An important transformation in exploration geophysics is from data as a function of shot-receiver offset to data as a function of apparent velocity. To go from offset to velocity, the transformation sums along hyperbolas of many velocities. The adjoint is a superposition of hyperbolas of all the different velocities. Pseudocode for these transformations is

dovdo doxif hyperbola superposition data(t,x)= data(t,x) + vspace else if velocity analysis vspace=vspace+data(t,x)

10/21/1998