High-precision and high-efficiency first-arrival slope tomography via eikonal solvers and the adjoint-state method

First-arrival slope tomography (FAST) introduces first-arrival slopes, corresponding to the horizontal components of the slowness vectors at the receiver and source positions to supplement first-arrival traveltime for better guiding ray propagation in the media until the best match is achieved with the observed data. FAST can recover the velocity model with higher resolution and precision than first-arrival traveltime tomography (FATT) but is computationally intensive. In this context, we propose an improved approach, referred to as high-precision and high-efficiency first-arrival slope tomography (HFAST). HFAST redefines one of the slopes using the reciprocity principle and simultaneously employs the first-arrival traveltime and slopes to ensure high-quality model building. On the other hand, HFAST extracts calculated data and derives the gradient of the misfit function from the solutions of relatively limited forward and inverse problems, resulting in a low computational cost. The cost of HFAST is proportional to the minimum between the receivers and sources, whereas the cost of FAST is scaled to the sum of the receivers and sources. Numerical experiments involving the checkerboard and SEAM II Foothill models demonstrate that HFAST can achieve a higher inversion precision than FATT, especially in the recovery of small-scale anomalies and the presence of velocity reversal. Moreover, HFAST is more computationally efficient than FAST and suitable for managing large data sets. Therefore, HFAST can be regarded as a valuable supplement to current first-arrival-based model building methods and has the potential to be applied in static corrections, prestack depth migration and waveform inversion in the future.