Continuously variable, orbital vibrators (OV) are beginning to see use in the petroleum and environmental industries as vibration sources and physical property sensors. These are mechanically simple devices that consist of a cylinder driven by an eccentric mass that rotates about the axis of the cylinder. The resulting motion of the device is transmitted to the surrounding rock formation via the acoustic coupling of the fluid-filled wellbore. While it has been shown that these devices are accurate sensors of the characteristics of the rock formation, no analysis has yet demonstrated this behavior or estimated its effect on the elastic energy radiated by these sources. A two-dimensional analysis is presented for the response of an oscillating cylinder within a fluid-filled annulus that is embedded within an elastic continuum. In particular, the cylinder is driven by a rotating unbalance. This solution is used to show that the radiated power into the elastic domain is highly frequency dependent and larger than previous analyses have estimated. In addition, the inclusion of an another elastic region (of different properties) far from the vibrator provides means of estimating the depth of penetration or the resolution of this sensor into the surrounding rock formation. This penetration depth is also found to be highly frequency dependent with a maximum value in the low-to-mid frequency range.
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