Method and system for suppressing power frequency noise of electromagnetic signals based on CDRN

Abstract

The application discloses a CDRN-based electromagnetic power frequency noise suppression method and system, and belongs to the field of geophysical exploration. In view of the problems that the existing method is inaccurate in physical modeling of power frequency noise, poor in suppression effect on low signal-to-noise ratio late channels, and weak in generalization ability for multiple layered geoelectric models, the application comprises a cascaded deep learning model, including a first-stage rough denoising network and a second-stage fine-tuning network connected in series. The first-stage rough denoising network adopts a residual network structure with a variable expansion factor to preliminarily denoise a noisy signal. The second-stage fine-tuning network adopts a residual network structure with a variable expansion factor to finely tune residual noise of the first-stage denoising result. An adaptive fusion module is used to select an optimal result as a final denoising output according to local statistical characteristics of output signals of the first-stage rough denoising network and the second-stage fine-tuning network. The application can significantly improve the signal-to-noise ratio and provide a new way for high-precision processing of electromagnetic exploration data.

Description

Technical Field

[0001] This application belongs to the field of geophysical exploration, specifically a method and system for suppressing power frequency noise of electromagnetic signals based on CDRN (cascaded expansion residual network). Background Technology

[0002] The electromagnetic method (EM) is an important geophysical exploration method widely used in groundwater exploration, mineral resource exploration, deep metal ore detection, and urban geological engineering surveys. During time-domain electromagnetic measurements, the transmitted loop generates a transient electromagnetic field at the Earth's surface. By observing the attenuation response of the secondary magnetic field induced in the subsurface medium by this electromagnetic field, the resistivity distribution of the subsurface medium can be inferred.

[0003] However, time-domain electromagnetic measurements are often subject to power frequency electromagnetic interference from three-phase high-voltage transmission lines in areas such as urban fringe, industrial zones, and mining areas. The power grid frequency is 50Hz, accompanied by higher harmonics such as the 3rd (150Hz) and 5th (250Hz). These power frequency and harmonic electromagnetic fields act on the TEM measurement loop, superimposing large-amplitude, frequency-distinct power frequency noise into the original signal.

[0004] Time-domain electromagnetic signals exhibit typical multi-time-segment characteristics in the time dimension: early channels (10⁻) 5 (S-level) reflects shallow strata information, with a large signal amplitude and relatively high signal-to-noise ratio; mid-range channels (10⁻) 4 Early channels (on the order of 10⁻³ to 10⁻²s) reflect information about intermediate-depth strata; late channels (on the order of 10⁻³ to 10⁻²s) reflect information about deep strata, but the signal amplitude attenuates drastically, sometimes by 3-5 orders of magnitude, resulting in extremely low signal-to-noise ratios. Power frequency noise is particularly severe in contaminating late channels, often obscuring the response of deep strata and seriously affecting the accuracy of time-domain electromagnetic data interpretation, especially its resolution capability for deep mineral exploration.

[0005] Existing electromagnetic detection power frequency noise suppression methods mainly include: (1) hardware-based filtering suppression methods, such as band-stop filters and adaptive filters, but they are prone to damaging the effective signal spectrum near 50Hz; (2) statistical denoising methods based on multiple superposition averaging, which require the collection of a large amount of repeated observation data, are inefficient and have limited effect on non-stationary noise; (3) denoising methods based on time-frequency analysis such as wavelet transform and empirical mode decomposition, which require manual setting of thresholds and have poor adaptability to different geoelectric models; (4) denoising methods based on traditional machine learning, which have limited generalization ability.

[0006] In recent years, with the development of deep learning technology, researchers have tried to apply convolutional neural networks to TEM signal denoising. However, existing deep learning methods have the following problems: (1) Most of them adopt a single network structure, and their ability to extract noise features at different time periods is uneven, especially the denoising effect on low signal-to-noise ratio signals in late channels is not ideal; (2) The training data generation lacks the diversity of layered geoelectric models, resulting in poor adaptability of the network to actual complex layered geoelectric models (H-type, K-type, Q-type); (3) The power frequency noise simulation adopts a simplified sine wave model, ignoring the physical effects of multi-cable coupling and high-order harmonics in three-phase transmission lines, resulting in inconsistent training-measured distribution; (4) There is a lack of protection mechanism for the differentiated signal features of early, middle and late channels, and the late channel deviates significantly from the theoretical signal after denoising.

