The philosophy behind program bref is that the computer does computations, but the user makes the decisions. The delay time formulation is described more fully in Michaels (9) . The formulation is a linear matrix equation of the form
where the matrix, G, contains information about the source and receiver geometry, m, is a vector of delay times and the refractor slowness, and the vector, d, holds the observed first arrival pick times. When multiplied out, a row of equation (32) can be written as where is a shot delay time, is a geophone delay time, is the horizontal shot to geophone separation divided by the refractor velocity, and is the first break pick time, assuming that the geophone is located far enough away from the source to have the refracted head wave arrive before any other waves.