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MODELING OF ELASTIC WAVE PROPAGATION IN A FLUID-FILLED BOREHOLE EXCITED BY A PIEZOELECTRIC TRANSDUCER
Sergio Kostek
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.
