Analytical Modeling of Wave Generation by the Borehole Orbital Vibrator Source
The orbital vibrator source (a fluid-coupled shear wave source) has many unique properties that are useful for cross-well, single-well, and borehole-to-surface imaging of both P- (compressional) and S- (shear) wave velocities of reservoir rocks. To this day, however, no standard models for this source have been established, and the mechanism of wave generation and the characteristics of wave field around the source are not well understood yet. In this article, we develop both two and three-dimensional analytical models of the orbital vibrator source, which allow us to examine the source characteristics such as radiation patterns, frequency-dependence of the wave energy, and guided-wave generation. These models are developed in the frequency-wave number domain using the partial wave expansion of the wavefield within and outside the borehole. The results show that the developed models successfully reproduce many characteristics of orbital vibrator source that have been observed in the field, including formation property-dependent vibrator amplitudes, uniform isotropic shear wave radiation pattern, and small tube-wave generation.