Inverting atmospheric ducts using automatic identification system (AIS) signals is a nonlinear and ill-posed problem, requiring knowledge of the types of ducts and the corresponding ranges of duct parameters that the inversion method can handle. For atmospheric duct inversion, effective inversion can only be achieved when minor changes in duct parameters significantly affect the received AIS signal power and do not exceed the maximum reception distance of the AIS signal. Therefore, this paper employs a ray tracing model to study the applicable range of AIS signal inversion for atmospheric duct parameters. It analyzes the types of ducts and their parameter ranges that can be inverted, evaluates the well-posedness of the inversion method, and validates the approach through simulations. The simulation results indicate that the proposed method can determine the inversion ranges for the base height of the trilinear duct and the thickness of the trapping layer, thereby improving the accuracy and reliability of atmospheric duct inversion and addressing the ill-posedness issue in the inversion process.