Geodesic
The inverse problem for the acoustic equation in a weakly horizontally inhomogeneous medium
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 37, Tome 354 (2008), pp. 81-99 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

The inverse problem of reconstruction of coefficients $A$ and $B$ for equation $$ AU_{tt} =\operatorname{div}(B\operatorname{grad}U) $$ in the half-plane $z>0$ is considered. It is assumed that instantaneous point source at $z=0$ generate wave field $U(t,z,x)$ that is known on the boundary. It is also known that coefficients $A$ and $B$ can be represented in the form \begin{gather*} A=A(z,\varepsilon x)=A_0(z)+\varepsilon xA_1(z)+O(\varepsilon^2),\\ B=B(z,\varepsilon x)=B_0(z)+\varepsilon xB_1(z)+O(\varepsilon^2). \end{gather*} Here $\varepsilon$ is a small parameter. The algorithm for the determination of coefficients $A_0,B_0,A_1,B_1$ with accuracy $O(\varepsilon ^2)$ is constructed. Bibl. – 5 titles. 
@article{ZNSL_2008_354_a2,
     author = {A. S. Blagoveshchenskii and D. A. Fedorenko},
     title = {The inverse problem for the acoustic equation in a~weakly horizontally inhomogeneous medium},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {81--99},
     year = {2008},
     volume = {354},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_354_a2/}
}
TY  - JOUR
AU  - A. S. Blagoveshchenskii
AU  - D. A. Fedorenko
TI  - The inverse problem for the acoustic equation in a weakly horizontally inhomogeneous medium
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2008
SP  - 81
EP  - 99
VL  - 354
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2008_354_a2/
LA  - ru
ID  - ZNSL_2008_354_a2
ER  - 
%0 Journal Article
%A A. S. Blagoveshchenskii
%A D. A. Fedorenko
%T The inverse problem for the acoustic equation in a weakly horizontally inhomogeneous medium
%J Zapiski Nauchnykh Seminarov POMI
%D 2008
%P 81-99
%V 354
%U http://geodesic.mathdoc.fr/item/ZNSL_2008_354_a2/
%G ru
%F ZNSL_2008_354_a2
A. S. Blagoveshchenskii; D. A. Fedorenko. The inverse problem for the acoustic equation in a weakly horizontally inhomogeneous medium. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 37, Tome 354 (2008), pp. 81-99. http://geodesic.mathdoc.fr/item/ZNSL_2008_354_a2/

[1] A. S. Blagoveschenskii, “O kvazidvumernoi obratnoi zadache dlya volnovogo uravneniya”, Trudy Mat. inst. im. V. A. Steklova, 115, 1971, 57–69 | Zbl

[2] A. S. Blagovestchenskii, Y. V. Kurylev, V. V. Zalipaev, Inverse problem in a weakly horizontally inhomogeneous layered medium, Preprint, Loughborough University, 2005

[3] M. I. Belishev, A. S. Blagoveschenskii, Dinamicheskie obratnye zadachi teorii voln, SPb., 1999

[4] L. D. Landau, E. M. Lifshits, Mekhanika sploshnykh sred, M., 1952 | Zbl

[5] A. S. Blagovestchenskii, Ya. V. Kurylev, V. V. Zalipaev, “Inverse problem of velocity reconstruction in a weakly lateral heterogeneous half-space”, Proceedings of the 5th International Conference on Inverse Problems in Engineering: Theory and Practice (Cambridge, UK, 11–15 July 2005)