[0007] Therefore, there is an urgent need for a smart TEM power frequency noise suppression method and system that can accurately model the physical characteristics of power frequency noise, have good denoising effects for all time channels, and have strong generalization ability for multiple types of layered geoelectric models. Summary of the Invention

[0008] This application aims to address the technical problems of existing TEM power frequency noise suppression methods, such as poor denoising effect on late channels, weak generalization ability to various types of layered geoelectric models, and inaccurate noise physical modeling. It provides an intelligent power frequency noise suppression method and system for electromagnetic signals based on CDRN.

[0009] The first aspect of this application provides an intelligent electromagnetic signal power frequency noise suppression system based on CDRN, comprising: The cascaded deep learning model includes a first-level coarse denoising network and a second-level refinement network connected in series. The first-level coarse denoising network adopts a residual network structure with a variable dilation factor to perform preliminary denoising on the noisy signal; the second-level refinement network adopts a residual network structure with a variable dilation factor to refine the residual noise of the first-level denoising result. The adaptive fusion module is used to select the optimal result segment by segment as the final denoised output based on the local statistical characteristics of the output signals of the first-level coarse denoising network and the second-level fine denoising network.

[0010] Furthermore, both the first-level coarse denoising network and the second-level refined network sequentially include a pre-convolutional layer, multiple dilated residual blocks, and a tail convolutional layer; the dilated residual block contains two convolutional layers with the same dilation factor, a batch normalization layer, and a nonlinear activation function, and forms a residual structure through identity mapping; the network size of the first-level coarse denoising network is larger than that of the second-level refined network, and the network size includes the total number of network layers, the number of convolutional layer channels, the total number of trainable parameters, or the receptive field size.

[0011] Furthermore, the expansion factor of the expanded residual block is distributed in a diamond shape along the network depth direction, first increasing and then decreasing, so that the network receptive field successively covers three levels: local details, global context and local refinement, so as to simultaneously capture the low-frequency envelope features and high-frequency oscillation features of power frequency noise.

[0012] Furthermore, the first-level coarse denoising network is trained using a weighted regression loss function, with a time weight function assigning higher weights to early and late channels and moderate weights to mid-stage channels; the second-level fine-tuning network is trained using a standard regression loss function.

[0013] Furthermore, the adaptive fusion module divides the noisy signal into several segments, and calculates the local fluctuation statistics of the output of the first-level coarse denoising network and the second-level fine denoising network for each segment. When the local fluctuation of the output of the second-level fine denoising network is greater than the threshold set by the first-level coarse denoising network, the output of the first-level coarse denoising network is selected for that segment; otherwise, the output of the second-level fine denoising network is selected.

[0014] Furthermore, it also includes a data generation module, which is used to generate time-domain electromagnetic signals using a layered geodetic forward model, and generate corresponding noise signals based on rigorous electromagnetic modeling of the power frequency and higher harmonics of the three-phase transmission line using Sommerfeld integral. The time-domain electromagnetic signals and noise signals are superimposed to form a noisy signal. A second aspect of this application provides a time-domain electromagnetic power frequency noise suppression method based on CDRN, comprising: Construct a training sample set, wherein the input data of the training sample set is a time-domain electromagnetic signal containing power frequency and higher harmonic noise, and the output data is the corresponding noise signal or a clean signal; Construct a cascaded deep learning model, including a first-level coarse denoising network and a second-level fine-tuning network; The cascaded deep learning model is trained in stages: first, the first-level coarse denoising network is trained, and then the second-level fine denoising network is trained based on the output of the first-level coarse denoising network. The noisy signal is sequentially input into the trained first-level coarse denoising network and the second-level fine denoising network, and the final denoising result is obtained through adaptive fusion.

[0015] Furthermore, the time-domain electromagnetic signal is generated using a layered geodetic forward model, including but not limited to various typical layered structural samples with resistivity exhibiting intermediate low resistance, intermediate high resistance, and monotonically decreasing resistivity; the noise component of the noisy signal is generated based on rigorous electromagnetic modeling of the Sommerfeld integral of the power frequency and harmonics of the three-phase transmission line.

