Ground-air transient electromagnetic data rapid processing and anomaly analysis method

Abstract

The invention belongs to the technical field of geophysical exploration, and discloses a ground-air transient electromagnetic data rapid processing and anomaly analysis method, which comprises the following steps of: preprocessing a pulse signal acquired by a receiving coil by adopting a time window interception strategy, and extracting an effective secondary field response signal; constructing a terrain-containing three-dimensional half-space resistivity model, and performing numerical simulation and interpolation to obtain a dense induced electromotive force data set; comparing the induced electromotive force calculated values of different resistivity measuring lines with the actually measured data, and analyzing an abnormal geologic body; the observed induced electromotive force is divided into a plurality of areas in a time domain and a space domain, the optimal apparent resistivity is searched in each area according to the change rule of the induced electromotive force along with the resistivity, and underground space abnormal distribution is displayed. According to the method, the problems of difficult interpretation, low inversion efficiency and large error of the existing air-ground transient electromagnetic data are solved, the processing efficiency and the analysis precision are considered, the dependence on computing resources is reduced, the underground anomalous body can be quickly identified, and the method is suitable for resource exploration scenes under various complex terrains.

Description

Technical Field

[0001] This invention belongs to the field of geophysical exploration technology, specifically relating to a method for rapid processing and anomaly analysis of transient electromagnetic data between the ground and the air. Background Technology

[0002] The ground-to-air transient electromagnetic method (SATEM), also known as the semi-airborne transient electromagnetic method, is a transient electromagnetic method that uses a long ground-based conductor source or large loop to transmit electromagnetic signals, while an unmanned aerial vehicle (UAV) carries a receiving coil for aerial observation. Compared to traditional ground-based electromagnetic methods, this transmitter-receiver configuration offers higher detection efficiency and can achieve greater detection depths compared to traditional airborne electromagnetic methods. Furthermore, it features wide spatial coverage, high sampling density, and simultaneous in-flight observation, resulting in outstanding experimental efficiency and excellent adaptability to complex terrain. Therefore, it has unique advantages in areas where conventional detection methods are difficult to implement, such as mountains, deserts, hills, lakes, and areas with vegetation cover, demonstrating broad application prospects in various resource exploration fields, including minerals, groundwater, and geothermal energy.

[0003] In recent years, researchers have made significant progress in SATEM data processing and imaging methods. However, this technology still faces many unresolved problems, and the commercialization of existing systems is low, making it difficult to meet the needs of practical engineering applications. Theoretically, based on the differentiated electromagnetic field attenuation characteristics exhibited by different underground media resistivity, SATEM has the ability to reconstruct the spatial distribution of underground resistivity, providing theoretical support for the detection of underground anomalies. However, existing research generally agrees that reliable interpretation of SATEM data remains one of the core issues restricting the engineering application and improvement of the method's fine imaging capabilities. The fundamental reason is that the spatial separation between the SATEM transmitter and receiver significantly complicates the propagation and attenuation process of the underground induced electromagnetic field. The superposition of the transmitted and diffused signals with the attenuation response signals corresponding to the underground anomalies makes the physical meaning of the observation data less intuitive, increasing the difficulty of interpretation. Simultaneously, the anomaly attenuation information directly related to the underground resistivity structure accounts for only a very small proportion of the total energy of the observation data, resulting in a low signal-to-noise ratio. Furthermore, the data is highly susceptible to interference from complex terrain conditions, changes in UAV flight attitude, environmental noise, and instrument noise, further affecting data quality. Against this backdrop, how to stably and effectively extract key information reflecting changes in underground resistivity from SATEM measured data has become a pressing technical challenge in the industry. This also places higher demands on the rationality of SATEM data processing procedures, the efficiency of inversion methods, and the reliability of noise suppression technologies.

[0004] To enhance the constraint of inversion results on underground resistivity structures, current research is gradually introducing large-scale 3D SATEM inversion imaging methods based on massive observational data, achieving some success in some applications. However, this type of 3D inversion is usually accompanied by extremely high computational costs and is highly dependent on computing resources and parallel computing power, limiting its promotion and rapid application in practical engineering. More importantly, in many engineering and resource exploration scenarios, research focuses on the identification and characterization of local anomalies rather than the overall imaging of the entire 3D region, making full 3D inversion not the optimal choice in terms of efficiency and target matching.

