Intelligent processing of electromagnetic data using detrended and identification

The application of the electromagnetic method has accelerated due to the demand for the development of mineral resource, however the strong electromagnetic interference seriously lowers the data quality, resolution and detect effect. To suppress the electromagnetic interference, this paper proposes an intelligent processing method based on detrended and identification, and applies for wide field electromagnetic method (WFEM) data. First, we combined the improved intrinsic time scale decomposition and detrended fluctuation analysis algorithm for removing the trend noise. Then, we extracted the time domain characteristics of the WFEM data after removing the trend noise. Next, the arithmetic optimization algorithm was utilized to search for the optimal smoothing factor of the probabilistic neural network (PNN) algorithm, which realized to intelligently identify the noise data and WFEM effective data. Finally, the Fourier transform was performed to extract the spectrum amplitude of the effective frequency points from the reconstructed WFEM data, and the electric field curve was obtained. In these studies and applications, the fuzzy c-mean and PNN algorithm are contrasted. The proposed method indicated that the trend noise can be adaptively extracted and eliminated, the abnormal waveform or noise interference can be intelligently identified, the reconstructed WFEM data can effectively recover the pseudo-random signal waveform, and the shape of electric field curves were more stable. Simulation experiments and measured applications has verified that the proposed method can provide technical support for deep underground exploration.


Introduction
Professor Jishan He of Central South University has proposed the WFEM, that is, a controlled source electromagnetic method (CSEM) with Chinese proprietary intellectual property rights [1,2].The WFEM can obtain geoelectric information of various frequencies by sending and receiving simultaneously, improving field work efficiency and anti-interference ability [3,4].Furthermore, the WFEM still strictly defines the calculation formula for the whole region of the apparent resistivity, which can be obtained by using a single electric field component.Unlike the MT and CSAMT methods, the WFEM only measures the Ex electric field component to obtain the apparent resistivity.The WFEM has been widely applied in shale gas exploration, metal ore exploration, engineering geophysical exploration, urban geophysical exploration and so on [5][6][7][8].
However, the CSEM data cannot avoid the influence of the noise or interference, resulting in low data quality and poor exploration effect.WFEM exploration is also seriously constrained by electromagnetic interference.As a result, several scholars have developed different CSEM data denoising techniques.Zhang et al proposed a novel adaptive bidirectional mean square deviation threshold method [9].Mo et al proposed the gray system theory and robust M-estimation method [10].Chen et al proposed the gray judgment criteria and rational function filtering method [11].The data quality of less interfered data can be greatly enhanced by using these frequency domain data processing method.These mentioned methods in refers [9][10][11] are to implement CSEM data processing in the frequency domain, while the most frequency points (the maximum spectral amplitude) are mixed up the noise of frequency spectrum, these methods will fail.In addition, Yang et al proposed a CSEM noise evaluation method based on wavelet transform and Hilbert analytic envelope in the frequency domain [12].For the CSEM data processing method in the time domain, Yang et al used the time domain fragments containing noiseless or random noise to solve the noise spectrum, and obtained high-quality data [13].Li et al proposed a CSEM denoising method based on the fast Fourier transform, CEEMD, and shift-invariant sparse coding [14].Yang et al proposed a subtraction and addition method for cancellation the powerline noise [15].Ling et al proposed a high frequency information extraction method based on time-domain signal reconstruction [16].Li et al proposed inception-temporal convolutional network-shift-invariant sparse coding method for CSEM noise elimination [17].These time series denoising methods can partially improve the data quality and achieve good results for the different type of noise.Therefore, we still need to solve a fundamental technical problem that how to effectively use the novel method to identify and eliminate the electromagnetic noise.
With the development of artificial intelligence technology, these techniques have been applied for practical engineering.Machine learning is also a typical artificial intelligence technology and is widely used to the signal processing.Therefore, this paper proposes an intelligent processing method based on detrended and identification.The IITD and DFA algorithms are combined to eliminate the trend noise, and the time domain characteristics are extracted after the detrended noise.The AOA is utilized to search the optimal smoothing factor in the PNN algorithm, which achieves intelligent identification of the noisy data and the effective data.In this paper, we selected time domain characteristic parameters, combined with IITD-DFA and AOA-PNN algorithms, which were applied to WFEM signal-noise separation, so as to improve the WFEM data quality.The experiments demonstrated that the trend noise and abnormal noise waveforms can be extracted, identified and removed, and the reconstructed WFEM data can reflect the characteristics of the pseudo-random signals.The relatively stable electric field curves show that the reliable WFEM data can provide technical support for electromagnetic inversion interpretation.

