Magnetotelluric signal noise suppression method and system based on feature contraction and expansion

Abstract

The invention discloses a magnetotelluric signal noise suppression method and system based on feature contraction and expansion, a brand new CLR-MLP AE network model is constructed and used for magnetotelluric signal noise reduction, the CLR-MLP AE model introduces a time sequence feature enhancement mechanism, time block processing and anomaly identification are performed on an input signal, and the noise suppression efficiency of the magnetotelluric signal is improved. Key information can be reserved in a feature extraction stage; besides, the constructed neural network adopts a CMLP-mix encoder and a decoder adopting adaptive transpose convolution, and a full connection layer is decomposed and fused by using an SVD matrix, so that low-rank conversion of the encoder is realized, feature information is effectively extracted, and efficient feature compression is realized; furthermore, the size and weight distribution of a transposed convolution kernel are adaptively adjusted in a decoder according to input data features or a learned mode, so that the calculation speed of the network is finally improved, and the noise reduction effect is ensured.

Description

Technical Field

[0001] The present invention belongs to the technical field of magnetotelluric signal processing, and particularly relates to a magnetotelluric signal noise suppression method and system based on feature contraction and expansion. Background Art

[0002] The magnetotelluric sounding method was first proposed by Tikhonov and Cagniard in the 1950s and is now widely used as an important geophysical exploration method for detecting the underground geoelectric structure. This method uses the naturally varying electromagnetic field as the field source and infers the electrical properties and their distribution characteristics underground by measuring the orthogonal electric and magnetic fields on the ground surface. This method has the advantages of large detection depth, low cost, simple construction, and high vertical and horizontal resolution capabilities, and has been widely applied in fields such as earthquake prediction, oil and gas field exploration and census, and mineral resource exploration. However, magnetotelluric signals are usually very weak, have a wide frequency band range, and are easily interfered by various noises. Moreover, with the progress of technology, the artificial electromagnetic interference generated by heavy industrial activities has become increasingly significant, greatly affecting the quality of the captured earth electromagnetic signals, thereby reducing the ability to deeply understand and analyze underground structures and resources.

[0003] Numerous scholars have actively developed and applied various advanced data processing technologies to effectively reduce different types of interference noises in order to improve the quality of magnetotelluric (MT) data. For example, the remote reference (RR) method, the least squares method, the MT robust processing method, and the Hilbert-Huang transform. These methods can suppress power frequency interference and highlight the useful information in seismic data, and to a certain extent, improve the quality of magnetotelluric data. However, the existing technologies mainly perform signal-to-noise separation in an overall processing manner, resulting in the filtering of some useful low-frequency information when strong interference is removed, seriously affecting the reliability of the magnetotelluric data itself. At the same time, the traditional time-frequency domain magnetotelluric signal signal-to-noise separation method also has the problem of low processing efficiency. Therefore, how to improve the denoising accuracy of magnetotelluric signals is a current hot research direction in this field, and the present invention is committed to improving the denoising accuracy and calculation efficiency based on neural networks. Summary of the Invention

[0004] The object of the present invention is to improve the noise reduction accuracy of magnetotelluric signals, and a magnetotelluric signal denoising method and system based on feature contraction and expansion are provided, that is, a neural network based on feature contraction and expansion of CLR-MLP AE is proposed for magnetotelluric signal denoising. The technical solution of the present invention uses a CLR-MLP AE, which includes a CMLP-mixer encoder that uses SVD matrix decomposition to achieve low-rank transformation and a decoder composed of an adaptive transposed convolutional layer. The core is to adopt a novel CLR-MLP-mixer encoder, which introduces an SVD matrix-full connection layer for low-rank transformation in the MLP-mixer, that is, embedding the full connection layer between the sequence dimensionality reduction and sequence dimensionality increase operations of the SVD matrix decomposition algorithm, so as to better achieve feature compression and expansion.

