基于ISTA算法的稀疏约束反演谱分解及应用

常规谱分解的分辨率难以满足地震解释的需求,稀疏约束反演谱分解可以很好地解决该问题。稀疏约束反演谱分解是把地震信号看成已知的子波矩阵库和伪反射系数的褶积,从而将谱分解问题转化为一个反问题来求解,其核心内容是如何快速获得最优解。采用L₁范数正则化的L₂范数作为稀疏约束反演谱分解的目标函数,并通过迭代阈值算法求解稀疏反问题。为了进一步提高计算速度,基于Ricker子波构建一种新的算子,并用ISTA算法进行计算。在此基础上,将稀疏约束反演谱分解用于模拟信号的数值试验,并与常规谱分解结果进行比较。结果表明,稀疏约束反演谱分解具有更好的时频聚集性和更高的时频分辨率;进一步应用于济阳坳陷沾化凹陷渤南洼陷义176井区地震资料,处理结果对油气响应十分敏感,可以较好地识别油气储集层。

Decomposition and Application of Constrained Sparse Inversion Spectrum Based on ISTA Algorithm

The resolution of conventional spectral decomposition can’t meet the needs of seismic interpretation, which can be well solved by the spectral decomposition of constrained sparse inversion. In this method, seismic signal is regarded as the convolution of known wavelet matrix library and pseudo-reflection coefficient, then the spectral decomposition is transformed into an inverse problem which focuses on how to obtain an optimum solution. The L₂ norm regularized by L₁ norm is used as the objective function for the constrained sparse inversion spectrum decomposition, then the iterative threshold algorithm is used to obtain the solution of the inverse problem. In order to improve the calculation speed of spectral decomposition, a new kind of operator is established on the basis of Ricker wavelet and the optimal solution can be obtained by ISTA algorithm. Based on which, the spectral decomposition of constrained sparse inversion is applied into numerical modeling and the results are compared with those of conventional spectral decomposition. The results show that the spectral decomposition of constrained sparse inversion has high time-frequency resolution. The actual application of the algorithm in the Wellblock Yi176 of Bonan sag in Jiyang depression indicates that the processing result is sensitive to oil and gas, which can be used to identify oil and gas reservoirs.