A Numerical Investigation of Head Waves and Leaky Modes in Fluid-Filled Boreholes
Name
1985.2 Paillet_Cheng.pdf
Size
723.56 KB
Format
Adobe PDF
Checksum (MD5)
7cf2f3251e1a70dfb5673b9f84f11468
Author(s)
Paillet, Frederick L.
Cheng, C. H.
Date Issued
1985
Publisher
Massachusetts Institute of Technology. Earth Resources Laboratory
Series/Report no.
Earth Resources Laboratory Industry Consortia Annual Report;1985-02
Abstract
Although synthetic borehole seismograms routinely can be computed for a wide
range of borehole conditions, the physical nature of shear and compressional head
waves in fluid-filled boreholes is poorly understood. This paper presents a series of
numerical experiments designed to provide insight into the physical mechanisms
controlling head wave propagation in boreholes. These calculations demonstrate the
existence of compressional normal modes equivalent to shear normal modes, or
pseudo-Rayleigh waves, with sequential cutoff frequencies spaced between the
cutoff frequencies for the shear normal modes. Major contributions to head wave
spectra are shown to occur in discrete peaks at frequencies just below mode cutoff
for both compressional and shear modes. This result is confirmed by calculations with
synthetic waveforms at frequencies corresponding to mode cutoff, and by branch cut
integrals designed to yield independent spectra for the compressional mode. In the
case of soft formations where shear velocity falls below acoustic velocity in the
borehole fluid, leaky compressional normal modes attain properties similar to those
observed for shear normal modes in the hard rock case. This result is formally related
to a fluid-fluid waveguide with undamped compressional normal modes in the limit of
vanishing shear velocity. Synthetic waveforms demonstrate that high amplitude
arrivals, traveling at velocities less than the acoustic velocity of the borehole fluid,
and at frequencies above a few kilohertz represent the Airy phase of the
compressional mode and not a tube wave. Comparison of synthetic waveforms with
waveforms obtained in soft sea sediments indicates that the predicted Airy phase
arrivals are present in the experimental data.
Persistent DSpace Link
