基于高分辨率Radon变换的VSP波场分离方法

VSP wavefield separation based on highresolution Radon transformation

(中国石油大学(华东)地球资源与信息学院，山东东营257061)

College of Georesources and Information, China University of Petroleum (East China), Dongying 257061, China

讨论了时间域线性Radon变换、频率域最小平方Radon变换和频率域高分辨率Radon变换等方法的基本原理。Radon变换在频率域通常采用最小平方反演的方式来实现，但由于最小平方法对于不同的p值(视慢度)范围采用相同的阻尼因子，得到的解不够精确。高分辨率Radon变换对这一缺陷进行了改进，即通过对不同的p值范围采用不同的加权值来提高解的稀疏性和精确性。具体方法是：在反演迭代过程中，根据前一次迭代的结果，通过Bayes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。设计了一个3层水平地层的地质模型，利用高分辨率Radon变换进行了VSP波场分离。τ-p域的结果表明，能量得到了很好的收敛。在分离出来的上、下行波波场记录上，波形恢复得很好，上、下行波波场的相互干扰被完全消除。

Principles of Radon transformation methods, including linear Radon transform in time domain, least square Radon transformation and highresolution Radon transformation in frequency domain are discussed. Radon transformation in frequency domain is usually implemented by least square inversion. However, for different values of p (slowness), the least square uses the same dummy factor, making the solution inaccurate. Highresolution Radon transformation can improve the deficiency. Different weights varied with the range of p values are used to enhance the accuracy and sparseness of the solution. 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. A three-layer acline geological model was designed so as to carry out the VSP wavefield separation by using high-resolution Radon transformation. The results in τ-p domain show that the energy can be converged well. In the separated up and down wave field record, the waveform is well recovered, with the interference being completely eliminated.