一类双曲反问题的逼近算法及收敛性

Appromaxlmation and Convergence of a Class of Hyperbolic Inverse Problem

该文考虑地球物理勘探中出现的间断特性阻抗的反演问题．利用样条插值理论，把无穷维空间上的反问题用有限维空间上的反问题来近似．利用半群理论，证明了近似反问题之解收敛于原反问题之解．据此可得到求解反问题的一种稳定的近似算法．

This paper deals with the impedance inverse problem arising in the seismic geophysics. By spline theory, we approximate the infinite dimensional inverse problem by a problem in the finite dimensional space. With the aid of semi-group theory, we prove that the solution of apprximate problem converges the solution of original inverse problem.