Perturbations caused by geophysical and anthropogenic events on the ground have been observed to propagate upward and impact the upper atmosphere. Gravity waves with wavelengths less than 750 km are known to be responsible for the total electron content (TEC) perturbations and to play a significant role in the mass, momentum, and energy budgets of the mesosphere and lower thermosphere. These waves are, however, difficult to continuously measure, globally resolve, and deterministically specify in first-principle ionosphere-thermosphere (IT) models. In this study, we investigate IT response to induced acoustic-gravity waves resulting from strong time-varying lower atmospheric wave forcing, including a traveling wave packet (TWP) and stochastic gravity wave (SGW) fields using the nonlinear Global Ionosphere Thermosphere Model (GITM) with high-resolution grids of 0.08° in longitude and latitude. When TWP and SGW forcing occurs concurrently, the induced gravity waves (GWs) cause variation of ±8.8% in neutral, ±6.2% in electron density, and ±1.5% in TEC. The magnitudes decrease by 2.4% (from ±8.8% to ±6.4%) with the SGW effects simulated separately and subtracted; importantly, interactions between TWP and SGW contribute to ±1.4% of the perturbations. On the other hand, the induced acoustic waves (AWs) cause variation of ±13.9% in neutral, ±2.1% in electron density, and ±0.4% in TEC. Furthermore, GWs sustain tens of minutes after the TWP has passed through the lower atmosphere and clear traveling ionospheric disturbances and traveling atmospheric disturbances are developed. We demonstrate that clear wave structures from an episodic event can be isolated even under a ubiquitously and overwhelmingly perturbed atmosphere.