J. Cent. South Univ. (2019) 26: 1011-1020
DOI: https://doi.org/10.1007/s11771-019-4067-x
Calculation and application of full-wave airborne transient electromagnetic data in electromagnetic detection
JI Yan-ju(嵇艳鞠)1, 2, ZHU Yu(朱宇)1, YU Ming-mei(于明媚)4,LI Dong-sheng(黎东升)3, GUAN Shan-shan(关珊珊)1
1. College of Instrumentation and Electrical Engineering, Jilin University, Changchun 130026, China;
2. Key Laboratory of Earth Information Detection Instrumentation of Ministry of Education, Jilin University, Changchun 130026, China;
3. National Geography Exploration Equipment Engineering Research Center, Jilin University,Changchun 130026, China;
4. StarNav Navigation Equipment Co., Ltd., Chongqing 400084, China
Central South University Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019
Abstract: Airborne electromagnetic transient method enjoys the advantages of high-efficiency and the high resolution of electromagnetic anomalies, especially suitable for mining detection around goaf areas and deep exploration of minerals. In this paper, we calculated the full-wave airborne transient electromagnetic data, according to the result of numerical research, the advantage of switch-off time response in electromagnetic detection was proofed via experiments. Firstly, based on the full-wave airborne transient electromagnetic system developed by Jilin University (JLU-ATEMI), we proposed a method to compute the full-waveform electromagnetic (EM) data of 3D model using the FDTD approach and convolution algorithm, and verify the calculation by the response of homogenous half-space. Then, through comparison of switch-off-time response and off-time response, we studied the effect of ramp time on anomaly detection. Finally, we arranged two experimental electromagnetic detection, the results indicated that the switch-off-time response can reveal the shallow target more effectively, and the full-waveform airborne electromagnetic system is an effective technique for shallow target detection.
Key words: airborne electromagnetic transient method; full-waveform; FDTD approach; convolution algorithm; anomaly detection
Cite this article as: JI Yan-ju, ZHU Yu, YU Ming-mei, LI Dong-sheng, GUAN Shan-shan. Calculation and application of full-wave airborne transient electromagnetic data in EM detection [J]. Journal of Central South University, 2019, 26(4): 1011–1020. DOI: https://doi.org/10.1007/s11771-019-4067-x.
1 Introduction
In the last decade, airborne time-domain electromagnetic method (ATEM) has become an effective technology for mineral exploration, geological survey, groundwater exploration and environmental monitoring owning to its advantages of high detection efficiency and low cost [1–3]. Particularly, with the developments of digital acquisition technology and data processing, airborne electromagnetic detection systems (including Aero-TEM, NEWTEM, Hoistem, VTEM, Heli-GEOTEM and SkyTEM systems) have been successfully applied to the geophysical exploration and resource investigations [4–7]. Previously, the airborne time-domain electromagnetic method records data at the off-time section. However, in recent years, it has been found that the secondary field data in the switch-off-time section carry a lot of valuable information about shallow targets [8, 9]. Therefore, a kind of full-waveform airborne electromagnetic system with trapezoidal current (JLU-ATEMI system, see Figure 1) was developed by Jilin University based on integrating the advantages of Aero-TEM and VTEM systems. This full-waveform electromagnetic system can efficiently record electromagnetic response during the switch-off-time section and off-time section. And hence, it is suitable for anomaly detection of shallow and deep targets.
Figure 1 Diagram of JLU-ATEMI system
In recent years, many researchers focused on the numerical modeling and inversion of airborne transient electromagnetic data. XU et al [8] used the source discrete method to calculated the full-waveform response of trapezoidal transmitting current. JI et al [9] used the equivalent approximation method to study the electromagnetic response of switch-off-time section and off-time section, and analyzed the detection resolution with the existence of cover layer. YIN et al [10, 11] calculated the full-waveform response of the homogenous half-space excited by the half-sine wave and trapezoidal wave current. QI et al [12] reported an algorithm of airborne transient electromagnetic modeling and inversion under the situation of full attitude change. JI et al [13] calculated the airborne transient electromagnetic response using the CFS-PML in Source-free Media. LIU et al [14] applied the resistivity-depth imaging method to airborne TEM data interpretation based on horizontal sheet model. CLAPROOD et al [15] utilized the weighted multi-linear regression method to study the detection and classification of airborne time-domain electromagnetic anomalies.
