Recent progress on full waveform inversion
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摘要: 全波形反演是一种基于声波/弹性/黏弹性波动方程来反演三维地球模型的高分辨率成像方法. 目前该方法已经被广泛应用于油气勘探、地壳与上地幔结构以及地幔对流的研究当中. 使用该方法，可以建立一个统一的理论和算法框架来反演地球内部的多个地震学参数模型，主要包括P波和S波速度、各向异性、黏滞性衰减、密度以及反射系数等. 通过联合解释这些地震学多参数结果，可以更好地约束地球内部的温度变化、物质构成、地幔对流以及水和挥发成分的分布. 目前，关于全波形反演的研究前沿主要包括目标函数的选取、多参数联合反演、模型正则化约束、分辨率和不确定性分析，以及其在新型地震数据，例如背景噪声和线性密集台阵中的应用. 此外，为了更好地解释反演所得到的地震学多参数模型以及探讨相关的地球科学问题，需要多学科之间的交叉合作，包括结合地震学以及岩石矿物实验和地球动力学模拟等的结果. 相关的成果对更好地认识油气储层构造、盆地结构、断层分布以及地幔对流具有重要的科学意义.Abstract: Full waveform inversion is an acoustic/elastic/anelastic wave equation-based high accuracy seismic imaging method for studying the Earth's interior structure. To date, it has been widely used in exploration seismology, studies on crustal and mantle structures at both regional and global scales. With this approach, we are able to build a unified theory and algorithm platform to constrain multi-parameter seismic models for the Earth's interior, including P and S wave velocities, anisotropy, attenuation, density and reflectivity, etc. By jointly interpreting these seismic parameters, we hope to better constrain variations in temperature and composition, mantle convection and distribution of water and volatiles. Recent developments include selection of optimal misfit functions, multi-parameter inversion, model regularization, resolution and uncertainty quantification, as well as its applications to special types of datasets, such as ambient-noise recordings and teleseismic scattered waves recorded by dense linear arrays. Furthermore, in order to better interpret inverted multi-parameters and investigate related problems in Earth sciences, we need collaboration among different disciplines, such as synthesizing results from seismology, mineral physics and geodynamic modeling. These results enable us to better understand reservoirs, basin structures, fault distribution and mantle convection.
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图 1 二维均匀速度模型下构建SH波的敏感核. 从左到右分别是正传波场、伴随波场、相互作用波场和剪切波速度的敏感核. 五角星和方块分别表示震源和接收台站的位置. 时间从下往上分别是8 s、16 s、24 s、32 s 和44 s. 地表使用的是自由表面边界条件（修改自Tromp et al., 2005中的图3）
Figure 1. Construction of an SH sensitivity kernel in a 2D homogeneous velocity model. From left to right are forward wavefield, adjoint wavefield, interaction wavefield and shear wave velocity sensitivity kernel. The star and rectangular represent source and receiver. The time steps from bottom to top are 8, 16, 24, 32 and 44 seconds. A traction free boundary condition is applied to the Earth's surface (modified from Figure 3 in Tromp et al., 2005)
图 2 对比九个不同理论模型下使用三种迭代方法所得到的收敛性，包括最速下降法（黑线），非线性共轭梯度法（绿线）和L-BFGS法（红线）. 不同的理论模型如每个图的标题所示（修改自 Modrak and Tromp, 2016中的图2）
Figure 2. Convergency comparison of three iterative methods for nine synthetic velocity models, including the steepest descent method (black lines), nonlinear conjugate gradient method (green lines) and L-BFGS method (red lines). The 2D synthetic velocity models are shown in the titles of each panel (modified from Figure 2 in Modrak and Tromp, 2016)
图 3 对比不同目标函数的特征. （a）显示的是子波波形. （b）和（c）分别显示的是基于最小二乘波形残差和最优化路径所得到的目标函数随着不同时间移动（s）的特征（修改自Engquist and Froese, 2014中的图1）
Figure 3. Comparison of misfit functions based on least-square waveform differences and optimal transport distances. Panel (a) shows the input source wavelet. Panels (b) and (c) are the misfits as functions of time shifts for the least-squares waveform differences and optimal distances, respectively (modified from Figure 1 in Engquist and Froese, 2014)
图 4 三维俯冲板块导致的地幔对流. （a）和（b）分别显示中美洲和卡斯凯迪亚俯冲带的反演结果. 绿色块体显示的是剪切波速度扰动大于1.5%的结果. 黄色箭头表示通过伴随方位各向异性成像所得到的地幔对流情况[（a）和（b）分别修改自 Zhu et al., 2020a中的图7 和 Zhu et al., 2020c中的图5 ]
Figure 4. Three dimensional subducting slabs and induced mantle flows. Panels (a) and (b) are results for the Middle American and Cascadian subduction zones. Green bodies represent regions with shear wave velocity perturbations greater than 1.5%. Yellow arrows represent horizontal mantle flows constrained by azimuthal anisotropy adjoint tomography [Panels (a) and (b) are modified from Figure 7 in Zhu et al., 2020a and Figure 5 in Zhu et al., 2020c, respectively]
图 5 对比三个全球尺度的上地幔地震波衰减成像结果. （a-c）分别来自于QRLW8（Gung and Romanowicz, 2004）、SEMUCB-UMQ（Karaoglu and Romanowicz, 2018）和QRFSI12（Dalton et al., 2008）. 每一个图的下方第一行和第二行分别显示的是各个深度的剪切模量衰减值及其扰动量，其中SEMUCB-UMQ是全波形衰减反演的结果（修改自Karaoglu and Romanowicz, 2018中的图9 ）
Figure 5. Comparison of three global scale upper mantle seismic attenuation tomography models. Panels (a-c) are results from QRLW8 (Gung and Romanowicz, 2004)，SEMUCB-UMQ (Karaoglu and Romanowicz, 2018) and QRFSI12 (Dalton et al., 2008). The first and second lines in each panel represent absolute and relative perturbations of shear modulus attenuation (modified from Figure 9 in Karaoglu and Romanowicz, 2018 )
图 6 不同正则化约束下二维弹性波全波形反演所得到的P波速度结果. （a-c）分别表示基于Tikhonov、全变差和改进的全变差正则化的结果（修改自 Lin and Huang, 2014中的图10）
Figure 6. P wave velocity models from an elastic full waveform inversion with different regularization schemes. Panels (a-c) are results constrained with Tikhonov, Total variation and modified Total variation regularization, respectively (modified from Figure 10 in Lin and Huang, 2014)
图 7 使用点扩散函数分析二维全波形反演所得到的不同位置上的分辨率. （a-i）分别显示点扩散函数在右下角图中不同区域的结果（修改自 Fichtner and van Leeuwen, 2015中的图5）
Figure 7. Using point-spread functions to analyze resolution at different locations in an 2D full waveform inversion. Panels (a-i) illustrate results at different locations as shown in the bottom right panel (modified from Figure 5 in Fichtner and van Leeuwen, 2015)
图 8 散射波对于不同模型参数组合的辐射样式. （a, b）分别表示散射波对于声波速度和密度组合所得到的辐射样式. （c, d）分别表示声波速度和波阻抗组合的结果. 蓝色和白色五角星分别表示激发震源和散射点. 绿色曲线表示由射线加上波恩近似所得到的理论波前（修改自 Operto et al., 2013中的图2）
Figure 8. Radiation patterns of scattered waves for different combinations of model parameters. Panels (a, b) show the radiation patterns for P wave velocity and density, respectively. Panels (c, d) are results for the combination of P wave velocity and impedance. Blue and white stars denote exciting source and scattering point. Green curves represent the amplitudes of scattered waves from Ray+Born approximation (modified from Figure 2 in Operto et al., 2013)
图 9 通过使用背景噪声信号改进南加州地壳剪切波速度模型. 从左到右分别是M16（只使用天然地震记录）、M21（结合天然地震记录和背景噪声互相关函数），以及两者之间的差（Diff）（修改自 Wang et al., 2019中的图9）
Figure 9. Comparison of shear wave velocity models by incorporating ambient noise cross correlation functions. From left to right are model M16 (only constrained by earthquake records), M21(further constrained by ambient noise cross correlation functions) and differences between M16 and M21 (modified from Figure 9 in Wang et al., 2019)
图 10 对比不同南加州地壳模型在二维LARSE-I（a）和LARSE-II（b）剖面上的P波速度结果. CVM-S4.26、CVM-S4和CVM-H11.9分别是三个南加州地震研究中心的标准公共地壳模型. Lutter等（1999, 2004）以及Fuis等（2003）分别是两个二维主动源地壳速度反演结果（修改自 Lee et al., 2014中的图8）
Figure 10. Comparisons of P wave velocities in different Southern Californian velocity models for 2D LARSE-I and LARSE-II cross sections. Models CVM-S4.26, CVM-S4 and CVM-H11.9 are three 3D reference crustal velocity models from the Southern California Earthquake Center (SCEC). Lutter et al. (1999, 2004) and Fuis et al. (2003) are 2D crustal velocity models constrained by active source experiments (modified from Figure 8 in Lee et al., 2014)
图 11 使用通过地幔转换带的SH波改进俯冲板块伴随层析成像结果. （a）显示的是二维剖面和所使用的地震台站的位置. （b）对比初始模型（左）和迭代改进之后的模型（右）对SH地幔转换波的影响. 黑色和红色地震图分别是实际观测和模拟计算所得到的结果. （c）和（d）分别是初始模型和迭代改进之后的模型在（a）中所示的二维剖面上的剪切波速度扰动（修改自 Tao et al., 2018中的图6）
Figure 11. Imaging subducting slabs by using SH triplication waveforms. Panel (a) shows the locations of 2D vertical cross sections and stations. Panel (b) compares observed (black) and synthetic (red) SH waveforms from the starting (left) and updated models (right). Panels (c) and (d) show shear wave velocity perturbations for the starting and updated models on the 2D vertical cross section shown in Panel (a) (modified from Figure 6 Tao et al., 2018)
图 12 对比三个全球尺度地幔剪切波成像模型在6个二维剖面上的结果. 从左到右分别是来自于GLAD-M25（Lei et al., 2020）、TX2015（Lu and Grand, 2016）和SEMUCB-WM1（French and Romanowicz, 2015）. （a-f）分别对应于以下的热点:（a）阿法尔州;（b）百慕大群岛和加那利群岛;（c）佛得角和哈加尔高原;（d）冰岛和艾费尔高原;（e）复活节岛 和加拉帕戈斯群岛；（f） 马里昂县和凯尔盖朗群岛（修改自 Lei et al., 2020中的图15）
