Direct surface wave tomography for three dimensional structure based on surface wave traveltimes: Methodology review and applications
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摘要: 利用面波频散数据进行各向同性和各向异性横波速度结构成像是研究全球和区域构造变形、获取地壳上地幔和近地表精细结构的一种非常有效的方法. 传统的基于频散数据的面波成像通常采用两步法，即首先反演二维相速度或群速度分布图，然后再基于格点的纯路径频散反演格点下方的一维横波速度模型，之后再拼合成三维速度模型. 在本文中我们较为详细地综述新发展的基于面波频散走时的三维面波直接成像方法体系，即面波一步法成像. 该方法体系包括通过所有路径、不同频率的面波频散走时直接反演三维各向同性横波速度结构的方法（DSurfTomo）、直接反演三维方位各向异性横波速度结构的方法（DAzimSurfTomo），以及直接反演三维径向各向异性横波速度结构的方法（DRadiSurfTomo）. 新的面波直接成像方法计算不同周期的面波射线路径，从而更好地考虑复杂结构下面波射线路径弯曲对成像精度的影响. 随后我们介绍面波直接成像方法的应用实例，包括地壳上地幔及地壳浅部的多尺度各向同性和各向异性横波速度结构的成像，这些成像研究为认识区域构造演化、孕震构造、断裂带浅部结构、成矿构造、城市地下结构等提供了重要的约束. 最后我们讨论面波直接成像方法的频散数据及模型参数化问题，以及基于有限频理论的面波直接成像和面波全波形成像，讨论并展望在面波直接成像方法框架下面波频散数据与其他地震或地球物理数据的联合成像问题.Abstract: Surface wave tomography using dispersion data to obtain isotropic and anisotropic shear wave velocity structures is a very efficient approach to study regional and global tectonics and deformation and to probe high-resolution crustal, upper mantle and near surface structures. Conventional surface wave tomography based on dispersion data usually has two steps, that is, inverting for 2D phase/group velocity maps first and then conducting point-wise inversion to obtain a 1D shear wave velocity model at each geographical grid point, which are then combined to obtain a 3D shear wave velocity model. In this paper, we review in detail the direct surface wave tomography framework based on surface wave dispersion traveltimes, that is, the one-step surface wave tomography. This framework includes direct inversion of 3D isotropic shear wave velocity model using all dispersion measurements at different periods and from all paths (DSurfTomo), direct inversion of both isotropic and azimuthally anisotropic shear wave velocity model (DAzimSurfTomo), and direct inversion of radially anisotropic shear wave velocity model (DRadiSurfTomo).The new direct tomography method computes surface wave ray paths at different periods, thus better considering the ray path bending effect of surface waves in complex media on the precision of tomographic images. We then introduce some applications of the new direct tomography methods, including multi-scale isotropic and anisotropic shear wave velocity tomography in the crust and upper mantle as well as shallow crust. These tomographic studies provide important constraints on regional tectonic evolution, seismogenic structures, shallow fault zone structures, ore deposit structures, and urban subsurface structures. At last, we discuss the dispersion data and model parameterization problems in surface wave tomography, direct surface wave tomography based on finite frequency theory and full waveform inversion, and perspective research of joint tomography problems using surface wave dispersion data and other seismological or geophysical data in the framework of direct surface wave tomography.
