Seismic inversion methods that are based on the analysis of traveltime rely on the most fundamental measurement of waveform and amplitude; either there is an arrival or there is not. Traveltime contains the basic information about an arrival's phase; the geometrical arrival time is equal to the stationary point of the phase term in the wave equation representation for any seismic arrival. Even when impedance and velocity series are determined from the amplitude and phase variations along a seismic trace, these can usually be interpreted only as fine scale deviations from a velocity function which changes relatively slowly as a function of depth. That 'long period' velocity function must itself be obtained by other means; typically from traveltime analysis.
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- Tau-p Analysis in One, Two and Three Dimensions
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