An account of the mathematical properties of velocity functions used in the seismic method of geophysical prospecting is presented. Basic equations are given for deriving various quantities of interest associated with a particular velocity function, such as average velocity as a function of depth, average velocity as a function of vertical travel time, parametric equations for displacement, depth, travel time, etc. In Part I the relations are based on a given instantaneous-velocity--depth function. Part II contains a similar analysis based on a given instantaneous-velocity--vertical-time function. The results are incorporated in Tables I and II.