Transient electromagnetic signal denoising method based on wtd-pc-vit

Abstract

The application discloses a transient electromagnetic signal denoising method based on WTD-PC-ViT, and belongs to the field of geophysical electromagnetic data processing researches. The method firstly performs preliminary denoising on the noisy transient electromagnetic signal by using an improved wavelet threshold denoising (WTD) method, so as to reduce the interference of random noise signals on network training. Then, multi-scale feature extraction and time sequence modeling are performed through a PC-ViT deep neural network, so as to realize adaptive suppression of residual random noise and strengthening of effective information. The application fully combines the time-frequency locality of wavelet analysis and the global feature capturing capability of the visual Transformer structure, significantly improves the signal-to-noise ratio of the denoised signal, and makes the output result closer to the ideal real signal. The method has strong robustness and generalization capability, and can solve the problems that the signal-to-noise ratio of the late transient electromagnetic signal is low and the traditional denoising method is difficult to effectively suppress the random noise.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of geophysical electromagnetic data processing research, in particular to a transient electromagnetic signal denoising method based on WTD-PC-ViT. BACKGROUND

[0002] Transient electromagnetic method is a geophysical exploration technology based on electromagnetic induction principle. Transient electromagnetic method has been widely used in urban engineering, environmental geology and mineral exploration.

[0003] The early signals of transient electromagnetic method reflect the information of the near-surface, while the late signals contain the deep information of the stratum. However, due to the exponential decay of transient electromagnetic signals with time, the late signals are inevitably affected by various noises, among which random noise is the most common. This kind of noise will cause serious distortion of the late transient electromagnetic signal, making it impossible to effectively detect the deep underground structure. Therefore, the effective suppression of random noise plays an important role in the field of transient electromagnetic signal processing.

[0004] The invention patent with publication number CN117056677A proposes a transient electromagnetic signal denoising method based on sparrow algorithm improved variational mode decomposition. This method uses sparrow search algorithm to globally optimize the penalty factor α and the mode number K in VMD to obtain the optimal parameter combination [K, α], and accordingly performs variational mode decomposition on the collected transient electromagnetic signal to realize adaptive denoising of the signal. However, this method may result in a long calculation time, increasing the calculation time and complexity.

[0005] The invention patent with publication number CN117786329A provides a transient electromagnetic time-frequency denoising method. This method uses fast Fourier transform to obtain the frequency spectrum of the transient electromagnetic signal and the background noise signal, then performs denoising on the transient electromagnetic signal in the frequency domain, and finally performs inverse Fourier transform on the denoised signal to obtain the denoised time-domain transient electromagnetic signal, thereby effectively suppressing noise and improving the signal-to-noise ratio of the late transient electromagnetic signal. However, since this method is a global transformation, it may not capture the local characteristics of the transient electromagnetic signal, resulting in loss of local signal details and affecting the denoising effect.

[0006] Random noise signal mainly comes from external environmental electromagnetic interference and instrument's own background noise. This kind of noise has randomness and disorder, lacks fixed characteristics, and it is difficult to establish an accurate mathematical model. Influenced by this, traditional denoising methods such as minimum noise separation, Kalman filtering and singular value decomposition have insufficient adaptive ability, limited denoising effect, complex processing flow and relatively complicated model structure, and it is often difficult to obtain ideal denoising results. SUMMARY

[0007] Therefore, the present application aims to provide a WTD-PC-ViT-based transient electromagnetic signal denoising method to solve the problems of low signal-to-noise ratio of late transient electromagnetic signals and difficulty of traditional denoising methods in effectively suppressing random noise.