[0005] On the one hand, the present invention provides a magnetotelluric signal noise suppression method based on feature contraction and expansion, constructs a signal-to-noise mapping model based on the CLR-MLP AE neural network for noise suppression of magnetotelluric signals, and the method includes the following steps:

[0006] Dataset construction, constructing noisy samples of magnetotelluric signals and training labels, where the training labels are defined as noise profiles or denoised magnetotelluric signals;

[0007] Model training, using the constructed dataset, inputting the noisy samples into the CLR-MLP AE neural network for training to obtain a signal-to-noise mapping model;

[0008] Actual signal denoising, inputting the magnetotelluric actual signal to be denoised into the signal-to-noise mapping model to obtain a noise profile or a denoised magnetotelluric signal, and subtracting the noise profile from the actual signal to obtain a denoised magnetotelluric signal;

[0009] Among them, the CLR-MLP AE neural network is a network that is provided with a CLR-MLP-Mixer encoder and a decoder based on low-rank transformation to achieve feature contraction and expansion. The CLR-MLP-Mixer encoder introduces an SVD matrix-full connection layer for low-rank transformation in both the parallel spatial mixing encoder and the temporal mixing encoder, to replace the corresponding full connection layer in the original MLP-Mixer encoder and add a convolutional layer. The SVD matrix-full connection layer embeds the full connection layer between the sequence dimensionality reduction and sequence dimensionality increase operations of the SVD matrix decomposition algorithm.

[0010] In the solution of the present invention, considering that traditional neural networks cannot capture global feature information well, it is proposed to use an MLP-Mixer to form an encoder to better obtain the global feature information of magnetotelluric signals, which can better shrink the global feature information. Convolution operations are good at extracting features locally. Therefore, adding a convolutional layer to the encoder can, in addition to the global information capture of the MLP-Mixer, supplement the local feature extraction and feature shrinkage of the input magnetotelluric signals. At the same time, the combination of the two can reduce the computational complexity and improve the accuracy of feature shrinkage of magnetotelluric signals while maintaining high performance.

[0011] The technical solution of the present invention introduces an SVD matrix - fully connected layer to replace the fully connected layer, and the SVD matrix - fully connected layer embeds the fully connected layer between the sequence dimensionality reduction and sequence dimensionality increase operations of the SVD matrix decomposition algorithm. It is fully considered that the SVD matrix decomposition combined with the fully connected layer is beneficial to reducing the computational complexity. The parameter matrix of the fully connected layer is usually very large, with high computational and storage costs. Through low-rank transformation, SVD only retains the main singular values and corresponding singular vectors, greatly reducing the amount of matrix multiplication calculations and improving the inference speed. It can also improve the generalization ability. The fully connected layer may overfit the training data, while the SVD low-rank approximation is equivalent to a kind of regularization of the weight matrix, removing the singular values with less influence on the data, thereby reducing the sensitivity of the model to noise and improving the generalization ability. It can also enhance the feature compression ability. What SVD extracts is the main change direction of the data, retaining key information while reducing the dimensionality, which helps to learn more representative features and improve the feature compression ability of the MLP.

[0012] The signal-to-noise mapping model provided by the present invention's technology is proposed to better extract the global and local features of magnetotelluric signals in the time domain and frequency domain. In the technical solution of the present invention, CLR-MLP-Mixer is used to replace the traditional convolutional encoder. Different from the traditional MLP for processing two-dimensional images, the CLR-MLP-Mixer encoder is divided into two parts: spatial mixing, also known as channel mixing, and time mixing. Spatial mixing mainly processes the interaction between different channels at each position, extracts its spatial distribution characteristics and spatial structure correlation, and adapts to the multi-channel and multi-component spatial characteristics of magnetotelluric signals; time mixing processes the information interaction between each time period, can capture the global dependence of magnetotelluric signals, capture its time dynamic trend, periodicity and abruptness, and model long-term and short-term dependence relationships. To ensure that CLR-MLP-Mixer can better learn temporal features, the present invention will preferably perform time delay processing on the input signal below, retain the historical information and evolution trajectory of the time series, effectively enhance the model's ability to capture long-term and short-term dependence relationships, help identify periodic changes, trend changes and abnormal fluctuations. At the same time, for the MLP-Mixer encoder part, an SVD matrix - fully connected layer is used. The SVD matrix - fully connected layer reduces the matrix multiplication calculation amount through low-rank decomposition, reduces the parameter scale, and improves the model inference speed; the SVD matrix - fully connected layer improves the model generalization ability. The SVD low-rank approximation is equivalent to regularizing the fully connected weight matrix, suppressing noise interference and reducing the risk of overfitting; the SVD matrix - fully connected layer can enhance the feature compression ability, extract the main change direction, retain key information while reducing the dimension, and improve the MLP feature expression and compression effect.

