Abstract: The invention is related to a method of determininng the instantaneous rotation speed of a drill string or a drill bit in a borehole or the lateral shocks applied to the string or bit. The centripetal acceleration of the drill string is measured at at least two opposite ends of a drill string diameter so as to obtain two centripetal acceleration signals ac1 and ac2; the signals ac1 and ac2 are combined and the instantaneous rotation speed or the lateral shocks are derived from said combined signal. The accelerometers must be of the type delivering a signal with a DC component. An important application of the invention is to transform drill string rotation speed dependent data acquired versus time with a constant sampling time increment T.sub.c separating successive data, into compensated data which would be obtained for a substantially constant drill string rotation speed S.sub.c. The compensated data are obtained either by adjusting the constant sampling time interval T.sub.

Abstract: Downhole Torque and Rate of Penetration are utilized to develop indications of formations having high porosity or of the development of an undergauge bit. Downhole torque is normalized by dividing it by the product of downhole weight on bit and bit size to produce Dimensionless Torque while Rate of Penetration is normalized by dividing it by the product of downhole weight on bit and rotary speed. The values of Dimensionless Torque and Normalized Rate of Penetration are compared to "normally" expected values of these quantities. Deviations from the normal values are taken as an indication of the occurrence of bit penetration of a highly porous formation or of the development of an undergauge or damaged bit.

Abstract: Information on tooth wear is obtained from the frequency distribution spectrum of a vibrational quantity influenced by the impact of cutter teeth on the bottom of a bore. For example, spectra may be obtained from the product of signals indicative of torque and torsional acceleration. Tooth wear is then indicated by the shift upwardly in frequency of peaks in the spectra. Other quantities which may be used, singly or together to enhance spectral information, are weight on bit, vertical acceleration, transverse acceleration, standpipe pressure. Abrupt changes in frequency distribution curves indicate abrupt occurrences such as broken teeth or stuck cones. A stuck cone is also indicated by unidirectional peaks in a plot of torsional acceleration against time.