A Case Study of 2-D Seismic Refraction Tomography and Regularization Effects, using the Tikhonov Approach Applied to Shallow Marine Environment

A common approach to stabilize the ill-posed inverse problem is to apply regularization, which restricts the possible solutions to these problems. Thus, a regularization term is often incorporated into the tomographic objective function to resolve the non-uniqueness of the inverse geophysical problem, restricting the possible solutions to these problems. This work evaluates the effects of regularization and analyzes its impact on the resulting seismic velocities. Grounded in a detailed case study, we investigate Tikhonov's regularization of order 1 and its variants, including order 2, utilizing a tomography program that employs ray tracing, a finite differences scheme with the eikonal equation for first arrivals, and the regularization algorithm. The velocity model is synthetic and based on shallow seabed channel geology. The true model was compared with the tomography results without regularization and with regularization schemes. The results clearly indicate that regularization parameters play a critical role in defining the outcomes of velocity models in tomography inversion. By applying regularization, we significantly reduce structural distortion in tomographic results — this approach proves to be not only effective but essential. Tikhonov’s regularization of order 2 consistently demonstrates faster convergence and notable improvements in the velocity model. Furthermore, our parameter sensitivity tests reveal the extent to which an inappropriate choice can distort geological structures, such as by creating artificial structural highs or lows, underscoring the necessity of careful selection in regularization techniques.