Full‐wave acoustic logging: synthetic microseismograms and frequency‐wavenumber analysis

The discrete wavenumber method is used to compute synthetic full‐waveform acoustic logs in axisymmetric multilayered boreholes and to perform the frequency‐wavenumber analysis of the radiated wave field. The stress‐displacement vector is propagated through the layers using a numerically improved formulation of the Thomson‐Haskell method. In the time domain, all the trapped and interface modes overlap. On the contrary, the representations of the spectral energy density of the scattered wave field in the frequency axial‐wavenumber domain, for various radial positions of observation, allow the recognition and identification of the different wave types as well as their repartition of energy. In particular, these diagrams show the close relation between the resonance frequencies of the borehole and the significant low‐frequency energy of the pseudo‐Rayleigh modes. They also facilitate the interpretation of some of the physical phenomena which occur during the propagation in a complex borehole environment. We present the configurations of a well‐bonded and unbonded cased hole, an invaded zone, and a mudcake. For all of these models, we consider a “fast” formation in which the S-wave velocity is higher than the bore fluid velocity and a “slow” formation. The presence of an elastic tool at the center of the borehole is also investigated. The associated microseismograms, computed for a series of source‐receiver spacings, characterize in the time domain the observations previously made.