[0016] Compared with the prior art, this application has the following advantages: (1) It adopts a cascaded two-stage denoising architecture. The first-stage coarse denoising network is responsible for coarse denoising, and the second-stage fine denoising network is responsible for fine denoising. The two complement each other and avoid the uneven denoising ability of a single network on different time channels; (2) It adopts a diamond-shaped dilatation residual network with variable dilatation factor. The multi-scale receptive field captures the high-frequency oscillation characteristics and low-frequency envelope characteristics of power frequency noise at the same time, and has a good denoising effect on early, middle and late channels; (3) The training data is generated based on the rigorous electromagnetic modeling of Sommerfeld integral, taking into account the coupling of 6 cables of three-phase transmission line and the 3rd and 5th harmonics, which is more in line with the actual physical characteristics of power frequency noise; (4) The training samples evenly cover three typical layered earth models of H, K and Q, and the model has a strong generalization ability for multiple geoelectric structures; (5) The adaptive segment selection fusion mechanism ensures the consistency of denoising effect in different time periods. After denoising, the root mean square error of late channel can be controlled at about 0.005, which is highly consistent with the theoretical curve and the signal-to-noise ratio can be significantly improved. Attached Figure Description

[0017] Figure 1 A block diagram of a CDRN electromagnetic signal power frequency noise intelligent suppression system provided in this application embodiment; Figure 2 A flowchart illustrating the process of the CDRN-based intelligent suppression system for power frequency electromagnetic signal noise in this application embodiment; Figure 3 The first-level coarse denoising network model structure diagram provided in the embodiments of this application; Figure 4 This is a denoising result image of the H-type layered land model provided in the embodiments of this application; Figure 5 This is a denoising result image of a K-type layered geodetic model provided in an embodiment of this application; Figure 6 This is a denoising result image of the Q-type layered land model provided in the embodiments of this application; Figure 7 A flowchart of a CDRN-based intelligent suppression method for power frequency noise of electromagnetic signals provided in an embodiment of this application. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, the following detailed description is provided in conjunction with embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0019] See Figure 1 Combination Figure 2 The illustrated intelligent electromagnetic signal power frequency noise suppression system based on CDRN includes: The cascaded deep learning model includes a first-level coarse denoising network and a second-level refinement network connected in series. The first-level coarse denoising network adopts a residual network structure with a variable dilation factor to perform preliminary denoising on the noisy signal; the second-level refinement network adopts a residual network structure with a variable dilation factor to refine the residual noise of the first-level denoising result. The adaptive fusion module is used to select the optimal result segment by segment as the final denoised output based on the local statistical characteristics of the output signals of the first-level coarse denoising network and the second-level fine denoising network.

[0020] Both the first-level coarse denoising network and the second-level refined network sequentially include a pre-convolutional layer, multiple dilated residual blocks, and a tail convolutional layer; the dilated residual block contains two convolutional layers with the same dilation factor, a batch normalization layer, and a nonlinear activation function, and forms a residual structure through identity mapping; the network size of the first-level coarse denoising network is larger than that of the second-level refined network, and the network size includes the total number of network layers, the number of convolutional layer channels, the total number of trainable parameters, or the receptive field size.

[0021] In one example, see [reference] Figure 3 As shown, the first-stage coarse denoising network is used to extract and remove the main noise components from the time-domain electromagnetic signal containing power frequency noise. It adopts a dilated residual network structure, consisting of a pre-convolutional layer, 14 residual blocks, and a tail 1×1 convolutional layer. The pre-convolutional layer has a kernel size of 1×7 and 96 channels, without stride dilation, followed by a batch normalization layer and a ReLU activation function, mapping the input signal to a 96-channel high-dimensional feature space. Each dilated residual block contains two convolutional layers with a kernel size of 1×5 and 96 channels, a corresponding batch normalization layer, and a ReLU activation function. The residual structure is constructed through an identity mapping, represented as: First convolutional layer (1×5 kernel, 96 channels, dilation factor d) → Batch normalization → ReLU activation function → Second convolutional layer (1×5 kernel, 96 channels, dilation factor d) → Batch normalization → Added with the block input identity connection → ReLU activation function. Dilated convolution expands the receptive field without increasing the number of parameters by inserting zero values ​​between standard convolutional kernels. Equatedly, this is equivalent to: , Where K=5 is the kernel size, d is the dilation factor, and w is the convolution weight. The equivalent receptive field of the d-th block is... .

[0022] The expansion factors of the 14 residual blocks are [1, 1, 2, 4, 4, 8, 16, 16, 32, 64, 32, 16, 8, 4], exhibiting a diamond-shaped distribution that first increases and then decreases. This allows the network's receptive field to gradually expand from local details to the global context, and then return to local refinement, enabling it to simultaneously capture the high-frequency characteristics of power frequency noise (such as fundamental and harmonic oscillations) and the low-frequency envelope (the overall change in noise amplitude over time). The expansion factors of the first 7 blocks increase (from 1 to 64), gradually expanding the network's receptive field from local details to almost covering the entire 1000 sampling points of the signal; the expansion factors of the last 7 blocks decrease (from 64 to 4), allowing the network to return to the local refinement stage after fusing the global context. This structure allows the first-stage coarse denoising network to simultaneously learn the high-frequency oscillation characteristics of power frequency noise (captured by small expansion factors) and the low-frequency envelope characteristics (captured by large expansion factors).

