Study on the detection technology and response of isolated anomalous bodies in transient electromagnetic wave logging of formations

Transient electromagnetic wave logging is one of the key methods for detecting underground formations, especially for identifying anomalies near wells using higher frequencies and resolutions. In this paper, the 3D TDFD (three-dimensional time-domain finite-difference) simulation method is used to investigate the detection technique of wellbore anomalies based on the scattered field of transient electromagnetic waves and its significance in underground structure identification and localization. The research results show that isolated anomalies can be effectively characterized by extracting the scattering field response generated by block-shaped anomalies while eliminating the contribution of background media. Analyzing the measurement response caused by scatterers provides important information about the position, size, and response magnitude of the anomalies, offering an effective method for detecting and identifying wellbore anomalies. Applying this detection technique enriches the existing methods for wellbore anomaly detection, providing important theoretical and technical foundations for petroleum and solid mineral exploration, as well as the construction of underground defense engineering.


Introduction
Transient electromagnetic wave logging is an effective geophysical exploration method widely used in underground resource exploration and geological engineering [1][2][3] .The detection and identification of isolated anomalous bodies are crucial in understanding the physical properties of subsurface media and hydrogeological characteristics and evaluating and developing mineral resources [4][5] .Transient electromagnetic wave logging technology excites transient electromagnetic fields.It measures the response of the subsurface media to electromagnetic waves, providing information about the physical properties and structural characteristics of the subsurface media.Unlike traditional direct current resistivity logging methods, transient electromagnetic wave logging offers higher resolution and greater detection depth, providing more accurate and detailed subsurface media information [6][7][8][9][10] .However, the

3D Time-Domain Finite-Difference Method for Transient Electromagnetic Fields
We expand the curl equations of the electric field and magnetic field in Maxwell's equation in a medium with losses in the Cartesian coordinate system (x, y, z) in component form. And, For B z , after obtaining B x and B y , we employ the low-frequency approximation [11][12] and solve for B z based on the condition of zero divergence.
In the equations, σ represents the conductivity of the geological formation, and γ represents the imaginary permittivity.
Based on the staggered grid of the electromagnetic field in the time-domain finite-difference algorithm, as shown in Figure 1, we discretize the computational space and time.By combining Figure 1 with Equations (1) and (2) in the Cartesian coordinate system, we can derive the difference equations for three-dimensional FDTD (Finite-Difference Time Domain).

