The inversion of logging-while-drilling azimuthal electromagnetic measurements is essential for geosteering in horizontal wells and optimizing reservoir development. Conventional fixed-layer inversion models lack adaptability to dynamically varying formations, resulting in limited applicability and a trade-off between accuracy and efficiency. This study introduces a trans-layer inversion method that adaptively optimizes model complexity. The method quantifies the tool's multi-boundary detection capability using eigenvalue analysis of the Fisher information matrix. Statistical analysis of synthetic models informs the construction of an inversion model library spanning two-to five-layer configurations, facilitating adaptation to diverse formation geometries. To address the dependence of multi-layer inversion on initial values, a progressively increasing model complexity hot-start mechanism is implemented, allowing lower-order inversion results to constrain higher-order models. A comprehensive quality score autonomously selects the optimal inversion model. Numerical examples demonstrate that: (1) in a three-layer sand-shale sequence, the method enhances early recognition of reservoir boundaries due to the model library's coverage of all tool positions; (2) in a six-layer thin-bed model, the trans-layer inversion reduces mean square error by 91.5% compared to conventional three-layer inversion, significantly improves thin-bed imaging resolution, and doubles computational efficiency relative to fixed five-layer inversion; (3) in an anticlinal reservoir model, the method accurately tracks both reservoir structure and internal oil-water contacts; (4) field data validation from a complex clastic reservoir confirms the method's ability to delineate thin shale layers and guide well trajectory in real drilling scenarios. This approach offers a robust solution to the challenges of model applicability and computational efficiency in LWD inversion.

The oil-based mud (OBM) borehole measurement environment presents significant limitations on the application of existing electrical logging instruments in high-resistance formations. In this paper, we propose a novel logging method for detection of high-resistance formations in OBM using high-frequency electrodes. The method addresses the issue of shallow depth of investigation (DOI) in existing electrical logging instruments, while simultaneously ensuring the vertical resolution. Based on the principle of current continuity, the total impedance of the loop is obtained by equating the measurement loop to the series form of a capacitively coupled circuit. and its validity is verified in a homogeneous formation model and a radial two-layer formation model with a mud standoff. Then, the instrument operating frequency and electrode system parameters were preferentially determined by numerical simulation, and the effect of mud gap on impedance measurement was investigated. Subsequently, the DOI of the instrument was investigated utilizing the pseudo-geometric factor defined by the real part of impedance. It was determined that the detection depth of the instrument is 8.74 cm, while the effective vertical resolution was not less than 2 cm. Finally, a focused high-frequency electrode-type instrument was designed by introducing a pair of focused electrodes, which effectively enhanced the DOI of the instrument and was successfully deployed in the Oklahoma formation model. The simulation results demonstrate that the novel method can achieve a detection depth of 17.40 cm in highly-resistive formations drilling with OBM, which is approximately twice the depth of detection of the existing oil-based mud microimager instruments. Furthermore, its effective vertical resolution remains at or above 2 cm, which is comparable to the resolution of the existing OBM electrical logging instrument.