3D ray tracing using a modified shortest-path method

We present an accurate 3D ray-tracing algorithm based on a modified (more flexible and economical) shortest-path method (SPM). Unlike the regular SPM in the 3D case, which uses only primary nodes at the corners of each cell and whose accuracy depends on actual cell size, the new method can work with much larger cell sizes by introducing secondary nodes along all bounding surfaces of the cell. This increases the ray angular coverage and permits detailed specification of the velocity field. The modified SPM simultaneously calculates first-arrival times and gradually locates the related raypaths on all grid nodes as the wave field evolves. Its advantages over the regular SPM are its ability to handle high-contrast velocity models more easily, lower memory requirements and less CPU time, and the capability to calculate a relatively large 3D model without losing accuracy. The maximum relative error bound in the computed traveltimes of the modified SPM is established for a uniform velocity field, which may be considered an upper error bound for the whole model in real problems. The modified method in this study is compared with the regular SPM theoretically and on two specific velocity models. The Marmousi model is used to further test the performance of the new approach for both accuracy and flexibility in a complex velocity field. The study shows that the modified SPM is preferable to regular SPM for real 3D problems.