Analysis of the Wavefields Around the Borehole During Acoustoelectric Logging
By
Hengshan Hu1, Jiaqi Liu1
(1) Harbin Institute of Technology, Harbin, China
This study is aimed at understanding the wave propagation mechanism of the
acoustic and electromagnetic fields during acoustoelectric well logging. The
coupled acoustic and electromagnetic fields excited by a point pressure source
in a fluid-filled borehole are formulated by introducing potential functions in
cylindrical coordinate system, and by applying Pride's governing equations and
the boundary conditions at the borehole wall. Transient full waveforms of
acoustic pressure and electric fields in a borehole are numerically simulated.
The components of the displacement vector and components of the electric and
magnetic fields in the porous formation outside the borehole are also
calculated. It is shown that both the acoustic and the electromagnetic waves
propagate along the borehole in a way different from plane waves in an unbounded
uniform medium. The critically refracted shear (S-) wave causes radial and axial
displacements. So does the critically refracted compressional (P-) wave. Both of
them cause accompanying electric and magnetic fields. The radiating
electromagnetic (EM) wave is stronger in the center of the borehole than on the
formation wall. This EM wave is comparatively large and can be the dominant
component wave in the full
waveform
when the frequency is high and the receiving
position is near to the acoustic transmitter. As a check of our simulation
process, we calculated the acoustic field separately using Biot's theory, and
simulated the converted electric field using simplified coupling equations and
by assuming the electric field to be quasi-static. Numeral examples show that
the calculated waveforms of the electric field by the approximate method are in
complete agreement with waveforms using the full coupling theory.