Detrended fluctuation analysis (DFA)
The DFA is proposed by Peng et al, is a scale signal analysis method that suitable for analyzing the long-range correlation of signals [18,19].The scaling exponent is a measure to define the strength of autocorrelation over an extended time series.Especially for the different trends with unknown duration, DFA is a novel method for obtaining more reliable scaling exponents when the signal has non-stationary properties [20], the principle of DFA algorithm can be seen in the previous research [21].Note that the scaling exponent α of the fluctuation function is determined by analyzing the log-log plots of the root mean square fluctuation F (s) versus the length s.
The scaling exponent α is also an important parameter in the paper, and is calculated by linear least-squares regression as follows: where C is the constant, the range of s is 4 ⩽ s ⩽ 16, which is the most popular and reliable linear region, and applied in electromagnetic signal processing.

The improved intrinsic time-scale decomposition (IITD) method
ITD is an adaptive time-frequency analysis method that can be used to adaptively decompose the signal into a series of independent PR components and a residual signal [22].For the ITD method, the baseline is obtained by using a linear transformation but this is not accurate enough to obtain high precision for the signal components.In addition, the termination condition and many pseudo components which have no physical meaning lead to an increase in decomposition time.To overcome this problem, the IITD method based on spline interpolation is proposed [23,24].Among them, the spline interpolation can be regarded as a piecewise function estimation problem, the main principle is the hypothesis of continuity and smoothness.The continuity shows that the piecewise function is equal at the contact point, the smoothness is equal at the lower order derivative of the contact point.
The details of the IITD method are presented below: (1) Calculate the extreme points of the original signal.We then obtain the sequence of extreme points.The mirror extension method is applied to the sequence of extreme points, and two additional extreme points on both ends of the signal are calculated.(2) Calculate the baseline control points.The baseline signal is obtained by using non-uniform spline interpolation to fit all baseline control points.(3) After subtracting the baseline signal from the original signal.We have the new signal into which the first PR component is to be decomposed.(4) The baseline signal serves as the original signal, and the above steps are repeated until the baseline signal is a constant or monotonic function.Finally, the original signal x (t), is decomposed into a series of PR components and a residual signal r n (t), PR n (t) + r n (t) . ( Figure 1 shows the comparison of decomposition results between the ITD and IITD methods.The synthetic signal is generated, which consists of AM-FM components of 70 Hz and single-frequency signals of 30 Hz and 4 Hz.The synthetic signal is defined as follows: According to analyze the figure 1, the synthetic signal can be effectively decomposed into three layers PR components and residual component.It is clear that the PR components decomposed using ITD have a distortion in the PR 2 and PR 3 .From figure 1(b), the IITD method use the spline interpolation instead of the linear transformation, which effectively improves the waveform distortion in PR 2 and PR 3 .Thus, the spline interpolation is an important parameter to balance computational efficiency and smoothness, which can improve the smoothness of PR components after using IITD.

Detrended process and analysis
In the paper, the advantage of DFA and IITD are combined to achieve adaptive signal decomposition and reconstruction, the aim to eliminate trend noise.Figure 2 shows the flow of detrended process.
As shown in figure 2, the pending signal is decomposed by using IITD, and multiple PR components and a residual component are obtained adaptively.The scaling exponent value in DFA algorithm of PR component is calculated.We select PR components with a scale exponent value larger than 0.75 for superposition, that is reconstructed signal is obtained.Among them, the choice of 0.75 refer as [21,25,26].Finally, the trend noise of the pending data is eliminated and the reconstructed signal is obtained.Next, we applied the detrended process to analyze the simulation signal.Among them, the possible source of trend noise is temperature drift, that is, the influence of instruments and equipment on temperature in complex geological environments.This is manifested as signal distortion caused by weather changes, making the original signal trend change.Figure 3 shows the detrended effect of simulation signal in time-frequency domain.
From figure 3, the simulation signal (pseudo-random signal) with trend noise distorts the signal waveform, and the corresponding low-frequency band of spectrum appears upward trend, and the maximum spectral amplitude value also increases.The IITD combined with DFA method is used to adaptively eliminate the trend noise, improve the influence of the trend noise on the spectrum, and restore the time and frequency domain characteristics of the pseudo-random signal.

