Improve numerical efficiency of three-dimensional seismic migration by compressing traveltime table

Traveltime data of seismic waves are indispensable for many seismic migration methods. Three-dimensional (3D) traveltime table is 3D scattered data, which has a large amount of data points. In process of 3D seismic migration, the enormous traveltime table file is frequently read, which significantly degrades the numerical efficiency. Research work has rarely been published to solve this problem by far. We propose a method to improve the calculation efficiency of 3D seismic migration by compressing the traveltime table: At first, we construct a least cuboidal region with regular grids in 3D space where all the traveltime data points are included. Then, the 3D cubic B-spline function is selected as a basal function to fit a curved surface body which covers all the 3D scattered traveltime data, and the values of the finite regular grids can be calculated using least square method, and then be stored into the memory. When the scattered traveltime data are needed by migration, they can be decompressed from the regular grids´ data by linear interpolation of 3D cubic B-spline function. Because of having sparse character, the least-square coefficient matrix is stored into the memory by Compressed Sparse Column method, which saves the memory greatly. Application to real seismic data shows the method can compress the traveltime table with compressing ratio more than 270 and local relative errors as little as 0.0002. Additionally, because of the enormous traveltime table file needn´t be read any more, the numerical efficiency of seismic migration can be enhanced by twice without any influence on the precision.