Torsional oscillations of the drillstring will lead to frequency modulation (FM) of the signal from a vibratory source (e.g., the bit). This results, in the frequency domain, in sidebands being present around a detected excitation frequency. In accordance with the present invention, it has been discovered that these sidebands may be used in advantageous methods for optimizing drillstring and drilling performance. In a first embodiment of this invention, these sidebands are used to discriminate between downhole and surface vibrational sources. Once the location of the drillstring vibration is determined, appropriate action may be taken to optimize drilling and drillstring performance. In a second embodiment of this invention, the sidebands are used to determine the rotary speed of BHA (bottom hole assembly) components. Using the method of this second embodiment, minimum and maximum rotary speeds of a given BHA component is determined as a function of the excitation frequency, the frequency of torsional oscillation and the modulation index. Once the minimum and maximum rotary speeds of the BHA components are determined, adjustments can be made to alter the rotary speeds and thereby enhance or optimize drilling and drillstring performance. This method is particularly well suited for use in those applications where torsional oscillations are not recognizable in the time domain, but are better recognized in the frequency domain.
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