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We developed a fast algorithm to calculate a response of cylindrically layered media excited by the vertical magnetic dipole eccentred with respect to the axis of symmetry. The algorithm calculates response in the range of frequencies typical for induction and dielectric logging. The media conductivity and dielectric constant are described by piecewise‐constant functions. The corresponding boundary value problem is solved by method of separation of variables. Fourier transform is applied to Maxwell equations and boundary conditions to express field components through Fourier transforms of vertical components of an electrical and magnetic field. In addition, an expansion of vertical components into an infinite series with respect to angular harmonics is used to reduce the original problem to a series of 1‐D problems that only depend on the radial coordinate. The solution to each 1‐D radial problem for the angular harmonics is presented as a linear combination of modified Bessel functions. Finally, inverse Fourier transformation is applied to the angular harmonics of vertical components to derive electrical and magnetic field of the original boundary value problem. We provide detailed discussion on the elements that are critical for the numerical implementation of the algorithm: a proper normalization, convergence, and integration. Specifically, we show how to perform integration in the complex plane by avoiding intersection of the integration pass with the cuts located on the Riemann surface. Numerical results show the usefulness of the algorithm for solving inverse problems and for studying the effect of eccentricity in induction and dielectric logging.

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A new wire-line high-definition formation resistivity imaging instrument employing a 'two-electrode' measurement configuration was developed for application in low-resistivity formations drilled with non-conductive (oil-based) mud. The new instrument and measurement principles are described with modeled synthetic responses. Several field log examples with image interpretation are shown.The high-spatial resolution of a 'two-electrode' arrangement has been well documented for nearly 25 years in conductive boreholes [1] and has been used in oil-based mud (OBM) for more than a decade [2]. However, the lower formation resistivity limit in OBM often precluded realizing the benefits in many important offshore deep-water plays, such as offshore East Malaysia and the Gulf of Mexico. The new instrument employs multi-frequency impedance measurements to overcome this low-resistivity low-contrast (LRLC) formation limitation.The imaging device measures electrical impedance across electrodes and produces two image logs: an image of the real part of impedance that is calibrated to yield formation resistivity and an image of the imaginary part of impedance that conveys information about image quality and borehole rugosity. The instrument employs six individually articulated pads, each containing ten sensor electrodes that provide a 79% surface coverage in an 8-in borehole. Typical spatial-resolution is better than 0.8-in vertically and 0.3-in azimuthally, providing a high-definition image of the near-wellbore formation. Pad-to-pad vertical offset is less than 6 inches. This short offset means there is never any pad overlap and guarantees high coverage of borehole surface while the instrument rotates during logging.Presented are field examples from typical logging environments found offshore Malaysia. Detailed geologic features such as turbidite thin-beds, slumping, debrites, faulting and fracturing in low resistivity formations are clearly resolved in highdefinition image logs. The high-definition images deliver information necessary for detailed sedimentological studies, reducing uncertainty when calculating hydrocarbon saturations in LRLC sandstone successions, and provide more precise and accurate net-to-gross calculations.

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