Full waveform inversion of anisotropic parameters in VTI media based on automatic differentiation

Conventional Full Waveform Inversion (FWI) requires explicit calculation of the adjoint source back-propagation wavefield, and the adjoint equations need to be derived to obtain the gradient of the objective function to the model parameters. However, the adjoint equations of complex equations containing multiple parameters are usually difficult to derive, which increases the difficulty of developing and applying multi-parameter full waveform inversions such as anisotropic equations. In response to the above problems, this paper realizes the solution of VTI medium wave equation and automatic differential inversion under the deep learning framework, simplifies full waveform inversion into an optimization problem of minimizing the objective function. The gradient is obtained directly through the chain rule, avoiding the explicit calculation and back-propagation of the adjoint source, significantly simplifying the FWI implementation process. Additionally, the Adam gradient optimization algorithm in the field of deep learning is introduced. Compared with the traditional conjugate gradient algorithm, it can further improve the multi-parameter inversion efficiency and inversion accuracy of VTI media, and finally realize the efficient and high-precision multi-parameter full waveform inversion of VTI media.