[0008] The purpose of the present application is realized by the following technical scheme: a WTD-PC-ViT-based transient electromagnetic signal denoising method, comprising the following steps:

[0009] Step S1: constructing an improved wavelet threshold denoising WTD threshold function, which is continuous and derivable at the threshold point;

[0010] Step S2: setting a base wavelet, a threshold type, and a wavelet decomposition layer number, and setting the threshold function to the improved wavelet threshold denoising WTD threshold function constructed in step S1, using the improved wavelet threshold denoising WTD threshold function to perform WTD pre-denoising on the transient electromagnetic signal containing random noise to obtain a pre-denoising signal;

[0011] Step S3: performing normalization processing on the pre-denoising signal obtained in step S2;

[0012] Step S4: constructing a PC-ViT neural network model, which sequentially includes a parallel convolutional neural network layer, an attention mechanism layer, a visual Transformer layer, and a linear mapping layer in order of signal processing, the parallel convolutional neural network layer being used for multi-scale feature extraction of an input signal; the attention mechanism layer being used for global context modeling of the output of the parallel convolutional neural network layer; the visual Transformer layer being used for deep temporal feature modeling of the output of the attention mechanism layer; and the linear mapping layer being used for mapping and restoring the output of the visual Transformer layer to a final denoising signal;

[0013] Step S5: inputting the normalized signal in step S3 to the PC-ViT neural network model constructed in step S4 for denoising processing to obtain a final denoising signal.

[0014] Further, in step S1, the improved wavelet threshold denoising WTD threshold function is specifically represented as:

[0015] ;

[0016] wherein is the threshold function corresponding to the layer of the wavelet; is the original wavelet coefficient; represents a sign function for keeping the amplitude direction of the signal unchanged; is a threshold value; is a smoothing adjustment factor, and the value range of the smoothing adjustment factor is .

[0017] Further, the value of the smoothing adjustment factor is 0.3.

[0018] Further, in step S2, the base wavelet is a sym8 wavelet, and the number of wavelet decomposition layers is 4 layers.

[0019] Further, in step S4, the parallel convolutional neural network layer includes three parallel convolutional branches, and each convolutional branch includes, in sequence, a first one-dimensional convolutional layer, a first ReLU activation function layer, a first maximum pooling layer, a self-attention layer, a second one-dimensional convolutional layer, a second ReLU activation function layer, and a second maximum pooling layer; and the outputs of the three convolutional branches are spliced in the channel dimension.

[0020] Further, in the three convolutional branches, the sizes of the convolutional kernels of the first one-dimensional convolutional layers are 3, 5, and 7, respectively.

[0021] Further, in step S4, the visual Transformer layer is configured as:

[0022] receiving an input signal, the size of the input signal being a first size, the first size being the size of an output signal of an attention mechanism layer;

[0023] performing a linear projection operation on the input signal to expand the size of the input signal to an embedding dimension, to obtain an embedding signal, the size of the embedding signal being a second size;

[0024] inputting the embedding signal into a Transformer block for processing;

[0025] wherein the linear projection operation is implemented by a fully connected layer to map the number of input channels from a first value to a second value, the first value corresponding to the channel dimension of the first size, and the second value corresponding to the channel dimension of the second size;

[0026] The Transformer block includes a multi-head self-attention sublayer and a feedforward neural network sublayer connected in sequence; the multi-head self-attention sublayer is configured to have attention heads, and the dimension of each attention head is ; the feedforward neural network sublayer includes a first linear layer, an activation function layer, and a second linear layer connected in sequence; the size of the output signal of the Transformer block is the same as the size of the embedding signal, both being the second size;

[0027] In the feedforward neural network sublayer, the first linear layer expands the input dimension to a magnification of the original dimension, and the second linear layer projects the dimension back to the same number of channels as the embedded signal.

[0028] Further, the linear mapping layer is configured to:

[0029] receive a multi-channel signal output by the visual Transformer layer;

[0030] linearly map the multi-channel signal to restore its channel number to a single channel, obtaining a single-channel signal amplitude;

[0031] linearly up-sample the time length dimension of the single-channel signal amplitude, and restore the time length to a target length through processing including at least one pooling operation;

[0032] extract a signal from the up-sampled signal, and output a final single-batch denoised signal.

