• diffusion model
• first arrival traveltimes
• Kirchhoff migration
• most energetic traveltimes
• NST
• seismic imaging
• U-Net

There is an extensive body of literature demonstrating that Prestack Kirchhoff Depth Migration (PSDM) using first-arrival traveltimes often produces suboptimal migrated images in regions with complex geology, which refers to areas with significant variations in the propagation velocity of seismic waves. To address this limitation, researchers since the 1990s have explored the use of the most energetic traveltimes for Kirchhoff migration instead of relying solely on the first arrivals. It has been shown that this approach yields more accurate and reliable subsalt images and offset image gathers. However, the primary drawback is the significant increase in computation time, as calculating the most energetic arrivals often requires solving the wave equation, which is more computationally intensive than the eikonal equation used for first arrivals.

Focusing on the 2D acoustic case, this study aims to reduce the computational burden of generating max-energy arrival times by leveraging machine learning techniques. Specifically, U-Net-like architectures were employed in a supervised learning framework to predict the most energetic traveltimes, using velocity models and first-arrival traveltimes as inputs. The choice of U-Net is motivated by its robustness and versatility across various applications. Additionally, diffusion models were applied to the U-Net outputs to further enhance the quality of the migrated images.

To validate the proposed approach, the Marmousi velocity model was migrated using the predicted traveltimes. The resulting migrated images were compared against those obtained using traditional Kirchhoff migration with first-arrival and most energetic arrival traveltimes. This thesis demonstrates that the U-Net-based approach substantially improves computational efficiency, reducing processing time by approximately two orders of magnitude. However, in particularly complex geological scenarios, the resolution of the U-Net outputs is sometimes lower than desired. Applying diffusion models improved image quality, but at the cost of increased computational time.