TRAVEL TIME TOMOGRAPHY WITH FORMALLY DETERMINED INCOMPLETE DATA IN 3D

被引：14

作者：

Klibanov, Michael, V ^{[1
]}

机构：

[1] Univ North Carolina Charlotte, Dept Math & Stat, Charlotte, NC 28223 USA

来源：

INVERSE PROBLEMS AND IMAGING | 2019年 / 13卷 / 06期

关键词：

Inverse kinematic problem; Carleman-like estimate for the Volterra operator; Lipschitz stability; convexification; globally convergent numerical method; INVERSE; CONVEXITY;

D O I：

10.3934/ipi.2019060

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For the first time, a globally convergent numerical method is developed and Lipschitz stability estimate is obtained for the challenging problem of travel time tomography in 3D for formally determined incomplete data. The semidiscrete case is considered meaning that finite differences are involved with respect to two out of three variables. First, Lipschitz stability estimate is derived, which implies uniqueness. Next, a weighted globally strictly convex Tikhonov-like functional is constructed using a Carleman-like weight function for a Volterra integral operator. The gradient projection method is constructed to minimize this functional. It is proven that this method converges globally to the exact solution if the noise in the data tends to zero.

引用

页码：1367 / 1393

页数：27

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