Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Earth, Atmospheric, and Planetary Sciences, 1991.Includes bibliographical references (leaves 71-74).M.S

Kostek, Sergio

DSpace@MIT

Modeling of elastic wave propagation in a fluid-filled borehole excited by a piezoelectric transducer.

Acoustic logging is an important geophysical method for obtaining relevant information
concerning rock properties in formations traversed by boreholes. Typically, the formation
parameters that are measured are the compressional, shear, and Stoneley wave
slownesses, which are related to important petrophysical parameters such as porosity,
permeability, etc. Theoretical waveform modeling has played an important role in helping
to understand the complex wave pattern setup in the borehole, and many processing
algorithms have come out of this improved understanding. However, in the presence
of formation inhomogeneities and borehole irregularities, which are the most common
situations found in practice, no satisfactory modeling scheme has yet been presented.
Furthermore, source and receivers have been treated as idealized pointwise transducers,
with isotropic radiation patterns. As new applications of full waveform acoustic logs
arise, such as sonic imaging, cross-well tomography, etc., a better understanding of the
wave phenomena including excitation, propagation, scattering, and detection is necessary
for inverting the recorded wavefield. In this paper a velocity-stress finite-difference
model is presented for a cylindrical piezoelectric transducer in a borehole. The transducer may be free-flooded or capped, and a variety of support and auxilliary structures may be included. The borehole may be irregular and the surrounding formation inhomogeneous. The model is two-dimensional in that azimuthal symmetry is assumed.
The description of the tranducer is a full elasto-electromagnetic one, including transverse isotropy in the elastic, dielectric, and piezoelectric parameters, and dissipation in the piezoelectric material. The borehole propagation portion of the model is verified by comparison with a standard transform technique. Predictions of the model for a piezoelectric cylinder radiating into a fluid medium are compared to experimental results with excellent agreement. The radiation patterns of a bare transducer near resonance frequencies are quite anisotropic. Acoustic waveforms in a borehole excited by a finite sized cylindrical transducer are displayed and are quite different from those excited by an ideal point pressure source. The effect of borehole loading upon the impedance of the transducer is shown to be small.Schlumberger-Doll Research Cente