三维地震数据离散光滑插值的共轭梯度法

针对三维地震数据插值,提出采用Laplacian算子进行光滑约束的插值方法,并借鉴Mallet研究的离散光滑插值思路,采用预条件共轭梯度法,直接生成网格节点上的值,从而回避寻求满足插值方程的函数. 为了实现其中Laplacian算子的快速求逆,文中引入Claerbout螺旋坐标系谱因式分解理论. 在螺旋坐标系下,Laplacian算子的表示矩阵具有Toeplitz结构,其快速求逆可由谱法LU分解实现. 基于二维离散光滑插值,文中还给出共轭梯度法与NMO相结合的沿时间切片逐层处理的离散光滑插值流程. 最后,应用该方法对模型数据和实际三维地震数据进行了处理.

3-D SEISMIC DATA DISCRETE SMOOTH INTERPOLATION USING CONJUGATE GRADIENT

An interpolation method is presented in this paper for interpolation of three dimensional seismic data by means of Laplacian algorithm of smooth restriction. Considering the idea of discrete smooth interpolation (DSI) studied by Mallet, we use precondition conjugate gradient method to compute the grid values directly and avoid finding the function fitting interpolating equation. In order to compute the converse of Laplacian algorithm rapidly, the theory of helical spectral factorization method is applied. In the helical coordinates, the matrix of Laplacian algorithm has the Topelitz structure, and its rapid converse can be got using spectral factorization. Based on the two dimensional DSI, one flow is presented in this paper to do DSI along the time slice by use of conjugate gradient method combined with NMO. The good results were achieved after the processing of model data and real three dimensional data using this method.