Abstract: The invention is concerned with the analysis of velocity data such as sonic data obtained from wells. The invention includes analyzing time versus depth data and generating velocity versus depth data and generating velocity versus depth function. A significant feature is the recognition that translating the observed time versus depth data along the time axis in time-depth domain can be used to obtain a match with a time versus depth curve corresponding a velocity versus depth function. The invention also makes use of visual displays which show degree-of-fit data in parameter spaces. These displays represent an important means for generating velocity versus depth functions.