Travel time tomography by ray tracing using the fast sweeping method

This paper presents a gradient-descent travel time tomography method for solving the acoustic-type velocity model inversion problem. Similarly to the adjoint-state method, the proposed method is based on the Eikonal equation, enabling simultaneous calculation of contributions from all common-source receivers to the gradient. This overcomes the inefficiency inherent in conventional travel time tomography methods, which rely on a two-point ray tracing process. By directly calculating Fréchet derivatives, our method avoids the complex derivation processes associated with the adjoint-state method. The key to calculating the Fréchet derivatives is to calculate a so-called ray-path term. Consequently, compared to the adjoint-state method, the proposed method can explicitly obtain the ray paths, resulting in a more concise and intuitive derivation process. Furthermore, our method retains the benefits of the adjoint-state method, such as speed, low memory usage, and robustness. This paper focuses on elucidating the principles and algorithms for calculating the ray-path term based on the fast sweeping method. The algorithms could be further speeded up by using parallel computational techniques. Synthetic tests demonstrate that our proposed travel time tomographic method accurately calculates ray paths, regardless of the complexity of the model and recording geometry.