Figure 12. Comparisons of shear wave velocity perturbations in three global-scale mantle tomography models. From left to right are results from GLAD-M25 (Lei et al., 2020)，TX2015 (Lu and Grand, 2016) and SEMUCB-WM1 (French and Romanowicz, 2015). Panels (a) to (f) show results for the following hotspots: (a) Afar; (b) Bermuda and Canary; (c) Cape Verde and Hoggar; (d) Iceland and Eifel; (e) Easter and Galapagos and (f) Marion and Kergulen (modified from Figure 15 in Lei et al., 2020)
图 13 对比全波形反演在北海Valhall油田勘探当中的应用. 左图和右图分别是使用反射波到时层析成像和全波形反演所得到的结果. （a-c）以及（h-j）分别是在175 m、500 m和1000 m所得到的P波速度结果. （d-g）以及（k-n）分别是相应虚线位置的二维剖面结果（修改自 Operto et al., 2015中的图4和图11）
Figure 13. Comparison of velocity models for the ocean bottom node data from the Valhall oilfield. The left panel and right panel are models from reflection travel time tomography and full waveform inversion, respectively. (a-c) and (h-j) in each panel are P wave velocities at 175 m, 500 m and 1000 m. (d-g) and (k-n) demonstrate results in corresponding vertical profiles as shown by dashed lines (modified from Figures 4 and 11 in Operto et al., 2015)
图 14 在二维均匀速度模型下对比直达波和反射波的梯度. （a）和（b）分别是直达波和反射波的梯度，其中反射界面如图（b）中的紫色直线所示. （c）直达波+反射波的梯度. （d）改进的联合全波形梯度结果（修改自 Zhou et al., 2015中的图3）
Figure 14. Gradients for direct and reflected waves in a 2D homogeneous velocity model. Panels (a) and (b) are gradients for direct and reflected P waves. The reflector is shown as the purple line in Panel (b). Panels (c) and (d) are gradients for direct+reflected waves, and joint full waveform inversion gradient (modified from Figure 3 in Zhou et al., 2015)
图 15 使用基于目标函数梯度的马尔科夫链蒙特卡罗方法反演二维Marmousi模型. （a-c）分别表示平均模型、标准差模型以及平均与真实模型之间的差. （d）显示6个采样点的一维边界后验概率分布情况（修改自 Zhao and Sen, 2021中的图9和10）
Figure 15. Results for the 2D Marmousi model from a gradient based Markov chain Monte Carlo sampling. Panels (a) to (c) are results for the mean velocity model, standard deviation and differences between the mean and true velocity models. Panel (d) shows the 1D marginal posteriori probability density functions at six different locations (shown in Panel a) (modified from Figures 9 and 10 in Zhao and Sen, 2021)
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[1] Adenis A, Debayle E, Richard Y. 2017a. Attenuation tomography of the upper mantle[J]. Geophysical Research Letters, 44(15): 7715-7724. doi: 10.1002/2017GL073751 [2] Adenis A, Debayle E, Richard Y. 2017b. Seismic evidence for broad attenuation anomalies in the asthenosphere beneath the Pacific ocean[J]. Geophysical Journal International, 209(3) : 1677-1698. doi: 10.1093/gji/ggx117 [3] Akcelik V, Biros G, Ghattas O. 2002. Parallel multiscale Gauss-Newton-Krylov methods for inverse wave propagation[C]//Proceedings of the 2002 ACM/IEEE Conference on Supercomputing, 1-15. [4] Akcelik V, Bielak J, Biros G, et al. 2003. High resolution foward and inverse earthquake modeling on terascale computers[C]//Proceedings of the 2003 ACM/IEEE Conference on Supercomputing, 52. [5] Aki K, Christoffersson A, Husebye E. 1977. Determination of the three-dimensional seismic structure of the lithosphere[J]. Journal of Geophysical Research: Solid Earth, 82(2) : 277-296. doi: 10.1029/JB082i002p00277 [6] Allen R. 1978. Automatic earthquake recognition and timing from single traces[J]. Bulletin of the Seismological Society of America, 68(5) : 1521-1532. doi: 10.1785/BSSA0680051521 [7] Askan A, Bielak J. 2008. Full anelastic waveform tomography including model uncertainty[J]. Bulletin of the Seismological Society of America, 98(6): 2975-2989. doi: 10.1785/0120080138 [8] Asnaashari A, Brossier R, Garambois S, et al. 2013. Regularized seismic full waveform inversion with prior model information[J]. Geophysics, 78(2) : R25-R36. doi: 10.1190/geo2012-0104.1 [9] Aster R, Borchers B, Thurber C. 2018. Parameter Estimation and Inverse Problems (3rd Edition)[M]. Amsterdam, Netherlands: Elsevier. [10] Backus G. 1965. Possible forms of seismic anisotropy of the uppermost mantle under oceans[J]. Journal of Geophysical Research, 70(14) : 3429-3439. doi: 10.1029/JZ070i014p03429 [11] Backus G, Gilbert F. 1968. The resolving power of gross Earth data[J]. Geophysical Journal International , 16(2) : 169-205. doi: 10.1111/j.1365-246X.1968.tb00216.x [12] Backus G, Gilbert F. 1970. Uniqueness in the inversion of inaccurate gross Earth data[J]. Philosophical Transactions of the Royal Society A , 266(1173) : 123-192. [13] Baek H, Calandra H, Demanet L. 2013. Velocity estimation via registration-guided least-squares inversion[J]. Geophysics, 79(2) : R79-R89. [14] Bao X Y, Dalton C A, Jin G, et al. 2016a. Imaging Rayleigh wave attenuation with USArray[J]. Geophysical Journal International, 206(1) : 241-259. doi: 10.1093/gji/ggw151 [15] Bao X Y, Dalton C A, Ritsema J. 2016b. Effects of elastic focusing on global models of Rayleigh wave attenuation[J]. Geophysical Journal International, 207(2) : 1062-1079. doi: 10.1093/gji/ggw322 [16] Barmin M, Ritzwoller M, Levshin A. 2001. A fast and reliable method for surface wave tomography[J]. Pure and Applied Geophysics, 158(8) : 1351-1375. doi: 10.1007/PL00001225 [17] Baysal E, Kosloff D, Sherwood J. 1983. Reverse time migration[J]. Geophysics, 48(11) : 1514-1524. doi: 10.1190/1.1441434 [18] Beller S, Monteiller V, Operto S, et al. 2017. Lithospheric architecture of the South-Western Alps revealed by multiparameter teleseismic full-waveform inversion[J]. Geophysical Journal International, 212(2) : 1369-1388. [19] Bensen G D, Ritzwoller M H, Barmin M P, et al. 2007. Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements[J]. Geophysical Journal International, 169(3) : 1239-1260. doi: 10.1111/j.1365-246X.2007.03374.x [20] Bercovici D, Karato S. 2003. Whole-mantle convection and the transition-zone water filter[J]. Nature, 425(6953) : 39-44. doi: 10.1038/nature01918 [21] 卞爱飞, 於文辉, 周华伟. 2010. 频率域全波形反演方法研究进展[J]. 地球物理学进展, 25（3）: 982-993 doi: 10.3969/j.issn.1004-2903.2010.03.037Bian A F, Yu W H, Zhou H W. 2010. Progress in the frequency-domain full waveform inversion method[J]. Progress in Geophysics, 25(3): 982-993 (in Chinese). doi: 10.3969/j.issn.1004-2903.2010.03.037 [22] Bijwaard H, Spakman W. 1999. Tomographic evidence for a narrow whole mantle plume below Iceland[J]. Earth and Planetary Science Letters, 166(3-4) : 121-126. doi: 10.1016/S0012-821X(99)00004-7 [23] Biondi B, Almomin A. 2014. Simultaneous inversion of full data bandwidth by tomographic full-waveform inversion[J]. Geophysics, 79(3) : WA129-WA140. doi: 10.1190/geo2013-0340.1 [24] Bozdağ E, Peter D, Lefebvre M, et al. 2016. Global adjoint tomography: first-generation model[J]. Geophysical Journal International, 207(3) : 1739-1766. doi: 10.1093/gji/ggw356 [25] Brenders A, Pratt G. 2007. Full waveform tomography for lithospheric imaging: results from a blind test in a realistic crustal model[J]. Geophysical Journal International, 168(1) : 133-151. doi: 10.1111/j.1365-246X.2006.03156.x [26] Brenguier F. Campilloc M, Hadziioannou C, et al. 2008a. Postseismic relaxation along the San Andreas Fault at Parkfield from continuous seismological observations[J]. Science, 321(5895) : 1478-1481. doi: 10.1126/science.1160943 [27] Brenguier F, Shapiro N M, Campillo M, et al. 2008b. Towards forecasting volcanic eruptions using seismic noise[J]. Nature Geoscience, 1(2) : 126-130. doi: 10.1038/ngeo104 [28] Bui-Thanh T, Ghattas O, Martin J, Stadler G. 2013. A computational framework for infinite-dimensional Bayesian inverse problem, Part I: the linearized case with application to global seismic inversion[J]. SIAM Journal on Scientific Computing, 35(6) : A2494-A2523. doi: 10.1137/12089586X [29] Bunks C, Saleck F, Zaleski S, Chavent G. 1995. Multiscale seismic waveform inversion[J]. Geophysics, 60(5) : 1457-1473. doi: 10.1190/1.1443880 [30] Buttles J, Olson P. 1998. A laboratory model of subduction zone anisotropy[J]. Earth Planetary Science Letter, 164(1-2) : 245-262. doi: 10.1016/S0012-821X(98)00211-8 [31] Carcione J, Kosloff D, Kosloff R. 1988. Wave propagation simulation in a linear viscoelastic medium[J]. Geophysical Journal International, 95(3) : 597-611. doi: 10.1111/j.1365-246X.1988.tb06706.x [32] Cerveny V. 2001. Seismic Ray Theory (1st Edition)[M]. Boston, MA: Cambridge University Press. [33] Chen M, Huang H, Yao H J, et al. 2014. Low wave speed zones in the crust beneath SE Tibet revealed by ambient noise adjoint tomography[J]. Geophysical Research Letters, 41(2) : 334-340. doi: 10.1002/2013GL058476 [34] Chen M, Niu F L, Liu Q Y, et al. 2015. Multiparameter adjoint tomography of the crust and upper mantle beneath East Asia: 1. Model construction and comparisons[J]. Journal of Geophysical Research: Solid Earth, 120(3) : 1762-1786. doi: 10.1002/2014JB011638 [35] Chen P, Jordan T, Zhao L. 2007a. Full three-dimensional tomography: a comparison between the scattering-integral and adjoint wavefield methods[J]. Geophysical Journal International, 170(1) : 175-181. doi: 10.1111/j.1365-246X.2007.03429.x [36] Chen P, Zhao L, Jordan T. 2007b. Full 3D tomography for the crustal structure of the Los Angeles region[J]. Bulletin of the Seismological Society of America, 97(4) : 1094-1120. doi: 10.1785/0120060222 [37] Chen P, Lee E. 2015. Full-3D Seismic Waveform Inversion: Theory, Software and Practice (1st Edition)[M]. Berlin, Germany: Springer. [38] Chen W, Molnar P. 1983. Focal depths of intracontinental and intraplate earthquakes and their implications for the thermal and mechanical properties of the lithosphere[J]. Journal of Geophysical Research: Solid Earth, 88(B5) : 4183-4214. doi: 10.1029/JB088iB05p04183 [39] Chow B, Kaneko Y, Tape C, et al. 2022. Strong upper-plate heterogeieity at the Hikurangi subduction margin (north Island, New Zealand) imaged by adjoint tomography[J]. Journal of Geophysical Research: Solid Earth, 127(1). doi: 10.1029/2021JB022865. [40] Claerbout J. 1971. Toward a unified theory of reflector mapping[J]. Geophysics, 36(3) : 467-481. doi: 10.1190/1.1440185 [41] Clouzet P, Masson Y, Romanowicz B. 2018. Box Tomography: first application to the imaging of upper-mantle shear velocity and radial anisotropy structure beneath the North America continent[J]. Geophysical Journal International, 213(3) : 1849-1875. doi: 10.1093/gji/ggy078 [42] Colli L, Fichtner A, Bunge H. 2013. Full waveform tomography of the upper mantle in the South Atlantic region: Imaging a wesward fluxing shallow asthenosphere[J]. Tectonophysics, 604(24) : 26-40. [43] Dahlen F, Hung S -H, Nolet G. 2000. Frechet kernels for finite-frequency traveltimes--I. Theory[J]. Geophysical Journal International, 141(1) : 157-174. doi: 10.1046/j.1365-246X.2000.00070.x [44] Dalton C, Ekstrom G, Dziewonski A. 2008. The global attenuation structure of the upper mantle[J]. Journal of Geophysical Research: Solid Earth, 113(B9) : B09, 303. doi: 10.1029/2007JB005429. [45] 董良国, 迟本鑫, 陶纪霞, 等. 2013. 声波全波形反演目标函数性态[J]. 地球物理学报, 56（10）, 3445-3460 doi: 10.6038/cjg20131020Dong L G, Chi B X, Tao J X, et al. 2013. Objective function behavoir in acoustic full-waveform inversion[J]. Chinese Journal of Geophysics, 56(10), 3445-3460 (in Chinese). doi: 10.6038/cjg20131020 [46] Dong X, Yang D, Zhu H, Chen Y. 2022. Geometry-perserving full-waveform tomography and its application in the Longmen Shan area[J]. Science China Earth Sciences, 65(3) : 437-448. doi: 10.1007/s11430-021-9849-5 [47] Douma H, Yingst D, Vasconcelos I, Tromp J. 2010. On the connection between artifact filtering in reverse-time migration and adjoint tomography[J]. Geophysics, 75(6) : S219-S223. [48] Durek J, Ritzwoller M, Woodhouse J. 1993. Constraining upper mantle anelasticity using surface wave amplitude anomalies[J]. Geophysical Journal International, 114(2) : 249-272. doi: 10.1111/j.1365-246X.1993.tb03914.x [49] Dziewonski A. 1971. Overtones of free oscillations and the structure of the Earth's interior[J]. Science, 172(3990) : 1336-1338. doi: 10.1126/science.172.3990.1336 [50] Dziewonski A, Woodhouse J. 1987. Global images of the Earth's interior[J]. Science, 236(4797) : 37-48. doi: 10.1126/science.236.4797.37 [51] Dziewonski A, Romanowicz B. 2015. Deep Earth seismology: An introduction and overview[J]//Schubert G. Treatise on Geophysics. Oxford: Elsevier, 1: 1-28. [52] Eddy C, Ekstrom G. 2014. Local amplification of Rayleigh wave in the continental United States observed on the USArray[J]. Earth and Planetary Science Letters, 402(15) : 50-57. [53] Ekstrom G, Tromp J, Larson E. 1997. Measurements and global models of surface wave propagation[J]. Journal of Geophysical Research: Solid Earth, 102(B4) : 8137-8157. doi: 10.1029/96JB03729 [54] Ellsworth W. 2013. Injection-induced earthquakes[J]. Science, 341(6142): 1225942. doi: 10.1126/science.1225942 [55] Engquist B, Ying L. 2011. Sweeping preconditioner for the Helmholtz equation: Moving perfectly matched layers[J]. Multiscale Modling and Simulation, 9(2) : 686-710. doi: 10.1137/100804644 [56] Engquist B, Froese B. 2014. Application of the Wasserstein metric to seismic signals[J]. Communications in Mathematical Sciences, 12(5) : 979-988. doi: 10.4310/CMS.2014.v12.n5.a7 [57] Engquist B, Yang Y. 2019. Seismic Imaging and optimal transport[J]. Communications in information and systems, 19(2) : 95-145. doi: 10.4310/CIS.2019.v19.n2.a1 [58] Epanomeritakis I, Akcelik V, Ghattas O, Bielak J. 2008. A Newton-CG method for large-scale three-dimensional elastic full-waveform seismic inversion[J]. Inverse Porblems, 24: 034015. doi: 10.1088/0266-5611/24/3/034015 [59] Ermert L, Villasenor A, Fichtner A. 2016. Cross-correlation imaging of ambient noise sources[J]. Geophysical Journal International, 204(1) : 347-364. doi: 10.1093/gji/ggv460 [60] Fichtner A, Kennett B, Igel H, Bunge H. 2008. Theoretical background for continental- and global-scale full-waveform inversion in the time-frequency domain[J]. Geophysical Journal International, 175(2) : 665-685. doi: 10.1111/j.1365-246X.2008.03923.x [61] Fichtner A, Kennett B, Igel H, Bunge H. 2009. Full seismic waveform tomography for upper-mantle structure in the Australasian region using adjoint methods[J]. Geophysical Journal International, 179(3) : 1703-1725. doi: 10.1111/j.1365-246X.2009.04368.x [62] Fichtner A. 2010. Full Seismic Waveform Modelling and Inversion (1st Edition)[M]. Switzerland AG: Springer Science & Business Media. [63] Fichtner A, Kennett B, Igel H, Bunge H. 2010. Full waveform tomography for radially anisotropic structure: new insights into present and past states of the Australasian upper mantle[J]. Earth and Planetary Science Letters, 290(3-4) : 270-280. doi: 10.1016/j.jpgl.2009.12.003 [64] Fichtner A, Trampert J. 2011. Hessian kernels of seismic data functionals base upon adjoint techniques[J]. Geophysical Journal International, 185(2) : 775-798. doi: 10.1111/j.1365-246X.2011.04966.x [65] Fichtner A, Sayginb E, Taymazc T, et al. 2013. The deep structure of the North Anatolian fault zone[J]. Earth and Planetary Science Letters, 373(1) : 109-117. [66] Fichtner A, Driel M. 2014. Models and Frechet kernels for frequency-(in)dependent Q[J]. Geophysical Journal International, 198(3) : 1878-1889. doi: 10.1093/gji/ggu228 [67] Fichtner A, van Leeuwen T. 2015. Resolution analysis by random probing[J]. Journal of Geophysical Research: Solid Earth, 120(8) : 5549-5573. doi: 10.1002/2015JB012106 [68] Fichtner A, Villasenor A. 2015. Crust and upper mantle of the western Mediterranean-Constraints from full-waveform inversion[J]. Earth and Planetary Science Letters, 428(1) : 52-62. [69] Fletcher R, Reeves C. 1964. Function minimization by conjugate gradients[J]. Computer Journal, 7(2) : 149-154. doi: 10.1093/comjnl/7.2.149 [70] French S, Lekic V, Romanowicz B. 2013. Waveform tomography reveals channeled flow at the base of the oceanic asthenosphere[J]. Science, 342(6155) : 227-230. doi: 10.1126/science.1241514 [71] French S, Romanowicz B. 2015. Broad plumes rooted at the base of the Earth's mantle beneath major hotspots[J]. Nature, 525(7567) : 95-99. doi: 10.1038/nature14876 [72] Fuis G, Clayton R, Davis P, et al. 2003. Fault systems of the 1971 San Fernando and 1994 Northridge earthquakes, Southern California: Relocated aftershocks and seismic images from LARSE II[J]. Geology, 31: 171-174. [73] Fukao Y, Obayashi M. 2013. Subducted slabs stagnant above, penetrating through, and trapped below the 660 km discontinuity[J]. Journal