| Linearization Ill-Posedness for 2.5-D Ware Equation Inversion Model |
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| 作者姓名： | Ji-jun Liu |
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| 作者单位： | Ji-jun LiuDepartment of Mathematics，Nanjing Normal University，Nanjing 210097，China & Department of Applied Mathematics，Southeast University，Nanjing 210018，China |
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| 基金项目： | Supported by the Science Foundation of Southeast University (No.9207011148) |
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| 摘 要： | Abstract For the weakly inhomogeneous acoustic medium in Ω={(x,y,z):z>0},we consider the inverse problemof determining the density function ρ(x,y).The inversion input for our inverse problem is the wave field givenon a line.We get an integral equation for the 2-D density perturbation from the linearization.By virtue of theintegral transform,we prove the uniqueness and the instability of the solution to the integral equation.Thedegree of ill-posedness for this problem is also given.
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Linearization Ill-Posedness for 2.5-D Wave Equation Inversion Model |
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| Ji-jun Liu.Linearization Ill-Posedness for 2.5-D Ware Equation Inversion Model[J].Acta Mathematicae Applicatae Sinica,2002,18(2):219-230. |
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| Authors: | Ji-jun Liu |
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| Institution: | (1) Department of Mathematics, Nanjing Normal University, Nanjing 210097, China & Department of Applied Mathematics, Southeast University, Nanjing 210098, China (E-mail: jjliu@seu.edu.cn), CN |
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| Abstract: | Abstract
For the weakly inhomogeneous acoustic medium in Ω={(x, y, z:z>0}, we consider the inverse problem of determining the density function p(x, y). The inversion input for our inverse problem is the wave field given on a line. We get an integral equation for the 2-D
density perturbation from the linearization. By virtue of the integral transform, we prove the uniqueness and the instability
of the solution to the integral equation. The degree of ill-posedness for this problem is also given.
Supported by the Science Foundation of Southeast University (No.9207011148) |
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| Keywords: | Linearization inversion integral geometry ill-posedness |
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