Arithmetic optimization algorithm (AOA)
The AOA is a meta-heuristic optimization algorithm proposed by Abualigah et al in 2021, which is designed based on the idea of four mixed operations (multiplication, division, subtraction, addition) [27].The AOA selects optimization strategy, global search and local development through MOA function, the multiplication and division strategy, and addition strategy and subtraction strategy, respectively.The AOA improves the dispersion of solution, and overcomes premature convergence ability, and realizes the global explore optimization and local optimization ability.Its optimization process is composed of the several steps, such as initialization, exploration and development [28].Figure 4 shows model of updating the position of math operators in AOA toward the optimum area.To verify the optimization performance of the AOA algorithm.A benchmark function (that is, the Sphere function) is used to compare their convergence.Among them, a variety of intelligence optimization algorithm such as PSO [29], ABC [30], MVO [31], MFO [32], GWO and its improved algorithm are applied [33,34].In this paper, we set the population size is 20, and the maximum number of iterations is 100.Figure 5 shows convergence comparison of the sphere function.
From figure 5, the Sphere function has many local minima except for the global one, which has the features of continuous, convex and unimodal.The left plot shows its two-dimensional form.The right plot shows the solution accuracy and convergence speed.The AOA is better than other intelligent optimization algorithms at the same population and the iteration number.Through the convergence analysis, we can see that the AOA algorithm has obvious advantages in the optimization ability and stability of sphere function and can better jump out of local optimization and obtain higher global optimization ability.

Probabilistic neural network (PNN)
The PNN is a kind of neural network commonly used for pattern identification [35,36].The PNN is a neural network model based on statistical principle.It is equivalent to the optimal Bayesian classifier in the classification function.The PNN is generally divided into four-layer networks [37].The input layer, as the initial layer, is responsible for normalizing the input vector following the input mode layer.The mode layer is the second layer of the PNN model, which links the input layer through the weights, and then calculates the matching degree between the input vector and the training set as follows: where K represents the input vector of the input layer and W i represents the weight.δ is the smoothing factor, which determines the accuracy of sample classification and is the core parameter of the PNN model, but it needs optimization [38].
The third layer network of PNN is the summation layer, whose function is to connect each mode layer, and then calculate the initial probability sum of each classification mode through linear summation.The last layer of PNN is the output layer.According to the initial probability sum of each classification mode in the summation layer, the classification mode of the input vector is determined.

The flow of AOA-PNN
The smoothing factor is the key parameter of PNN algorithm, which usually selects a fixed value according to several experiments.However, this method lacks a theoretical basis and cannot give full play to the role of PNN, which has a few of limitations in practical problems.Therefore, the optimized PNN is conducive to improving the performance of PNN, and realizing intelligent classification processing.In this paper, the prediction error is taken as the fitness function, and the AOA is used to optimize the smoothing factor parameters of PNN, so as to improve the problem of the identification rate reduction caused by the empirical selection of the smoothing factor parameters.
The specific process of AOA-PNN is as follows: Step 1: Initialization of AOA parameters, such as population size, spatial dimension, maximum number of iterations.
Step 2: Take the prediction error as a fitness function, calculate the fitness value, and update the optimal value.
Step 3: Update the MOA function and the MOP according to the principle of AOA.
Step 4: Judge the size of r 1 and MOA.When r 1 > MOA, AOA algorithm is in the global exploration stage.When r 1 < MOA, AOA algorithm entered the local development stage.
Step 5: Iterate until the maximum number of iterations, output the target position and the global optimal solution, that is, obtain the smoothing factor value of the optimal PNN.

