GEOsynchronous orbit Synthetic Aperture Radar (GEO SAR) has a long synthetic aperture and large observation region; therefore, it is easily affected by atmospheric spatial-temporal changes, which results in a serious degradation in the focusing quality and performance of differential interference processing. In this paper, a high-precision spatial-temporal hybrid GEO SAR signal model is established for the slowly disturbed parts of the atmosphere such as the background troposphere and the ionosphere. The effects of the time rate of different atmospheric parameters on the image quality and accuracy of differential interference processing are analyzed. Considering the influence of random disturbances such as tropospheric turbulence and ionospheric scintillation in atmosphere, a quantitative analysis model is established based on a power law power spectrum model using the atmospheric disturbance and imaging quality parameters. The relationships of the random disturbances intensity in the atmosphere and the imaging evaluation index are obtained. Finally, the model is verified by simulations, and the effects of slow-varying atmospheric errors in a long aperture time on the quality of imaging and differential interference processing are analyzed. Simulation results show that spatial-temporal variable ionospheric disturbances seriously affect L-band GEO SAR imaging and differential interference processing, which must be compensated, and they are slightly affected by tropospheric disturbances. Moreover, it is necessary to consider the tropospheric effects on imaging performance only when the integration time reaches several hundred seconds.