Abstract

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.

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