[0013] Further optionally, the noisy signal input to the CLR-MLP-Mixer encoder is divided into several patch sequences according to the patch length k, a noisy signal matrix X is constructed, and then the patch sequences in the noisy signal matrix X are used as subsequences and input into the spatial mixing encoder in the CLR-MLP-Mixer encoder, and the time dimension vectors composed of the elements at the same position in each patch sequence in the noisy signal matrix X are used as subsequences and input into the time mixing encoder in the CLR-MLP-Mixer encoder;

[0014] The SVD matrix - fully connected layer processes each subsequence as follows:

[0015] First, perform SVD matrix decomposition on each subsequence to obtain the left singular matrix, diagonal matrix, and right singular matrix;

[0016]

[0017] In the formula, respectively represent the left singular matrix, the diagonal matrix, and the right singular matrix, and T is the matrix transpose symbol;

[0018] The left singular matrix and the diagonal matrix are respectively subjected to non-linear transformation by using the fully connected layer, specifically:

[0019]

[0020]

[0021] In the formula, is the left singular matrix obtained through the fully connected layer, is the diagonal matrix obtained through the fully connected layer, are respectively learnable weight matrices, is the bias term, and sigmoid is the non-linear transformation function corresponding to the fully connected layer;

[0022] Finally, the left singular matrix and the diagonal matrix obtained through the fully connected layer are combined with the right singular matrix to obtain the output feature map in the SVD matrix - fully connected layer, specifically:

[0023] .

[0024] Further preferably, the method further includes: before inputting the CLR-MLP-Mixer encoder, introducing the idea of delayed embedding to enhance the temporal features of the noisy signal, specifically as follows:

[0025] First, the original noisy signal is segmented according to the patch length k to obtain an initial noisy signal matrix, and the noisy signal matrix is composed of segmented patch sequences, and the noisy signal matrix is expressed as: , each row corresponds to a patch sequence, is the signal at the kth sampling point in the noisy signal;

[0026] Secondly, the delay sequence length and the value range of are defined, and is traversed and valued within the value range, and the autocorrelation function is calculated for each delay sequence length ;

[0027]

[0028] In the formula, Denotes the row number marker in matrix X, which represents the th row and th column element in matrix X, and is the average value of the th row;

[0029] Then, all the results are normalized, and the minimum value of the delay sequence length is found based on the normalized results and regarded as the optimal value :

[0030] ,

[0031] wherein, is the delay sequence length is the autocorrelation function when it is 0, is the normalized result;

[0032] Finally, based on the optimal value the patch sequence in the original noisy signal matrix is delay-embedded to obtain a new patch sequence, and the noisy signal matrix X is reconstructed as: .

