Traditional full waveform inversion uses the L₂ norm as the misfit function and applies a local optimization algorithm in the inversion process. When the initial model is inaccurate or the low-frequency information is deficient, the inversion results converge to a local minimum. Elastic full waveform inversion needs to obtain multi-parameter information, the nonlinearity is stronger, and the parameter crosstalk problem exists. The graph space optimal transport distance can effectively alleviate the cycle skipping of waveform inversion due to the convexity in the signal time shift and amplitude change. Therefore, we take the graph space optimal transport distance as the metric and construct the objective function, use the Hungarian algorithm to solve the linear distribution problem, and use the automatic differential to obtain the gradient to realize the graph space optimal transport automatic differentiation elastic full waveform inversion. According to graph space optimal transport characteristics, we propose a graph space optimal transport automatic differentiation elastic full waveform inversion method based on point cloud allocation strategy to ensure the inversion effect and improve the computing efficiency. Model test results show that the proposed method has noise robustness and low dependence on the initial model and low-frequency information