This paper presents a theory describing the acoustic waves set up in a fluid-filled borehole by the passage of plane elastic waves in the surrounding solid. It consists of a mathematical development of the following process. A stress in the solid around the borehole will in general cause the hole to contract or expand. A contraction compresses the fluid and causes pulses to radiate in both directions as tube waves. At some observation point, one of these pulses is observed after a delay due to the propagation as a tube wave. A complex wave in the solid is expressed as a combination of stresses distributed along elementary lengths of the borehole, and the total acoustic wave received at a point is expressed as the summation of elementary pulses arriving after suitable delays. The expressions derived give pressure or fluid particle velocity in terms of motion or stresses in the solid for plane compressional waves and plane shear waves arriving at any angle. The method can be extended to the case of a spherical wave cutting the borehole
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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.