压制截断效应的Radon变换在波场分离中的应用

由于离散运算,Radon变换方法中存在截断效应,传统的最小二乘约束反演并不能有效抑制这种效应。介绍了一种频域空间稀疏约束算法,在反演迭代过程中,根据前一次迭代的结果,通过贝叶斯原理将加权矩阵与前一次迭代的结果联系起来,得到新的加权矩阵;然后求解这个加权矩阵方程,得到频率域的稀疏解。比较了用最小二乘反演和压制截断效应的Radon域变换的效果,后者效果明显优于前者。模拟了一个5层的水平地层的地质模型,用这种压制截断效应的Radon变换进行了VSP资料的上下行波场的分离,得到了较好的效果。

Wave Filed Decomposition Via Eliminating Truncation Artifacts of Radon Transform

A commonly used discrete form of the Radon transform integral formula results truncation artifacts.Traditional method of Least-squares inversion is not effective eliminating truncation artifacts.This paper presents frequency-domain sparseness constraint algorithm.In the inversion iterations,according to the previous solution,the weighted matrix is linked to the result of previous iteration by Bayes rule,resulting in a new weighted matrix.Then the sparse solution in frequency domain can be obtained through computing the weighted matrix equation.Comparing Least-squares inversion and eliminating truncation artifacts Radon transform,the resolution of the latter is obviously better than the former.A five-layer acline geological model was designed so as to carry out the VSP wave field decomposition by using eliminating truncation artifacts Radon transform.This method can be satisfying results.