Optimization method of first-arrival waveform inversion based on the L-BFGS algorithm

The first arrival waveform inversion (FAWI) has a strong nonlinearity due to the objective function using L2 parametrization. When the initial velocity is not accurate, the inversion can easily fall into local minima. In the full waveform inversion method, adding a cross-correlation function to the objective function can effectively reduce the nonlinearity of the inversion process. In this paper, the nonlinearity of this process is reduced by introducing the correlation objective function into the FAWI and by deriving the corresponding gradient formula. We then combine the first-arrival wave travel-time tomography with the FAWI to form a set of inversion processes. This paper uses the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) algorithm to improve the computational efficiency of inversion and solve the problem of the low efficiency of the FAWI method. The overthrust model and field data test show that the method used in this paper can effectively reduce the nonlinearity of inversion and improve the inversion calculation efficiency at the same time.