[0033] Further, before step S5, a training step of the PC-ViT neural network model is further included, and a training data set used in the training step is constructed in the following manner:

[0034] generate a plurality of groups of noise-free transient electromagnetic signals corresponding to different formation resistivity models through one-dimensional forward modeling;

[0035] superimpose random noise signals with different signal-to-noise ratios on the noise-free transient electromagnetic signals to form a noisy transient electromagnetic signal sample set;

[0036] divide the noisy transient electromagnetic signal sample set into a training set and a test set;

[0037] train the PC-ViT neural network model using the training set.

[0038] Further, in the one-dimensional forward modeling, a multi-layer formation model is constructed, wherein the thickness of the first layer is a fixed value, and the resistivity is randomly generated within a first preset resistivity range; starting from the second layer, the thickness of the current layer is a fixed multiple of the thickness of the previous layer, and the resistivity of the current layer is randomly generated within a second preset resistivity range; and the signal-to-noise ratio of the random noise signal is distributed within a preset signal-to-noise ratio interval.

[0039] Compared with the prior art, the present application has the beneficial effects that:

[0040] Firstly, the present application is aimed at the problems of difficulty in obtaining measured signals and insufficient signal sample quantity, and proposes a dataset construction method based on superposition of forward simulation signals and random noise signals; by designing various different stratum structure models, using forward algorithm to generate noiseless transient electromagnetic signals, and adding different types and intensity of random noise signals on this basis, a dataset with diversity and representativeness is formed; this method can greatly improve the sample size while ensuring the authenticity and complexity of the signal, and make up for the high cost and long acquisition period of measured signals;

[0041] Secondly, in the wavelet threshold denoising (WTD) process, an improved threshold function is proposed; the traditional hard threshold function has the problems of signal mutation and waveform distortion, and the soft threshold function will cause effective signal loss near the threshold; the improved threshold function constructed by the present application has continuity and derivability near the threshold point, can weaken the noise amplitude smoothly while retaining the effective signal components, thereby reducing the waveform distortion and pseudo-oscillation phenomenon of the denoised signal; this improvement improves the stability and fidelity of the WTD method in processing non-stationary and weak signals;

[0042] Thirdly, the present application innovatively combines the wavelet threshold denoising method with the PC-ViT deep neural network structure, and constructs an end-to-end multi-stage noisy transient electromagnetic signal denoising framework; firstly, the WTD method is used to preliminarily denoise the noisy transient electromagnetic signal, reducing the interference of random noise signal on network training; then, the PC-ViT deep neural network is used for multi-scale feature extraction and time series modeling, realizing adaptive suppression of residual random noise and strengthening of effective information; this method fully combines the time-frequency locality of wavelet analysis and the global feature capturing ability of visual Transformer structure, significantly improves the signal-to-noise ratio of the denoised signal, and makes the output result closer to the ideal real signal; this method has strong robustness and generalization ability. BRIEF DESCRIPTION OF DRAWINGS

[0043] The accompanying drawings are included to provide a further understanding of the present application, constitute a part of the present application application, and the illustrative embodiments of the present application and their descriptions are used to understand the present application, and do not constitute improper limitations of the present application, and in the drawings:

[0044] Figure 1 The wavelet threshold denoising (WTD) method based on WTD-PC-ViT for transient electromagnetic signals provided for the embodiments of the present application is shown in the flowchart;

[0045] Figure 2 The improved wavelet threshold denoising (WTD) threshold function provided for the embodiments of the present application is compared with the traditional soft and hard threshold functions in the graph;

[0046] Figure 3This is a diagram of the PC-ViT deep neural network structure provided in an embodiment of the present invention;

[0047] Figure 4 A comparison chart of denoising of a random set of noisy transient electromagnetic signals in the synthetic signal test set provided in the embodiments of the present invention;