of Geophysical Research: Solid Earth, 118(11) : 5920-5938. doi: 10.1002/2013JB010466 [74] Gao H, Shen Y. 2014. Upper mantle structure of the Cascades from full-wave ambient noise tomography: Evidence for 3D mantle upwelling in the back-arc[J]. Earth Planetary Science Letters, 309(1): 222-233. [75] Gauthier O, Virieux J, Tarantola A. 1986. Two-dimensional nonlinear inversion of seismic waveforms: numerical results[J]. Geophysics, 51(7) : 1387-1403. doi: 10.1190/1.1442188 [76] Gebraad L, Boehm C, Fichtner A. 2020. Bayesian elastic full-waveform inversion using Hamiltonian Monte Carlo[J]. Journal of Geophysical Research, 125(3): e2019JB018428. [77] Grand S, Van der Hilst R, Widiyantoro S. 1997. High resolution global tomography: a snapshot of convection in the Earth[J]. Geological Society of America Today, 7(4) : 1-6. [78] Gung Y, Romanowicz B. 2004. Q tomography of the upper mantle using three-dimensional long-period waveforms[J]. Geophysical Journal International, 157(2) : 813-830. doi: 10.1111/j.1365-246X.2004.02265.x [79] Hale D. 2013. Dynamic warping of seismic images[J]. Geophysics, 78(2) : S105-S115. doi: 10.1190/geo2012-0327.1 [80] Hall C, Fischer K, Parmentier E. 2000. The influence of plate motions on three-dimensional back arc mantle flow and shear wave splitting[J]. Journal of Geophysical Research: Solid Earth, 105(B12) : 28009-28033. doi: 10.1029/2000JB900297 [81] Hess H. 1964. Seismic anisotropy of the upper mantle under oceans[J]. Nature, 203(4945) : 629-631. doi: 10.1038/203629a0 [82] 胡勇, 韩立国, 许卓, 张天泽. 2017. 基于精确震源函数的解调包络多尺度全波形反演[J]. 地球物理学报, 60（3）: 1088-1105 doi: 10.6038/cjg20170321Hu Y, Han L G, Xu Z, Zhang T Z. 2017. Demodulation envelope multi-scale full waveform inversion based on precise seismic source function[J]. Chinese Journal of Geophysics, 60(3): 1088-1105 (in Chinese). doi: 10.6038/cjg20170321 [83] Huang H, Yao H, van der Hilst R. 2010. Radial anisotropy in the crust of SE Tibet and SW China from ambient noise interferometry[J]. Geophysical Research Letters, 37(21): L21310. doi: 10.1029/2010GL044981. [84] Huang X, Xu Y, Karato S. 2005. Water content in the transition zone from electrical conductivity of wadsleyite and ringwoddite[J]. Nature, 434(7034) : 746-749. doi: 10.1038/nature03426 [85] Hung S -H, Dahlen F, Nolet G. 2000. Frechet kernel for finite-frequency traveltimes-II. Examples[J]. Geophysical Journal International, 141(1) : 175-203. doi: 10.1046/j.1365-246X.2000.00072.x [86] Ishii M, Tromp J. 1999. Normal-mode and free-air gravity constraints on lateral variations in velocity and density of Earth's mantle[J]. Science, 285(5431) : 1231-1236. doi: 10.1126/science.285.5431.1231 [87] 蒋梦凡, 孙伟家, 塔力哈尔·哈帕尔, 等. 2021. 地震全波形反演及其探测壳—幔结构的研究进展[J]. 地球物理学进展, （2）: 464-480 doi: 10.6038/pg2021EE0024Jiang M F, Sun W J, Talihaer H, et al. 2021. Progress of seismic full-waveform inversion and its applications in investigating the crust-mantle structure[J]. Progress in Geophysics, (2): 464-480 (in Chinese). doi: 10.6038/pg2021EE0024 [88] Jung H, Karato S. 2001. Water-induced fabric transition in olivine[J]. Science, 293(5534) : 1460-1463. doi: 10.1126/science.1062235 [89] Kamei R, Pratt R G. 2013. Inversion strategies for visco-acoustic waveform inversion[J]. Geophysical Journal International, 194(2) : 859-884. doi: 10.1093/gji/ggt109 [90] Karaoglu H, Romanowicz B. 2017. Global seismic attenuation imaging using full-waveform inversion: a comparative assessment of different choices of misfit function[J]. Geophysical Journal Intenrational, 212(2) : 807-826. [91] Karaoglu H, Romanowicz B. 2018. Inferring global upper-mantle shear attenuation structure by waveform tomography using the spectral element method[J]. Geophysical Journal International, 213(3) : 1536-1558. doi: 10.1093/gji/ggy030 [92] Karato S, Jung H, Katayama I, Skemer P. 2008. Geodynamic significance of seismic anisotropy of the upper mantle: new insights from laboratory studies[J]. Annual Review of Earth and Planetary Sciences, 36(1) : 59-95. doi: 10.1146/annurev.earth.36.031207.124120 [93] Kincaid C, Griffiths R. 2003. Laboratory models of the thermal evolution of the mantle during rollback subduction[J]. Nature, 425(6953) : 58-62. doi: 10.1038/nature01923 [94] Kohlstedt D, Evans B, Mackwell S. 1995. Strength of the lithosphere-constraints imposed by laboratory experiments[J]. Journal of Geophysical Research: Solid Earth , 100(B9) : 17587-17602. doi: 10.1029/95JB01460 [95] Komatitsch D, Tromp J. 1999. Introduction to the spectral-element method for 3-D seismic wave propagation[J]. Geophysical Journal International, 139(3) : 806-822. doi: 10.1046/j.1365-246x.1999.00967.x [96] Komatitsch D, Xie Z N, Bozdağ E, et al. 2016. Anelastic sensitivity kernels with parsimonious storage for adjoint tomography and full waveform inversion[J]. Geophysical Journal International, 206(3) : 1467-1478. doi: 10.1093/gji/ggw224 [97] Krischer L, Fichtner A, Boehm C, Igel H. 2018. Automated large-scale full seismic waveform inversion for North America and the North Atlantic[J]. Journal of Geophysical Research: Solid Earth, 123(7) : 5902-5928. doi: 10.1029/2017JB015289 [98] Lailly P. 1984. Migration Methods: Partial but Efficient Solutions to the Seismic Inverse Problem[M]//Inverse Problem of Acoustic and Elastic Waves. Philadelphia : Society for Industrial and Applied Mathematics, 182-214. [99] Lee E, Chen P, Jordan T, Wang L. 2011. Rapid full-wave centroid moment tensor (CMT) inversion in a three-dimensional earth structure model for earthquakes in Southern California[J]. Geophysical Journal International, 186(1) : 311-330. doi: 10.1111/j.1365-246X.2011.05031.x [100] Lee E, Chen P, Jordan T H, et al. 2014. Full 3-D tomography for crustal structure in southern California based on the scattering-integral and the adjoint-wavefield methods[J]. Journal of Geophysical Research: Solid Earth , 119(8) : 6421-6451. doi: 10.1002/2014JB011346 [101] Leeuwen T, Mulder W. 2010. A correlation-based misfit criterion for wave-equation traveltime tomography[J]. Geophysical Journal International, 182(3) : 1383-1394. doi: 10.1111/j.1365-246X.2010.04681.x [102] Lei W, Youyi Ruan Y Y, Bozdağ E, et al. 2020. Global adjoint tomography-model GLAD-M25[J]. Geophysical Journal International, 223(1) : 1-21. doi: 10.1093/gji/ggaa253 [103] Lekic V, Matas J, Panning M, Romanowicz B. 2009. Measurement and implications of frequency dependence of attenuation[J]. Earth and Planetary Science Letters, 282(1) : 285-293. [104] Leveque J, Rivera L, Wittlinger G. 1993. On the use of the checkerboard test to assess the resolution of tomographic inversion[J]. Geophysical Journal International, 115(1) : 313-318. doi: 10.1111/j.1365-246X.1993.tb05605.x [105] Lindsey N, Dawe T, Ajo-Franklin J. 2019. Illuminating seafloor faults and ocean dynamics with dark fiber distributed acoustic sensing[J]. Science, 366(6469) : 1103-1107. doi: 10.1126/science.aay5881 [106] Lin F, Moschetti M, Ritzwoller M. 2008. Surface wave tomography of the western United States from ambient seismic noise: Rayleigh and Love wave phase velocity maps[J]. Geophysical Journal International, 173(1) : 281-298. doi: 10.1111/j.1365-246X.2008.03720.x [107] Lin F, Tsai V, Ritzwoller M. 2012. The local amplification of surface waves: a new observable to constrain elastic velocities, density and anelastic attenuation[J]. Journal of Geophysical Research: Solid Earth , 117(B6): B06302. [108] Lin F C, Ritzwoller M H, Yang Y J, et al. 2011. Complex and variable crustal and uppermost mantle seismic anisotropy in the western United States[J]. Nature Geoscience, 4(1) : 55-61. doi: 10.1038/ngeo1036 [109] Lin G Q, Clifford H. Thurber C H, Haijiang Zhang H J. 2010. A California statewide three-dimensional seismic velocity model from both absolute and differential times[J]. Bulletin of the Seismological Society of America, 100(1) : 225-240. doi: 10.1785/0120090028 [110] Lin Y, Huang L. 2014. Acoustic- and elastic-waveform inversion using a modified total-variation regularization scheme[J]. Geophysical Journal International, 200(1) : 489-502. doi: 10.1093/gji/ggu393 [111] Lioyd A J, Wiens D A, Zhu H, et al. 2019. Seismic structure of the Antarctic upper mantle imaged with adjoint tomography[J]. Journal of Geophysical Research: Solid Earth, 125(3): 2019JB017823. [112] Liu H, Anderson D, Kanamori H. 1976. Velocity dispersion due to anelasticity: implicitions for seismology and mantle composition[J]. Geophysical Journal Research Astro Society, 47(1) : 41-58. doi: 10.1111/j.1365-246X.1976.tb01261.x [113] 刘璐, 刘洪, 张衡, 等. 2013. 