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图 1 面波成像中离散化的三维网格点模型及面波射线路径示意图. （a）水平向的二维慢度网格点；（b）垂直向的VS网格点（黑点）和插值得到的层状模型（黑色阶梯状实线）. 图（a）中的黑色实线表示某个周期面波在AB间的传播路径，路径上的p点的慢度由周围4个水平网格点（1、2、3、4）的双线性值插值获得. 图（b）中垂直格点模型通过扰动（如红色圆点和虚线所示）来计算频散相对于参数模型的深度敏感核（修改自Fang et al., 2015）
Figure 1. Discretized 3D grid model of surface wave tomography and illustration of surface wave ray path. (a) 2D slowness grids in the horizontal direction; (b) VS grids (black dots) in the vertical direction and the interpolated layered model (black staircase lines). In (a) the black solid line represents the propagation path between two stations A and B for the surface wave at some period. The phase slowness at any point p along the path is determined from the values at four surrounding horizontal grid points (1, 2, 3, 4) using a bilinear interpolation method. In (b) the vertical grid model is perturbed (as shown by the red dots and red dashed lines) to compute the depth sensitivity kernel of dispersion data to model parameters (modified from Fang et al., 2015)
图 2 一维速度模型（a）及其相应的
$ \mathrm{d}c/\mathrm{d}L $ （实线）和$ \mathrm{d}c/\mathrm{d}A $ （虚线）在不同周期的深度敏感核（b）（修改自Liu et al., 2019）Figure 2. Depth sensitivity kernels (b) of
$ \mathrm{d}c/\mathrm{d}L $ (solid line) and$ \mathrm{d}c/\mathrm{d}A $ (dashed line) at different periods from a 1D velocity model (a) (modified from Liu et al., 2019)
图 3 面波直接成像方法（DSurfTomo、DAzimSurfTomo和DRadiSurfTomo）的简介图
Figure 3. The sketch diagrams of the direct surface wave tomography methods (DSurfTomo, DAzimSurfTomo, and DRadiSurfTomo)
图 4 不同周期瑞利波和勒夫波相速度深度敏感核的对比. （a）计算深度敏感核所采用的横波速度模型；（b）5 s、20 s、40 s 周期的瑞利面波相速度的深度敏感核；（c）5 s、20 s、40 s 周期的勒夫面波相速度的深度敏感核
Figure 4. The comparison of depth sensitivity kernels of Rayleigh wave and Love wave at different periods. (a) The shear wave velocity model used to compute depth sensitivity kernels; (b) Depth sensitivity kernels of Rayleigh wave phase velocities at periods of 5 s, 20 s, and 40 s; (c) Depth sensitivity kernels of Love wave phase velocities at periods of 5 s, 20 s, and 40 s
图 5 考虑面波射线路径弯曲（a）和大圆路径假设下（b）的300 m深度处的横波速度反演结果. （a, b）图中三角形表示本研究中使用的地震台站位置，灰线表示合肥市区内的主要道路. 黑色实线表示蜀山断层（SSF）位置. 红色直线PP'表示横跨断层的一条剖面的位置，其速度剖面如（c）所示. （c）中黑色三角形指示根据速度差异推测的蜀山断层（SSF）的位置（修改自 Li et al., 2016）
Figure 5. Shear wave velocity inversion results at the depth of 300 m considering the surface wave ray path bending effect (a) and with the great-circle propagation hypothesis (b). In (a, b) the triangles show the stations used in the study, gray lines show the main roads in the Hefei city, the black line shows the location of the Shushan Fault (SSF), and the red line PP' represents the profile location across the fault, with its velocity profile shown as (c). In (c) the black triangle indicates the location of the Shushan fault (SSF) (modified from Li et al., 2016)
图 6 云南地区三维方位各向异性横波速度结构模型. （a-c）图中的红色短棒显示方位异性的大小和快波方向；图（c）中的蓝色短线显示远震横波分裂测量结果（常利军等，2015），黑色箭头指示板块绝对运动方向（Argus et al., 2011）（修改自Liu et al., 2019）
Figure 6. 3D azimuthally anisotropic shear wave velocity model in the Yunnan area. In (a-c) the red bars give the amplitude and fast direction of azimuthal anisotropy. The blue bars show the teleseismic shear wave splitting measurements (Chang et al., 2015) and the black arrow indicates the absolute plate motion (Argus et al., 2011) (modified from Liu et al., 2019)
