Abstract: The invention relates to a method of monitoring the drilling of a borehole through an earth formation with a rotating drill bit fixed at the lower end of a drillstring. At least one physical quantity associated with the vibrations resulting from the interaction of the rotating drill bit with the earth formation is detected and an oscillatory signal is generated in response thereto. Filter coefficients a.sub.k of an auto-regressive filter model are determined by fitting the filter output signal with the oscillatory signal. The reflection coefficients of the vibrations propagating along the drill string and being reflected by a mis-match of impedance of two successive elements of the system earth formation/drillstring are derived from the filter coefficients. Finally, the hardness of the formation being drilled, the contact of the drillstring with the borehole and the vibration level of the vibration along the drillstring are determined from the reflection coefficients.