[0048] Figure 5 The time-domain waveform of random noise signal measured in the field is provided in the embodiments of the present invention;

[0049] Figure 6 Frequency domain waveform of random noise signal measured in the field, provided in an embodiment of the present invention;

[0050] Figure 7 A comparison of the results of different methods for processing transient electromagnetic signals containing random noise from field measurements;

[0051] Figure 8 This is a comparison image of apparent resistivity imaging of transient electromagnetic signals after and without denoising using the WTD-PC-ViT method. Detailed Implementation

[0052] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0053] Figure 1 A flowchart of a transient electromagnetic signal denoising method based on WTD-PC-ViT is shown, combined with... Figure 1 As shown, the transient electromagnetic signal denoising method based on WTD-PC-ViT proposed in this invention includes the following steps:

[0054] Step S1: Construct an improved wavelet thresholding (WTD) threshold function:

[0055] The improved WTD threshold function is continuous and smooth near the threshold point, which can reduce waveform distortion and spurious oscillation in the denoised signal.

[0056] Step S2: Set the base wavelet, threshold type, number of wavelet decompositions, and threshold function; wherein the threshold function uses the improved WTD threshold function constructed in step S1 to perform WTD pre-denoising on transient electromagnetic signals containing random noise.

[0057] Step S3: Normalize the signal after WTD pre-denoising in step S2 to change the signal amplitude range to [0,1].

[0058] Step S4: Construct a PC-ViT neural network model. The model consists of a parallel convolutional neural network and a visual Transformer architecture. The PC-ViT neural network model includes, in sequence according to the signal processing order, a parallel convolutional neural network layer, an attention mechanism layer, a visual Transformer layer, and a linear mapping layer. The parallel convolutional neural network layer is used to extract multi-scale features from the input signal; the attention mechanism layer is used to perform global context modeling on the output of the parallel convolutional neural network layer; the visual Transformer layer is used to perform deep temporal feature modeling on the output of the attention mechanism layer; and the linear mapping layer is used to map the output of the visual Transformer layer and restore it to the final denoised signal.

[0059] Step S5: The normalized signal from step S3 is then denoised using the PC-ViT neural network model constructed in step S4 to obtain the final denoised signal result.

[0060] Furthermore, in step S1 above, the improved WTD threshold function is specifically expressed as follows:

[0061] ;

[0062] in For the corresponding to the first Layer Threshold function for wavelets; These are the original wavelet coefficients; These are the original wavelet coefficients, representing the first wavelet coefficient obtained after wavelet transforming the signal. Layer Each wavelet coefficient represents the characteristics of the transient electromagnetic signal at different scales; The sign function is used to ensure that the amplitude and direction remain unchanged when the signal is restored. The threshold is used to determine the boundary for retaining or weakening wavelet coefficients. In this invention, the threshold is adaptively determined by the VisuShrink method, which is a commonly used threshold selection method and will not be described in detail here. This is a smoothing adjustment factor used to control the smoothness of the threshold function's shape; its value range is typically... In this invention, The improved threshold function graph is derived from... Figure 2 express, Figure 2 A comparison chart of the improved WTD threshold function provided in the embodiments of the present invention with the traditional soft threshold function and hard threshold function.

[0063] Furthermore, in step S2 above, the fundamental wavelet is selected as the sym8 wavelet, which is a type of symmetric wavelet. It has good smoothness and symmetry and is often used for denoising noisy geophysical signals. The wavelet decomposition number is 4 levels to ensure the best denoising effect. Therefore, the signal after WTD pre-denoising is represented as follows:

[0064] ;

[0065] in The signal after WTD pre-denoising. The inverse of the basis wavelet function. For threshold function Wavelet coefficients of the signal retained after nonlinear compression As a scale factor, The translation factor is... For time, Scale factor Scaling and translation factors The translated basis wavelet function.

