Global Positioning System (GPS) allows the detection of ionospheric disturbances associated with the vertical displacements of most of the major shallow seismic events. We describe a method to model the time and space distributions of Rayleigh wave induced total electron content (TEC) patterns detected by a dense GPS array. We highlight the conditions for which a part of the ionospheric pattern can be directly measured, at teleseismic distance and above the epicenter. In particular, a satellite elevation angle lower than 40 degrees is a favorable condition to detect Rayleigh wave induced ionospheric waves. The coupling between the solid Earth and its atmosphere is modeled by computing the normal modes of the solid Earth-atmosphere system. We show the dependency of the coupling efficiency on various atmospheric conditions. By summation of the normal modes we model the atmospheric perturbation triggered by a given earthquake. This shows that a part of the observation is a Rayleigh-induced radiation pattern and therefore characteristic of the seismic rupture. Through atmosphere-ionosphere coupling, we model the ionospheric perturbation. After the description of the local geomagnetic field anisotropic effects, we show how the observation geometry is strongly affecting the radiation pattern. This study deals with the related data for two earthquakes with far-field and near-field observations using the Japanese GPS network GEONET: after the 12 May 2008 Wenchuan earthquake (China) and after the 25 September 2003 Tokachi-Oki earthquake (Japan), respectively. Waveforms and patterns are compared with the observed TEC perturbations, providing a new step toward the use of ionospheric data in seismological applications.