一维介质双参数反演的适定性分析

ON WELL-POSEDNESS ANALYSIS FOR RECOVERING 1-D MEDIUM PARAMETERS

考虑一维波动方程模型了重建不均匀介质的密度ρ(z)小和吸收系数α(z)的反问题．首先将其化为一阶双曲方程组低阶项系数重建的问题，借助于方程组基本解的技术，将原反问题的附加信息（反射数据f（t）和透射数据g(t)转化到基本解上，得到一个新的反问题．对此问题，借助于本文发展起来的逐层递推方法，利用不动点技术，证明了大范围内解的唯一性．本文的结果使得反演计算不再局限于在小的区间上进行，这对多参数的数值反演计算具有很强的指导性．

Consider the inverse problem of recovering media density and dissipative coefficient. After converting this problem into the coefficients inversion for 1-D hyperbolic equations, we discussed the wellposedness with aid of the fundamental solution. By applying the recursion technique layer by layer, we prove the uniqueness result on large scale inversion iliterVal, which will be helpful in the numerical inversion procedure.