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.