基于修正拟牛顿公式的全波形反演[J]. 地球物理学报, 56（7）: 2447-2451 doi: 10.6038/cjg20130730Liu L, Liu H, Zhang H, et al. 2013. Full waveform inversion based on modified quasi-Newton equation[J]. Chinese Journal of Geophysics, 56(7): 2447-2451 (in Chinese). doi: 10.6038/cjg20130730 [114] Liu Q, Polet J, Komatitsch D, Tromp J. 2004. Spectral-element moment tnesor inversions for earthquakes in southern California[J]. Bulletin of the Seismological Society of America, 94(5) : 1748-1761. doi: 10.1785/012004038 [115] Liu Q, Tromp J. 2006. Finite-frequency kernels based on adjoint method[J]. Bulletin of the Seismological Society of America, 96(6) : 2383-2397. doi: 10.1785/0120060041 [116] Liu Q, Gu Y. 2012. Seismic imaging: from classical to adjoint tomography[J]. Tectonophysics, 566-567(1) : 31-66. [117] Liu Q, Peter D. 2019. Square-root variable metric based elastic full-waveform inversion-part 2 uncertainty estimation[J]. Geophysical Journal International, 218(2): 1100–1120. doi: 10.1093/gji/ggz137 [118] Long M, Silver P. 2008. The subduction zone flow field from seismic anisotropy: a global view[J]. Science, 319(5861) : 315-318. doi: 10.1126/science.1150809 [119] Long M, Becker T. 2010. Mantle dynamics and seismic anisotropy[J]. Earth and Planetary Science letters, 297(3-4) : 341-354. doi: 10.1016/j.jpgl.2010.06.036 [120] Lu C, Grand S. 2016. The effect of subducting slabs in global shear wave tomography[J]. Geophysical Journal International, 205(2) : 1074-1085. doi: 10.1093/gji/ggw072 [121] Luo Y, Schuster G. 1991. Wave-equation travel time inversion[J]. Geophysics, 56(6) : 645-653. [122] Luo Y, Ma Y, Wu Y, et al. 2016. Full-traveltime inversion[J]. Geophysics, 81(5) : R261-R274. doi: 10.1190/geo2015-0353.1 [123] Lutter W, Fuis G, Thurber C, Murphy J. 1999. Tomographic images of the upper crust from the Los Angeles Basin to the Mojave Desert, California: Results from the Los Angeles Region Seismic Experiment[J]. Journal of Geophysical Research: Solid Earth, 104: 25543-25565. [124] Lutter W J, Fuis G S, Ryberg T, et al. 2004. Upper crustal structure from the Santa Monica mountains to the Sierra Nevada, southern California: Tomographic results from the Los Angeles regional seismic experiment, Phase II (LARSE II)[J]. Bulletin of the Seismological Society of Americ, 94(2): 619–632. [125] Ma Y, Hale D. 2013. Wave-equation reflection traveltime inversion with dynamic warping and full-waveform inversion[J]. Geophysics, 78(6) : R223-R233. doi: 10.1190/geo2013-0004.1 [126] Ma Z, Masters G, Mancinelli N. 2016. Two-dimensional global Rayleigh wave attenuation model by accounting for finite-frequency focusing and defocusing effect[J]. Geophysical Journal International, 204(1) : 631-649. doi: 10.1093/gji/ggv480 [127] Maggi A, Tape C, Chen M, et al. 2009. An automated time-window selection algorithm for seismic tomography[J]. Geophysical Journal International, 178(1) : 257-281. doi: 10.1111/j.1365-246X.2009.04099.x [128] Marone F, Romanowicz B. 2007. The depth distribution of azimuthal anisotropy in the continental upper mantle[J]. Nature, 447(7141) : 198-201. doi: 10.1038/nature05742 [129] Masson Y, Romanowicz B. 2017. Box tomography: localised imaging of remote targets buried in an unknown medium, a step toward for understanding key structures in the deep Earth[J]. Geophysical Journal International, 211(1) : 141-163. doi: 10.1093/gji/ggx141 [130] Masters G, Jordan T, Silver P, Gilbert F. 1982. Aspherical Earth structure from fundamental spheroidal-mode data[J]. Nature, 298(5875) : 609-613. doi: 10.1038/298609a0 [131] Masters G, Johnson S, Laske G, Bolton H. 1996. A shear-velocity model of the mantle[J]. Philosophical Transactions of The Royal Society A, 354(1711) : 1385-1411. doi: 10.1098/rsta.1996.0054 [132] McMechan G. 1983. Migration by extrapolation of time-dependent boundary values[J]. Geophysical Prospecting, 31(3) : 413-420. doi: 10.1111/j.1365-2478.1983.tb01060.x [133] Meschede M, Romanowicz B. 2015. Lateral heterogeneity scales in regional and global upper mantle shear velocity models[J]. Geophysical Journal International, 200(2) : 1076-1093. [134] Métivier L, Bretaudeau F, Brossier R, et al. 2014. Full waveform invesion and the truncated Newton method: quantitative imaging of complex subsurface structures[J]. Geophysical Prospecting, 62(6) : 1353-1375. doi: 10.1111/1365-2478.12136 [135] Métivier L, Brossier R, Mérigot Q, et al. 2016. An optimal transport approach for seismic tomography: application to 3D full waveform inversion[J]. Inverse Problems, 32(11): 115008. doi: 10.1088/0266-5611/32/11/115008 [136] Modrak R, Tromp J. 2016. Seismic waveform inversion best practices: regional, global and exploration test cases[J]. Geophysical Journal International, 206(3) : 1864-1889. doi: 10.1093/gji/ggw202 [137] Montagner J, Nataf H. 1986. A simple method for inverting the azimuthal anisotropy of surface waves[J]. Journal of Geophysical Research: Solid Earth , 91(B1) : 511-520. doi: 10.1029/JB091iB01p00511 [138] Monteiller V, Chevrot S, Komatitsch D, Wang Y. 2015. Three-dimensional full waveform inversion of short-period teleseismic wavefields based upon the SEM-DSM hybrid method[J]. Geophysical Journal International, 202(2) : 811-827. doi: 10.1093/gji/ggv189 [139] Monteiller V, Beller S, Plazolles B, Chevrot S. 2021. On the validity of the planar wave approximation to compute synthetic seismograms of teleseismic body waves in a 3-D regional model[J]. Geophysical Journal International, 224(3) : 2060-2076. [140] Montelli R, Noletf G, Dahlen F A, et al. 2004a. Finite-frequency tomography reveals a variety of plumes in the mantle[J]. Science, 303(5656) : 338-343. doi: 10.1126/science.1092485 [141] Montelli R, Nolet G, Masters G, et al. 2004b. Global P and PP traveltime tomography: rays versus waves[J]. Geophysical Journal International, 158(2) : 637-654. doi: 10.1111/j.1365-246X.2004.02346.x [142] Montelli R, Nolet G, Dahlen F, Masters G. 2006. A catalogue of deep mantle plumes: New results from finite-frequency tomography[J]. Geochemistry, Geophysics and Geosystems, 7(11): Q11007. [143] Mora P. 1987. Nonlinear two-dimensional elastic inversion of multi-offset seismic data[J]. Geophysics, 52(9) : 1211-1228. doi: 10.1190/1.1442384 [144] Morgan W J. 1971. Convection plumes in the lower mantle[J]. Nature, 230(5288) : 42-43. doi: 10.1038/230042a0 [145] Moschetti M, Ritzwoller M, Lin F, Yang Y. 2010. Seismic evidence for widespread western-US deep crustal deformation caused by extension[J]. Nature, 464(7290) : 885-889. doi: 10.1038/nature08951 [146] Nettles M, Dziewonski A. 2008. Radial anisotropic shear velocity structure of the upper mantle globally and beneath North America[J]. Journal of Geophysical Research: Solid Earth, 113(B2): B02303. DOI: 10. 1029/2006JB004819. [147] Nicolas A, Christensen I. 1987. Formation of Anisotropy in Upper Mantle Peridotites-a Review[M]// Composition, Structure and Dynamics of the Lithosphere-Asthenosphere system. Washington D C : American Geophysical Union, 111-123. [148] Nocedal J, Wright S. 2006. Numerical Optimization (2nd Edition)[M]. Switzerland AG: Springer. [149] Nolet G, Dahlen F. 2000. Wave front healing and the evolution of seismic delay times[J]. Journal of Geophysical Research: Solid Earth , 105(B8) : 19043-19054. doi: 10.1029/2000JB900161 [150] Nolet G. 2011. A Breviary of Seismic Tomography: Imaging the Interior of the Earth and Sun (1st Edition)[M]. Princeton N J: Cambridge University Press. [151] Nolet G, Hello Y, van der Lee S, et al. 2019. Imaging the Galapagos mantle plume with an unconventional application of floating seismometers[J]. Scientific Report, 9(1326) : 1-12. [152] Operto S, Virieux J, Dessa X, Pascal G. 2006. Crustal imaging from multifold ocean bottom seismometers data by frequency-doamin full-waveform tomography: Application to the eastern Nankai trough[J]. Journal of Geophysical Research: Solid Earth, 111: B09306. doi: 10.1029/2005JB003835. [153] Operto S , Jean Virieux J, Amestoy P, et al. 2007. 