(19DZ1201702)联合资助

详细信息
    作者简介:

    董良国, 同济大学海洋与地球科学学院教授, 博士生导师, 主要从事地震波传播理论与数值模拟、地震波反演等方面的研究.E-mail: dlg@tongji.edu.cn

  • 中图分类号: P631

The improved first-arrival traveltime tomography based on the adjoint-state method

  • 目前,有关伴随状态法初至波走时层析成像方法的文献,基本上都是基于面积分来定义目标函数,由此得到的伴随方程也都依赖于地表的法向量.这样,一方面会因为伴随变量计算的不准确而造成梯度的不合理,另一方面也无法合理地处理井中观测问题.本文从理论或数值试验角度指出了这些问题,并提出了不依赖地表法向量的改进的伴随状态法走时层析成像方法.主要改进包括:(1)采用体积分定义目标函数,避免了传统方法不能较好处理井中观测数据的缺陷,可以适应任意地表或井中观测系统.(2)采用摄动法得到了新的伴随方程,克服了传统方法中伴随场计算需要依赖于地表法向量的缺陷,使得检波点处的走时残差可以正确地反传播至地下,进而得到更加合理的速度修正方向,提高了速度反演的精度.

  • 加载中
  • 图 1 

    不同地表法向量的对称接收点试验的真实模型

    Figure 1. 

    The true velocity model with two symmetrical receivers but different surface normal vectors

    图 2 

    初始速度模型

    Figure 2. 

    The initial velocity model

    图 3 

    传统AST方法得到的归一化后的伴随场分布

    Figure 3. 

    The normalized adjoint field distribution by the conventional AST method

    图 4 

    传统AST方法计算的梯度

    Figure 4. 

    The gradient obtained by the conventional AST method

    图 5 

    计算区域的拓展示意图

    Figure 5. 

    The extended sketch map of the computational domain

    图 6 

    改进的AST方法计算的归一化后的梯度分布

    Figure 6. 

    The normalized gradient obtained by the improved AST method

    图 7 

    简单起伏地表速度模型及改进前后AST反演结果

    Figure 7. 

    The simple topographic velocity model and the AST inversion results

    图 8 

    传统与改进的AST方法不同迭代次数的归一化梯度

    Figure 8. 

    The normalized gradients of different iterations for the conventional and the improved AST methods From top to bottom show the gradients corresponding to 1, 20, 100 and 300 iterations.

    图 9 

    归一化后的目标函数收敛曲线

    Figure 9. 

    The normalized objective function iteration curves

    图 10 

    起伏地表真实速度模型

    Figure 10. 

    The true complex topographic velocity model

    图 11 

    初始速度模型

    Figure 11. 

    The initial velocity model

    图 12 

    传统AST方法反演结果

    Figure 12. 

    The inversion result by the conventional AST method

    图 13 

    改进AST方法反演结果

    Figure 13. 

    The inversion result by the improved AST method

    图 14 

    第80代反演结果地表下不同深度的速度剖面对比

    Figure 14. 

    The inverted lateral velocity slices with depth of (a) 20 m, (b) 30 m, (c) 40 m and (d) 50 m below the surface for the 80th iteration

    图 15 

    方法改进前后反演结果的剩余走时对比

    Figure 15. 

    The residual first-arrival traveltime of the final inversion results for different shots with sources located at (a) 15 km, (b) 20 km and (c) 25 km

  •  

    Ao R D, Dong L G, Chi B X. 2015. Source-independent envelope-based FWI to build an initial model. Chinese Journal of Geophysics (in Chinese), 58(6): 1998-2010, doi:10.6038/cjg20150615.

     

    Benaichouche A, Noble M, Gesret A. 2015. First arrival traveltime tomography using the fast marching method and the adjoint state technique. 77th Annual International Conference and Exhibition, EAGE, Extended Abstracts.

     

    Bishop T N, Bube K P, Cutler R T, et al. 1985. Tomographic determination of velocity and depth in laterally varying media. Geophysics, 50(6): 903-923. doi: 10.1190/1.1441970

     

    Bretaudeau F, Brossier R, Métivier L, et al. 2014. First-arrival delayed tomography using 1st and 2nd order adjoint-state method.//84th Ann. Internat Mtg., Soc. Expl. Geophys.. Expanded Abstracts, 4757-4762.

     

    Choi Y, Alkhalifah T. 2013. Frequency-domain waveform inversion using the phase derivative. Geophysical Journal International, 195(3): 1904-1916. doi: 10.1093/gji/ggt351

     

    Fichtner A, Trampert J. 2011. Hessian kernels of seismic data functionals based upon adjoint techniques. Geophysical Journal International, 185(2): 775-798. doi: 10.1111/j.1365-246X.2011.04966.x

     

    Han P E, Dong L G, Ma Q P, et al. 2019. First-arrival traveltime tomography based on the adjoint state method with independence of surface normal vectors. 81th Annual International Conference and Exhibition, EAGE, Extended Abstracts.

     

    Huang J W, Bellefleur G. 2012. Joint transmission and reflection traveltime tomography using the fast sweeping method and the adjoint-state technique. Geophysical Journal International, 188(2): 570-582. doi: 10.1111/j.1365-246X.2011.05273.x

     

    Leung S, Qian J L. 2006. An adjoint state method for three-dimensional transmission traveltime tomography using first-arrivals. Communications in Mathematical Sciences, 4(1): 249-266. doi: 10.4310/CMS.2006.v4.n1.a10

     

    Li W B, Leung S. 2013. A fast local level set adjoint state method for first arrival transmission traveltime tomography with discontinuous slowness. Geophysical Journal International, 195(1): 582-596. doi: 10.1093/gji/ggt244

     

    Li W B, Leung S, Qian J L. 2014. A level-set adjoint-state method for crosswell transmission-reflection traveltime tomography. Geophysical Journal International, 199(1): 348-367. doi: 10.1093/gji/ggu262

     

    Li Y D, Dong L G, Liu Y Z. 2017. First-arrival traveltime tomography based on a new preconditioned adjoint-state method. Chinese Journal of Geophysics (in Chinese), 60(10): 3934-3941, doi:10.6038/cjg20171021.