[0033] Before the technical solution of the present invention inputs the signal into the encoder, temporal feature enhancement is performed on the original data, that is, the original data is delay-embedded, and the information of the past time points of the time series is embedded into the representation of the current time point to capture historical dependence, and the one-dimensional time series is transformed into a multi-dimensional embedding matrix. Each row subsequence contains the information of the current and several past moments, which is convenient for the subsequent spatial mixing and temporal mixing encoders to jointly model the local and global spatio-temporal characteristics. In the temporal signal of magnetotellurics, the state of the current time point is often affected by multiple past time points, and there is obvious historical dependence. Directly modeling the original data is likely to ignore the potential dynamic patterns of the signal in the time dimension. Therefore, before the signal is input into the encoder, the present invention constructs a temporal feature matrix through delay embedding, embeds the observed values of historical time points into the current representation, effectively enhances the expression ability of the temporal signal, and captures the short-term trends and long-term dependence relationships of the time series. And the present invention selects the autocorrelation function to determine the delay length in the delay embedding matrix, determines the delay length according to the decay situation of the autocorrelation coefficient, ensures that the main dependence structure of the signal is retained, and avoids redundant information. By setting a reasonable threshold, the optimal delay length is determined, so that the delay embedding matrix can retain the main correlation and does not introduce too many irrelevant features, improving the effectiveness and generalization ability of the model.

[0034] Further preferably, the method further includes: before inputting the CLR-MLP-Mixer encoder, performing anomaly detection and marking on the patch sequence of the noisy signal, that is, marking the abnormal patch sequence, and the unmarked patch sequence is not used as a subsequence to input the spatial mixing encoding;

[0035] Among them, the anomaly detection process is as follows:

[0036] First, calculate the distance between each patch sequence and other patch sequences; then extract the nearest neighbor distance corresponding to each patch sequence based on the distance, and then calculate the distance average value of the

[0037]

[0038]

[0039] In the formula, is the neighbor distance between two patch sequences , is the patch sequence and its nearest neighbor distance average value, is the length of the patch sequence, is the patch sequence the l-th sequence value in, is the patch sequence the nearest neighbor set composed of Generally,

[0040] takes a value of 5% of the total number of all patches; Then, determine the anomaly point judgment threshold

[0041]

[0042] In the formula, is a preset coefficient, define the variable , There is: , , T is the length of the noisy signal matrix X;

[0043] Finally, in the magnetotelluric signal sequence, if there is noise data, the amplitude is usually several times or even dozens of times that of the high-quality signal, which will cause the distance average value , indicating that there is a noise segment in this patch sequence, then the th window is regarded as abnormal, that is, the patch sequence 。The spatial mixture encoder in the present invention mainly learns the noise characteristics in different signal sequences. An abnormal subsequence usually contains a noise segment, while a non-abnormal subsequence does not. To effectively extract the abnormal characteristics of the noise segment inside the abnormal subsequence and avoid over-modeling of high-quality data, it is designed that abnormal data passes through the spatial mixture encoder, and non-abnormal data does not need to pass through.

[0044] Further preferably, when constructing the noisy samples of magnetotelluric signals, the Nonlinear SMOTE algorithm and non-linear interpolation are introduced to expand the noisy samples;

[0045] Among them, the noise part with non-zero amplitude in the noise profile is extracted, and then Nonlinear SMOTE is introduced to find its k nearest neighbor samples in the feature space;

[0046] Then, new noisy samples are generated through non-linear interpolation according to the k nearest neighbor samples. The formula for non-linear interpolation is:

[0047]

[0048] In the formula, is the vector composed of the noise part with non-zero amplitude in the noise profile, is 's k-nearest neighbor samples, is a random number, taking values in [0,1], is the parameter controlling the non-linear degree.

[0049] In the process of deep learning, although the network structure is important, the type and quantity of the data sample set also play a very important role and influence on the performance of the network model. Therefore, the present invention proposes to use Nonlinear SMOTE to further enhance the data of the noise profile sample library of the network for feature contraction and expansion. Further temporal feature enhancement is more conducive to feature compression and extraction by the time and space encoders. Nonlinear SMOTE can generate a large number of noise samples similar to the original noise profile, greatly enriching the type and quantity of the noise profile, enabling the network to better learn the characteristics of the noise profile and improving the generalization ability of the network. Therefore, the present invention can greatly improve the denoising effect and reliability of magnetotelluric signals.

