For macro-velocity-model building, the ray-based formulation of classic stereotomography is replaced by eikonal solvers with simultaneous introduction of adjoint-state method for an efficient matrix free optimization scheme. In this approach, named adjoint stereotomography, forward modelling is performed from sources and receivers, making the approach independent of the data complexity. In this work, the adjoint stereotomography is extended to anisotropic media where vertical velocity, Thomsen anisotropic parameters and scattering-point positions are inverted jointly. In this multi-parameter inversion, the matrix-free framework of optimization reduces drastically the computational burden of the workflow. The inversion is based on a weighted leastsquares misfit function as we mix different data. Explicit expressions of gradients for the different parameters are provided and are illustrated through sensitivity kernels. A very simple example of a circular anomaly will show how are recovered parameters when using a quasi-Newton lBFGS method of optimization, giving us the confidence that more realistic examples could be investigated in the future.


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