Building the System of Delay Time Equations ( bref )

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

$$Gm=d,$$ (32)

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

$$T_{s}+T_{g}+\frac{x}{V_{2}}=t_{p}\,,$$ (33)

where $T_{s}$ is a shot delay time, $T_{g}$ is a geophone delay time, $\frac{x}{V_{2}}$ is the horizontal shot to geophone separation divided by the refractor velocity, and $t_{p}$ 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.