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In this paper, we consider the inverse problem of determining on a compact Riemannian manifold the electric potential and the absorption coefficient in the wave equation with Dirichlet data from measured Neumann boundary observations. This information is enclosed in the dynamical Dirichlet-to-Neumann map associated with the wave equation. We prove in dimension $$n\ge 2$$n≥2 that the knowledge of the Dirichlet-to-Neumann map for the wave equation uniquely determines the absorption coefficient and the electric potential, and we establish Hölder-type stability.

Simultaneous determination of two coefficients in the Riemannian hyperbolic equation from boundary measurements