图 7 郯庐断裂带巢湖段主要地质单元、地震台站分布和成像结果. （a）研究区域主要地质单元和地震台站分布. 其中黑色三角形为地震台站位置，五角星表示主要的城市位置，深灰色实线为主要断裂位置，包括六安断裂（LAF）、巢湖断裂（CLF）、照明山断裂（ZMSF）、滁河断裂（CHF）、嘉山—庐江断裂（JSLJF）、池河—太湖断裂（CHTHF）、盛桥—柏山断裂（SQBSF）. 由西至东，主要地质单元包括合肥盆地、张八岭隆起、郯庐断裂带、巢湖、银屏山（YPM）. （b-d）深度分别为1 km、4.5 km和8 km深度的各向同性和方位各向异性横波速度分布. 其中小短线的长度和方位分别指示方位各向异性的强度和方位角，灰色小短线表示该方位各向异性具有较大误差（修改自Luo and Yao, 2021）
Figure 7. Distribution of main geological units, seismic stations, and tomographic results in the Chao Lake segment of the Tanlu fault zone. (a) Distribution of major geological units and seismic stations within the study area. The black triangle represents the location of the seismic station. The pentagram represents the location of the main city. The dark gray solid lines indicate the main fault locations, including the LuAn fault (LAF), the Chao Lake fault (CLF), the Zhaomingshan fault (ZMSF), the Chuhe fault (CHF), the Jiashan-Lujiang fault (JSLJF), the Chihe-Taihu fault (CHTHF), and the Shenqiao-Baishan fault (SQBSF). From west to east, the main geological units are the Hefei basin, the Zhangbaling uplift, the Tanlu fault zone, the Chao lake, and the Yinping mountain (YPM). (b-d) Slices of isotropic and azimuthally anisotropic shear wave velocity at depths of 1 km, 4.5 km, and 8 km, respectively. The length and azimuth of the short line indicate the strength and azimuth of the anisotropy, respectively. The gray short line indicates that the anisotropy has a large error (modified from Luo and Yao, 2021)
图 8 喜马拉雅东构造结5 km、25 km和35 km深度的平均横波速度结构Vs（a, c, e）及其相对应深度的径向各向异性结构
$ \xi $ （b, d, f）. 白线和灰线代表划分的不同子区域间的边界. （a）中灰色三角为南迦巴瓦峰的位置，粉色三角为台站位置；（c）和（e）中的紫线代表25 km和35 km深度地壳中带状软弱物质的位置. （a）和（b）中英文缩写为：BNS：班公—怒江缝合带；ITS：印度—雅鲁藏布江缝合带；JLF：嘉犁断裂；BB-LLF：边坝—洛龙断裂；CR：Comei 裂谷；MLF：米林断裂；MTF：墨脱断裂；NB：南迦巴瓦（修改自 Hu et al., 2020）Figure 8. Average shear wave velocity VS (a, c, e) and corresponding radial anisotropy ξ (b, d, f) around the eastern Himalayan syntaxis shown at depths of 5 km, 25 km, and 35 km, respectively. White and gray dashed lines denote the boundaries for different subregions. Pink triangles in (a) denote the stations used in this study. The gray triangle in (a) denotes the location of Namche Barwa peak. Purple lines in (c) and (e) denote the proposed channelized weak zones at depths of 25 km and 35 km, respectively. Abbreviations in (a) and (b) are as follows: BNS, Bangong-Nujiang Suture; ITS, Indus-Tsangpo Suture; JLF, Jiali Fault; BB-LLF,Bianba-Luolong Fault; CR, Comei Rift; MLF, Mainling Fault; MTF, Motuo Fault; NB, Namche Barwa (modified from Hu et al., 2020)
图 9 台北盆地两个台站间0.8 s周期瑞利面波走时的三维敏感核函数. （a）显示了0.4 km深度处的三维敏感核的水平剖面，黑色实线表示射线路径. （b）显示了三维敏感核的一条纵剖面，位置如（a）中红色实线所示（修改自李成，2019）
Figure 9. The 3D sensitivity kernel of the 0.8 s period Rayleigh wave travel-time between two stations in the Taipei Basin. (a) Shows the horizontal cross-section of the 3D sensitivity kernel at 0.4 km depth with the black curve representing the ray path. (b) Shows the vertical cross-section of the 3D sensitivity kernel with its location given as the red line in (a) (modified from Li, 2019)
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