Cauchy稀疏约束Bayesian估计地震盲反褶积框架与算法研究

以二阶统计学方法为基础，从Canadas等提出的非最小相位子波和非白噪反射系数地震盲反褶积框架出发，给出了Cauchy稀疏约束Bayesian估计地震盲反褶积框架。基于反射系数与子波相互独立（或弱相关）的假设，分别构建了反射系数和子波最优估计方程，并采用预条件共轭梯度法迭代反演实现反射系数和子波的同时估计。在方法具体实现时，以传统脉冲反褶积结果作为迭代初值，通过迭代得到反射系数和任意相位子波；然后再对子波进行最小相位化，通过反演得到反子波；最后将反子波与地震道褶积，得到反褶积结果。利用理论模型和实际数据对算法进行了试算，结果表明，给出的地震盲反褶积理论框架是正确的；与直接（共轭梯度求解正则方程）稀疏同时迭代反演法的对比显示，预条件共轭梯度算法稳定，精度高，收敛快。

Based on second order statistics,starting from the seismic blind deconvolution frame proposed by Canadas for non-minimum phase wavelet and non-white reflectivity,the Cauchy sparseness constrained Bayesian estimation based seismic blind deconvolution frame was proposed.Assuming the independence (or the weak-correlation) between the reflectivity and wavelet,the optimal estimation equations for the wavelet and reflectivity were derived respectively.Furthermore,pre-conditional conjugate gradient algorithm iteration inversion was applied to realize the simultaneous estimation of reflectivity and wavelet.During the procedures,taking traditional impulse devonvolution result as initials for iteration inversion,the reflectivity and wavelet with arbitrary phase was obtained from iteration.Then,the minimum phase of wavelet was achieved,and reversed wavelet was obtained by inversion.Finally,reversed wavelet was carried out convolution with seismic traces to get deconvolution results.Theoretical model and real 2-D seismic data were applied to test the algorithm.The results show that the proposed deconvolution theoretical frame is correct.Compared the above method to direct sparse simultaneous iteration inversion (solving canonical equation by conjugate gradient),the results indicate that pre-conditional conjugate gradient algorithm is stable,with high accuracy and fast converging speed.