[0050] Further preferably, the decoder is a decoder based on adaptive transposed convolution, which is composed of an adaptive transposed convolution layer, a batch normalization layer, and an activation function. The mathematical model is expressed as:

[0051]

[0052] In the formula, It represents the result after the transposed convolution operation; It represents performing the transposed convolution operation; stride represents the stride size, It represents the output of the concat layer of the CLR-MLP-Mixer encoder. The definition formula of the transposed convolution is as follows:

[0053]

[0054] In the above formula, represents the th input value, is the th output value in the output sequence after the transposed convolution calculation, represents the weight size of the transposed convolution kernel, represents the step size, and N represents the total length of the output sequence of the concat layer;

[0055] Among them, the size of the transposed convolution kernel is adaptively adjusted according to the following rules:

[0056]

[0057] In the formula, is the size of the convolution kernel after the th round of training, represents the th round of training, the mean square error between the output and the true value, is the adjustment step size of the convolution kernel size, with a default value of 1, is the threshold of the loss change, used to judge whether to continue the adjustment.

[0058] After each round of training, according to the current convolution kernel size, the mean square error (MSE) between the output and the true value, and the loss change situation, the convolution kernel size is adaptively adjusted. According to the size of the loss, the convolution kernel size is dynamically adjusted, and it is gradually adjusted by the step size (default value is 1). If the current loss is decreasing, it means that the current convolution kernel scale has a certain expressive ability, but it may be possible to further capture a larger receptive field and more global information to assist the current feature extraction. Therefore, continue to increase the convolution kernel, which can introduce more large-scale context information on the basis of maintaining the existing small-scale information, and can also avoid falling into local optima and improve the global structure restoration ability; if the current loss is increasing, it means that the previous convolution kernel scale has caused over-smoothing, loss of details, or capture of too much irrelevant global information, which instead affects the accurate restoration of local features. Reducing the convolution kernel can pay more attention to the local information in the neighborhood and avoid expanding the receptive field when the features are too blurred, resulting in information distortion.

[0059] The core idea of the adaptive transposed convolution proposed in this invention is to utilize information of different scales simultaneously to enhance the model's ability to capture complex data patterns. By adaptively and dynamically adjusting the parameters of the transposed convolution kernel based on the semantic information or structural features of the input features, while expanding the spatial dimension, the structural expression ability and semantic consistency of the output feature map are enhanced, thereby improving the decoder's ability to restore high-frequency and low-frequency information, reducing the network's dependence on a single scale, making the reconstruction result more delicate, and at the same time enhancing the ability to preserve detailed information.

[0060] Further preferably, after the feature fusion of the outputs of each channel of the spatial encoder and the temporal encoder, a learnable weight coefficient is introduced for the fused feature to perform focusing, expressed as:

[0061]

[0062] In the formula, is the output result adjusted by the weight coefficient , and the weight coefficient is adaptively adjusted during network training.

[0063] In the second aspect, the technical solution of this invention provides a system based on the magnetotelluric signal denoising method, including:

[0064] Sample library construction module: used to construct noisy samples of magnetotelluric signals and training labels, where the training labels are defined as noise profiles or denoised magnetotelluric signals;

[0065] CLR-MLP AE denoising model construction module: using the constructed data set, inputting the noisy samples into the CLR-MLP AE neural network for training to obtain a signal-to-noise mapping model;

[0066] Among them, the CLR-MLP AE neural network is a network with a CLR-MLP-Mixer encoder and decoder based on low-rank transformation to achieve feature contraction and expansion. The CLR-MLP-Mixer encoder introduces an SVD matrix - fully connected layer for low-rank transformation in both the parallel spatial mixing encoder and the temporal mixing encoder to replace the corresponding first fully connected layer in the original MLP-Mixer encoder. The SVD matrix - fully connected layer embeds the fully connected layer between the sequence dimensionality reduction and sequence dimensionality increase operations of the SVD matrix decomposition algorithm;

[0067] Denoising module: inputting the measured magnetotelluric signal to be denoised into the signal-to-noise mapping model to obtain a noise profile or a denoised magnetotelluric signal, and subtracting the noise profile from the measured signal to obtain a denoised magnetotelluric signal.

