Solving the eikonal equation for compressional and shear waves in anisotropic media using peridynamic differential operator

The traveltime of compressional (P) and shear (S) waves have proven essential in many applications earthquake exploration seismology. An accurate efficient computation for P S is crucial the success these applications. However, solutions to Eikonal equation with a complex phase velocity field anisotropic media challenging. first-order, hyperbolic, nonlinear partial differential (PDE) that represents high-frequency asymptotic approximation wave equation. fast marching sweeping methods are commonly used due their efficiency numercally solving suffer from numerical inaccuracy sharp heterogeneity, irregular surface topography fields. This study presents new method by employing peridynamic operator (PDDO). PDDO provides nonlocal form introducing an internal length parameter (horizon) weight function directional nonlocality. immune discontinuities changes or model variables invokes direction consistent manner. controls degree association among points within horizon. Solutions constructed manner without upwind assumptions through simple discretization. capability this approach demonstrated considering different types equations on models media. examples demonstrate its unconditional stability results compare well reference solutions.