Drill-bit displacement-source model: Source performance and drilling parameters

The emission properties of a drill-bit source and the signature of the drill-bit seismograms depend on the dynamic action of the drill bit, which in turn is a function of thregeological conditions, rock properties, and drilling parameters. In fact, drilling is a variable dynamic process, in which the vibrations produced by the drill bit are transmitted into the drillstring and formation with a partition of energy determined by the impedances at the bit. In this analysis, we study drill-bit performance and calculate the forces produced by an ideal drill bit to determine the variations in the signal signature and, ultimately, the conditions of source repeatability as a function of average drilling parameters and signal frequency. The model includes near-field effects and assumes the drill bit acts as a displacement source, producing axial bit forces with relative bit/formation displacement and vertical penetration in the formation. The analysis shows that the expected bit signature, which is equivalent to the ground force in Vibroseis, depends on average tooth impact area, percussion frequency, rate of penetration, formation strength, bit wear, and downhole pressure. In particular, the results show that larger amplitudes of axial forces are expected at a lower rate of penetration, higher formation strength, and lower formation pressure.