[0066] In step S4 above, the PC-ViT neural network model is constructed, as follows: Figure 3 As shown, the PC-ViT neural network model, in the order of processing noisy transient electromagnetic signals, includes a parallel convolutional neural network layer, an attention mechanism layer, a visual Transformer layer, and a linear mapping layer. Specifically:

[0067] The parallel convolutional neural network layer is designed with three parallel convolutional branches, each with the same internal structure, including: a first one-dimensional convolutional layer with kernel sizes of 3, 5, and 7 respectively, and 32 output channels, followed by a first ReLU activation function layer; then a first max pooling layer with a kernel size of 2 and a stride of 2, reducing the input signal duration to 500, followed by a self-attention layer to enhance model relevance, then a second one-dimensional convolutional layer (32 output channels, all with a kernel size of 3) and a second ReLU activation function layer; finally, a second max pooling layer is applied, further halving the duration from 500 to 250, meaning the feature vector size output by each parallel convolutional branch is [16, 32, 250]; finally, the outputs of the three parallel convolutional branches are concatenated along the channel dimension to form a fused multi-scale feature representation with an output signal size of [16, 96, ...]. 250]; where 16 is the batch size (determined by the input data, representing the processing of 16 samples at a time). It should be noted that in neural networks, the batch size represents the number of samples processed at one time. Throughout the entire network layer, the batch size remains unchanged (all operations are applied independently to each sample), so the output is still 16.

[0068] The attention mechanism layer takes the output of the parallel convolutional neural network layer as input and performs channel compression through a linear projection layer to map 96-dimensional channels to 64-dimensional channels, thereby reducing the number of parameters and further extracting features; at this time, the size of the signal becomes [16, 64, 250]; subsequently, an attention mechanism is introduced. This part calculates three attention weight matrices Query (query), Key (key), and Value (value) with a dimension of 64, and performs weighted summation on the sequence features through the attention weight matrix to realize global context modeling. After global attention processing, the size of the output signal remains unchanged, still [16, 64, 250].

[0069] The visual Transformer layer takes the output signal of the attention mechanism layer as input and performs linear projection to expand the size of the signal to [16, 128, 250] to form the embedding dimension of the Transformer; then, the input passes through the Transformer Block (Transformer block), which includes: a multi-head self-attention layer (8 attention heads, each head has a dimension of 16) and two linear layers; after passing through the Transformer Block, the size of the output remains unchanged, still [16, 128, 250].

[0070] The linear mapping layer takes the output signal of the visual Transformer layer as input and first passes through a linear mapping layer to restore the 128-scale channel to a single-channel signal amplitude. At this time, the output size becomes [16, 1, 250]. Then it passes through a linear upsampling layer, which includes two times of 2x2 pooling, to restore the time length dimension to 1000. That is, the output size is [16, 1, 1000], and then it passes through the signal extraction layer to output [1, 1000], which is the final denoised signal.

[0071] Further, the PC-ViT neural network model needs to obtain a synthetic noisy transient electromagnetic signal through one-dimensional forward modeling to train.

[0072] The process of obtaining the synthesized noisy transient electromagnetic signal through one-dimensional forward modeling specifically includes: During the forward modeling, a random method is used to simulate the real terrain. The model has 30 layers, with the first layer having a thickness of 1.8 meters and a resistivity that is a random value within the range of (1 Ω•m–1000 Ω•m). Starting from the second layer, the thickness of the current layer is 1.1 times that of the previous layer, and the resistivity of the current layer is also a randomly generated value within the range of (1 Ω•m–1000 Ω•m). In the process of constructing the synthetic model, this invention created a total of 20,000 different resistivity models with a total thickness of 300 meters. Simultaneously, a synthetic signal with a sampling frequency of 1 MHz and a duration of 1 ms was generated. Based on this, 30 random noise signals with different signal-to-noise ratios were randomly added. The signal-to-noise ratio is distributed in the range [−10dB, 10dB]; that is, a total of 600,000 sets of noisy transient electromagnetic signals with different signal-to-noise ratios were generated, of which 70% were used as the training set and 30% as the test set; both the training set and the test set signals need to be pre-denoised by WTD before being input into the PC-ViT deep neural network for training and testing.