[0005] Under these circumstances, two-dimensional inversion imaging has been widely used in transient electromagnetic methods due to its lower computational complexity and higher efficiency. For the conventional overlapping loop transient electromagnetic (TEM) method, simplifying the subsurface medium into a two-dimensional structure has a reasonable physical basis, as the transmitter and receiver coils are highly spatially overlapping, and the observed signal is mainly controlled by the subsurface structure in the vicinity of the receiver point. However, for the SATEM method, this two-dimensional assumption is often difficult to hold. Due to the significant spatial separation between the transmitter and receiver, the electromagnetic response recorded at the receiver point is not only closely related to the properties of the nearby subsurface medium but also influenced by the combined effects of the subsurface electrical structure along the propagation path from the transmitter to the receiver, further compounded by the modulation effects of three-dimensional topographic undulations and non-uniform surface conditions. Therefore, simply using a two-dimensional model approximation in SATEM data interpretation often ignores crucial three-dimensional propagation and coupling effects, introducing significant systematic errors and severely limiting the reliability and interpretation accuracy of the inversion results. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention provides a method for rapid processing and anomaly analysis of ground-to-air transient electromagnetic data. During data processing and imaging, it fully considers the three-dimensional diffusion characteristics of electromagnetic fields in underground media and the influence of complex terrain conditions on the observation response. It is applicable to various types of emission source configuration scenarios, such as magnetic sources and electrical sources, and has strong versatility and adaptability.

[0007] The method for rapid processing and anomaly analysis of transient electromagnetic data between ground and air as described in this invention includes the following steps: Step 1: Preprocess the pulse signal acquired by the receiving coil in the time domain to obtain an effective secondary field response signal; Step 2: Based on the secondary field response signal, construct a three-dimensional half-space resistivity model including terrain; Step 3: Identify and analyze anomalous geological bodies by comparing the calculated values ​​of induced electromotive force from different resistivity survey lines with actual observation data; Step 4: Divide the observed induced electromotive force into multiple regions in the time and spatial domains. Based on the variation law of induced electromotive force with resistivity, search for the optimal apparent resistivity in each region. Visualize all apparent resistivities to obtain the results of the anomaly distribution in underground space.

[0008] Furthermore, step 1 specifically includes: For each transient electromagnetic attenuation signal, a time window truncation strategy is applied. The time window truncation strategy is as follows: taking the maximum amplitude point of each impulse response curve as the starting point, truncates to within 1ms after the peak value as the effective secondary field response time window.

[0009] Furthermore, step 2 specifically involves: A three-dimensional geological model with topography was created for the exploration target area, and finite volume numerical simulation of the electromagnetic field was performed using the open-source software SIMPEG to obtain a dataset of induced electromotive force containing three dimensions: resistivity, spatial coordinates, and time. Where E is the induced electromotive force, ρ is the resistivity, x is the spatial coordinate, and t is the time. Interpolate the data along the resistivity dimension to obtain a denser dataset of induced electromotive force. , This is the interpolated resistivity.

[0010] Furthermore, step 4 specifically involves: In the time domain, the induced electromotive force is divided into three regions, each representing a different detection depth. Spatially, it is divided into 35 regions with 10 measuring points per group. The optimal resistivity sought simultaneously satisfies the minimum residuals of both the observed data and the background resistivity. Since the induced electromotive force always increases and then decreases with the change of apparent resistivity, the optimal resistivity can always be found that satisfies the following formula: , in, For the nth time window, the actual observed induced electromotive forces in the kth measuring point area, For the theoretically calculated and interpolated nth time window, the region of the kth measuring point contains all induced electromotive forces. This is the optimal background resistivity found. For all nth time windows, the apparent resistivity of the kth measurement point region; Background resistivity The search method is as follows: , in, For all induced electromotive forces actually observed, All induced electromotive forces obtained from theoretical calculations;