[0023] The tail 1×1 convolutional layer maps the 96-channel high-dimensional features back to the single-channel noise prediction.

[0024] The loss layer of the first-stage coarse denoising network uses the weighted mean square error loss function (weighted RegressionLaye-r), and the time weight function w[i] is segmented according to the following rules: , , , , , , Normalize the weights This weighting design improves the network's fitting accuracy for early traces (signal rising edge, crucial for shallow formation accuracy) and late traces (weak signal, dominated by power frequency noise), while avoiding underfitting of mid-range traces. The final weighted MSE loss is: , where N is the batch size, T is the signal length, Y is the network prediction value, and T is the actual noise label.

[0025] The second-stage refinement network is configured to perform further refinement processing on the denoised signal output by the first-stage coarse denoising network, so as to eliminate residual noise and restore signal details. The second-stage refinement network adopts a dilated residual network that is independent of but similar in structure to the first-stage coarse denoising network, which consists of a front convolution layer, 7 residual blocks, and a trailing 1×1 convolution layer. The convolution kernel of the front convolution layer is 1×7, with 64 channels. Each dilated residual block includes two convolution layers with a convolution kernel of 1×5 and 64 channels. The dilation factors of the 7 residual blocks are [1, 2, 4, 8, 16, 8, 4] in sequence. The parameter scale of the second-stage refinement network is approximately one third of that of the first-stage coarse denoising network, which focuses on fine removal of residual noise without damaging the main signal structure already restored by the first-stage coarse denoising network. This arrangement is also diamond-shaped but has fewer layers, and focuses on fine removal of residual noise in the Stage1 output. The second-stage refinement network uses a standard mean square error loss function (regressionLayer).

[0026] The input of the second-stage refinement network is the output of the first-stage coarse denoising network, and the target is the difference between the output of the first-stage coarse denoising network and the clean signal. That is, the training samples of the second-stage refinement network are: , , where net1(·) is the inference output of the first-stage coarse denoising network. The second-stage refinement network learns the correction amount of the residual predicted by the first-stage coarse denoising network, and forms a strong complementary relationship with the first-stage coarse denoising network.

[0027] The adaptive segment selection and fusion module is configured to select the output of the first-stage coarse denoising network or the second-stage refinement network segment by segment as the final denoising result according to the local signal variance feature, so as to avoid the problems that the second-stage refinement network over-smooths in some low-noise segments, or the first-stage coarse denoising network performs insufficient denoising in high-noise segments.

[0028] The first-stage coarse denoising network uses weighted mean square error as the loss function, and the time weight function is a piecewise function: the weight of the very early traces with index i≤80 is 2.2; the weight of the early-middle transition region with 80<i≤200 decreases linearly from 2.2 to 1.5; the weight of the middle traces with 200<i≤500 is 1.5; the weight of the middle-late transition region with 500<i≤700 increases linearly from 1.5 to 2.0; the weight of the late traces with 700<i≤850 increases linearly from 2.0 to 2.3; the weight of the very late traces with i>850 increases linearly from 2.3 to 2.5.

[0029] The adaptive fusion module divides the noisy signal into several segments. For each segment, it calculates the local fluctuation statistics of the outputs of the first-level coarse denoising network and the second-level fine denoising network. When the local fluctuation of the output of the second-level fine denoising network is significantly greater than that of the first-level coarse denoising network, the output of the first-level coarse denoising network is selected for that segment; otherwise, the output of the second-level fine denoising network is selected.

[0030] In one example, the adaptive segment selection fusion module divides the signal length into 10 equal segments. For each segment, it calculates the first-order difference variance of the output of the first-level coarse denoising network and the output of the second-level fine denoising network. If the first-order difference variance of the output of the second-level fine denoising network is greater than 1.5 times the variance of the output of the first-level coarse denoising network, it is determined that the second-level fine denoising network has overprocessed, and the output of the first-level coarse denoising network is selected as the final result for that segment; otherwise, the output of the second-level fine denoising network is selected.

[0031] In one embodiment, a data generation module is also included, which generates a pure time-domain electromagnetic signal based on a layered geodetic forward model and generates a corresponding noise signal based on rigorous electromagnetic modeling of the power frequency and higher harmonics of a three-phase transmission line using Sommerfeld integral. The pure time-domain electromagnetic signal and the noise signal are superimposed to form a noisy signal. A cascaded deep learning model and an adaptive fusion module are trained using the noisy signal.

