A disturbance at one point of a dispersive medium resulting from an impulse applied at another point may be represented as a superposition of traveling plane waves. The phase and period of the disturbance at any instant are related by the principle of stationary phase to the phase and period of a traveling wave component. For the instantaneous phase of that traveling wave component the following equation may be written.
Ct‐x=(N‐ϕ0/2π)CT
where C is the phase velocity, x the distance, T the period, t the travel time, N an integer, and ϕ0 the initial phase of the traveling wave component. Since t and T may be measured from a record of the disturbance and x may be determined, the equation may be used to compute the phase velocity as a function of period, if the initial phases are known. If distance and the dispersion are known, initial phases may be determined. From distance, initial phases, and phase velocities the disturbance at any point may be constructed. The practical use of the method is demonstrated by application to antisymmetric waves in a cylindrical rod, Rayleigh waves from United States and Russian nuclear explosions, Rayleigh waves from the Hudson Bay earthquake of January 30, 1959, and Love waves from the Fairview Peak and Fallen, Nevada, earthquakes of 1954.