MODELING OF A PIEZOELECTRIC TRANSDUCER AND ITS APPLICATION TO FULL-WAVE-FORM ACOUSTIC LOGGING

A velocity-stress finite-difference (VS-FD) model is presented for a c ylindrical piezoelectric transducer in a borehole. The borehole may be irregular and the surrounding formation inhomogeneous. The model is t wo dimensional in that azimuthal symmetry is assumed. The description of the tranducer is a full elasto-electromagnetic one, including trans verse isotropy in the elastic, dielectric, and piezoelectric parameter s, and dissipation in the piezoelectric material. The borehole propaga tion portion of the model is verified by comparison with a standard tr ansform technique. Predictions of the model for a piezoelectric cylind er radiating into a fluid medium are compared to experimental results with excellent agreement. The radiation patterns of a bare transducer near resonance frequencies are found to be anisotropic. Acoustic wavef orms in a borehole excited by a finite sized cylindrical transducer ar e displayed and are quite different from those excited by an ideal poi nt pressure source. The effect of borehole loading upon the impedance of the transducer is shown to be small.