  Let (M,g) be a compact Riemmanian manifold with non-empty boundary. Consider
the 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 the
Laplace-Beltrami operator on (M,g). Let b and q be the covector field and the
potential of P(x,D), respectively, in M. We prove H\"older type stability
estimates near generic simple Riemannian metrics for the inverse problem of
recovering g, b, and q from the hyperbolic Dirichlet-to-Neumann(DN) map
associated, f maps to <\nu,u>_g - i<\nu,b>_g u|_{\delta M x [0,T]} where v is
unit conormal to the boundary, modulo a class of transformations that fixed the
DN map.