[0032] The generation of pure time-domain electromagnetic signals employs a one-dimensional three-layered layered geodetic TEM forward model. The conductivity of the first layer is assumed to be... Thickness is The conductivity of the second layer is Thickness is The conductivity of the third layer is Furthermore, it is a half-space. This application uses the Hankel transform numerical integration method to calculate the magnetic flux density. The response is calculated using the following formula: , In the formula: For transmitting current; The radius of the equivalent circular hysteresis loop; The vacuum permeability; For the Hankel transform wavenumber; For parameters of propagation in the air, ; , , These are the propagation parameters in the three-layer medium; This refers to the height of the transmitting coil. Height of the receiving coil; The TE mode reflection coefficient is given by the recursive formula for layered earth: , , It is a first-order Bessel function; This represents the inverse transform from the frequency domain to the time domain. The calculation time window is... 1000 sampling points are taken at logarithmic intervals every second.

[0033] To ensure that the training samples cover a variety of typical layered structures, this application generates the following four types of typical layered geodetic model samples with equal probability (25% each): H-type: The first layer is high resistivity, the second layer is low resistivity, and the third layer is medium resistivity (ρ1>ρ2<ρ3), representing geoelectric structures with a low resistivity layer in the middle, such as aquifers, sandy layers, etc. K-type: The first layer is low resistivity, the second layer is high resistivity, and the third layer is low resistivity (ρ1<ρ2>ρ3), representing a geoelectric structure with a high resistivity layer in the middle, such as dense layers like sandstone and limestone; Q type: Resistivity decreases with depth (ρ1>ρ2>ρ3), representing a geoelectric structure with high resistance in shallow areas and low resistance in deep areas.

[0034] For each type of model, the resistivity reference value Random samples were taken from the layer within the range of [10, 300] Ω·m, achieving an interlayer resistivity contrast of 10:1. The thicknesses of the first two layers were randomly selected from the range of [15, 95] m. A total of 30,000 sets of sample data were generated and divided into training and validation sets at a ratio of 9:1.

[0035] Because the TEM magnetic flux density response spans multiple orders of magnitude, direct training can easily lead to a bias towards high-amplitude early channels in the network. This application employs a logarithmic normalization method to map the original amplitude Bz to the [0, 1] interval. The normalization formula is as follows: , In the formula, ε is a small quantity to prevent taking the logarithm of zero. and These are the minimum and maximum values ​​after taking the logarithm of a single signal, respectively. This normalization preserves the relative slope characteristics of channels in different time periods and balances the contribution of each time period to the training loss.

[0036] This application strictly models power frequency electromagnetic noise according to the physical layout of a three-phase double-circuit transmission line. The positions of the six transmission lines are assumed to be horizontally offset. meters, height above the ground Meters. The phase relationship of the three-phase currents is determined by phase markings. Description. The amplitude of the fundamental current is Considering the 3rd (150Hz) and 5th (250Hz) harmonics, the ratios of harmonic amplitude to the fundamental frequency are 1.0, 0.20, and 0.10, respectively.

[0037] For each harmonic Calculate the frequency domain magnetic field response generated by each transmission line at the measuring point. The frequency domain magnetic field response generated by the j-th transmission line is: , In the formula: Let be the current amplitude of the h-th harmonic on the j-th transmission line; The angular frequency of the h-th harmonic is It is the power frequency base frequency; For propagation parameters in the earth, The electrical conductivity of the earth; Let be the height of the j-th transmission line above the ground surface; ξ is the horizontal distance from the measuring point to the j-th transmission line, and ξ is the vertical distance from the measuring point to the center of the transmission line; λ is the integral variable, corresponding to the electromagnetic wave propagation wavenumber; This is the upper limit of the integral. This integral is in the typical Sommerfeld integral form, reflecting the electromagnetic field distribution generated by a three-phase transmission line in the layered earth.

[0038] The MATLAB adaptive numerical integration method (using the integral function, with a relative tolerance of 1×10⁻) was employed. 5 Absolute tolerance 1×10⁻ 8 Calculate the Sommerfeld integral for each frequency point. Then, synthesize the frequency-domain magnetic fields generated by the six transmission lines and three harmonic components at the measuring points: , In the formula: The initial phase of each harmonic; to simulate the non-strict synchronization between the harmonic phase and the fundamental phase in a real-world scenario, the fundamental phase... exist Uniformly randomized values ​​are taken within the range, and the phase shifts of the 3rd and 5th harmonics relative to the fundamental phase are... Internal random distribution. This is for the operation of taking the real part.

