Extensions for the Reversibility of First-Arrival Travel Times Investigated Using PINNs

ABSTRACT In this study, the forward and reverse propagation of first-arrival travel times is investigated for homogeneous and heterogeneous media. After the formation of caustics, the information in the first-arrival wavefronts becomes increasingly incomplete as the wavefronts fold back on themselves, resulting in a loss of reversibility in the first arrivals. This is investigated using physics-informed neural networks that, once trained, offer advantages in speed and flexibility in comparison to direct numerical solvers. If slope discontinuities can be identified in the first-arrival wavefronts and the corresponding caustics positions found, then a combined solution with the reversed wavefront and the contributions from the caustics can be used to obtain an improved reversibility of the results, while still using just first-arrival wavefront tracking. This assumes that the propagation distance is not too great and that the effects of the caustics are not overlapping. Several tests are performed using forward and reverse propagation of first-arrival wavefronts for curved initial wavefronts in homogeneous and inhomogeneous media. An example is then given using first-arrival travel times from a small, curved fault and recorded by a geophone array. By combining the reversed wavefront with contributions from caustics as identified by the slope discontinuities along the first-arrival wavefront, better reversibility can be found and an improved reconstruction of the fault obtained.