3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver: A feasibility study[J]. Geophysics, 72(5) : SM195-SM211. doi: 10.1190/1.2759835 [154] Operto S , Gholami Y, Prieux V, et al. 2013. A guided tour of multiparameter full-waveform inversion with multicomponent data: from theory to practice[J]. The Leading Edge, 32(9) : 1040-1054. doi: 10.1190/tle32091040.1 [155] Operto S, Miniussi A, Brossier R, et al. 2015. Efficient 3-D frequency-domain mono-parameter full-waveform inversion of ocean-bottom cable data: application to Valhall in the visco-acoustic vertical transverse isotropic approximation[J]. Geophysical Journal International, 202(2) : 1362-1391. doi: 10.1093/gji/ggv226 [156] Operto S, Miniuss A. 2018. On the role of density and attenuation in three-dimensional multiparameter viscoacoustic VTI frequency-domain FWI: an OBC case study from the North Sea[J]. Geophysical Journal International, 213(3) : 2037-2059. doi: 10.1093/gji/ggy103 [157] Pan W, Wang Y. 2020. On the influence of different misfit functions for attenuation estimation in viscoelastic full-waveform inversion: synthetic study[J]. Geophysical Journal International, 221(2) : 1292-1319. doi: 10.1093/gji/ggaa089 [158] Park J, Levin V. 2002. Seismic anisotropy: tracing plate dynamics in the mantle[J]. Science, 296(5567) : 485-489. doi: 10.1126/science.1067319 [159] Pienkowska M, Monteiller V, Nissen-Meyer T. 2021. High-frequency global wavefields for local 3-D structure by wavefield injection and extrapolation[J]. Geophysical Journal International, 225(3) : 1782-1798. doi: 10.1093/gji/ggaa563 [160] Plessix R. 2006. A review of the adjoint-state method for computing the gradient of a functional with geophysical appliations[J]. Geophysical Journal International, 167(2) : 495-503. doi: 10.1111/j.1365-246X.2006.02978.x [161] Poulson J, Engquist B, Li S, Ying L. 2013. A parallel sweeping preconditioner for heterogeneous 3D Helmholtz equation[J]. SIAM Journal on Scientific Computing, 35(3) : C194-C212. doi: 10.1137/120871985 [162] Pratt G, Shin C, Hicks G. 1998. Gauss-Newton and full Newton methods in frequency-space seismic waveform invesion[J]. Geophysical Journal International, 133(2) : 341-362. doi: 10.1046/j.1365-246X.1998.00498.x [163] Pratt G. 1999. Seismic waveform inversion in the frequency domain, Part 1: Theory and verification in a physical scale model[J]. Geophysics, 64(3) : 888-901. doi: 10.1190/1.1444597 [164] Pratt G, Shipp R. 1999. Seismic waveform inversion in the frequency domain, Part 2: Fault delineation in sediments using crosshole data[J]. Geophysics, 64(3) : 902-914. doi: 10.1190/1.1444598 [165] Pratt R, Worthington M. 1990. Inverse theory applied to multi-source cross-hole tomography. Part I: Acoustic wave-equation method[J]. Geophysical Prospecting, 38(3) : 287-310. doi: 10.1111/j.1365-2478.1990.tb01846.x [166] Prieux V, Brossier R, Operto S, Virieux J. 2013. Multiparameter full waveform inversion of multicomponent ocean-bottom-cable data from the Valhall field. Part 1: Imaging compressional wave speed, density and attenatuion[J]. Geophysical Journal International, 194(3) : 1640-1664. doi: 10.1093/gji/ggt177 [167] Rawlinson N, Pozgay S, Fishwick S. 2010. Seismic tomography: A window into deep Earth[J]. Physics of the Earth and Planetary Interiors, 178(3-4) : 101-135. doi: 10.1016/j.pepi.2009.10.002 [168] Richers F, Fichtner A, Trampert J. 2013. The Icealand-Jan Mayen plume system and its impact on mantle dynamics in the North Atlantic region: Evidence from full-waveform inversion[J]. Earth Planetary Science Letters, 367(1) : 39-51. [169] Ritsema J, van Heijst H, Woodhouse J. 1999. Complex shear wave velocity structure imaged beneath Africa and Iceland[J]. Science, 286(5446) : 1925-1928. doi: 10.1126/science.286.5446.1925 [170] Ritsema J, Lekic V. 2020. Heterogeneity of seismic wave velocity in Earth's mantle[J]. Annual Review of Earth and Planetary Sciences, 48(1) : 377-401. doi: 10.1146/annurev-earth-082119-065909 [171] Robertsson J, Blanch J, Symes W. 1994. Viscoelastic finite-difference modeling[J]. Geophysics, 59(9) : 1444-1456. doi: 10.1190/1.1443701 [172] Rocha D, Tanushev N, Sava P. 2016. Acoustic wavefield imaging using the energy norm[J]. Geophysics, 81(4) : S151-S163. doi: 10.1190/geo2015-0486.1 [173] Romanowicz B. 1987. Multiplet-multiplet coupling due to lateral heterogeniety: asymptotic effects on the amplitude and frequency of the Earth's normal modes[J]. Geophysical Journal International, 90(1) : 75-100. doi: 10.1111/j.1365-246X.1987.tb00676.x [174] Romanowicz B. 1995. A global tomographic model of shear attenuation in the upper mantle[J]. Journal of Geophysical Research: Solid Earth , 100(B7) : 12375-12394. doi: 10.1029/95JB00957 [175] Romanowicz B. 2003. Global mantle tomography: progress status in the past 10 years[J]. Annual Review of Earth and Planetary Sciences, 31(1) : 303-328. doi: 10.1146/annurev.earth.31.091602.113555 [176] Ross Z, Meier M, Hauksson E. 2018. P wave arrival pickingg and first-motion polarity determination with deep learning[J]. Journal of Geophysical Research: Solid Earth, 123(6) : 5120-5129. doi: 10.1029/2017JB015251 [177] Ruan Y, Zhou Y. 2010. The effects of 3-D anelasticity (Q) structure on surface wave phase delays[J]. Geophysical Journal International, 181(1) : 479-492. doi: 10.1111/j.1365-246X.2010.04514.x [178] Ruan Y, Zhou Y. 2012. The effect of 3-D anelasticity (Q) structure on surface wave amplitudes[J]. Geophysical Journal International, 189(2) : 967-983. doi: 10.1111/j.1365-246X.2011.05356.x [179] Rusmanugroho H, Modrak R, Tromp J. 2017. Anisotropic full-waveform inversion with tilt-angle recovery[J]. Geophysics, 82(3) : R135-R151. doi: 10.1190/geo2016-0025.1 [180] Russo R, Silver P. 1994. Trench-parallel flow beneath the Nazca plate from seismic anisotropy[J]. Science, 263(5150) : 1105-1111. doi: 10.1126/science.263.5150.1105 [181] Schaeffer A, Lebedev S. 2013. Global shear speed structure of the upper mantle and transition zone[J]. Geophysical Journal International, 194(1) : 417-449. doi: 10.1093/gji/ggt095 [182] Schellart W. 2004. Kinematics of subduction and subduction-induced flow in the upper mantle[J]. Journal of Geophysical Research: Solid Earth , 109(B7): B07401. [183] Schellart W P , Freeman J, Stegman D R, et al. 2007. Evolution and diversity of subduction zones controlled by slab width[J]. Nature, 446(7133) : 308-311. doi: 10.1038/nature05615 [184] Schmandt B, Jacobsen S D, Becker T W, et al. 2014. Dehydration melting at the top of the lower mantle[J]. Science, 344(6189) : 1265-1268. doi: 10.1126/science.1253358 [185] Sen M, Stoffa P. 2013. Global Optimization Methods in Geophysical Inversion (2nd Edition)[M]. Cambridge, United Kingdom: Cambridge University Press. [186] Shapiro N, Campillo M, Stehly L, Ritzwoller M. 2005. High-resolution surface-wave tomography from ambient seismic noise[J]. Science, 307(5715) : 1615-1618. doi: 10.1126/science.1108339 [187] Shen W, Ritzwoller M, Schulte-Pelkum V, Lin F. 2013. Joint inversion of surface wave dispersion and receiver function: a Bayesian Monte-Carlo approach[J]. Geophysical Journal International, 192(2) : 807-836. doi: 10.1093/gji/ggs050 [188] Shin C, Cha Y. 2008. Waveform inversion in the Laplace domain[J]. Geophysical Journal International, 173(3) : 922-931. doi: 10.1111/j.1365-246X.2008.03768.x [189] Shin C, Cha Y. 2009. Waveform inversion in the Laplace-Fourier domain[J]. Geophysical Journal International, 177(3) : 1067-1079. doi: 10.1111/j.1365-246X.2009.04102.x [190] Sieminski A, Liu Q, Trampert J, Tromp J. 2007a. Finite-frequency sensitivity of body waves to anisotropy based on adjoint methods[J]. Geophysical Journal International, 171(1) : 368-389. doi: 10.1111/j.1365-246X.2007.03528.x [191] Sieminski A, Liu Q, Trampert J, Tromp J. 2007b. Finite-frequency sensitivity of surface wave to anisotropy based on adjoint methods[J]. Geophysical Journal International, 168(3) : 1153-1174. doi: 10.1111/j.1365-246X.2006.03261.x [192] Silver P, Chan W. 1991. Shear wave splitting and