Shear wave logging in elastic formations

The analysis of the dispersion and attenuation of the modes generated both by a dipole and a quadrupole source in a fluid-filled borehole surrounded by a (multilayered) elastic formation is performed. The displacement-stress vectors are propagated through the layers using the Thomson–Haskell method. Only the well-bonded configuration is investigated. In the time domain, the effects of the source center frequency on synthetic full waveform microseismograms computed using the discrete wavenumber method are investigated. Whatever the formation (fast or slow) and the configuration, the low-frequency part of both the flexural and screw modes follows the virgin formation shear wave characteristics. Their high-frequency parts behave like that of the Stoneley wave excited by a monopole source. As a result, the fundamental modes are very sensitive to the properties of the inner layers at intermediate and high frequencies. In the presence of an invaded zone, the internal dynamics of the waveforms can be significantly modified, while the useful starting energy of the fundamental modes is shifted toward lower frequencies. The reverse phenomenon occurs when the borehole is cased. For this last configuration, it is only with low source center frequencies that multipole sources can log a slow formation shear wave due to the leaky character of the fundamental modes. Such behaviors emphasize the need for useful low-frequency energy for the actual logging tools.