Recently, atmospheric perturbations residing over around epicenters of forthcoming earthquakes were remotely sensed by the multiple instruments of the MVP-LAI (Monitoring of Vibrations and Perturbations in Lithosphere, Atmosphere and Ionosphere) system. In this study, we found another way and proposed a theory for the evolution of the perturbations in the atmosphere from the aspect of numerical simulation. We started from the fundamental hydromechanics equations for the perturbations based on the atmospheric dynamics in the cylindrical symmetric coordinate to solve their analytical solution. The solution shows that a persistent vibration at the bottom of the cylindrical symmetric coordinate tends to decay exponentially with along altitude. In other words, a persistent ground vibration in a wide area can rapidly evolve into small-scale perturbations in the atmosphere. The preliminary theoretical model in this study shows the kernel concept for the coupling of geospheres.