We investigate the stability of the inverse problem of recovering general wave speed in a bounded domain from the boundary measurements. The problem arises in geophysics where people are interested in finding the inner structure of the earth from measurements on the ground. Two types of measurements are considered. One is the wave fields. The other is the scattering relation, which is the counterpart of the travel time in a simple metric setting. We show the relations between these two types of data and also derive the stability of the associated inverse problems.