TomoATT: A Software Package of Adjoint-State Traveltime Tomography for Imaging Subsurface Velocity Heterogeneity and Seismic Anisotropy.

Adjoint-state traveltime tomography (ATT) is a new modality of traveltime tomography for determining subsurface velocity heterogeneity and seismic anisotropy. It formulates the tomographic inverse problem as an eikonal equation-constrained optimization problem solved by the ray-free adjoint-state method. Instead of using the ray-based methods, the theoretical traveltime is predicted by solving the anisotropic eikonal equation in spherical coordinates using the robust grid-based fast sweeping method. The influences of the seismic anisotropy and the Earth’s curvature are taken into account. Besides, the Fréchet derivatives of the objective function with respect to velocity and anisotropy are computed based on the adjoint field obtained by solving the adjoint equation without ray tracing. These two improvements ensure the accuracy of the forward modeling and avoid the potential failure of ray tracing techniques. Meanwhile, compared with wave-equation-based tomography methods, the computational cost of solving eikonal and adjoint equations is drastically cheaper. The usage of the reciprocity principle makes the computation cost nearly independent of the number of earthquakes, enabling the inversion involving massive earthquakes but with moderate computational cost. Due to these advantages, we develop the TomoATT package based on the ATT method, accommodating the tomographic problems on local, regional, and global scales. To be used on high performance computing systems, TomoATT implements a multilevel hybrid parallel algorithm, which utilizes MPI for inter-node parallelization and MPI Shared Memory for intra-node parallelization. The performance on single CPU is also improved using the Single Instruction Multiple Data (SIMD) instructions. This traveltime tomography package has been tested and verified in central California near Parkfield.