The major drivers of the ionospheric variations are solar inputs and seasonal changes in the thermosphere. The solar radio flux on 10.7 cm wavelength (F10.7) is widely used as a proxy of solar EUV irradiance that ionizes the neutral atmosphere. However, F10.7 is not a perfect proxy of EUV. Variability of the 10.7 cm flux is mostly due to coronal activities, while EUV originates in various solar atmospheric regions. We used multiple indices to model the solar influences on the ionospheric total electron content (TEC) variations; Mg II c-w-r as a proxy of lower chromospheric activity, SOHO_SEM measurements at 26-34 nm as a proxy of upper chromospheric and transition region activity, and F10.7 as a proxy of transition region to coronal activity. Further, in order to take account of delayed evolutions of activities of active regions related to different proxies, mean values over several preceding periods were used along with the daily values. To deal with multiple solar parameters (9 in total), a seasonal parameter, and ∑Kp representing geomagnetic activities, an artificial neural network (ANN) was used to model the solar, seasonal, and geomagnetic influences. The training of the ANN was conducted for the TEC database covering one solar cycle from 1997 to 2008. The difference (ΔTEC) between the predicted TEC by the trained ANN and the measured TEC is considered to give a time series of TEC variations without solar and seasonal influences, which are most probably driven by the lower atmosphere. A wavelet analysis was applied to the time series of ΔTEC. Strong bursty wave activities with periods of approximately 13 and 27 days were recognized, which are not directly influenced by the solar activity modulations.