Journal of Inverse and Ill-posed Problems
Editor-in-Chief: Kabanikhin, Sergey I.
6 Issues per year
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Inversion of the Radon transform, based on the theory of A-analytic functions, with application to 3D inverse kinematic problem with local data
- Department of Mathematics and Statistics, Wichita State University, 1845 N. Fairmount, Wichita, KS, 67260-0033, USA. E-mail: Boukhgueim@math.wichita.edu
- Schlumberger, Aslakveien 14E, 0753 Oslo, Norway. E-mail: ABoukhgueim@slb.com
In the introduction we show that the inverse problems for transport equations are naturally reduced to the Cauchy problem for the so called A-analytic functions, and hence the solution is given in terms of operator analog of the Cauchy transform. In Section 2 we develop elements of the theory of A-analytic functions and obtain stability estimates for our Cauchy transform. In Section 3 we discuss numerical aspects of this transformation. In Section 4 we apply this algorithm to the 3-dimensional inverse kinematic problem with local data on the Earth surface, using modified Newton method and discuss numerical examples.
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