Eccentric dipole sources in fluid-filled boreholes: Numerical and experimental results

Abstract

A frequency-wavenumber (ω−k) representation is given for the response of eccentric multipole sensors in a fluid-filled borehole. Specializing to eccentric dipole sensors, synthetic time-domain waveforms from an array of receivers deployed along the axis of the borehole are displayed for a range of eccentricity magnitude and orientation, formation slowness, and borehole radius. Flexural wave slowness estimates within several frequency bands are extracted from the synthetic waveforms using a semblance technique. For eccentricity small relative to the borehole radius, the character of dipole waveforms and the estimated flexural slowness are little changed. When the eccentricity is a substantial fraction of the borehole radius, flexural wave amplitude is greatly increased, and strong nonmonotonic trends are introduced due to interference with other modes. If eccentricity is not parallel to the transmitting dipole axis, substantial signals are detected on cross-dipole receivers, perpendicular to that of the transmitting dipole. Eccentricity effects decrease with frequency. Even for large eccentricity, flexural slowness estimates are affected only slightly. Scaled laboratory experiments confirm the numerical results. Comparison of the experimental and numerical waveforms is made for both centered and eccentric dipoles in several model formations. The predicted increase and nonmonotonic variation of flexural wave amplitude versus receiver offset for eccentric sensors is observed. Experimental and numerical waveforms overlay with excellent agreement.