Smoothness: The key factor in well-log information-assisted PINNtomo

Seismic traveltime tomography is popularly used to provide a smooth background model for subsequent depth migration or full waveform inversion (FWI). The core of the traveltime tomography process requires an eikonal solver for seismic traveltime calculation. Most of the conventional eikonal solvers, suffer from first-order convergence errors and difficulties in dealing with irregular topography, which will lead to inaccurate seismic tomography results. To solve these issues, physics-informed neural networks (PINNs) have been developed and demonstrated remarkable success in simultaneous traveltime calculation and velocity construction, which is referred to as PINNtomo. It combines the physics constraint (eikonal equation) and data constraint (traveltime fitting) to form the loss function of the networks. Though PINNtomo can manage to recover a smooth background velocity, it will fail in the inversion for a complicated high-resolution velocity model. We take advantage of the well-log velocity as a prior information to provide an additional model constraint in the loss function to improve the performance of PINNtomo. We found that the well-log information will provide high-resolution components in the inverted velocity model. However, it will destroy the lateral structure of the true model. We propose to use a smoothed version of the well-log velocity as the prior model constraint in PINNtomo. As a result, the accuracy of the inverted background velocity will be improved, which will be beneficial to the subsequent FWI.