  We consider the inverse hyperbolic problem of recovering all spatial
dependent coefficients, which are the wave speed, the damping coefficient,
potential coefficient and gradient coefficient, in a second-order hyperbolic
equation defined on an open bounded domain with smooth enough boundary. We show
that by appropriately selecting finite pairs of initial conditions we can
uniquely and Lipschitz stably recover all those coefficients from the
corresponding boundary measurements of their solutions. The proofs are based on
sharp Carleman estimate, continuous observability inequality and regularity
theory for general second-order hyperbolic equations.