Simulation and Analysis of Isolated Anomalous Body Response to Transient Electromagnetic Waves
To investigate the relationship between the position of anomalies and the distance from the detection instrument, a 3D-FDTD method was used for simulation.In the simulation, the source-to-detector distance was set to 40 inches.The background was modeled as an infinitely thick homogeneous formation with a 20 Ω•m resistivity.The anomaly was a 2 m × 2 m × 2 m isolated three-dimensional block with a resistivity of 1 Ω•m.The distances between the anomaly and the transmitting axis were 2, 3, 5, and 7 meters.Figure 2 illustrates the measured induced electromotive force curves when the instrument is positioned at the longitudinal center of the anomaly and different distances from a lowresistivity anomaly on the right.The simulation results show that the overall field response of the transient electromagnetic field measurement, as shown in Figure 2(a), is not sensitive to isolated anomalies near the well.The response curve exhibits minimal noticeable changes.However, the contribution of the scattered part caused by the three-dimensional isolated anomaly is obtained by subtracting the background medium response, as shown in Figure 2(b).The graph shows that the appearance time of the scattered contribution caused by the anomaly is directly proportional to its distance from the instrument.When the anomaly is closer to the instrument, the scattered contribution appears earlier, and the response amplitude of the contribution is greater.As time progresses, eddy currents pass through the low-resistivity anomaly and propagate deeper into the geological formation.This leads to accelerated attenuation of the induced electromotive force generated by the scattered part.Eventually, it coincides with the response of the background medium.In the case of a three-dimensional isolated anomaly model, the anomaly size was set at 2 m×2 m×2 m, with an anomaly resistivity of 10 Ω•m and a background resistivity of 100 Ω•m.When the target body was located 2 m to the right of the transmitting axis, the total field response was obtained by moving the instrument along the axis and measuring the induced electromotive force at various depth points, as shown in Figure 3. From the figure, it can be observed that no apparent detection of any anomaly is observed in the total field response, and the amplitude variations at different depth points are similar.
Figure 3 Total field response of Three-Dimensional Block-Like Anomaly Near a Well Therefore, we subtract the contribution of the background medium from the total measured response to isolate the scattering contribution caused by the three-dimensional isolated block-like anomaly.Figure 3(a) illustrates the two-dimensional spectrum of the scattering response.By observing the abnormal region in the plot, it is evident that the scattering contribution spectrum exhibits exceptional signals in a specific area.The longitudinal position of this abnormal region corresponds to the longitudinal position of the anomaly, with the center of the abnormal region corresponding to the center of the anomaly's longitudinal position.Additionally, the half-width points of the abnormal region correspond to the upper and lower boundaries of the anomaly's longitudinal position.
After moving the anomaly to a position 7 m to the right of the transmitting axis, the 2D spectral analysis of the measurement response caused by the scattering body was performed using the same measurement method, as shown in Figure 4(b).By observing the image, the longitudinal center position of the anomaly can be identified, demonstrating the effectiveness of the scattering field contribution.Additionally, it can be noted that the axial position of the anomaly remains the same but is shifted backward on the time axis.Furthermore, the scattering field response area is significantly reduced compared to the case where the anomaly is 2 m away from the receiving coil.Despite this, the central position of the anomaly can still be recognized.
Furthermore, when two isolated anomalies with the same resistivity, size, and radial distance from the instrument are present 2 m to the right of the instrument, one located above the receiving coil and the other below, with a vertical distance of 3 m from the receiving coil.By excluding the field contributions caused by the background medium, the 2D spectrum in Figure 4(c) is obtained.The abnormal regions are clearly separated for these two anomalies near the well, allowing for clear observation and accurate identification of their presence.Therefore, by analyzing the scattering field contribution generated by the scattering body, we can conclude that the anomaly identification method based on the scattering field has significant feasibility and can provide accurate and intuitive information about isolated anomalies.By analyzing the measurement response caused by the scattering body, we can obtain important information about the position, size, and response scale of the anomaly.This provides an effective method for the detection and identification of isolated anomalies.

Conclusions
The study on three-dimensional block-shaped anomalies near a well reveals that the total field response of transient electromagnetic wave measurements is not sensitive to these anomalies, as there is no significant change in the response curve.However, by excluding the contribution of the background medium, the scattering portion caused by these anomalies can be successfully isolated.Simulation results indicate that the response time of block-shaped anomalies is directly related to their distance from the instrument, with closer anomalies generating earlier and stronger scattering contributions.
Greater contrast between the geological formation and the anomalies leads to higher induced electromotive force and more pronounced responses.The anomaly identification method based on the scattering field shows promising feasibility in detecting well vicinity anomalies in transient electromagnetic wave logging, providing valuable information for subsurface structure identification and localization.However, practical applications require further consideration of background medium complexity, instrument parameter optimization, and data processing algorithm improvement to enhance detection effectiveness and accuracy.These research findings offer valuable guidance for underground resource exploration and engineering applications, with the potential for significant advancements in subsurface exploration.

Figure 1
Figure 1 Staggered grid in the Cartesian coordinate system

Figure 2
Figure 2 Response of Low-Resistivity Anomalies at Different Locations (a) Total field response (b) Scattered object contribution

Figure 4
Figure 4 3D block anomaly scattered response near the wellbore (a) Anomaly body at a distance of 2 m from the receiver coil (b) Anomaly body at a distance of 7 m from the receiver coil (c) Scattered response of two isolated anomaly bodies