[0068] In a third aspect, the technical solution of the present invention further provides a computer-readable storage medium storing a computer program, which is called by a processor to implement the steps of a magnetotelluric signal denoising method based on feature fusion.

[0069] Beneficial effects

[0070] Compared with the existing methods, the advantages of the present invention are as follows:

[0071] 1. The present invention provides a magnetotelluric signal denoising method based on feature contraction and expansion, which uses an SVD matrix decomposition to implement a CMLP-mixer encoder for low-rank transformation and a decoder composed of an adaptive transposed convolutional layer. Among them, an SVD matrix - fully connected layer for implementing low-rank transformation is introduced in the MLP-mixer. When processing magnetotelluric signals, considering that feature extraction is not perfect enough, the technical solution of the present invention introduces a CLR-MLP-Mixer encoder composed of channel mixing and time mixing. Channel mixing integrates information of different channels on a global scale, and the convolutional layer further captures local dependencies between channels. Time mixing processes the global relationships between time segments, and the convolutional layer effectively extracts local features of magnetotelluric signals in the time dimension. The application of SVD matrix decomposition on the MLP can effectively reduce the data dimension, remove redundant data information, make the feature representation more compact, and improve the generalization ability. The combination of the three can fully explore and utilize the feature information in magnetotellurics, contract the feature information in magnetotellurics, extract the most critical data information, and then expand and restore the feature information in magnetotellurics through a decoder including multi-scale feature extraction to map deeper and more complex feature representations of magnetotelluric signals, ultimately improving the noise reduction accuracy of magnetotelluric signals.

[0072] 2. In a further optimization scheme of the present invention, Nonlinear SMOTE and corresponding time series feature enhancement are used to perform data enhancement on the training sample library of the CLR-MLP AE network. Nonlinear SMOTE generates new samples through nonlinear interpolation, which can expand the original data sample library, enabling the network to better learn the features of noise profiles and pure signals, and improving the denoising performance of the network. In addition, a time series feature enhancement mechanism is also introduced. The time embedding matrix constructs multiple subsequences through a sliding window, maps the one-dimensional time series into a high-dimensional structure, retains local patterns and dynamic characteristics in time, and helps the model understand short-term and long-term dependence relationships; and through abnormal feature identification, the Euclidean distance between each time window and other windows is calculated to measure the similarity between subsequences, which can more accurately distinguish the features of noise and signals. Description of the drawings

[0073] Figure 1 is the flow chart provided by the embodiment of the present invention;

[0074] Figure 2 is the network diagram provided by the embodiment of the present invention;

[0075] Figure 3 is the noise profile sample diagram generated by partial Nonlinear SMOTE;

[0076] Figure 4 is the denoising effect diagram of simulated noisy data;

[0077] Figure 5 is the denoising effect diagram of measured data;

[0078] Figure 6 is the original apparent resistivity-phase curve of the measured data and the apparent resistivity-phase curve diagram after being processed by the inventive method. (a) and (b) are the comparisons of the apparent resistivity curves, and (c) and (d) are the comparisons of the phase curves; Specific Embodiments

[0079] As Figure 1 shown, the technical solution of the present invention provides a magnetotelluric signal denoising method and system based on a feature contraction and expansion network. The technical idea of the denoising method is as follows: First, construct a noise profile sample library and a pure signal sample library, and then input the noisy signal sample obtained by adding these two sample libraries into the CLR-MLP AE network for training, and use the pure signal or the noise profile as the training label to train a signal-to-noise mapping model based on feature contraction and expansion. Finally, input the magnetotelluric noisy signal to be denoised into the signal-to-noise mapping model to obtain the noise profile or the denoised magnetotelluric signal. Among them, if the noise profile is obtained, the signal to be denoised is subtracted from the corresponding noise profile to obtain the denoised magnetotelluric signal. Among them, the core of the present invention is to construct and train a signal-to-noise mapping model based on the CLR-MLP AE neural network based on the magnetotelluric signal characteristics and the noise reduction performance requirements. The signal-to-noise mapping model based on the CLR-MLP AE neural network will be specifically described below.

