Dictionary:Velocity function

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A mathematical expression relating velocity to depth or reflection arrival time, used to approximate the actual velocity distribution that usually involves abrupt discontinuities. The most common forms of velocity function are (a) linear with depth and (b) linear with arrival time. The use of any functional form is an approximation because lithology and the other factors involved in velocity do not vary systematically and smoothly. Especially the extrapolation of velocity functions can lead to errors. A number of functional forms are given by Al-Chalabi (1997).