     

    Lions J L. 1971. Optimal Control of Systems Governed by Partial Differential Equations. Berlin Heidelberg: Springer-Verlag.

     

    Liu Z Y, Zhang J. 2017. Joint travel-time, waveform, and waveform envelope inversion for near-surface imaging. Geophysics, 82(4): 235-244. http://www.researchgate.net/publication/315461862_Joint_travel-time_waveform_and_waveform_envelope_inversion_for_near-surface_imaging

     

    Luo Y, Schuster G. 1991. Wave-equation traveltime inversion. Geophysics, 56(5): 645-653. doi: 10.1190/1.1443081

     

    Moser T. 1991. Shortest path calculation of seismic rays. Geophysics, 56(1): 59-67. doi: 10.1190/1.1442958

     

    Noble M, Thierry P, Taillandier C, et al. 2010. High-performance 3D first-arrival traveltime tomography. The Leading Edge, 29(1): 86-93. doi: 10.1190/1.3284057

     

    Nocedal J, Wright S J. 2006. Numerical Optimization. 2nd ed. New York, USA: Springer.

     

    Olson K B. 1989. A stable and flexible procedure for the inverse modeling of seismic first arrivals. Geophysical Prospecting, 37(5): 455-465. doi: 10.1111/j.1365-2478.1989.tb02217.x

     

    Plessix R E. 2006. A review of the adjoint-state method for computing the gradient of a functional with geophysical applications. Geophysical Journal International, 167(2): 495-503. doi: 10.1111/j.1365-246X.2006.02978.x

     

    Sei A, Symes W W. 1994. Gradient calculation of the traveltime cost function without ray tracing.//64th Ann. Internat Mtg., Soc. Expl. Geophys.. Expanded Abstracts, 1351-1354.

     

    Sheng J M, Leeds A, Buddensiek M, et al. 2006. Early arrival waveform tomography on near-surface refraction data. Geophysics, 71(4): U47-U57. doi: 10.1190/1.2210969

     

    Taillandier C, Noble M, Chauris H, et al. 2009. First-arrival traveltime tomography based on the adjoint-state method. Geophysics, 74(6): WCB1-WCB10. doi: 10.1190/1.3250266

     

    Waheed U, Yarman C, Flagg G. 2014. An efficient eikonal solver for tilted transversely isotropic and tilted orthorhombic media. 76th Annual International Conference and Exhibition, EAGE, Extended Abstracts.

     

    Waheed U, Flagg G, Yarman C E. 2016. First-arrival traveltime tomography for anisotropic media using the adjoint-state method. Geophysics, 81(4): R147-R155. doi: 10.1190/geo2015-0463.1

     

    Xie C, Liu Y Z, Dong L G, et al. 2014. First-arrival traveltime tomography based on the adjoint-state method. Oil Geophysical Prospecting (in Chinese), 49(5): 877-883. http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=GPYSA700007400000600WCB1000001&idtype=cvips&gifs=Yes

     

    Xie C, Liu Y Z, Dong L G, et al. 2015. First arrival tomography with finite frequency adjoint-state method based on acoustic wave equation. Oil Geophysical Prospecting (in Chinese), 50(2): 274-282.

     

    Zhang J M, Dong L G, Wang J H. 2021. A first arrival multi-information joint inversion method based on wave-equation for near-surface velocity model building. Chinese Journal of Geophysics (in Chinese), doi:10.6038/cjg2021O0278.

     

    Zhao H K. 2005. A fast sweeping method for eikonal equations. Mathematics of Computation, 74(250): 603-627. http://doi.ieeecomputersociety.org/resolve?ref_id=doi:10.1090/S0025-5718-04-01678-3&rfr_id=trans/tp/2007/09/ttp2007091563.htm

     

    敖瑞德, 董良国, 迟本鑫. 2015. 不依赖子波、基于包络的FWI初始模型建立方法研究. 地球物理学报, 58(6): 1998-2010, doi:10.6038/cjg20150615. http://www.geophy.cn//CN/abstract/abstract11582.shtml

     

    李勇德, 董良国, 刘玉柱. 2017. 一种新的预条件伴随状态法初至波走时层析. 地球物理学报, 60(10): 3934-3941, doi:10.6038/cjg20171021. http://www.geophy.cn//CN/abstract/abstract14058.shtml

     

    谢春, 刘玉柱, 董良国等. 2014. 伴随状态法初至波走时层析. 石油地球物理勘探, 49(5): 877-883. https://www.cnki.com.cn/Article/CJFDTOTAL-SYDQ201405012.htm

     

    谢春, 刘玉柱, 董良国等. 2015. 基于声波方程的有限频伴随状态法初至波旅行时层析. 石油地球物理勘探, 50(2): 274-282. https://www.cnki.com.cn/Article/CJFDTOTAL-SYDQ201502018.htm

     

    张建明, 董良国, 王建华. 2021. 基于波动方程的初至波多信息联合反演方法. 地球物理学报, doi:10.6038/cjg2021O0278.

  • 加载中

(15)

计量
  • 文章访问数:  491
  • PDF下载数:  319
  • 施引文献:  0
出版历程
收稿日期:  2020-11-06
修回日期:  2021-01-11
上线日期:  2021-03-10

目录