Transient Electromagnetic Response of Electrode Excitation and Geometric Factors of Desired Signal

Cross-hole exploration is of great significance to the detection and efficient utilization of remaining oil between wells. In order to achieve cross-hole formation resistivity measurement in open-hole wells, this paper proposes an electrode-excited transient electromagnetic method and defines an electric vector potential function to describe the transient electromagnetic field excited by the electrode. The radial eddy currents and circular magnetic fields in the conductive ring of the Doll formation are analyzed by the retardation potential. According to the reciprocal symmetry of electric field and magnetic field in Maxwell’s equations and Biot-Savart Law, the characteristics of transient electric field excited by changing circular magnetic field are described, the variation law of eddy current field is explored, and the response of electrode excitation was reclassified into undesired signal and desired signal. The full-space geometric factors of desired signals in the transient electromagnetic field excited by a single electrode are calculated by referring to the inference ideas of the Doll conductive ring model and Ampere circuital theorem. The results show that the eddy current in the area surrounded by the magnetic ring is proportional to the conductivity of the formation, and the intensity of the re-excited electric field, which can also be called a secondary field, can be used as the desired signal of the excited response of the electrode. The signal can be expressed as a weighted average of geometric factors and formation conductivity. This paper describes a new way for the data processing of transient electromagnetic responses excited by electrodes. The spatial distribution of geometric factors of the desired signal excited by electrodes received along the x, y, and z directions in the test well and an adjacent well is presented and compared with the Doll geometric factor. This new method allows the spatial distribution to be measured by the transient electromagnetic response of the electrode excitation and provides a theoretical basis for cross-hole exploration.