Simulation experiments
By observing a large number of measured WFEM data, it can be seen that typical noise types (impulse noises, attenuation noises, triangle wave noises and square wave noises) usually appear in time domain.In order to analyze the time domain characteristics and distinguishing relationship between WFEM pseudo-random signal and abnormal noise waveform, we constructed a data sample library of pseudo-random signal and four types of noise.Among them, the sample library contains 30 pseudo-random signals, 30 impulse noises,  30 attenuation noises, 30 triangle wave noises and 30 square wave noises.The sampling length of each sample signal is 1200, and the sampling rate is 200 Hz. Figure 6 shows a group of sample library signal.
As can be seen from figure 6, the pseudo-random signal with noise results in abnormal mutation, disorder and amplitude increase in the time and frequency domain, which cannot reflect the inherent features of the pseudo-random signal.While the pseudo-random signal has the characteristics of periodicity, stable amplitude, relatively stable spectrum, and its frequency point information can be completely retained.Therefore, the sample library can effectively realize the simulation noise analysis and provide targeted processing for the subsequent feature extraction.
Figure 7 shows the characteristic distribution of the first ten sample signal of each type in the sample library.As shown in figure 7, we extracted three kinds of characteristic parameters (pulse factor, peak factor, margin factor) to analyze the characteristic distribution of the sample points, it is obvious to distinguish the samples of signal and noise types.From the feature values, the feature values of the signal samples are small, while those of the other four types of noise samples are higher than that of the signal samples.As a result, feature extraction can qualitatively divide the types of sample library.From figure 8, when the FCM clustering method and PNN method classify the sample library data, it is obvious that the part of the noise samples are divided into signal type (the right figure of figures 8(a) and (b)), so the classification effect is not ideal.According to the classification and prediction error, a small number of noise samples were divided into signal type, resulting in misjudgment in figures 8(a) and (b).Therefore, the proposed method can effectively divide signal and noise in the sample library, and the prediction error is 0. It is obvious that the actual results are in agreement with the predicted results, thus verifying the prediction effect of the AOA optimized PNN, and providing a favorable way for the subsequent WFEM signal-noise identification.
Figure 9 shows the effect of simulation signal detrended and signal-noise identification.As shown in figure 9, the simulation signal (pseudo-random signal) with trend noise and various typical noise waveform, make the signal waveform appear upward trend change, signal disturbance and amplitude increase.The spectrum of the corresponding noisy signal fluctuates at different frequency points, so that the effective signal below 30 Hz is completely affected, and the truth value of the main frequency of the original pseudo-random signal cannot be extracted.Through using the proposed method, the trend noise is effectively eliminated, and a variety of noise waveform can be effectively identified and eliminated.The reconstructed signal and its spectrum is agreed with the characteristics of pseudo-random signal.Meanwhile, compared with FCM clustering method, it can be seen that attenuation noise is still retained in the reconstructed signal, and the corresponding spectrum fluctuated accordingly in the main frequency.Thus, the FCM clustering method cannot realize effectively signal-noise identification.
Therefore, the feature distribution of the sample library, the AOA optimized PNN and the simulation experiment show that the proposed method can provide the detrended and intelligent identification, and improve the data quality of pseudo-random signal and spectrum characteristic.

