This research focuses on both developing computational tools to model transient wave propagation in coupled acoustic-viscoelastic-poroviscoelastic media and estimating material properties from the simulated/recorded full-waveform data. Numerical simulation of wave-dominated problems is computationally demanding. Efficient parallelization, capability to handle complex geometries, and sufficient numerical accuracy are some of the requirements for a suitable full-waveform simulation technique. On the other hand, robustness and prediction accuracy is needed from the method used to solve the corresponding inverse problem. Here, the discontinuous Galerkin method is used to solve the forward model while the convolutional neural networks is used to solve the estimation problem. The applicability of the studied computational tools is demonstrated by numerical examples.