The most important element in the depth imaging process for reflection seismograms is the velocity field. This field predicts the travel paths of seismic waves, and therefore determines the placement of reflector positions to explain the data. This paper investigates the mathematical structure of a number of velocity estimation algorithms, both conventional and speculative. All of these are based on optimization of an objective function of velocity.
William Woodbury Symes,
"Objective functions for velocity inversion", Proc. SPIE 2033, Mathematical Methods in Geophysical Imaging, (1 December 1993); doi: 10.1117/12.164836; https://doi.org/10.1117/12.164836