Directional Interpolation of velocity model based on Partial Differential Equations used in ray tracing
HAN Fu-Xing, SUN Jian-Guo, Wang Kun
1. Theory of Ministry for Land and Resources, College for Geoexploration Science Technology, Jilin University, Changchun, 130026, china.
2. Jilin Communications Polytechnic, Jilin Changchun 130012, china.
Abstract：
The interpolation of velocity and velocity derivative at non-grid nodes of velocity model is an important part of ray type migration imaging, it affects the efficiency and accuracy of ray tracing, and affects the quality and efficiency of the whole migration imaging. In this paper, according to the characteristics of the velocity model and considering the gradient effect of the velocity at the interpolated point, that is based on the minimum velocity gradient of the interpolated points along the x-direction and the z-direction of velocity model, the directional interpolation algorithm based on partial differential equation developed in digital image processing in recent years is introduced into ray type migration imaging, to achieve the velocity and velocity derivative interpolation problem of non-grid nodes. In view of the partial differential equation method have linear superposition characteristic, uniqueness of the model solution, the local features of retention, therefore, using the PDE interpolation algorithm can be achieved the velocity and velcity derivative interpolation problem of non-grid nodes based on the spatial structure of the original velocity mode. Through interpolation of Marmousi and Sigsbee velocity model, comparative analysis of ray paths, interpolation results and migration imaging results of rough and steep slope rugged seabed velocity model, it can be concluded that the application of partial differential equation interpolation to velocity model can better maintain the edge characteristics of velocity model and improve the quality of migration imaging.
. Directional Interpolation of velocity model based on Partial Differential Equations used in ray tracing[J]. APPLIED GEOPHYSICS, 2018, 15(3-4（2）): 600-612.
2018, Vol. 15 