subcontinental mantle deformation[J]. Journal of Geophysical Research: Solid Earth, 96(B10) : 16429-16454. doi: 10.1029/91JB00899 [193] Silver P. 1996. Seismic anisotropy beneath the continents: probing the depths of geology[J]. Annual Review of Earth and Planetary Sciences, 24(1) : 385-432. doi: 10.1146/annurev.earth.24.1.385 [194] Simutė S, Steptoe H, Cobden L, et al. 2016. Full-waveform inversion of the Japanese Islands region[J]. Journal of Geophysical Research: Solid Earth, 121(5) : 3722-3741. doi: 10.1002/2016JB012802 [195] Smith M, Dahlen F. 1973. The azimuthal dependence of Love and Rayleigh wave propagation in a slightly anisotropoic medium[J]. Journal of Geophysical Research, 78(17) : 3321-3333. doi: 10.1029/JB078i017p03321 [196] Stegman D R, Freeman J, Schellart W P, et al. 2006. Influence of trench width on subduction hinge retreat rates in 3-D models of slab rollback[J]. Geochemistry, Geophysics, Geosystems, 7(3): Q03012. [197] Stern R. 2002. Subduction zones[J]. Reviews of Geophysics, 40(4) : 1-38. [198] Stuart G, Minkoff S, Pereira F. 2019. A two-stage Markov chain Monte Carlo method for seismic inversion and uncertainty quantification[J]. Geophysics, 84(6) : R1003-R1020. doi: 10.1190/geo2018-0893.1 [199] Su W, Dziewonski A. 1992. On the scale of mantle heterogeneity[J]. Physics of the Earth and Planetary Interiors, 74(1-2) : 29-54. doi: 10.1016/0031-9201(92)90066-5 [200] Su W J, Woodward R L, Dziewonski A. 1994. Degree-12 model of shear velocity heterogeneity in the mantle[J]. Journal Geophysical Research Solid Earth, 99(B4) : 6945-6980. doi: 10.1029/93JB03408 [201] 孙史磊, 毛伟建, 任志明, 李振春. 2020. VTI介质速度与δ参数qP波全波形反演[J]. 地球物理学进展, 35（6）: 2203-2210 doi: 10.6038/pg2020EE0011Sun S L, Mao W J, Ren Z M, Li Z C. 2020. Velocity and δ parameter quasi-P waves full waveform inversion in VTI media[J]. Progress in Geophysics, 35(6): 2203-2210 (in Chinese). doi: 10.6038/pg2020EE0011 [202] Tang Y, Youcai Tang Y C, Obayashi M, Niu F L, et al. 2014. Changbaishan volcanism in northeast China linked to subduction-induced mantle upwelling[J]. Nature Geoscience, 7(5) : 470-475. [203] Tao K, Grand S, Niu F. 2018. Seismic structure of the upper mantle beneath eastern Asia from full waveform seismic tomography[J]. Geochemistry, Geophysics, Geosystems, 19(8) : 2732-2763. [204] Tape C, Liu Q, Tromp J. 2007. Finite-frequency tomography using adjoint methods-Methodology and examples using membrane surface waves[J]. Geophysical Journal International, 168(3) : 1105-1129. doi: 10.1111/j.1365-246X.2006.03191.x [205] Tape C, Liu Q, Maggi A, Tromp J. 2009. Adjoint tomography of the southern California crust[J]. Science, 325(5943): 450. [206] Tape C, Liu Q, Maggi A, Tromp J. 2010. Seismic tomography of the southern California crust based on spectral-element and adjoint methods[J]. Geophysical Journal International, 180(1) : 433-462. doi: 10.1111/j.1365-246X.2009.04429.x [207] Tarantola A. 1984. Inversion of seismic reflection data in the acoustic approximation[J]. Geophysics, 49(8) : 1259-1266. doi: 10.1190/1.1441754 [208] Tarantola A. 1986. A strategy for nonlinear elastic inversion of seismic reflection data[J]. Geophysics, 51(10) : 1893-1903. doi: 10.1190/1.1442046 [209] Tarantola A. 1988. Theoretical background for the inversion of seismic waveforms, including elasticity and attenuation[J]. Pure and Applied Geophysics, 128(1) : 365-399. [210] Tarantola A. 2005. Inverse Problem Theory and Methods for Model Parameter Estimation (2nd Edition)[M]. Philadelphia, P A : Society for Industrial and Applied Mathematcs. [211] Thurin J, Brossier R, Metivier L. 2019. Ensemble-based uncertainty estimation in full waveform inversion[J]. Geophysical Journal International, 219(3) : 1613-1635. [212] Tong P, Chen C W, Komatitsch D, et al. 2014. High-resolution seismic array imaging based on SEM-FK hybrid method[J]. Geophysical Journal International, 197(1) : 369-395. doi: 10.1093/gji/ggt508 [213] Tromp J, Tape C, Liu Q. 2005. Seismic tomography, adjoint method, time reversal and banana-doughnut kernels[J]. Geophysical Journal International, 160(1) : 195-216. [214] Tromp J, Luo Y, Hanasoge S, Peter D. 2010. Noise cross-correlation sensitivity kernels[J]. Geophysical Journal International, 183(2) : 791-819. doi: 10.1111/j.1365-246X.2010.04721.x [215] Tromp J. 2020. Seismic wavefield imaging of Earth's interior across scales[J]. Nature Reviews Earth & Environment, 1(1) : 40-53. [216] Van der Hilst R, Widiyantoro S, Engdahl E. 1997. Evidence for deep mantle circulation from global tomography[J]. Nature, 386(6625) : 578-584. doi: 10.1038/386578a0 [217] van Leeuwen T, Herrmann F. 2013. Mitigating local minima in full-waveform inversion by expanding the search space[J]. Geophysical Journal International, 195(1) : 661-667. doi: 10.1093/gji/ggt258 [218] Virieux J, Operto S. 2009. An overview of full-waveform inversion in exploration geophysics[J]. Geophysics, 74(6) : WCC127-WCC152. doi: 10.1190/1.3237087 [219] Virieux J, Calandra H, Plessix R. 2011. A review of the spectral, pseudo-spectral, finite-difference and finite-element modelling techniques for geophysical imaging[J]. Geophysical Prospecting, 59(5) : 794-813. doi: 10.1111/j.1365-2478.2011.00967.x [220] Waldhauser F, Ellsworth W. 2000. A double-difference earthquake location algorithm: Method and application to the northern Hayward fault, California[J]. Bulletin of the seismological society of America, 90(6) : 1353-1368. doi: 10.1785/0120000006 [221] Wang K, Liu Q, Yang Y. 2019. Three-dimensional sensitivity kernels for multicomponent empirical Green's functions from ambient noise: Methodology and application to adjoint tomography[J]. Journal of Geophysical Research: Solid Earth, 124(6) : 5794-5810. doi: 10.1029/2018JB017020 [222] Wang K, Jiang C X, Yang Y J, et al. 2020. Crustal deformation in Southern California constrained by radial anisotropy from ambient noise adjoint tomography[J]. Geophysical Research Letters, 47(12): e2020GL088580. [223] Wang X, Zhan Z. 2020. Moving from 1-D to 3-D velocity model: automated waveform-based earthquake moment tensor inversion in the Los Angeles region[J]. Geophysical Journal International, 220(1) : 218-234. doi: 10.1093/gji/ggz435 [224] Wang Y, Chevrot S, Monteiller V, et al. 2016. The deep roots of the western Pyrenees revealed by full waveform inversion of teleseismic P waves[J]. Geology, 44(6) : 475-478. doi: 10.1130/G37812.1 [225] 王毓玮, 董良国, 黄超, 刘玉柱. 2016. 降低弹性波全波形反演强烈非线性的分步反演策略[J]. 石油地球物理勘探, 51（2）: 288-294Wang Y W, Dong L G, Huang C, Liu Y Z. 2016. A multi-step strategy for mitigating severe nonlinearity in elastic full-waveform inversion[J]. Oil Geophysical Prospecting, 51(2): 288-294 (in Chinese) [226] Warner M, Guasch L. 2016. Adaptive waveform inversion: Theory[J]. Geophysics, 81(6) : R429-R445. doi: 10.1190/geo2015-0387.1 [227] Woodhouse J, Dziewonski A. 1984. Mapping the upper mantle: three dimensional modelling of earth structure by inversion of seismic waveforms[J]. Journal Geophysical of Research, 89(B7) : 5953-5986. doi: 10.1029/JB089iB07p05953 [228] Woodward M. 1992. Wave-equation tomography[J]. Geophysics, 57(1) : 15-26. doi: 10.1190/1.1443179 [229] Wortel M, Spakman W. 2000. Subduction and slab detachment in the Mediterranean-Carpathian region[J]. Science, 290(5498) : 1910-1917. doi: 10.1126/science.290.5498.1910 [230] Wu R -S, Aki K. 1985. Scattering characteristics of elastic waves by an elastic heterogeneity[J]. Geophysics, 50(4) : 582-595. doi: 10.1190/1.1441934 [231] Wu R, Luo J, Wu B. 2014. Seismic envelop inversion and modulation signal model[J]. Geophysics, 79(3) : WA13-WA24. doi: 10.1190/geo2013-0294.1 [232] Xue Z, Zhu H, Fomel S. 2017. Full waveform inversion using seislet regularization[J]. Geophysics, 82(5) : A43-A49. doi: 10.1190/geo2016-0699.1 [233] 杨积忠, 刘玉柱, 董良国. 2014. 变密度声波方程多参数全波形反演策略[J]. 