层状不均匀介质的一维地球模型物性参数反演

INVERSION OF 1-DIMENSIONAL IMPEDANCE IN LAYERED INHOMOGENEOUS NONABSORBING MEDIA

本文建立了层状不均匀非吸收介质的反问题模型，与已有的模型相比，它更切合实际．讨论了这种模型下介质的物性参数和几何参数的反演问题，它包括特性阻抗Ｋ（ｘ），间断状态参数ｃｉ，ｘｉ，ｎ．借助于行波传播算子Ｋｉ和有间断系数的方程的弱Ｒｉｅｍａｎｎ函数，得出每一层上波场正问题的表达式．借助于此表达式把反演物性参数的问题，转化为确定Ｍｋ（ｘ，ｙ，０）的问题，而关于Ｍｋ（ｘ，ｙ，０）我们得到的是一个第二类Ｆｒｅｄｈｏｌｍ积分方程，因而可用适定性方法求解．所有的过程都直接在时空域上进行，避免了Ｆｏｕｒｉｅｒ变换，减少了运算量，为数值计算提供了一条途径．

In this paper,we consider a impedance inverse problem model in geophysics for 1-dimensional layered inhomogeneous nonabsorbing media.By introducing shift operator and weak Riemann function for PDE with discontinuous coefficients,we give the expression of wave in every layer. By virtue of this expression and reflection function R(s),we get a well-posed method to reconstruct impedance K(x).Then we give a way to find constants ci,xi and n under some assumptions.All these are carried out in time-domain directly which avoids the Fourier transformation.