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May  2009, 3(2): 275-294. doi: 10.3934/ipi.2009.3.275

Full identification of acoustic sources with multiple frequencies and boundary measurements

Carlos J. S. Alves 1, , Nuno F. M. Martins 2, and  Nilson C. Roberty 3,

1. 

CEMAT-IST, Departamento de Matemática, Instituto Superior Técnico (TULisbon), Avenida Rovisco Pais, 1049-001 Lisboa, Portugal
2. 

CEMAT-IST and Departamento de Matemática, Faculdade de Ciências e Tecnologia (NULisbon), Universidade Nova de Lisboa, Quinta da Torre, Caparica, Portugal
3. 

Programa de Engenharia Nuclear, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil

Received  December 2008 Revised  March 2009 Published  May 2009

In this paper we study the identification of acoustic sources in a domain $\Omega$ from boundary data. With a single frequency, we show that identification is possible if, besides the boundary data, considerable information regarding the type of the source is considered. For the general case, we present an identification result using multiple frequencies and boundary measurements. We show that for compactly supported sources in $\Omega$, the completion of Cauchy data has at most one solution and thus for this type of sources, identification is possible using variable frequencies and incomplete boundary measurements. A numerical method based on the reciprocity functional is proposed and tested for several numerical examples. For compact sources, a data completion method is proposed and tested in order to apply the previous method.
Keywords: Inverse acoustic source problem, method of fundamental solutions for Cauchy data fitting, reciprocity gap functional..
Mathematics Subject Classification: 65N21; 65N35; 35J2.
Citation: Carlos J. S. Alves, Nuno F. M. Martins, Nilson C. Roberty. Full identification of acoustic sources with multiple frequencies and boundary measurements. Inverse Problems & Imaging, 2009, 3 (2) : 275-294. doi: 10.3934/ipi.2009.3.275
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