The ever-expanding need for energy, including those related to fossil fuels, is behind the drive to explore more complicated regions, such as salt and subsalt provinces. This exploration quest relies heavily on recorded surface seismic data to provide precise and detailed subsurface properties. However, conventional seismic processing algorithms including the state-of-the-art full-waveform inversion (FWI) fail to recover those features in many areas of salt provinces. Even the industrial solution with substantial involvement of manual human-interpretation has faced challenges in many regions. In this thesis, I attempt to replace those manual, and somewhat erroneous, steps to the velocity building in salt provinces with a mathematically robust algorithm under the FWI machinery. I, specifically, regularize FWI by penalizing the velocity drops with depth with a new more flexible function. Although promising, FWI is computationally very expensive, especially for large 3D seismic data. It updates an initial guess of the model iteratively using the gradient of the misfit function, which requires lengthy computations and large memory space/disc storage. Based on the adjoint state method, gradient computation usually requires us to store the source wavefield, or include an additional extrapolation step to propagate the source wavefield from its temporary storage at the boundary. To mitigate this computational overburden, I propose an amplitude excitation gradient calculation based on representing the source wavefield history by a single, specifically the most energetic arrival. In this thesis, I also propose a novel-multiscale scheme based on ux-corrected transport (FCT) to reduce artifacts in the gradient direction due to the noise present in seismic data. FCT comprises of two finite difference schemes: a transport and a diffusion to compute the flux at a grid point. I observe a couple of benefits in FCT-based FWI. First, it yields a smooth gradient at the earlier iterations of FWI by promoting the lower frequency content of the seismic data. Second, it is easily compatible with the existing FWI code, and with any objective function. The multiscale strategy starts with a large smoothing parameter and relaxes it progressively to zero to achieve the final inverted model from traditional FWI.