Geophone differencing is a matter of taking the difference of the output response of two geophone elements that are vertically separated by a small distance. The primary purpose of this technique is to attenuate all horizontally propagating energy, such as ground roll, regardless of whether propagation is in line with the shot or out of the plane. The objective is met because horizontally propagating energy is received by the two elements in-phase and is subtracted out. Vertically propagating energy, however, is slightly phase shifted due to the element separation. Differencing, rather than cancellation, results.
The response operator of differencing depends upon several factors: (1) the vertical separation distance of the geophone elements; (2) the propagational velocity in the ground adjacent to and between the elements; (3) the distance of the upper element from the free surface; (4) the reflectivity of the free surface; and (5) the amplitude response of the lower geophone element relative to the response of the upper element. Models show that the best response may be obtained when the upper element is on or very near the free surface, and the other element is at a depth equal to half the shortest expected signal wavelength (highest frequency).
Experimental results confirm the expectation that ground roll tends to be in-phase with depth. In (mild) contrast with the model results, actual data show that best results might be obtained when the geophone elements are as close as possible, because the decay of ground-roll amplitude depends upon wavelength and depth. Very shallow burial minimizes the amount of decay. How shallow the burial depth can be before it interferes with the reflection signal is unclear, although .9 m is not too shallow. Upcoming compressional (P)-waves are out-of-phase and have a reduced amplitude even when the geophone is buried only .9 m. Geophone differencing attenuates ground roll and does not adversely affect upcoming P-waves; it has a gentle high-pass filtering effect on P-waves.