Angle Domain Common-Image Gathers (ADCIGs) are crucial for seismic amplitude-versus-angle analysis, facilitating the prediction of lithology, fluid properties. ADCIGs, which represent angle-dependent reflectivities, are challenging to compute accurately due to the high accuracy requirements of migration and inversion algorithms. This thesis focuses on developing an new algorithm to integrate the modeling, migration, and inversion of ADCIGs. The modeling of ADCIGs is based on acoustic and elastic wave equations, and the results are compared with the exact Zoeppritz equations to validate the accuracy of the modeling process. The migration of ADCIGs is based on reflection angle extraction methods in Reverse Time Migration (RTM) fullfilling the requirement of the true amplitude migration. The inversion of ADCIGs predicts both velocity and angle-dependent reflectivity based on Full Waveform Inversion (FWI). Advances in high-performance computing and FWI algorithms have significantly improved the generation of accurate velocity models and other parameters across diverse geological settings. However, the FWI sensitivity kernel in acoustic variable-density media differs by parameterization method, and the time-domain gradient equation in velocity-density media has multiple arguments. I tested several velocity-density gradient equations in time-domain full waveform inversion (FWI) for acoustic variable-density media. Additionally, I derived a new FWI sensitivity kernel based on scattering theory, and proposed an iterative non-linear inversion method to predict both velocity and amplitude-preserved reflectivity. This method combines angle domain RTM migration with FWI. The iterative inversion method is based on time-domain FWI using the nonlinear conjugate-gradient method. The results demonstrate that the new FWI sensitivity kernel has higher resolution in certain high-dip structures compared to previously published methods, and the angle domain FWI can predict ADCIGs in shallow zones with high accuracy.