In this paper, the performance of switch-off time response in shallow target detection was well demonstrated. For this purpose, we calculated the full-wave airborne transient electromagnetic response using the FDTD approach and convolution algorithm, and proofed the advantage of switch-off time response in electromagnetic detection through comparison of numerical response (switch-off-time response and off-time response). According to the results of numerical research, the experimental electromagnetic surveys were arranged to further verify effectiveness of switch-off-time response in shallow target identification.
2 Full-waveform transient electro- magnetic response calculation of 3D model
In this section, the FDTD method is used to calculated the 3D electromagnetic response of step-wave, and the step-wave response is transformed to ramp-step-wave response by the convolution algorithm.
2.1 3D transient modeling based on FDTD
In this study, the FDTD method is applied to the transient-electromagnetic modeling. Under the quasi-static approximation, Maxwell’s equations are used as the governing equations to describe the transient electromagnetic fields in linear, isotropic and source-free media. The two Maxwell’s curl equations are employed to advance the electric fields and the magnetic fields of Bx and By. Moreover, Maxwell’s divergence equation of magnetic field is incorporated into the calculation, and the magnetic field of Bz is advanced by using Bx and By [16]. The governing equations can be expressed as formulas (1) and (2).
(1)
(2)
where γ is the fictitious dielectric constant, σ is the electric conductivity. As shown in Figure 2, the computational earth model is divided into a number of prisms using Yee staggered grids. The electric and magnetic fields are defined at the edge and face of grid, the electric field components (Ex, Ey and Ez) are located at the center of the edges, while the magnetic field components (Hx, Hy and Hz) are located at the center of the faces. For the time-staggering scheme, we define the electric field at integer time indices and the magnetic field at intermediate time indices, the electric fields are extrapolated at t=tn+1 and the magnetic fields are extrapolated at t=tn+1+Δtn+1/2. The semi-analytical solutions of the homogeneous half-space are employed for field initialization, a upward- continuation boundary condition is implemented at the air-earth interface [16]. The formulas of electric and magnetic fields advance are presented in the appendix. At the initial time t0 (t0=1.13 μσΔ2, where μ, σ and Δ are respectively, the magnetic permeability, conductivity and grid spacing), the semianalytical responses of a homogeneous half-space are calculated for field initialization.
As the numerical verification method used by SUN et al [17], we also check our FDTD solution against analytical solution. Figure 3 shows the FDTD solutions of homogeneous half-space (0.1 S/m and 0.01 S/m), and the analytical solutions are used as the comparison. We can see that the FDTD solutions are highly in agreement with the analytical solutions.
2.2 Full-waveform electromagnetic response transformation using convolution algorithm
According to the research proposed by YIN et al [11], the time-domain electromagnetic response using any transmitting current can be expressed by the convolution equations:
(3)
(4)
where I(t) is the transmitting current, h(t) is the impulse response of magnetic field and Bs(t) is the step response of magnetic field.
Figure 2 Discretization of earth model by staggered grids (a) and location of electromagnetic fields in Yee grid (b)
Figure 3 Comparison of FDTD solution with analytical solution:
Figure 4 Ramp-step wave and step-wave
To verify the correctness of full-waveform electromagnetic calculation, the ramp-step-wave response (dBR) and step-wave response (dB) are compared (shown in Figure 5). The relationship between dBR and dB can be expressed as the following equation:
(5)
F(t, tr) is a correction function, it can be wrote as Eq. (6) when the response of homogenous ground is calculated [18].
