We consider a problem of identification of physical properties of the Earth using the damped wave equation, based on the linearized inversion associated with Horn's inversion theory. We assume that damping and sound speed are well approximated by the background plus the perturbation. Application of the method leads to a linear integral equation involving variations in sound speed and damping. Our aim is to recover these variations in velocity and damping, what in turn yields a map of the interfaces in the interior of the Earth. We consider the three-dimensional inverse problem of determining three-dimensional variations in the propagation speed and damping by considering the damped wave equation. We exploit the high-frequency character of seismic data to simplify the problem.
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