Resistivity information of formation in transient electromagnetic response of cased well

To measure formation resistivity in a cased well by transient electromagnetic (TEM) method, it is necessary to understand the way of TEM energy passing through the casing into the formation, the electromagnetic field distribution area in the formation, and the response waveform of each point in the well and the formation. In this paper, the transient electromagnetic field distribution at different time and response in and out of cased well are studied using the real-axis integral. The transient electromagnetic field excited by a coil in the cased well diffuses radially and is reflected in the well wall. A few part of the energy transmits into the casing and continues to diffuse, and the most of the energy is reflected and diffused back in the well along the radius opposite direction. After collecting in the well axis, the transient field continues to diffuse along the radial direction and reaches the wall to be reflected and transmitted,…. In the casing, the transient field diffuses slowly, entering the formation, it diffuses rapidly to form transient distribution and response. It is greatly affected by the casing, and the whole transient response changes slowly. The response for each point in and outside the cased well increasing fast to peak and decreased slowly. At the moment of its the fastest rise and fall, the secondary field stimulated by the formation eddy is the strong, but the polarities are opposite. The information of the conductivity for formation at any moment t is the superposition of secondary fields generated by all formation, in which the polarity of secondary fields generated by responses is different, and in-phase superposition the amplitude of second field increases, while the anti-phase superposition decreases. The responses at different time correspond to the conductivity of formations of different radial depths.