A successive three-point perturbation method for fast ray tracing in complex 2D and 3D geological models

This paper presents new 2D and 3D ray-tracing methods that can be applied to traveltime and ray path computations for transmitted, reflected and turning seismic waves in complex geologic models. The new ray-tracing scheme combines segmentally iterative ray tracing (SIRT) and pseudo-bending methods to address both stratified and arbitrarily shaped block models. The new method robustly extends our previous constant block models and constant gradient block models to generally heterogeneous block models, and incorporates cubic splines or triangulated interfaces to boundaries of complex geological bodies. The method is thus more widely applicable to practical problems. A successive three-point perturbation scheme is formulated that iteratively updates the midpoints of a segment based on an initial ray path. The midpoints are corrected by applying first-order analytic formulae to locations of the midpoint inside the block or on the boundaries of the blocks, which are then updated with the pseudo-bending method and SIRT algorithm instead of the traditional iterative methods. Empirical applications, including an example addressing the Bohemian Massif, demonstrate that this successive three-point perturbation scheme successfully performs kinematic ray tracing in heterogeneous complex 2D and 3D media.