[0039] First of all Calculated on a uniform sampling time grid of seconds (200,000 sampling points) Then, it is mapped to the logarithmic equidistant time sampling of the TEM signal through spline interpolation. The above process yields a power frequency noise waveform synchronized with the pure time-domain electromagnetic signal. Finally, the noise waveform is mean-removed and scaled according to its physical amplitude (scaling formula: ...). ,in ξ is the current scaling factor and ξ is the horizontal distance from the measuring point to the transmission line. Random white noise with a standard normal distribution of 0.002 times is superimposed to simulate the background noise of the measuring instrument.

[0040] The normalized pure time-domain electromagnetic signal Adding it to the generated power frequency noise signal yields the noisy signal. The noisy signal is truncated within the range of [-1.0, 2.0] to simulate the dynamic range limitation of actual measuring instruments. Corresponding training labels. That is, the regression target of the network is the noise itself.

[0041] The cascaded deep learning model is trained in stages.

[0042] Training the first-level coarse-coarse denoising network: The Adam adaptive learning rate optimization algorithm is employed. The initial learning rate is set to 1×10⁻³, and a segmented decreasing learning rate scheduling strategy is used, with the learning rate decaying to 50% of its original value every 40 training epochs. The maximum number of training epochs is 200, the training batch size is 128, the gradient clipping threshold is set to 1.0 to prevent gradient explosion, and the L2 regularization coefficient is 1×10⁻³. 5 A validation is performed every 500 iterations, with the validation patience value set to infinity to disable early stopping (to avoid premature convergence and missing better solutions). Checkpoints are automatically saved every 10 rounds for resuming training if interrupted.

[0043] Second-level refinement of network data preparation.

[0044] After the first-level coarse denoising network is trained, all training and validation samples are input into the first-level coarse denoising network for batch inference to obtain the noise prediction values ​​of the first-level coarse denoising network. and Calculate the training data for the second-level refinement network: , , , , in This is a clean signal.

[0045] Level 2 Refinement Network Training.

[0046] The second-stage refinement network also uses the Adam optimizer, with an initial learning rate of 2×10⁻. 4 (Smaller than the first-level coarse denoising network, as the second-level refinement network learns smaller residuals), the learning rate decays by 50% every 20 epochs. The maximum number of training epochs is 80, the batch size is 128, the gradient threshold is 0.5, and the L2 regularization coefficient is 5 × 10⁻⁻⁻⁶. 5 (Stronger than the first-level coarse denoising network, preventing overfitting).

[0047] For the noisy TEM signal to be denoised To obtain the final denoising result, follow these steps: The first-stage coarse denoising network denoises the area. Noise prediction is obtained by inputting the first-level coarse denoising network. The first-stage coarse denoising network outputs the following: .

[0048] Level 2 Refinement (Network Refinement). [The following is likely a separate, unrelated sentence:] ... (The sentence is incomplete and requires further context.) Inputting the second-level refined network yields residual predictions. The second-level refined network refined output is .

[0049] Piecewise adaptive Sgolay smoothing. This applies to the output of the first-stage coarse denoising network. Second-level refinement network output Segmented Savitzky-Golay filtering smoothing is performed: the early channel (first 250 sampling points) uses a Savitzky-Golay filter with a window length of 5; the middle channel (150-750 sampling points) uses a Savitzky-Golay filter with a window length of 7; and the late channel (650-1000 sampling points) uses a Savitzky-Golay filter with a window length of 9. Linear fusion is used for smooth transition between segments (150-250 sampling points and 650-750 sampling points), with a fusion weight of [value missing]. This segmented processing allows the early channels to retain signal details, the middle channels to balance fidelity and smoothness, and the late channels to achieve a stronger smoothing effect to cope with low signal-to-noise ratio.

[0050] Adaptive segment selection fusion. The signal length of 1000 is divided into 10 equal segments, with 100 sampling points in each segment. For each segment, the smoothing result of the first-level coarse denoising network is calculated. Second-level refined network smoothing results The first-order difference variance. The judgment condition is: if var(diff(s2_smooth[ir])) > 1.5 · var(diff(s1_smooth[ir])): denoised[ir] = s1_smooth[ir] # Select Stage 1 output; else: denoised[ir] = s2_smooth[ir] # Select Stage 2 output; Where ir represents the index range of that segment. The physical meaning of this judgment criterion is: if the second-level refinement network introduces more severe local fluctuations (larger first-order difference variance) in a certain segment than the first-level coarse denoising network, it indicates that the second-level refinement network has overprocessed in that segment and should revert to the result of the first-level coarse denoising network; otherwise, the second-level refinement network works normally and its refinement result is selected.