(6)
We know from the Eq. (6) that, for one certain sampling time t, the shorter the ramp time (tr) is, the closer the values for dBR/dt and dB/dt. When limtr=0, the value of F(t,tr) approximately equals to 1, this is an important factor to validate our calculations. According to this characteristic, we calculated the ramp-step-wave response by reducing the ramp time gradually, and verified the calculation by comparing the ramp-step-wave response with step-wave response. Figure 5 shows the comparison of different ramp time, we can see that the ramp-step-wave response is very close to the step-wave response when the ramp time is 0.001 ms.
To further verify the calculation, the relative errors between ramp step-wave response and step- wave response are calculated. Figure 6 shows the relative error curves of three ramp times. It can be seen that the relative errors get smaller with the decreasing of the ramp time, and the relative error is less than 0.1% after 6 ms when the ramp time is 1 μs. The results in Figures 5 and 6 indicate that the calculation of full-wave response is correct.
Figure 5 Comparison of ramp-step responses with different turn-off time
Figure 6 Relative errors between ramp step-wave response and step-wave response.
3 Effect of ramp time in anomaly detection
To analyze the effect of ramp time in anomaly detection, the full-wave electromagnetic responses of a 3D model are calculated, and three ramp times (0.2, 0.5 and 1 ms) are selected in the calculation. In this model, the surrounding medium is 0.01 S/m and a anomaly body with 0.1 S/m is placed at a shallow depth of 50 m (as shown in Figure 7). All the parameters in the calculation are the same as JLU-ATEMI system.
Figure 7 Sketch map of 3D model
JI et al [19] proposed a method to remove the primary field form TEM data, and this method is also used in the current study. After the removal of primary field, the anomaly responses of switch-off- time section and off-time section are shown in Figures 8–10.
From Figures 8–10, whether the switch off time response or off time response, we can see that the early sampling time signal has the larger amplitude. When the ramp time is 1 ms (Figure 8), the amplitude differences of the switch-off-time response and off-time response (at the same sampling time) are the smallest, the maximum amplitude difference is only about 0.8 nT/s. When the ramp time is 0.5 ms, the maximum amplitude difference is 2.8 nT/s. When the ramp time is 0.2 ms, the amplitude of switch-off-time response is 65 nT/s (sampling time is 0.066 ms), while that of the off-time response is 5 nT/s, the maximum amplitude difference can reach 60 nT/s. Therefore, we can get the higher anomaly response by reducing the ramp time, which is benefit for the anomaly detection of shallow target. According to the EM diffusion theory [20], the TEM method is not good to reveal the high resistive material, so the high resistive detection is not studied in this paper.
Figure 8 Switch-off-time response and off-time response (ramp time is 1 ms)
Figure 9 Switch-off-time response and off-time response (ramp time is 0.5 ms)
Figure 10 Switch-off-time response and off-time response (ramp time is 0.2 ms)
4 Detection experiment of full-waveform electromagnetic response
To validate the detectivity of full-waveform electromagnetic response, we designed two experimental EM surveys, the anomaly loops were used to instead of 3D target.
4.1 Performance of full-wave detection on laboratory experiment
The laboratory detection experiment was arranged at a mobile platform, as shown in Figure 11. The EM system can be moved with the platform along x, y and z directions, and an anomaly loop (radius 0.3 m) was placed at 1 m below the receiving coil. Table 1 shows the parameters of the laboratory detection experiment.
Figure 11 Laboratory detection experiment on a mobile platform
Table 1 Experimental parameters for indoor anomaly loop test
After the data acquisition, the noise reduction methods were used to remove the noise from EM data [21–23]. Figure 12 shows the profile curves of switch-off-time section, and the profile curves of off-time section were used as the comparison. From this figure, we can see that the amplitude of switch-off-time response is clearly larger than the off-time response. The curves of switch-off-time section can clearly describe the high-conductivity target.
To further study the full-wave electromagnetic response in anomaly detection, the slice maps of switch-off-time response are shown in Figure 13, and the slice maps of off-time response are also used as the comparison. In Figures 13(a)–(c), a circular electromagnetic anomaly can be distinctly observed in the center of the figure even under the influence of noise, its size is basically the same as the anomaly loop. Although we also can observe the electromagnetic anomaly in Figure 13(d)–(f), but the size and location of anomaly are not well revealed.
