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Let (M,g) be a compact Riemmanian manifold with non-empty boundary. Considerthe second order hyperbolic initial-boundary value problem (\delta_t^2 +P(x,D))u = 0 in (0,T) x M, u(0,x) = \delta_t u(0,x) = 0 for x in M, u(t,x) =f(t,x) on (0,T) x \delta M; where P(x,D) is a first-order perturbation of theLaplace-Beltrami operator on (M,g). Let b and q be the covector field and thepotential of P(x,D), respectively, in M. We prove H\"older type stabilityestimates near generic simple Riemannian metrics for the inverse problem ofrecovering g, b, and q from the hyperbolic Dirichlet-to-Neumann(DN) mapassociated, f maps to <\nu,u>_g - i<\nu,b>_g u|_{\delta M x [0,T]} where v isunit conormal to the boundary, modulo a class of transformations that fixed theDN map.

Stable determination of a simple metric, a covector field and a potential from the hyperbolic Dirichlet-to-Neumann map