基于最大特征值估计的C3算法及应用

A fast algorithm to estimate the dominant eigenvalue of Real Symmetric Matrices and its application to C3 algorithm

第三代相干体算法(C3算法)具有分辨率高、压制噪声能力强的优点,但是该算法需要计算协方差矩阵的特征值,所以耗时较多。为提高大矩阵特征值分解的运算速度,提出了一种估计最大特征值的快速收敛算法,通过运用A2k矩阵的迹来构造一种收敛速度更快的特征值估计方法,并给出了这种方法的误差估计表达式,实现计算精度的有效控制。文中还讨论了地震数据体边缘补地震道方法,解决了将递推算法应用到平面方向时空间窗越过边界的问题。实例表明,本算法的计算效率明显高于常规的C3算法。

The third-generation coherence algorithm, C3,is robust to suppress noise and posseses high resolution. However, the process of computing eigenvalues of the covariance matrix in C3 is time-consuming.To avoid computing all eigenvalues, this paper proposes a fast convergence algorithm based an eigenvalue estimation of real symmetric matrices to calculate the dominant eigenvalue.To control the precision of the algorithm, this paper presents an error evaluation formula.By adding traces along the boundary of the seismic data volume,we avoid judging whether the spatial window oversteps the boundary when recursion strategy is applied in a horizontal direction. The application to real data shows that the efficiency of C3 is improved by approxinately 3 times.