[0051] Finally, a light smoothing is applied. The adaptively fused result is then subjected to a final Sgolay filter with a window length of 5 to eliminate any abrupt transitions between segments and to limit the result to the range [0, 1] to obtain the final denoised signal denoised_test.

[0052] See Figure 7 As shown, this application also provides a time-domain electromagnetic power frequency noise suppression method based on a cascaded dilated residual network, comprising: Construct a training sample set, wherein the input data of the training sample set is a time-domain electromagnetic signal containing power frequency and higher harmonic noise, and the output data is the corresponding noise signal or a clean signal; Construct a cascaded deep learning model, including a first-level coarse denoising network and a second-level fine-tuning network; The cascaded deep learning model is trained in stages: first, the first-level coarse denoising network is trained, and then the second-level fine denoising network is trained based on the output of the first-level coarse denoising network. The noisy signal is sequentially input into the trained first-level coarse denoising network and the second-level fine denoising network, and the final denoising result is obtained through adaptive fusion.

[0053] Pure time-domain electromagnetic signals are generated using a layered geodetic forward model, including but not limited to samples of various typical layered structures with resistivity ranging from low to high in the middle to monotonically decreasing. The noise components of the noisy signals are generated based on rigorous electromagnetic modeling of the Sommerfeld integral of the power frequency and harmonics of three-phase transmission lines.

[0054] This application provides an electronic device, including a processor and a memory, wherein the memory stores a computer program that, when executed by the processor, implements the method described above.

[0055] A processor can be a central processing unit (CPU) or other form of processing unit with data processing and / or instruction execution capabilities, and can control other components in an electronic device to perform desired functions.

[0056] The memory may include one or more computer program products, which may include various forms of computer-readable storage media, such as volatile memory and / or non-volatile memory. The volatile memory may include, for example, random access memory (RAM) and / or cache memory. The non-volatile memory may include, for example, read-only memory (ROM), hard disk, flash memory, etc. One or more computer program instructions may be stored on the computer-readable storage medium, and a processor may execute the program instructions to implement the methods of the various embodiments of this disclosure described above and / or other desired functions.

[0057] Depending on the specific application, electronic devices may also include any other suitable components.

[0058] In addition to the methods and apparatus described above, embodiments of this disclosure may also be computer program products comprising computer program instructions that, when executed by a processor, cause the processor to perform the steps of the methods according to various embodiments of this disclosure as described in the "Exemplary Methods" section above.

[0059] The computer program product can be written in any combination of one or more programming languages ​​to perform the operations of the embodiments of this disclosure. The programming languages ​​include object-oriented programming languages ​​such as Java and C++, as well as conventional procedural programming languages ​​such as C or similar languages. The program code can be executed entirely on a user's computing device, partially on a user's computing device, as a standalone software package, partially on a user's computing device and partially on a remote computing device, or entirely on a remote computing device or server.

[0060] Furthermore, embodiments of this disclosure may also be computer-readable storage media having computer program instructions stored thereon, which, when executed by a processor, cause the processor to perform the steps in the methods according to various embodiments of this disclosure described in the "Exemplary Methods" section above.

[0061] The computer-readable storage medium may be any combination of one or more readable media. A readable medium may be a readable signal medium or a readable storage medium. A readable storage medium may be, for example, an electrical, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any combination thereof. More specific examples of readable storage media (a non-exhaustive list) include: an electrical connection having one or more wires, a portable disk, a hard disk, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fiber, portable compact disk read-only memory (CD-ROM), optical storage device, magnetic storage device, or any suitable combination thereof.

[0062] To verify the denoising effect of this application, the following typical layered geodetic test models were constructed. Each model uses a specific combination of resistivity, layer thickness, and noise parameters (distance ξ from the measuring point to the transmission line, current scaling factor). ): Test 1: H-type model, resistivity ρ=[100, 10, 200]Ω·m, layer thickness h=[50, 30]m, ξ=200m, I_scale=0.9; Test 2: K-type model, resistivity ρ=[50, 500, 20]Ω·m, layer thickness h=[40, 60]m, ξ=150m, I_scale=1.0; Test 3: Q-type model, resistivity ρ=[500, 100, 20]Ω·m, layer thickness h=[40, 40]m, ξ=300m, I_scale=0.8; The system of this application is used to denoise the noisy signals of the above four types of test models. The denoising results are as follows: Figure 4 , Figure 5 , Figure 6 As shown. The quantitative evaluation metrics for each test model are as follows: For the H-type test model, including the comparison of theoretical signal, noisy signal and denoised signal, the original signal-to-noise ratio was 33.6dB, and the final signal-to-noise ratio after denoising was 44.5dB, with a total improvement of 10.9dB in signal-to-noise ratio; the early channel RMSE was 0.0021, and the late channel RMSE was 0.0014.

