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MODELING OF ELASTIC WAVE PROPAGATION IN A FLUID-FILLED BOREHOLE EXCITED BY A PIEZOELECTRIC TRANSDUCERby Submitted to the Department of Earth, Atmospheric, and Planetary Sciences on February, 1990 in partial fulfillment of the requirements for the degree of Master of Science ABSTRACT
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 from 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 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 thesis 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. Return to Theses Return to ERL Home Updated: May, 1999
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