Wavefront Construction Using a Two-dimensional Cubic Convolution Interpolation

Liu, Chuncheng (CNOOC Research Institute) | Han, Fuxing (Jilin University) | Sun, Zhangqing (Jilin University) | Sun, Jianguo (Jilin University)


Wavefront construction is a method used for fast seismic ray tracing. An essential process in the method is the interpolation of traveltimes from an irregular grid to a regular grid. Usually, this interpolation is realized by using bilinear interpolation. However, bilinear interpolation cannot give continuous derivatives across the grid element used for realizing interpolation. Therefore, it is not adequate for ray tracing in complex media with certain smoothness, because for computing rays traveltime derivatives should be continuous everywhere in the smoothed model. To have an interpolation scheme that meets the requirements for solving ray tracing system numerically, we introduce a two-dimensional cubic convolution interpolation. It is found that the two-dimensional cubic convolution interpolation is efficient and accurate in comparison to bilinear interpolation. Also, it is found that the difference between the ray families respectively computed by the two-dimensional cubic convolution interpolation and by bilinear interpolation is large when the velocity change in the model used is strong. This leads to the conclusion that for obtaining correct ray trajectories in the complex velocity model, an interpolation formula with a smoothness order higher than that of bilinear interpolation formula is necessary.