Ray tracing in discontinuous velocity model with implicit Interface

Ray tracing in the velocity model containing complex discontinuities is still facing many challenges. The main difficulty arises from the detection of the spatial relationship between the rays and the interfaces that are usually described in non-linear parametric forms. We propose a novel model representation method that can facilitate the implementation of classical shooting-ray methods. In the representation scheme, each interface is expressed as the zero contour of a signed distance field. A multi-copy strategy is adopted to describe the volumetric properties within blocks. The implicit description of the interface makes it easier to detect the ray-interface intersection. The direct calculation of the intersection point is converted into the problem of judging the signs of a ray segment's endpoints. More importantly, the normal to the interface at the intersection point can be easily acquired according to the signed distance field of the interface. The multiple storage of the velocity property in the proximity of the interface can provide accurate and unambiguous velocity information of the intersection point. Thus, the departing ray path can be determined easily and robustly. In addition, the new representation method can describe velocity models containing very complex geological structures, such as faults, salt domes, intrusions, and pinches, without any simplification. The examples on synthetic and real models validate the robustness and accuracy of the ray tracing based on the proposed model representation scheme.