Geosynchronous orbit synthetic aperture radar (GEO SAR) has a long integration time and a large imaging scene. Therefore, various nonideal factors are easily accumulated, introducing phase errors and degrading the imaging quality. Within the long integration time, tropospheric status changes with time and space, which will result in image shifts and defocusing. According to the characteristics of GEO SAR, the modeling, and quantitative analysis of background troposphere and turbulence are conducted. For background troposphere, the accurate GEO SAR signal spectrum, which takes into account the time-varying troposphere, is deduced. The influences of different rates of changing (ROC) of troposphere with time are analyzed. Finally, results are verified using the refractive index profile data from Fengyun (FY) 3C satellite and the tropospheric zenith delays data from international GNSS service (IGS). The time-space changes of troposphere can cause image shifts which only depend on the satellite beam-foot velocity and the linear ROC of troposphere. The image defocusing is related to the wavelength, resolution requirement, and the second and higher orders of ROC. The short-wavelength GEO SAR systems are more susceptible to impacts, while L-band GEO SAR will be affected when the integration time becomes longer. Tropospheric turbulence will cause the amplitude and phase random fluctuations resulting in image defocusing. However, in the natural environment, radio waves are very weakly affected by turbulence, and the medium-inclined GEO SAR of L- to C-band will not be affected, while the Xband will be influenced slightly.@en