High-order accurate adjoint-state methods for three-dimensional high-resolution first-arrival traveltime tomography

The original first-order accurate adjoint-state method for first-arrival traveltime tomography (Leung and Qian (2006) [12]) is based on first-order eikonal solvers and first-order adjoint-state solvers so that the resulting algorithm provides only low-resolution images. Therefore, to produce high-resolution images in first-arrival traveltime tomography, we propose a novel high-order accurate adjoint-state method which consists of three crucial ingredients: a high-order point-source eikonal solver to compute accurate traveltimes, a novel advection equation to uniformly back-propagate traveltime residuals, and a high-order adjoint-state solver to compute accurate adjoint states. 2-D and 3-D numerical results demonstrate that the new algorithm is able to produce high-resolution images in the setting of first-arrival transmission traveltime tomography.