[0011] The beneficial effects of this invention are as follows: 1) High efficiency and low computational overhead: This invention can achieve data overlay through time window truncation, thereby improving the signal-to-noise ratio; at the same time, it can complete anomaly identification and rapid imaging with only ten or fewer 3D forward modeling calculations. Compared with traditional large-scale 3D inversion methods, it can significantly reduce the demand for computing resources and time costs, saving several to tens of times. It is particularly suitable for scenarios with high timeliness requirements such as engineering exploration and rapid decision-making. 2) Avoiding systematic errors of traditional two-dimensional methods: This invention does not rely on the assumption of simplifying the underground medium into a two-dimensional structure, thus avoiding systematic errors introduced by the simplification of model dimensions; through a finite number of three-dimensional forward modeling calculations, the spatial distribution of the underground electromagnetic response is quickly constrained and analyzed, which can more realistically reflect the resistivity distribution characteristics of the underground medium and provide more reliable underground structural information for the detection of underground anomalies; 3) High-precision anomaly identification and semi-quantitative imaging: Even with a significant reduction in computational load, the method described in this invention can still accurately determine the spatial location and scale of low-resistivity anomalies (such as goaf, water bodies, ore bodies, etc.); it is also adaptable to complex terrain (such as mountains, swamps, lakes) and various emission source configurations (magnetic sources, electrical sources), demonstrating strong adaptability. 4) Strong versatility and practicality: This invention fully considers the three-dimensional diffusion characteristics of electromagnetic fields and the influence of terrain. It is not only suitable for data processing of small-scale, two-dimensional survey lines, but also takes into account the detection depth (inheriting the advantages of ground-to-air TEM, reaching several kilometers) and work efficiency (airborne reception and rapid on-site processing). It is superior to pure airborne electromagnetic methods in terms of signal-to-noise ratio and adaptability to complex terrain, and superior to pure ground electromagnetic methods in terms of processing efficiency and cost control. It has a wide range of applications. 5) Outstanding engineering application value: This invention is particularly suitable for scenarios that require fast, efficient and reliable results, such as resource exploration, goaf detection, tunnel advanced geological prediction, and hydrogeological survey; compared with existing ground-to-air transient electromagnetic technology, it further improves the speed and practicality of data processing while maintaining a high signal-to-noise ratio. Attached Figure Description

[0012] Figure 1 This is a flowchart of the method described in this invention; Figure 2 This is a schematic diagram of the original acquired signal and the time window truncation result; Figure 3 It is the induced electromotive force curve of a certain receiving point simulated before and after interpolation at different resistivities; Figure 4 It is the induced electromotive force curve of a certain receiving point simulated by different resistivities after interpolation; Figure 5It is a time-division windowed apparent resistivity imaging of transient electromagnetic fields between ground and air. Detailed Implementation

[0013] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings.

[0014] like Figure 1 As shown, the method for rapid processing and anomaly analysis of ground-to-air transient electromagnetic data according to the present invention includes the following steps: Step 1: Preprocess the pulse signal acquired by the receiving coil in the time domain to obtain an effective secondary field response signal; Step 2: Based on the secondary field response signal, construct a three-dimensional half-space resistivity model including terrain; Step 3: Identify and analyze anomalous geological bodies by comparing the calculated values ​​of induced electromotive force from different resistivity survey lines with actual observation data; Step 4: Divide the observed induced electromotive force into multiple regions in the time and spatial domains. Based on the variation law of induced electromotive force with resistivity, search for the optimal apparent resistivity in each region. Visualize all apparent resistivities to obtain the results of the anomaly distribution in underground space.

[0015] In a ground-to-air electromagnetic system, the transmitter alternately emits shut-off pulse signals in the positive and negative directions, and the receiving coil on the UAV collects a large number of pulse signals in the time domain. In this invention, it is first necessary to perform time window truncation on each transient electromagnetic attenuation signal. Since the energy of each pulse signal is weak in the later stage (usually more than 10ms), it is more susceptible to interference; there is a region of increased energy in the early stage (i.e., the signal has not yet started to attenuate, and the energy in the Z direction is in the rising stage due to the influence of the primary diffusion field). This part of the signal is mainly a primary field signal and needs to be cut off. Therefore, the time window truncation of this invention is selected within 1ms after the maximum energy.