[0073] The above signal-to-noise ratio calculation formula is as follows:

[0074] ;

[0075] in This represents a transient electromagnetic signal sequence. Represents a sequence of random noise signals. For time;

[0076] In this example, a random set of noisy transient electromagnetic signals from the synthetic test set was first selected for method verification, such as... Figure 4 As shown, Figure 4 This is a comparison chart of denoising a randomly selected set of noisy transient electromagnetic signals from the synthetic signal test set provided in this embodiment of the invention. By comparing WTD denoising using traditional soft thresholding functions (green line), traditional hard thresholding functions (orange line), improved thresholding functions (blue line), and the WTD-PC-ViT denoising method of this invention, it is found that WTD denoising using the improved thresholding function is superior to traditional soft and hard thresholding functions, and does not cause signal distortion. The WTD-PC-ViT method of this invention achieves the best denoising effect.

[0077] Secondly, random noise signals were collected and tested in the field. The time-domain and frequency-domain waveforms of the random noise signals in the field are shown below. Figure 5 and Figure 6 As shown, random noise signals from the field are superimposed on synthesized noiseless transient electromagnetic signals to form noisy transient electromagnetic signals for testing. The denoising results of the noisy transient electromagnetic signals obtained by the conventional method and the method of this invention are compared as follows: Figure 7As shown, the method WTD-PC-ViT of the application achieves the best performance; Figure 8 The comparison results of the apparent resistivity imaging of the signal denoised by the method of the application and the apparent resistivity imaging of the signal without denoising are shown; it can be found that the signal denoised by the method of the application effectively restores the real model. The method of the application can effectively select and reconstruct the signal and suppress random noise. A new and effective solution is provided for transient electromagnetic random noise denoising.

[0078] The above merely describes preferred embodiments of the application and is not used to limit the application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the application shall be included in the protection scope of the application.

Claims

1. A transient electromagnetic signal denoising method based on WTD-PC-ViT, characterized in that, Includes the following steps: Step S1: Construct an improved wavelet threshold denoising WTD threshold function, wherein the improved wavelet threshold denoising WTD threshold function is continuous and differentiable at the threshold point; Step S2: Set the base wavelet, threshold type, and wavelet decomposition level, and set the threshold function to the improved wavelet threshold denoising WTD threshold function constructed in step S1. Use the improved wavelet threshold denoising WTD threshold function to perform WTD pre-denoising on transient electromagnetic signals containing random noise to obtain a pre-denoised signal. Step S3: Normalize the pre-denoised signal obtained in step S2; Step S4: Construct a PC-ViT neural network model. The PC-ViT neural network model includes, in sequence according to the signal processing order, a parallel convolutional neural network layer, an attention mechanism layer, a visual Transformer layer, and a linear mapping layer. The parallel convolutional neural network layer is used to extract multi-scale features from the input signal; the attention mechanism layer is used to perform global context modeling on the output of the parallel convolutional neural network layer. The visual Transformer layer is used to perform deep temporal feature modeling on the output of the attention mechanism layer; the linear mapping layer is used to map the output of the visual Transformer layer and restore it to the final denoised signal. Step S5: Input the normalized signal from step S3 into the PC-ViT neural network model constructed in step S4 for denoising to obtain the final denoised signal. In step S1, the improved wavelet threshold denoising WTD threshold function is specifically expressed as follows: ； in For the corresponding to the first Layer Threshold function for wavelets; These are the original wavelet coefficients; The sign function is used to keep the amplitude and direction of the signal unchanged. It is a threshold; It is a smoothing adjustment factor, with a value range of [value range missing]. .

2. The transient electromagnetic signal denoising method based on WTD-PC-ViT according to claim 1, characterized in that, The smoothing adjustment factor The value is 0.

