Tube Waves and Borehole Coupling
More than a century ago Horace Lamb showed that pressure waves in a fluid-filled pipe or borehole travel at a speed which depends on the yielding of the hole wall. These tube waves have been discussed quite fully in the literature including permeability of the rock, reflection at a change in hole size, lithologic boundary and other structural details.
Oil wells have been “shot for velocity,” that is, the time (T) from a surface source and a geophone at depth (D) yields an average velocity V = D/T. Without a theory for guidance, one had to accept as fact that the signal was sometimes too weak to measure or was of reverse polarity. The theory published in 1953 explained these and other oddities.
If fluid volume changes in a short length of a hole, a pressure pulse travels outward. If changes in the diameter are caused by seismic waves in the solid, a summation of these pressure pulses produces the response in the borehole, resulting from external plane waves. This is an example of borehole coupling.
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.