Recent studies have shown that upper atmospheric observations can be used to examine the properties of acoustic and gravity waves (AGWs) induced by natural hazards (NHs), including earthquakes and tsunamis (e.g., Komjathy et al., Radio Sci., 51, 2016). In addition to rapid processing, analysis, and retrieval of the AGW signals in data, the need remains to investigate a broad parameter space of atmospheric and ionospheric state observables for the robust constraint of coupled and nonlinear processes. Here, we present several earthquake/tsunami-atmosphere-ionosphere case studies that demonstrate the possibility to detect AGWs and constrain the characteristics of their sources. Direct numerical simulations of the triggering and wave dynamical processes, from Earth's interior to the exobase, are carried out based on coupled forward seismic wave and tsunami propagation models and our state-of-the-art nonlinear neutral atmosphere and ionosphere models MAGIC and GEMINI (Zettergren and Snively, JGR, 120, 2015).