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