Improving parsimonious refraction interferometry through U-Net-based correction of first-arrival traveltimes

Parsimonious refraction interferometry (PRI) is a useful technique for generating dense virtual traveltimes when the seismic survey is performed with sparse acquisition geometry. However, PRI has limitations in accurately calculating the traveltimes of direct and diving waves, leading to inaccurate velocity structures when applying first-arrival traveltime tomography (FATT). To address this issue, we develop an improved approach using a deep-learning network called U-Net. We first examine the feasibility of our algorithm analytically through the traveltime interpretation of a simple model. Then, the U-Net model is trained on various data sets to learn the relationship between PRI results and actual traveltimes. Subsequently, the trained network corrects the traveltime errors of the PRI results. As a result, we can obtain accurate first-arrival traveltimes using only two shot gathers without additional information such as infilled shots. Our technique enables virtual traveltime corrections, allowing for improved FATT results, even in cases for which dense shots are difficult to deploy. Numerical results demonstrate that our method can achieve accuracy comparable to picked traveltime data, indicating its high effectiveness in increasing the resolution of FATT results. Our approach maximizes the cost-saving benefits of PRI and can be advantageous in obtaining high-resolution FATT results when dense shot geometry is unavailable.