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Recovery of Perturbations in an Acoustic Medium with Attenuation from Several Plane Wave Responses

A linearized inverse problem is studied for recovering a stratified acoustic medium with attenuation from reflection data known at the medium’s surface. The inverse problem is based on a plane wave decomposition of the medium’s response to a point-source input. This paper shows that the inverse problem for recovering perturbations in density, wave speed, and the coefficient of attenuation from known perturbations in three plane wave responses is well posed in the appropriate function spaces. The question of whether the medium itself can be recovered from the point-source response is discussed.The primary focus of this paper is on applications in reflection seismology and oil exploration. The work also has direct application to some inverse problems in electromagnetics.