SERIES APPROXIMATION IN VELOCITY AND TRAVELTIME COMPUTATIONS *

A rigorous proof is presented to show that over a horizontally layered ground the rms velocity cannot exceed the stacking velocity. The proof helps to illustrate the difference between stacking and rms velocities in a quantitative manner. The series of Taner and Koehler (1969) is used for the purpose. Convergence of this series is tested. Including more terms will not necessarily improve the convergence. Although the series is rapidly convergent when the spread length/depth ratio is small, strong oscillations are observed when this ratio is high.