Figure 12 Switch-off-time response with 14 ms time constant (a) and off-time response with 14 ms time constant (b)
4.2 Performance of full-wave detection on simulated ATEM survey
In 2010, we carried out the full-waveform detection experiments in Changchun, Jilin province, China. The place was far away from downtown with lower artificial noise. The experimental diagram and field work picture are shown in Figure 14, and the experimental parameters are shown in Table 2. The experiment used a crane for JLU- ATEMI carrying to simulate the ATEM detection, we also used an anomaly loop to instead of 3D target.
Figure 15 shows the profile curves of switch- off-time section and off-time section, we can see that the amplitude of switch-off-time response is obviously higher than that of off-time response. This characteristic is beneficial to anomaly detection, especially for the shallow anomaly. The slice maps of switch-off-time response and off-time response at 0.066 ms are shown in Figure 16, showing that the anomaly loop is well revealed by the switch-off-time response.
Figure 13 Slice maps of switch-off-time response at three sampling time:(The anomaly loop is indicated by the red line)
Figure 14 Measuring diagram with crane (a) and field work picture (b)
Table 2 Parameters of simulated ATEM experiment
Figure 15 Switch-off-time response with 14 ms time constant (a) and off-time response with 14 ms time constant (b)
5 Conclusions
In this paper, the full-wave transient electromagnetic response of 3D target calculation was proposed by using the FDTD method and convolution algorithm. Based on the calculation result, we studied the full-wave transient electromagnetic response on shallow anomaly detection, showing that the switch-off-time response had the higher than the off-time response, this characteristic is beneficial to anomaly detection. We also arranged two experimental EM surveys to test the detectivity of full-waveform electromagnetic response, the results indicated that the switch-off-time response can reveal the shallow target more effectively, and the full-waveform airborne electromagnetic system is an effective technique for shallow target detection.
Figure 16 Slice maps of switch-off-time response and off-time response at 0.066 ms:
Acknowledgements
We thank editors and reviewers for their helpful comments. Our study was carried out within the framework of the projects ‘Research on The Anomalous Diffusion of Time-domain Electromagnetic Detection based on Fractional- order Finite-difference (41674109)’ supported by the National Natural Science Foundation of China, the authors thank the members of the two project committees.
Appendix
The advance formulas of electric fields:
(A1)
(A2)
(A3)
The advance formulas of magnetic fields:
(A4)
(A5)
(A6)
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(Edited by HE Yun-bin)
中文导读
全波形时域航空电磁数据的计算及其在电磁探测中的应用
摘要：航空瞬变电磁法具有探测效率高、电磁异常分辨率高等优点，尤其适用于深部矿产及老矿区周边的资源探测。本文模拟了全波形航空电磁数据，结合数值研究的结果，通过实验验证了关断期间段电磁响应在异常探测中的优势。首先，基于吉林大学研制的航空瞬变电磁系统(JLU-ATEMI型)，采用时域有限差分方法和卷积算法计算了三维模型的全波形航空瞬变电磁响应，并通过均匀半空间模型验证了计算的正确性；然后，对比关断期间段和关断后段的电磁响应，研究了下降沿时间对于异常探测的影响；最后，开展了两组电磁探测实验，结果表明关断期间段的电磁响应能够更有效地揭示浅层目标体，航空瞬变电磁系统对于浅层目标探测是一种有效的技术手段。
关键词：航空瞬变电磁法；全波形；时域有限差分；卷积算法；异常探测
Foundation item: Project(41674109) supported by the National Natural Science Foundation of China
Received date: 2017-12-13; Accepted date: 2018-09-04
Corresponding author: LI Dong-sheng, PhD, Engineer; Tel: +86-17790096370; E-mail: lidongsheng@jlu.edu.cn; ORCID: 0000-0003- 0008-6687; GUAN Shan-shan, PhD, Lecturer; Tel: +86-17790072253; E-mail: guanshanshan@jlu.edu.cn; ORCID: 0000-0003-4168-8502