[0016] In ground-to-air transient electromagnetic detection systems, ground-based transmitters typically employ a bipolar alternating turn-off pulse pattern (positive current → turn-off → negative current → turn-off, repeating cyclically) to effectively suppress static background field interference and improve the signal-to-noise ratio. A high-sensitivity receiving coil (measuring the Z component) mounted on the UAV rapidly acquires the transient response signal generated after each transmit pulse is turned off in the time domain. The typical attenuation curve after each pulse is turned off exhibits obvious stage characteristics: In the very early stage (usually within a few hundred μs), the primary field dominates, with extremely large amplitude and often accompanied by system turn-off effects (such as ramp-off overshoot); in the early stage (about a few hundred μs to 1–3 ms), the primary field decays rapidly but still leaves significant residues. At the same time, affected by the primary diffusion field, the Z component response often shows a brief amplitude increase or plateau / slow decrease. This part mainly reflects the near-surface and primary field residues, contributing very little to deep information, and is extremely susceptible to interference from UAV attitude jitter, flight altitude changes, and electromagnetic noise; in the middle and late stages (after about 3 ms, especially after 10 ms), the primary field is basically attenuated, and the signal is mainly dominated by the underground secondary field, exhibiting classical exponential or power-law attenuation. However, the energy in the late stage is extremely weak and easily submerged by cultural noise, atmospheric electric field, and plateau interference, resulting in a significant decrease in signal-to-noise ratio.

[0017] To balance deep resolution with primary field interference suppression, the time window truncation strategy of this invention is as follows: taking the maximum amplitude point (peak value, usually corresponding to the vicinity of the end of the rapid decay of the primary field) of each impulse response curve as the starting point, and truncating to within approximately 1 ms after the peak value as the effective secondary field response window. This selection is based on the following reasons: the secondary field begins to gradually dominate at the peak value; within 1 ms after the peak value, it can effectively avoid the early primary diffusion field rise / plateau region, while retaining as much early-mid secondary field information as possible (most sensitive to shallow structure resolution); at the same time, it avoids truncation that introduces a large amount of primary field residue and system distortion too early, or truncation that leads to severe loss of shallow information.

[0018] To achieve this time window truncation, the pulse position must first be located. Typically, 70% of the peak value is set as a threshold, and all pulse positions exceeding this threshold are recorded. Then, a time window is truncated by taking a 0.2ms forward and a 1.2ms backward, and the time windows within each second are superimposed to improve the signal-to-noise ratio. The truncated window, starting from the pulse peak value, takes a 1ms backward to obtain the Z-component induced electromotive force recording once per second. Figure 2 As shown, where, Figure 2 (a) is the original data. Figure 2 (b) is Figure 2 Enlarged schematic diagram of the gray area in (a).

[0019] To suit complex 3D terrain scenarios, a 3D half-space resistivity model incorporating terrain needs to be constructed based on the actual layout of the transmitter and receiver points, as well as the terrain conditions within the work area. First, a terrain-integrated model of the exploration target area is created, and then finite-volume numerical simulations of the electromagnetic field are performed using the open-source software SIMPEG to simulate the induced electromotive force distribution under different resistivity half-space conditions. In this process, it is assumed that there are no anomalies, and only the influence of the diffusion field is considered. The set resistivity... The range covers common rock resistivity (typically 1000 ppm). Furthermore, the resistivity follows a uniform logarithmic distribution, and the source and receiver settings are completely consistent with the actual scenario. Through 8 to 10 forward simulations, a dataset containing resistivity, spatial, and temporal dimensions was obtained. .

[0020] Next, the data is interpolated along the resistivity dimension to obtain a denser dataset of induced electromotive force. Considering the diffusion characteristics of transient electromagnetic field propagation, the trend of induced electromotive force (EMF) changing with resistivity is consistent at any point in space; that is, the induced EMF first increases with increasing resistivity, reaches a certain inflection point, and then decreases with further increases in resistivity. For example... Figure 3 As shown, where, Figure 3 (a) is the induced electromotive force curve of a receiving point simulated with different resistivities before interpolation. Figure 3 (b) shows the induced electromotive force (EMF) curves at a receiving point simulated at different resistivities after the difference. Therefore, by simulating the induced EMF at a small number of resistivities, the induced EMF data corresponding to other resistivities can be calculated using interpolation methods, such as... Figure 4 As shown, the horizontal axis represents the measurement point, and the vertical axis represents the induced electromotive force. Figure 4 (a), (b), (c), (d), and (e) represent resistivity, respectively. , , , , The induced electromotive force curve at time, Figure 4 (f) represents the observed induced electromotive force curve.

