基于李代数积分的薄层多重散射消除技术

目前消除薄层多重散射的影响主要采取Q值补偿和Levinson算法的预测反褶积.Q值补偿经常存在不稳定问题,且会加强高频噪音;Levinson算法的预测反褶积受阶数限制,层数多时不稳定,且容易伤害有效波.本文采用基于李代数积分的薄层反射系数Picard迭代反演技术来消除这种地层滤波效应.本文将微分方程e指数解方法用于预测算子方程,提出一种称为李代数积分的新方法,给出了预测算子和地层反射系数序列的关系式,普通O'Doherty-Anstey公式为该关系式的一阶李代数表达,高阶李代数积分是对一阶李代数积分的修正.同时基于该关系式本文提出了Picard迭代反演算法由预测算子求取地层有效反射波,并分析了不同阶李代数反演效果.模型试验和实际应用说明该算法消除薄层多重散射的可行性和可靠性.依托李代数积分本身的优点,该算法快速、稳定、收敛.

Elimination of multiple scattering for thin layers based on the Lie algebra integral

Q-compensation and predictive deconvolution are usually used for the elimination of multiple scattering for thin layers. But both of them have some disadvantages, the former is often instable or may enhance the high frequency noise, and the latter which is based on the Levinson algorithm is also instable when the order of autoregressive (AR) filter is bigger than 12 and may do harm to the primary seriously. In this paper we present the Picard iterative inversion algorithm to eliminate the stratigraphic filtering effect. Firstly, we suggest a new method called Lie algebra integral by putting the exponent solution to the prediction operator equation, then the expression of the relationship between the prediction operator and the reflection coefficients of sedimentary sequence is given. O' Doherty-Anstey is just the first order of this expression while the high order of the Lie algebra integral is the correction to the first order. Based on this expression, we suggest the Picard iterative inversion method to recover the primary from the prediction operator and mainly focus on the effect of different order Lie algebra in inversion. Model test and the practical application show that the inversion result about high order Lie algebra integral is better than that of low order Lie algebra integral. What's more, the Picard iterative inversion algorithm is fast, stable and convergent.