Measured applications
Based on sample library division and simulation experiment analysis, the proposed method is further applied to the measured data.Note that the used WFEM data are the Ex component of electric field data in this paper.Figure 10 shows the signal-noise identification effect of measured data.
As can be seen from figure 10, with different sampling rates and acquisition duration of the measured data, it is inevitable that the data will be affected by complex noises (typical noise types), and different abnormal waveform will appear in the time domain sequence, leading to the increase or distortion of the amplitude of the pseudo-random signal.Through time domain feature extraction combined with the optimized PNN prediction and identification, the abnormal waveform can be effectively identified and eliminated.The abnormal waveform or noise are completely eliminated in the reconstructed signal, which accords with the characteristics of the measured effective data.
Figure 11 shows the detrended and signal-noise identification effect of the measured data, and compared with PNN method.Among them, the measured data contain the obvious trend noise and common noise types, which shows the abnormal trends and mutations.
From figure 11, the trend noise and abnormal abrupt signals cause the deflection of baseline and the unstable of amplitude.Similarly, these types of noise prevent the original data from providing reliable information for subsequent processing.The combination of DFA and IITD method can effectively extract the trend noise, and reconstruct the original data after the detrended, which satisfies the fluctuation of the measured signal near the baseline.Furthermore, compared the signal-noise identification effect of PNN and AOA-optimized PNN methods, the proposed method can effectively distinguish the abnormal or noise waveform in the data after the trend is removed, and the parts identified as signals are merged, and integrated to obtain the reconstructed data according to the original sampling rate.
Then, the WFEM measured sites are collected and processed from Yunnan province of mining area.Among them, the time domain sequence of these original data contain trend noise and typical noise types.Note that the electric field curve is drawn by the electric field amplitude (the red circle in figure 13(b)) of the required frequency points is extracted from the spectrum.Thus, we connect the red circle in figure 13(b), that is an electric field curve.
Figure 12 is the comparison diagram of electric field curve effect.The red curve represents the original data, while the black curve represents the processed data.
As shown in figure 12, the electric field curve of the original data presented fluctuations and jumps at different frequency points in the middle and low frequency bands.Due to the typical noise and abnormal waveform in the original time domain sequence, especially for a few measured sites still contain the trend noise, that led to the spectrum amplitude value increases in the 2-0.5 Hz, the quality of the original WFEM data was reduced.Therefore, the shape of electric field curve cannot accurately reflect the information of underground electrical structure.By using the proposed method, the electric field curve presents a more stable shape without abnormal jump.
Furthermore, the electric field amplitude (red circle) and spectrum effect of the measured point S 5 are analyzed before and after processing.Figure 13 shows the spectrum of measured points S 5 .From figure 13, the part of effective frequency information in the original data is drowned by noise.The difference between adjacent frequency points (red circle) is large.Especially, the time domain of original data also contain trend noise, resulting in an upward trend in the frequency spectrum at low frequencies.By the proposed method, the effective frequency information is obtained and the difference between adjacent frequency points is reduced.
Meanwhile, table 1 shows the comparison of electric field values before and after treatment of the real measured points in figures 12 and 13 (taking the measured points S 5 and S 7 as examples).Through the analysis of table 1, it can be seen that the electric field amplitudes of the two measured points differ greatly before and after the frequency of 2.5 Hz, 1.5 Hz, 1 Hz and 0.5 Hz respectively, which leads to fluctuations in the electric field curve, indicates that the original data of those frequency is affected by noise.The processed WFEM data obviously show the stability of the electric field amplitude, and the fluctuation of the electric  field amplitude between different frequencies is small, and it also verifies that the proposed method can effectively improve the stability of the electric field curve.
Thus, the results of figures 12, 13 and table 1 indicated that the noise can be effectively eliminated, and the data quality can be improved, the proposed method can provide reliable electromagnetic exploration data.

Discussion
Identifying noise and improving data quality through the artificial intelligent technique is conducive to enhance the WFEM detection effect.In this paper, the combination of an adaptive and intelligent algorithm is proposed, and applied to the WFEM data processing.Firstly, the DFA algorithm is a scale analysis method used to estimate the correlation of time series.Among them, the scaling exponent is one of the key parameter in the DFA algorithm, which determines if a time series is stationary.As a result, we choose the scaling exponent bigger than 0.75 for analysis [21,25,26].At the same time, an example is given and verified below in figure 14(a).A noisy signal is decomposed by IITD algorithm, the result can obtain 11 PR components and one residual component.By calculating the scaling exponent of all components as shown in figure 14(b), it can be seen that the best denoising effect of the last row of figure 14(c) can be obtained by selecting PR components for superposition, that is the scaling exponent greater than 0.75 for superposition, and obtain the reconstructed signal.
Secondly, the ITD is a non-stationary signal decomposition and time-frequency analysis method.The PR component is distorted due to the 'burr' phenomenon when ITD decomposes the signal waveform.Meanwhile, the baseline signal is obtained through spline interpolation rather than linear transformation, which improved the ITD algorithm.The IITD algorithm can enhance the stability of PR components and reduce the distortion of PR components when used with figure 1.Additionally, the adaptive signal decomposition is performed using the combination of DFA and IITD algorithm (figures 2 and 3), and the PR components with scaling exponent bigger than 0.75 are chosen for superposition (figure 14), and reconstructed signal is obtained.The combination of DFA and IITD method can eliminate trend noise from the original data, and improve the reconstruction effect, and remove the phenomenon of trend change in the low frequency band of the spectrum.Thirdly, the AOA is an intelligent optimization algorithm that optimizes the model primarily using the mathematical definition of addition, subtraction, multiplication and division (figure 4).The AOA is a simple algorithm, easy to implement, and has the capacity to achieve the fastest convergence when compared to other intelligent optimization methods (figure 5).Then, the PNN is a simple forward propagation network that does not require backpropagation optimization parameters.Among them, the smoothing factor plays a crucial role in network performance.A stronger network may be developed to accomplish accurate classification by carefully tweaking this parameter.So the combination of AOA and PNN algorithm can improve the empirical selection of parameter, and achieve the signal-noise identification of the time series signals of sample library (figures 6-8).
Finally, the measured point S 5 is taken as an example for comprehensive analysis.The original time-domain sequence of the measured point contains abnormal waveform (noise) and trend noise, and the spectrum of original data is shown in figure 13(a).After processing by the proposed method, the abnormal waveform and trend noise are effectively eliminated in the time-domain sequence, and the corresponding spectrum is stable as shown in figure 13(b), and the difference of spectrum amplitude (red circle) between adjacent frequency points is reduced.Therefore, the electric field curve before and after the processing of this measured point is observed as shown in figure 12, the overall curve trend becomes smoother, and the phenomenon of abnormal changes also decreases correspondingly.The adaptive detrended method (DFA-IITD) and intelligent identification method (AOA-PNN) were combined in the simulation experiment and the measured data processing (figures 9-12), and the electric field curve and frequency spectrum amplitudes before and after processing of the measured points in figures 12 and 13 were quantitatively analyzed (table 1).The combined algorithm proposed (DFA-IITD and AOA-PNN) can obtain more stable reconstructed data and improve the quality of WFEM data by the adaptive elimination of trend noise and intelligent identification of abnormal waveform or noise.
Thus, the satisfactory performance in the results verifies the effectiveness of the design and optimization methods.Furthermore, the proposed method can be generalized or applied to natural source electromagnetic method (MT/AMT) signal processing and controlled source electromagnetic method data processing in different ore concentration areas, and can improve the data quality, obtain more stable apparent resistivity curve and more real underground electrical structure information, and continue to provide technical support for electromagnetic inversion interpretation.

