Application of Snell's law in reflection raytracing using the multistage fast marching method

Accurate calculations of travel times and raypaths of reflection waves are important for reflection travel time tomography. The multistage shortest path method (MSPM) and multistage fast marching method (MFMM) have been widely used in reflection wave raytracing, and both of them are characterized by high efficiency and accuracy. However, the MSPM does not strictly follow Snell's law at the interface because it treats the interface point as a sub-source, resulting in a decrease in accuracy. The MFMM achieves high accuracy by solving the Eikonal equation in local triangular mesh. However, the implementation process is complex. Here we propose a new method which uses linear interpolation to compute the incident travel time of interface points and then using Snell's law to compute the reflection travel time of grid points just above the interface. Our new method is much simpler than the MFMM; furthermore, numerical simulations show that the accuracy of the MFMM and our new method are basically the same, thus the reflection tomography algorithms which use our new method are easier to implement without decreasing accuracy. Besides, our new method can be extended easily to other grid-based raytracing methods.