Static-constrained first-arrival traveltime tomography for near-surface velocity estimation

Seismic data processing and interpretation encounter the challenges of near-surface static problems. Long-wavelength statics can be calculated using the near-surface velocity model. While being efficient for deriving the near-surface velocity model, the first-arrival traveltime tomography (FTT) may not be sufficiently precise due to ray assumptions and limited traveltime information. The static-optimized traveltime tomography (SOTT) method has been developed to derive near-surface velocities with more accurate long-wavelength statics. However, this method does not account for short-wavelength static effects, potentially introducing artifacts into the derived velocity model. To address these limitations, we propose a novel static-constrained first-arrival traveltime tomography (SFTT) method that simultaneously incorporates both long- and short-wavelength statics. Our method introduces a static-constrained term in the objective function by minimizing variances of static-processed traveltimes in common-offset sections. This constrained inversion framework fits the traveltime data and ensures the accuracy of the static solutions simultaneously. We demonstrate the effectiveness of the new method by comparing it with conventional traveltime tomography and static-optimized traveltime tomography in both synthetic and field data examples. The application results show that the static-constrained traveltime tomography has high reconstruction accuracy, especially for the high-velocity objects in the weathering layers, which are challenging to estimate by the conventional traveltime tomography. Furthermore, the static-constrained traveltime tomography mitigates the artifacts in the velocity model estimated from static-optimized traveltime tomography and achieves higher accuracy in both velocity reconstructions and static calculations compared with the other two methods.