[0021] By comparing the induced electromotive force combinations of survey lines with different resistivities with observational data, a preliminary analysis of anomalous geological bodies can be achieved. First, a comparison... Figure 4 The observed data and resistivity are relatively low ( and The observations show that both curves exhibit the same overall shape, indicating that this invention simulates the anomalous induced electromotive force characteristics caused by shallow surface topography. The early data at both ends of the observed induced electromotive force dB / dt are closer to the resistivity. In the scenario where the resistivity is close to that of the later stages, the latter stage is closer to that of the later stages. The scene, and overall the later stages of the observation data are consistent with... The scenarios are quite similar. This indicates that the resistivity of the shallow surface at both ends and the middle of the survey line is similar. As the depth increases (up to 200 meters), the deep portion of the entire survey line exhibits low resistivity, approaching... In the middle section of the survey line, at measuring point 110, a vertical strip-shaped low-resistivity structure is observed, presumably a channel between groundwater and the surface. Within the range of measuring points 120-300, the surface resistivity is generally close to 10. In this scenario, the area around measuring point 220 is somewhat of an exception. Early dB / dt values ​​are relatively flat, and the dB / dt values ​​corresponding to low resistivity cannot explain the observed data. Meanwhile, resistivity and high resistivity... The scenario might be better described, which suggests that the shallow surface resistivity in this area may be very high.

[0022] Finally, the optimal apparent resistivity is searched, and its spatial distribution can intuitively demonstrate the spatial anomaly distribution. In the time domain, the induced electromotive force is divided into three regions, each representing a different detection depth. Spatially, it is divided into 35 regions with 10 measuring points per group. The searched optimal resistivity simultaneously satisfies the minimum residuals of both the observed data and the background resistivity. The essence of this strategy is to treat the model corresponding to each spatiotemporal region as a restricted half-space, thus determining its optimal resistivity. Since the induced electromotive force always increases and then decreases with the change in apparent resistivity, the optimal resistivity can always be found that satisfies the following formula: , in, For the nth time window, the actual observed induced electromotive forces in the kth measuring point area, For the theoretically calculated and interpolated nth time window, the region of the kth measuring point contains all induced electromotive forces. This is the optimal background resistivity found. For all n-th time windows, the apparent resistivity of the k-th measurement point region.

[0023] Background resistivity The search method is as follows: , in, For all induced electromotive forces actually observed, The induced electromotive force is calculated theoretically. The SATEM observation signal can be considered as a combination of a diffuse field and an attenuation field. The diffuse field reflects the influence of background resistivity and topographic features, while the attenuation field mainly consists of residual information caused by anomalous resistivity. Since the diffuse field dominates the signal, it contains most of the information related to background resistivity and topography. Therefore, there exists a background resistivity value that minimizes the residual signal after removing the diffuse field. This is the basis for finding the optimal background resistivity.

[0024] This method was applied to ground-to-air electromagnetic (GTE) field data collected in a mountainous area. The work area contained several abandoned coal mine shafts, and the presence of water accumulation in these areas was unclear. During the survey, a drone flew over a canyon and returned along the same route to identify potential water-bearing goaf areas beneath the surface, as well as identified aquifers. The terrain elevation difference along the flight path was nearly 40 meters. To reduce costs, a large coil magnetic source was used instead of a high-power wire power transmitter. The flight measurement points were located inside the coil, with a total flight length of approximately 300 meters. The flight path traversed the underground main tunnels of the abandoned mines; since the area within 30 meters of the tunnels had been waterproofed, the likelihood of water accumulation in this area was low. Figure 5 The image shows the attenuation field imaging results and their comparison with ground-based TEM data. Figure 5 (a) is the measured GATEM data. Figure 5 (b) is ground-based TEM data. Figure 5 (c) shows the terrain distribution and the locations of TEM data measurements on the surface. Due to the round-trip flight path of the aircraft, some measurement locations were projected as two. Figure 5 (d) represents the apparent resistivity imaging results. Black circles indicate possible tunnel passages, and blue dashed lines indicate water bodies and possible seepage channels. P1-P4 represent the locations of the ground transient electromagnetic acquisition curves, respectively.

