Transient waveforms have been computed for a family of source and receiver types and for geometry corresponding to plausible acoustic logging tools in oil wells. The acoustic tool now in commercial use is one member of the family. The computations also treat flexural waves and torsional waves. All quantities are expressed in terms of appropriate vector and scalar potentials, and output waveforms are obtained by numerical evaluation of triple Fourier transforms. When loss parameters are included in the stress-strain relations, the Fourier inversion formulas are free of singularities and numerical integration is straightforward. For the purely elastic case, it is necessary to cope with the singularities of the integrands in performing the numerical integrations. Dispersion curves and other features agree with earlier publications on wave propagation along concentric cylinders.
Figures & Tables
Seismic Wave Propagation: Collected Works of J. E. White
This first chapter sets the stage for the later technical development of Dr. Whit’s career in applied seismics. Experiments, f’wst at the Acoustics Laboratory of the Massachusetts Institute of Technology and later at Mobil Oil and Marathon Oil, provided insight into the general problems of impedance measurements, transduction, filtering, and attenuation. These papers also serve as a bridge to show geophysicists how theft own experiments in seismology naturally interface with (indeed, arose out of) the larger world of sound measurements in air and water. These experiments demonstrate the power of geometrically constrained experiments to allow verification of approximate (and in some cases, exact) theories of sound.