[0063] For the K-type test model, including the comparison of theoretical signal, noisy signal and denoised signal, the original signal-to-noise ratio was 30.6dB, and the final signal-to-noise ratio after denoising reached 39.8dB, with a total improvement of 9.2dB in signal-to-noise ratio; the early channel RMSE was 0.0039, and the late channel RMSE was 0.0042.

[0064] For the Q-type test model, the original signal-to-noise ratio (SNR) was 29.2 dB, and the final SNR after denoising reached 42.2 dB, with a total SNR improvement of 13 dB; the early track RMSE was 0.0026, and the late track RMSE was 0.0020.

[0065] The above results demonstrate that this application can achieve high-quality denoising for TEM signals from various typical layered geodetic models (H-type, K-type, and Q-type). The RMSE of the early, middle, and late traces of the denoised curves is controlled within 0.007, especially the RMSE of the late trace, which can be as low as 0.005, which is in high agreement with the theoretical curves and achieves the accuracy level required for fine interpretation of deep targets in geophysical exploration.

[0066] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. An electromagnetic power frequency noise suppression system based on CDRN, characterized in that, include: The cascaded deep learning model includes a first-level coarse denoising network and a second-level refinement network connected in series. The first-level coarse denoising network adopts a residual network structure with a variable dilation factor to perform preliminary denoising on the noisy signal; the second-level refinement network adopts a residual network structure with a variable dilation factor to refine the residual noise of the first-level denoising result. The adaptive fusion module is used to select the optimal result segment by segment as the final denoised output based on the local statistical characteristics of the output signals of the first-level coarse denoising network and the second-level fine denoising network.

2. The system according to claim 1, characterized in that, Both the first-level coarse denoising network and the second-level refined network sequentially include a pre-convolutional layer, multiple dilated residual blocks, and a tail convolutional layer; the dilated residual block contains two convolutional layers with the same dilation factor, a batch normalization layer, and a nonlinear activation function, and forms a residual structure through identity mapping; the network size of the first-level coarse denoising network is larger than that of the second-level refined network, and the network size includes the total number of network layers, the number of convolutional layer channels, the total number of trainable parameters, or the receptive field size.

3. The system according to claim 2, characterized in that, The expansion factor of the expanded residual block is distributed in a diamond shape along the network depth direction, first increasing and then decreasing, so that the network receptive field successively covers three levels: local details, global context and local refinement, so as to simultaneously capture the low-frequency envelope characteristics and high-frequency oscillation characteristics of power frequency noise.

4. The system according to claim 1, characterized in that, The first-stage coarse denoising network is trained using a weighted regression loss function, with a time weight function that assigns higher weights to early and late channels and moderate weights to mid-stage channels; the second-stage fine-tuning network is trained using a standard regression loss function.

5. The system according to claim 1, characterized in that, The adaptive fusion module divides the noisy signal into several segments, and calculates the local fluctuation statistics of the output of the first-level coarse denoising network and the second-level fine denoising network for each segment. When the local fluctuation of the output of the second-level fine denoising network is greater than the threshold set by the first-level coarse denoising network, the output of the first-level coarse denoising network is selected for that segment; otherwise, the output of the second-level fine denoising network is selected.

6. The system according to claim 1, characterized in that, It also includes a data generation module, which generates time-domain electromagnetic signals based on a layered geodetic model and generates corresponding noise signals based on rigorous electromagnetic modeling of the power frequency and higher harmonics of three-phase transmission lines using Sommerfeld integral. The time-domain electromagnetic signals and noise signals are superimposed to form a noisy signal.

7. A time-domain electromagnetic power frequency noise suppression method based on CDRN, based on the system described in any one of claims 1-6, characterized in that, include: Construct a training sample set, wherein the input data of the training sample set is a time-domain electromagnetic signal containing power frequency and higher harmonic noise, and the output data is the corresponding noise signal or a clean signal; Construct a cascaded deep learning model, including a first-level coarse denoising network and a second-level fine-tuning network; The cascaded deep learning model is trained in stages: first, the first-level coarse denoising network is trained, and then the second-level fine denoising network is trained based on the output of the first-level coarse denoising network. The noisy signal is sequentially input into the trained first-level coarse denoising network and the second-level fine denoising network, and the final denoising result is obtained through adaptive fusion.

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