Abstract:      Full waveform inversion is an inversion method to obtain the physical parameters of subsurface media by using the dynamic characteristics of seismic wave propagation, which can provide an important basis for revealing the fine structure of subsurface. In this paper, the elastic wave equation is used as mathematical model to simulate the propagation law of seismic wave and the corresponding inversion method is studied. In order to improve the computational efficiency and the accuracy of the inversion results, the nearly analytic discrete ( NAD ) operator can be used for the forward modeling of the frequency-domain elastic wave equation. In this paper, based on the NAD discretization, the sparse block structure of the impedance matrix and the gradient calculation formula of the inversion objective function to the model parameters are derived, and the frequency-domain elastic wave full waveform inversion method based on the NAD operator is established. In order to verify the effectiveness of the method, a variety of typical medium models are inverted by numerical experiments, and the ideal inversion results are obtained.