Abstract: Deep learning has gained significant prominence across various fields due to its ability to learn complex statistical relationships between input and target data. In geophysics, problems associated with the application of deep learning can be categorized into two classes: data-driven and physics-oriented problems. This thesis addresses two challenges using deep learning spanning the two categories. The first problem is equalizing time-lapse (TL) seismic data as an example of the data-driven application. The second challenge is related to full waveform inversion (FWI) in recovering salt models, which involves the physics of wave propagation. Ideally, the surveys in TL data should be identical such that their differences only correspond to the changes in the reservoir. However, many factors affect the repeatability of the surveys, leading to data differences from the non-reservoir regions. This thesis develops a deep learning-based processing for TL seismic. Neural networks are adopted to replace the standard matching filters to equalize the monitor surveys with its reference (base) survey. Various architectures were proposed, including recurrent neural network, convolutional autoencoder, and temporal convolutional network. The level of equalization accuracy achieved by the deep learning approach is on par with that attained by the standard matching filter. The industry approach to imaging the salt bodies involves significant manual interpretation, which is time-consuming and subject to the interpreter’s skills. Even the more advanced state-of-the-art full-waveform inversion (FWI) has limitations with salt models. It requires a good initial model with some prior salt knowledge, an advanced acquisition with long offsets, and low frequencies. All this amounts to a high cost required to properly address the salt body in seismic exploration. This thesis addresses these limitations of FWI by utilizing deep learning tools to inject statistical salt information in the inversion algorithm, considering also the case when we have poor data acquisition and the absence of low frequencies. Specifically, a deep learning-based unflooding algorithm is developed to detect the salt base and approximate the subsalt velocity, resulting in improved subsalt inversion. The approach is then extended to construct the entire salt body using a multi-scale FWI in a multi-stage flooding-unflooding scheme. Remarkably, this workflow can delineate the salt body even in the absence of long offsets and low frequencies. Furthermore, I investigate the uncertainty in FWI with salt models, which is rarely explored due to the high dimensional nature of the problem. In particular, I apply the Stein variational gradient descent (SVGD) as an efficient Bayesian inference method for high-dimensional problems. SVGD demonstrates its ability to assess the uncertainty in inverting the salt bodies in a manner aligned with the physics of wave propagation.