Topography-dependent first-arrival traveltime and slope tomography: method and application

SUMMARY Compared to first-arrival traveltime tomography (FATT), first-arrival traveltime and slope tomography (FASTT) integrates both traveltimes and local slopes of first arrivals at sources and/or receivers to construct more accurate subsurface velocity models. Local slopes serve as additional constraints, helping to mitigate the ill-posedness of tomography by better constraining ray directions. This is particularly beneficial in regions with complex topography, where shadow zones arise due to strong velocity contrasts. However, representing complex topography or bathymetry can be less accurate when using classical rectangular grid discretization. To address these complexities with greater versatility and accuracy, we compute traveltimes of locally coherent events using a factored topography-dependent eikonal solver on curvilinear grids. Slopes are then estimated by finite differences in the traveltime maps after a back-and-forth coordinate transform from the curvilinear grid to a rectangular computational grid. Additionally, we solve the inverse problem with the matrix-free approach, where the data misfit gradient is computed with the adjoint-state method. This adjoint-state formulation avoids the explicit construction and storage of large Fréchet derivative matrices and does not require a tedious posterior ray tracing on curvilinear grids. A land synthetic example first illustrates the sensitivity of slopes to topography and the more accurate velocity models with FASTT than with FATT in the presence of topography. We then perform a first application of the topography-dependent FASTT method on a real redatumed ocean-bottom node data set, where the bathymetry exhibits a steep scarp. We show that the topography-dependent FASTT generates a velocity model that matches more closely a legacy reflection tomography model than conventional FATT. We conclude that the topography-dependent FASTT provides a versatile approach for handling complex surfaces during velocity model building in both marine and land environments.