A numerical study of the effects of seismically generated acoustic waves in the ionosphere is conducted using a three-dimensional (3-D) ionospheric model driven by an axisymmetric neutral atmospheric model. A source consistent with the 2011 Tohoku earthquake initial ocean surface uplifting is applied to simulate the subsequent responses. Perturbations in electron density, ion drift, total electron content (TEC), and ground-level magnetic fields are examined. Results reveal strong latitude and longitude dependence of ionospheric TEC, and of ground-level magnetic field perturbations associated with acoustic wave-driven ionospheric dynamo currents. Results also demonstrate that prior two-dimensional models can capture dominant meridional responses of TEC over latitude, even though dynamics at other longitudes are not resolved. Conclusions support that TEC and magnetic signatures can arise from nonlinear acoustic waves generated by strong earthquakes; simulations elucidate the comprehensive physics of their 3-D ionospheric responses.