[0025] Through interpolation and optimization, the background resistivity was determined to be 130 Ω·m based on field data. Then, an attenuation field contour plot was drawn to visualize the results. Figure 5 (d), where the higher the Y-axis channel, the greater the detection depth. The X-axis corresponds to... Figure 5 The measurement point numbers are listed. A shallow negative anomaly appears in the central area, possibly reflecting low resistivity, consistent with the water-rich area at the canyon floor. The resistivity is relatively high in the middle and deep layers, while the resistivity remains low at the deepest point, indicating the presence of significant groundwater in the mined-out area below 100 meters. From... Figure 5 The imaging results show that the resistivity is higher near the flight initiation point, while the resistivity is significantly lower in the middle of the measurement line, especially near measurement point 110. This pattern is consistent with the ground transient electromagnetic response. Figure 5Consistent with (b). An exception exists near measuring point 220, where the dB / dt corresponding to low resistivity cannot explain the observed data, while resistivity and high resistivity... The scenario might correspond better, which also aligns with the electromagnetic field anomaly analysis. Measurement points P2 and P3 are located within the canyon. Figure 5 As shown in (c), their curves are significantly higher than those of P1 and P4, and their decay rate is slower, indicating that their resistivity may be lower. Furthermore, the weaker positive anomalies near measurement points 160 and 280 suggest the presence of impermeable, waterless tunnel regions. Figure 5 As shown in (d).

[0026] The above description is merely a preferred embodiment of the present invention and is not intended to further limit the present invention. All equivalent changes made based on the description and drawings of the present invention are within the protection scope of the present invention.

Claims

1. A method for rapid processing and anomaly analysis of ground-to-air transient electromagnetic data, characterized in that, Includes the following steps: Step 1: Preprocess the pulse signal acquired by the receiving coil in the time domain to obtain an effective secondary field response signal; Step 2: Based on the secondary field response signal, construct a three-dimensional half-space resistivity model including terrain; Step 3: Identify and analyze anomalous geological bodies by comparing the calculated values ​​of induced electromotive force from different resistivity survey lines with actual observation data; Step 4: Divide the observed induced electromotive force into multiple regions in the time and spatial domains. Based on the variation law of induced electromotive force with resistivity, search for the optimal apparent resistivity in each region. Visualize all apparent resistivities to obtain the results of the anomaly distribution in underground space.

2. The method for rapid processing and anomaly analysis of ground-to-air transient electromagnetic data according to claim 1, characterized in that, Step 1 is as follows: For each transient electromagnetic attenuation signal, a time window truncation strategy is applied. The time window truncation strategy is as follows: taking the maximum amplitude point of each impulse response curve as the starting point, truncates to within 1ms after the peak value as the effective secondary field response time window.

3. The method for rapid processing and anomaly analysis of ground-to-air transient electromagnetic data according to claim 1, characterized in that, Step 2 is as follows: A three-dimensional geological model with topography was created for the exploration target area, and finite volume numerical simulation of the electromagnetic field was performed using the open-source software SIMPEG to obtain a dataset of induced electromotive force containing three dimensions: resistivity, spatial coordinates, and time. Where E is the induced electromotive force, ρ is the resistivity, x is the spatial coordinate, and t is the time. A volumetric numerical simulation of the induced electromotive force dataset was performed in the resistivity dimension to obtain an induced electromotive force dataset containing three dimensions: resistivity, spatial coordinates, and time. Interpolation is performed to obtain a denser dataset of induced electromotive force. ,in, This is the interpolated resistivity.

4. The method for rapid processing and anomaly analysis of ground-to-air transient electromagnetic data according to claim 1, characterized in that, Step 4 is as follows: In the time domain, the induced electromotive force is divided into 3 regions, each corresponding to a different detection depth. In the spatial domain, the induced electromotive force is divided into 35 regions with 10 measuring points as a group. The optimal apparent resistivity is searched within each region. This optimal resistivity simultaneously minimizes both the observed data residual and the background resistivity residual, and satisfies the following formula: ， in, For the nth time window, there are all the induced electromotive forces actually observed in the kth measuring point area; For the nth time window and the kth measurement point region, which are obtained by theoretical calculation and interpolation, there are all induced electromotive forces. This is the optimal background resistivity found. For all nth time windows, the apparent resistivity at the kth measurement point; Among them, the optimal background resistivity The search method is as follows: ， in, For all induced electromotive forces actually observed, This represents all induced electromotive forces obtained from theoretical calculations.

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