3.

3. The transient electromagnetic signal denoising method based on WTD-PC-ViT according to claim 1, characterized in that, In step S2, the base wavelet is the sym8 wavelet, and the wavelet decomposition layer has 4 layers.

4. The transient electromagnetic signal denoising method based on WTD-PC-ViT according to claim 1, characterized in that, In step S4, the parallel convolutional neural network layer includes three parallel convolutional branches, each of which sequentially includes a first one-dimensional convolutional layer, a first ReLU activation function layer, a first max pooling layer, a self-attention layer, a second one-dimensional convolutional layer, a second ReLU activation function layer, and a second max pooling layer. The outputs of the three convolutional branches are concatenated along the channel dimension.

5. The transient electromagnetic signal denoising method based on WTD-PC-ViT according to claim 4, characterized in that, In the three convolutional branches, the kernel sizes of the first one-dimensional convolutional layer are 3, 5, and 7, respectively.

6. The transient electromagnetic signal denoising method based on WTD-PC-ViT according to claim 1, characterized in that, In step S4, the visual Transformer layer is configured as follows: Receive an input signal, the size of which is a first size, which is the size of the output signal of the attention mechanism layer; A linear projection operation is performed on the input signal to expand the size of the input signal to the embedding dimension, resulting in an embedded signal, the size of which is a second dimension. The embedded signal is input to the Transformer block for processing; The linear projection operation is implemented through a fully connected layer, which maps the number of input channels from a first value to a second value. The first value corresponds to the channel dimension of the first size, and the second value corresponds to the channel dimension of the second size. The Transformer block includes a multi-head self-attention sub-layer and a feedforward neural network sub-layer connected in sequence; the multi-head self-attention sub-layer is configured to have There are 1 attention head, and each attention head has 1 dimension. The feedforward neural network sublayer comprises a first linear layer, an activation function layer, and a second linear layer connected in sequence; the size of the output signal of the Transformer block is the same as the size of the embedded signal, both being the second size; In the feedforward neural network sublayer, the first linear layer expands the input dimension to the magnification factor of the original dimension, and the second linear layer projects the dimension back to the same number of channels as the embedded signal.

7. The transient electromagnetic signal denoising method based on WTD-PC-ViT according to claim 1, characterized in that, The linear mapping layer is configured as follows: Receives multi-channel signals output from the visual Transformer layer; The multi-channel signal is linearly mapped to restore its channel number to a single channel, thus obtaining the amplitude of the single-channel signal. The time length dimension of the amplitude of the single-channel signal is linearly upsampled, and the time length is restored to the target length through a process including at least one pooling operation; The upsampled signal is extracted to output the final single-batch denoised signal.

8. The transient electromagnetic signal denoising method based on WTD-PC-ViT according to claim 1, characterized in that, Prior to step S5, a training step for the PC-ViT neural network model is also included, wherein the training dataset used in the training step is constructed in the following manner: Multiple sets of noiseless transient electromagnetic signals corresponding to different formation resistivity models are generated through one-dimensional forward modeling. Random noise signals with different signal-to-noise ratios are superimposed on the noiseless transient electromagnetic signal to form a noisy transient electromagnetic signal sample set; The noisy transient electromagnetic signal sample set is divided into a training set and a test set; The PC-ViT neural network model is trained using the training set.

9. The transient electromagnetic signal denoising method based on WTD-PC-ViT according to claim 8, characterized in that, In the one-dimensional forward modeling, a multi-layer geological model is constructed, wherein the thickness of the first layer is a fixed value and the resistivity is randomly generated within a first preset resistivity range; starting from the second layer, the thickness of the current layer is a fixed multiple of the thickness of the previous layer, and the resistivity of the current layer is randomly generated within a second preset resistivity range; the signal-to-noise ratio of the random noise signal is distributed within a preset signal-to-noise ratio range.

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