地球物理学报, 57（2）: 628-643 doi: 10.6038/cjg20140226Yang J Z, Liu Y Z, Dong L G. 2014. A multi-parameter full waveform inversion strategy for acoustic media with variable density[J]. Chinese Journal of Geophysics, 57(2): 628-643 (in Chinese). doi: 10.6038/cjg20140226 [234] Yang J, Zhu H. 2018. A time-domain complex-valued wave equation for modeling visco-acoustic wave propagation[J]. Geophysical Journal International, 215(2) : 1064-1079. doi: 10.1093/gji/ggy323 [235] Yang J, Zhu H, Li X, Zhang S. 2020. Estimating P wave velocity and attenuation structures using full waveform inversion based on a time domain complex-valued viscoacoustic wave equation: the method[J]. Journal of Geophysical Research, 125(6): e2019JB019129. [236] 杨勤勇, 胡光辉, 王立歆. 2014. 全波形反演研究现状及发展趋势[J]. 石油物探, 53（1）: 77-83 doi: 10.3969/j.issn.1000-1441.2014.01.011Yang Q Y, Hu G H, Wang L X. 2014. Research status and development trend of full waveform inversion[J]. Geophysical Prospecting for Petroleum, 53(1): 77-83 (in Chinese). doi: 10.3969/j.issn.1000-1441.2014.01.011 [237] 杨午阳, 王西文, 雍学善, 陈启燕. 2013. 地震全波形反演方法研究综述[J]. 地球物理学进展, 2013, 28（2）: 766-776 doi: 10.6038/pg20130225Yang W Y, Wang X W, Yong X S, Chen Q Y. 2013. The review of seismic full waveform inversion method[J]. Progress in Geophysics, 28(2): 766-776 (in Chinese). doi: 10.6038/pg20130225 [238] Yang Y, Ritzwoller M, Levshin A, Shapiro N. 2007. Ambient noise Rayleigh wave tomography across Europe[J]. Journal of Geophysical Research, 168(1) : 259-274. doi: 10.1111/j.1365-246X.2006.03203.x [239] Yang Y, Engquist B, Sun J, Hamfeldt B. 2018. Application of optimal transport and the quadratic Wasserstein metric to full-waveform inversion[J]. Geophysics, 83(1) : R43-R62. doi: 10.1190/geo2016-0663.1 [240] 姚刚, 吴迪. 2017. 反射波全波形反演[J]. 中国科学: 地球科学, 47（10）: 1220-1232.Yao G, Wu D. 2017. Reflection full waveform inversion[J]. Science China Earth Sciences, 60: 1783–1794 (in Chinese). [241] Yao H, van der Hilst R, de Hoop M. 2006. Surface-wave array tomography in SE Tibet from ambient seismic noise and two-station analysis-I. phase velocity maps[J]. Geophysical Journal International, 166(2) : 732-744. doi: 10.1111/j.1365-246X.2006.03028.x [242] Yao H, van der Hilst R, Montagner J. 2010. Heterogeneity and anisotropy of the lithosphere of SE Tibet from surface wave array tomography[J]. Journal of Geophysical Research, 115(B12) : 1978-2012. [243] Yuan Y, Simons F. 2014. Multiscale adjoint waveform-difference tomography using wavelet[J]. Geophysics, 79(3) : W79-W95. doi: 10.1190/geo2013-0383.1 [244] Yuan Y, Simons F, Tromp J. 2016. Double-difference adjoint seismic tomography[J]. Geophysical Journal International, 206(3) : 1599-1618. doi: 10.1093/gji/ggw233 [245] Zhan Z W, Cantono M, Kamalov V, et al. 2021. Optical polarization-based seismic and water wave sensing on transoceanic cable[J]. Science, 371(6532) : 931-936. doi: 10.1126/science.abe6648 [246] Zhang H, Thurber C. 2003. Double-difference tomography: The method and its application to the Hayward fault, California[J]. Bulletin of the Seismological Society of America, 93(5) : 1875-1889. doi: 10.1785/0120020190 [247] Zhang S, Karato S. 1995. Lattice preferred orientation of olivine aggregates deformed in simple shear[J]. Nature, 375(6534) : 774-777. doi: 10.1038/375774a0 [248] 张文生, 罗嘉, 滕吉文. 2015. 频率多尺度全波形速度反演[J]. 地球物理学报, 58（1）: 216-228 doi: 10.6038/cjg20150119Zhang W S, Luo J, Teng J W. 2015. Frequency multiscale full-waveform velocity inversion[J]. Chinese Journal of Geophysics, 58(1): 216-228 (in Chinese). doi: 10.6038/cjg20150119 [249] Zhao D, Hasegawa A, Horiuchi S. 1992. Tomographic imaging of P and S wave velocity structure beneath northeastern Japan[J]. Journal of Geophysical Research: Solid Earth, 97(B13) : 19909-19928. doi: 10.1029/92JB00603 [250] Zhao D, Hasegawa A, Kanaamori H. 1994. Deep structure of Japan subduction zone as derived from local, regional, and teleseismic events[J]. Journal of Geophysical Reserach: Solid Earth, 99(B11) : 22313-22329. doi: 10.1029/94JB01149 [251] Zhao D. 2004. Global tomographic images of mantle plumes and subducting slabs: insight into deep Earth dynamics[J]. Physics of the Earth and Planetary Interiors, 146(1-2) : 3-34. doi: 10.1016/j.pepi.2003.07.032 [252] Zhao L, Jordan T, Chapman C. 2000. Three-dimensional Frechet differential kernels for seismic delay times[J]. Geophysical Journal International , 141(3) : 558-576. doi: 10.1046/j.1365-246x.2000.00085.x [253] Zhao L, Jordan T, Olsen K, Chen P. 2005. Frechet kernels for imaging regional earth structure based on three-dimensional reference models[J]. Bulletin of the Seismological Society of America, 95(6) : 2066-2080. doi: 10.1785/0120050081 [254] Zhao L, Chen P, Jordan T. 2006. Strain Green's tensors, reciprocity, and their applications to seismic source and structure studies[J]. Bulletin of the Seismological Society of America, 96(5) : 1753-1763. doi: 10.1785/0120050253 [255] Zhao Z, Sen M. 2021. A gradient-based Markov chain Monte Carlo method for full-waveform inversion and uncertainty analysis[J]. Geophysics, 86(1) : R15-R30. doi: 10.1190/geo2019-0585.1 [256] Zhou W, Brossier R, Operto S, Virieux J. 2015. Full waveform inversion of diving & reflected waves for velocity model building with impedance inversion based on scale separation[J]. Geophysical Journal International, 202(3) : 1535-1554. doi: 10.1093/gji/ggv228 [257] Zhou Y, Dahlen F, Nolet G. 2004. Three-dimensional sensitivity kernels for surface wave observables[J]. Geophysical Journal International, 158(1) : 142-168. doi: 10.1111/j.1365-246X.2004.02324.x [258] Zhu H J, Luo Y, Nissen-Meyer T, et al. 2009. Elastic imaging and time-lapse migration based on adjoint method[J]. Geophysics, 74(6): WCA167-WCA177. doi: 10.1190/1.3261747 [259] Zhu H, Bozdag E, Peter D, Tromp J. 2012. Structure of the European upper mantle revealed by adjoint tomography[J]. Nature Geoscience, 5(7) : 493-498. doi: 10.1038/ngeo1501 [260] Zhu H, Bozdag E, Duffy T, Tromp J. 2013. Seismic attenuation beneath Europe and the North Atlantic: Implicition for water in the mantle[J]. Earth and Planetary Science Letters, 381(1) : 1-11. [261] Zhu H, Tromp J. 2013. Mapping tectonic deformation in the crust and upper mantle beneath Europe and the North Atlantic Ocean[J]. Science, 341(6148): 871-875. doi: 10.1126/science.1241335 [262] Zhu H, Bozdag E, Tromp J. 2015. Seismic structure of the European upper mantle based on adjoint tomography[J]. Geophysical Journal International, 201(1) : 18-52. doi: 10.1093/gji/ggu492 [263] Zhu H, Fomel S. 2016. Building good starting models for full-waveform inversion using adaptive matching filtering misfit[J]. Geophysics, 81(5): U61-U72. doi: 10.1190/geo2015-0596.1 [264] Zhu H J, Li S W, Fomel S, et al. 2016. A Bayesian approach to estimate uncertainty for full waveform inversion using a priori information from depth migration[J]. Geophysics, 81(5): R307-R323. doi: 10.1190/geo2015-0641.1 [265] Zhu H, Komatitsch D, Tromp J. 2017. Radial anisotropy of the North American upper mantle based on adjoint tomography with USArray[J]. Geophysical Journal International, 211(1): 349-377. doi: 10.1093/gji/ggx305 [266] Zhu H. 2018a. Crustal wave speed structure of North Texas and Oklahoma based on ambient noise cross-correlation functions and adjoint tomography[J]. Geophysical Journal International, 214(1) : 716-730. doi: 10.1093/gji/ggy169 [267] Zhu H. 2018b. Seismogram registration via Markov chain Monte Carlo optimization and its applications in full waveform inversion[J]. Geophysical Journal International, 212(2) : 976-987. doi: 10.1093/gji/ggx461 [268] Zhu H, Stern R, Yang J. 2020a. Seismic evidence for subduction-induced mantle flows underneath Middle America[J]. Nature Communications, 11(2075)doi: 10.1038/s41467-020-15492-6. [269] Zhu H, Yang J, Li X. 2020b. Azimuthal anisotropy of the North American upper mantle based on full waveform inversion[J]. Journal of Geophysical Research: Solid Earth, 125(2): e2019JB018432. [270] Zhu H J, Li X Y, Yang J D, et al. 2020c. Poloidal- and toroidal-mode mantle flows underneath the Cascadia Subduction Zone[J]. Geophysical Research Letters, 47(14): e2020GL087530. [271] Zhu T, Harris J. 2014. Modeling acoustic wave propagation in heterogeneous attenuating media using decoupled fractional Laplacians[J]. Geophysics, 79(3): T105-T116. doi: 10.1190/geo2013-0245.1 [272] Zhu T, Sun J. 2017. Viscoelastic reverse time migration with attenuation compensation[J]. Geophysics, 82(2): S61-S73. doi: 10.1190/geo2016-0239.1 -
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