1. DSurfTomo Package: direct inversion for 3-D isotropic Vsv model from all path dependent dispersion data

We propose a method to invert surface wave dispersion data directly for 3-D variations of shear wave speed, that is, without the intermediate step of phase or group velocity maps, using frequency-dependent ray tracing and a wavelet-based sparsity-constrained tomographic inversion. A fast marching method (Rawlinson & Sambridge, 2004) is used to compute, at each period, surface wave traveltimes and ray paths between sources and receivers. This avoids the assumption of great-circle propagation that is used in most surfacewave tomographic studies, butwhich is not appropriate in complex media. To simplify the problem we consider quasi-stratified media with smoothly varying seismic properties. We represent the 3-D shear wave speed model by means of 1-D profiles beneath grid points, which are determined from all dispersion data simultaneously using a wavelet-based sparsity-constrained tomographic method. The wavelet coefficients of the wave speed model are estimated with an iteratively reweighted least squares algorithm, and upon iteration the surface wave ray paths and the data sensitivity matrix are updated using the newly obtained wave speed model. 

Reference: Fang H., Yao, H. *, Zhang H, Huang, YC, van der Hilst R.D., 2015. Direct inversion of surface wave dispersion for 3-D shallow crustal structure based on ray tracing: methodology and application, Geophys. J. Int. , 2011, 1251-1263). 

DSurfTomo code download: https://github.com/HongjianFang/DSurfTomo

2. DAzimSurfTomo Package: direct inversion for 3-D azimuthally anisotropic Vsv model from all path dependent dispersion data

Azimuthal anisotropy retrieved from surface waves is important for constraining depthvarying deformation patterns in the crust and upper mantle. We present a direct inversion technique for the three‐dimensional shear wave speed azimuthal anisotropy based on mixed‐path surface wave traveltime data. This new method includes two steps: (1) inversion for the 3‐D isotropic Vsv model directly from Rayleigh wave traveltimes and (2) joint inversion for both 3‐D Vsv azimuthal anisotropy and additional 3‐D isotropic Vsv perturbation. The joint inversion can significantly mitigate the trade‐off between strong heterogeneity and anisotropy. With frequency‐dependent ray tracing based on 2‐D isotropic phase speed maps, the new method takes into account the ray‐bending effect on surface wave propagation. 

Reference：Liu, C., Yao, H.*, Yang, H.‐Y.*, Shen, W., Fang, H., Hu, S., & Qiao, L. (2019). Direct inversion for three‐dimensional shear wave speed azimuthal anisotropy based on surface wave ray tracing: Methodology and application to Yunnan, southwest China. Journal of Geophysical Research: Solid Earth, 124(11), 11394-11413,  https://doi.org/10.1029/2018JB016920

DAzimSurfTomo package Download: https://github.com/Chuanming-Liu/DAzimSurfTomo

3. DRadiSurfTomo Package: direct inversion for 3-D radially anisotropic Vs model from all path dependent dispersion data

A novel method is implemented to invert Rayleigh and Love wave dispersion curves of all paths jointly for 3-D shear wave velocity and radial anisotropy parameter simultaneously without intermediate steps. This new approach is based on our previous method of direct inversion of 3-D isotropic Vs model (DSurfTomo, Fang, Yao, et al., 2015). Conventional approach requires the computation of division Vsh over Vsv after inversion, which is sometimes unstable. The new parameterization in our approve allows for direct inversion of the 3-D radial anisotropy parameter (Vsh/Vsv). Therefore, spatial smoothing can be directly applied to  (Vsh/Vsv), which ensures a more stable inversion of (Vsh/Vsv). 

Reference: Hu, S., Yao, H., & Huang, H. (2020). Direct surface wave radial anisotropy tomography in the crust of the eastern Himalayan syntaxis. Journal of Geophysical Research: Solid Earth, 125, e2019JB018257. https://doi.org/10. 1029/2019JB018257

DRadiSurfTomo code download: https://github.com/ShaoqianHu/DRadiSurfTomo

4. Recent review paper for the above three mthods (in Chinese)

姚华建*，罗松，李成，胡少乾，方洪健. 2023. 基于面波走时的三维结构面波直接成像：方法综述与应用. 地球与行星物理论评， 54(3)，231-251, doi：10.19975/j.dqyxx.2022-063. （Yao H J*,  Luo S, Li C, Hu S Q, Fang H J. 2022. Direct surface wave tomography for  three dimensional structure based on surface wave traveltimes:  Methodology review and applications. Reviews of Geophysics and Planetary Physics, 54(3)， 231-251，doi:10.19975/j.dqyxx.2022-063 (in Chinese)）.