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We consider a restricted Dirichlet-to-Neumann map associated to a wave typeoperator on a Riemannian manifold with boundary. The restriction corresponds tothe case where the Dirichlet traces are supported on one subset of the boundaryand the Neumann traces are restricted on another subset. We show that therestricted Dirichlet-to-Neumann map determines the lower order terms in thewave equation, up the natural gauge invariances, along a convex foliation ofthe manifold. We allow the lower order terms to be non-self-adjoint, and inparticular, the corresponding physical system may have dissipation of energy.

Hyperbolic inverse problem with data on disjoint sets