CAJ | 학술논문

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.
이이계통계학방법위기출,종Canadas등제출적비최소상위자파화비백조반사계수지진맹반습적광가출발,급출료Cauchy희소약속Bayesian고계지진맹반습적광가.기우반사계수여자파상호독립(혹약상관)적가설,분별구건료반사계수화자파최우고계방정,병채용예조건공액제도법질대반연실현반사계수화자파적동시고계.재방법구체실현시,이전통맥충반습적결과작위질대초치,통과질대득도반사계수화임의상위자파;연후재대자파진행최소상위화,통과반연득도반자파;최후장반자파여지진도습적,득도반습적결과.이용이론모형화실제수거대산법진행료시산,결과표명,급출적지진맹반습적이론광가시정학적;여직접(공액제도구해정칙방정)희소동시질대반연법적대비현시,예조건공액제도산법은정,정도고,수렴쾌.
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.