论文详情
基于层状介质的声波方程,将自回归算子的逆用于表示透射波,称为透射波的线性预测表示。将该表示与反射波的透射波自相关表示相结合,可以得到层状介质的Yule-Walker方程和Levinson递归反演方法。Levinson递归反演方法的缺陷是反演层数一般小于12层,而当反演层数再增加的时候不够稳定。已有的研究表明,自回归算子是一个齐次方程的解,采用李代数方法进行正、反演,其反演结果比采用Levinson递归反演方法得到的结果更为稳定。在横向非均匀弹性介质情况下,采用拟微分算子的象征方法,推导出自回归算子齐次方程,并利用该齐次方程,进一步研究强不均匀介质的共振现象,这对强耦合裂缝介质响应的研究有重要意义,可合理地解释低频阴影现象。此外,纠正了以往推导中存在的一个符号错误。
In the case of a layered medium,based on the acoustic wave equation,transmission waves can be expressed by the inverse of the autoregressive operator,which is called the expression of linear prediction of the transmission wave.Combining the expression of reflected waves with the autocorrelation representation of transmitted waves can lead to the Yule-Walker equation and Levinson recursive inversion method for layered media.The disadvantage of the Levinson recursive inversion method is that the calculation is not stable enough when the number of inversion layers is too large,such as when there are more than 12 layers.The previous studies indicated that the autoregressive operator satisfies a homogeneous equation and is more stable than the Levinson recursive inversion if the Lie algebra method is used for forward modeling and inversion.By using the symbolic method in pseudo-differential operators,the homogeneous equation of the autoregressive operator can be derived in the case of a laterally inhomogeneous elastic medium.By using the homogeneous equation,it is possible to further study the resonance phenomenon of a strong heterogeneous medium,which is of great significance to the study of the response of a strong coupling crack medium.It is also possible to explain the phenomenon of a low-frequency shadow more reasonably.There is a symbol error in the previous deduction,and it is corrected in the derivation presented.
国家自然科学基金重点项目(41630319)资助。