Zhu, J.G., Qu, Y.M., Duan, W.W., Zhang, Q.H. and Yang, C.Y., 2023. Frequency domain acoustic wave full waveform inversion based on average-derivative optimization. Journal of Seismic Exploration, 32: 509-508. Full waveform inversion is a geophysical inversion method. Based on the residuals of observation records and simulation records as the objective function, it combines travel time, amplitude and other information to invert subsurface parameters to achieve high-precision inversion of subsurface media. Seismic wave forward modeling is the key theoretical basis of full waveform inversion, and its accuracy is directly related to subsequent seismic data processing. In the frequency domain, the conventional difference scheme cannot adapt to the situation of unequal spatial sampling intervals. In order to improve the adaptability of the forward modeling algorithm in the frequency domain, this paper deduces a 21-point finite-difference scheme based on the average derivative method, and calculates the difference coefficient and Dispersion condition. The model trial calculation proves that the method is not only suitable for the non-uniform space sampling interval but also improves the operation efficiency. Then, the method in this paper is applied to the full waveform inversion in the frequency domain. The inversion effect of the method is verified by the Marmousi model, which can effectively restore the underground structure in the Marmousi model, especially for the subtle underground structure, and the inversion results are more accurate, fine and accurate.