This thesis provided a mathematically rigorous framework linking the gravitational potential and atmospheric wind fields in gas giants such as Jupiter and Saturn. It developed two models that established criteria for determining unique wind-induced densities and potentials within planetary interiors. However, the study’s assumptions–such as spherical symmetry and the use of a polytropic index-one model–introduced limitations due to the significant ellipticity of gas giants. It also noted unresolved issues, including the lack of physical justification for certain uniqueness conditions and discontinuities in modeled wind fields. Despite these limitations, the thesis offers a mathematically rigorous contribution to inverse gravimetry of gas giant atmospheres.