Institute of Computational Mathematics and Mathematical Geophysics SB RAS

International Conference on Mathematical Methods in Geophysics «MMG-2008»

Akademgorodok, Novosibirsk, Russia, October 13-15, 2008

Abstracts

Inverse Problems of Geophysics

The Carleman formula and recovering the refractive index of the two-dimensional Helmholtz equation

Arbuzov E.V., Bukhgeim A.A., Bukhgeim A.L.

Ин-т Математики им С.Л. Соболева СОРАН Россия;
Schlumberger Oslo Norway;

Ин-т Математики им С.Л. Соболева СОРАН Россия
и Wichita State University USA

We consider the Cauchy problem for the Helmholtz equation with given bounded refractive index in an arbitrary planar domain with Cauchy data only on part of the boundary of the domain. We derive a Carleman-type formula for a solution to this problem.

From another side we obtain the inversion formula for smooth unknown refractive index using the Cauchy date set on the boundary. Based of this inversion formula we numerically reconstruct the refractive index on the unit disk.

Note. Abstracts are published in author's edition

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