Conclusion
An intelligent method using detrended and identification for electromagnetic data was developed.We used spline interpolation instead of linear transformation to improve ITD algorithm, and combined DFA algorithm to adaptively select the appropriate PR component for reconstructing, which obtained the effective data after detrending.The smoothing factor the PNN algorithm are optimized by using AOA to improve the identification effect, and the intelligent identification method (AOA-PNN) has realized the signal-noise identification and separation.The simulation and measured experimental results show that the proposed method can remove the trend noise, identify typical noise, and the processed electric field curves and frequency spectrum amplitudes are stable, and the data quality is improved.The proposed method has proven the advantages of the detrended processing, feature extraction, intelligent optimization and machine learning in the WFEM data processing.In the future, we will conduct a more explicit analysis to improve the reliability of the prediction and denoising, and explore the application of WFEM signal processing for the other mining areas.

Figure 1 .
Figure 1.The comparison of decomposition results between the ITD and IITD methods.

Figure 2 .
Figure 2. The flow of the detrended process.

Figure 3 .
Figure 3. Detrended effect of simulation signal in time-frequency domain.

Figure 4 .
Figure 4. Model of updating the position of math operators in AOA toward the optimum area.

Figure 5 .
Figure 5.The convergence comparison of the sphere function.

Figure 6 .
Figure 6.A group of sample library signal.

Figure 7 .
Figure 7. Characteristic distribution of sample library signal.

8 .
Classification and prediction effect of sample library signal (a) FCM clustering; (b) PNN classification and prediction; (c) AOA optimized PNN classification and prediction.

Figure 8
Figure 8 shows the classification effect of sample library signals.Multiple time-domain characteristic parameters are extracted for classification analysis, and FCM clustering and PNN classification are compared.From figure8, when the FCM clustering method and PNN method classify the sample library data, it is obvious that the part of the noise samples are divided into signal type (the right figure of figures 8(a) and (b)), so the classification effect is not ideal.According to the classification and prediction error, a small number of noise samples were divided into signal type, resulting in misjudgment in figures 8(a) and (b).Therefore, the proposed method can effectively divide signal and noise in the sample library, and the prediction error is 0. It is obvious that the actual results are in agreement with the predicted results, thus verifying the prediction effect of the AOA optimized PNN, and providing a favorable way for the subsequent WFEM signal-noise identification.Figure9shows the effect of simulation signal detrended and signal-noise identification.

Figure 9 .
Figure 9. Detrended and signal-noise identification effect of simulation signal.

Figure 10 .
Figure 10.Signal-noise identification effect of measured data.

Figure 11 .
Figure 11.The detrended and signal-noise identification effect of measured data.

Figure 12 .
Figure 12.Comparison of electric field curves of measured sites before and after processed.

Figure
FigureThe spectrum of measured points S5.

Figure 14 .
Figure 14.The comparison of denoising effect of noisy signal.

Table 1 .
The compared effect of measured electric field value.