[0080] As Figure 2The following is the basic network diagram of the technical solution of the present invention. First, the input data is preprocessed by a temporal feature enhancement module, and a temporal path and a spatial path are respectively constructed to extract key features. In both paths, singular value decomposition (SVD) is used for feature dimensionality reduction and compression. Combined with feature screening and a fully connected layer, the dimensionality-reduced features are further modeled, and the feature expression ability is enhanced through a dimensionality increase operation. Subsequently, the ReLU activation function and a convolutional layer are introduced to extract deep local features, and preliminary modeling is completed through a fully connected layer. After the temporal and spatial features are fused in the Concat layer, an adaptive transposed convolutional layer is used to implement feature transformation or upsampling, and then through batch normalization and the ReLU activation, the target result is finally generated by the output layer.

[0081] As Figure 3 shown are a noise profile sample and the corresponding noisy sample respectively. By analyzing the magnetotelluric measurement point QH401504, it is obtained that the main types of noise interference in the signal are complex noise interferences such as pulse waves, triangular wave-like waves, and square wave-like waves, and the waveform amplitude range is between (-100000:100000). Therefore, first, single smooth noise profiles of these types are generated according to the data function, and then the Nonlinear SMOTE is used to generate noise profile samples. The generated sample amplitude range is between (-100000:100000), and finally, a large number of different smooth noise profile samples are obtained. The amplitude of the measured magnetotelluric interference-free data is between (-500:500), and because its data characteristics are extremely similar to Gaussian white noise with a similar amplitude, Gaussian white noise with the same length as the noise profile and an amplitude between (-500:500) is generated as the simulated interference-free data. The noise profile and the simulated interference-free data are added to obtain the noisy data, and finally, the noisy data is used as the training input of the CLR-MLP AE neural network. In the embodiment of the present invention, the sample length is set to 100.

[0082] Therefore, a magnetotelluric signal noise suppression method based on feature contraction and expansion in this embodiment includes the following steps:

[0083] Step 1: Dataset construction, constructing a noisy sample of the magnetotelluric signal and a training label, where the training label is defined as a noise profile or a denoised magnetotelluric signal.

[0084] Among them, in this field, wavelet analysis method is often used to extract a large number of smooth noise profiles from measured magnetotelluric data, and high-quality measured magnetotelluric data is extracted as simulated high-quality magnetotelluric data, and then relevant mathematical functions are used to construct more smooth noise profiles. In addition, a pure signal sample is constructed, and then the noise profile is superimposed on the pure signal to form a noisy signal. It should be understood that the construction of the noise profile sample, the pure signal sample, and the noisy signal sample can all be realized by conventional technical means in this field. Therefore, no specific description is given to them, nor are specific constraints imposed on their implementation means.

[0085] In this embodiment, in order to increase the number and diversity of samples, the noise samples are preferably expanded as follows:

[0086] Step 1.1: Use wavelet analysis method to extract a large number of smooth noise profiles from measured magnetotelluric data, and extract smooth noise profile waveforms such as pulse waves, triangular wave-like waves, square wave-like waves, etc.

[0087] Step 1.2: Divide the smooth noise profiles into two categories. One category is the safe part with an amplitude of 0 without noise, and the other category is the noise part with a non-zero amplitude of the noise profile. Determine that the noise part in the dataset is the minority class samples, and these samples will be used to generate new synthetic samples.

[0088] Step 1.3: For each minority class sample, the Nonlinear SMOTE algorithm will find its K nearest neighbor samples in the feature space (usually using Euclidean distance);

[0089] Step 1.4: According to the minority class sample and its selected nearest neighbor samples, Nonlinear SMOTE generates a new sample x through non-linear interpolation. The formula for non-linear interpolation is:

[0090]

[0091] In the formula, is the vector composed of the noise part with a non-zero amplitude in the noise profile, is the K-nearest neighbor sample of is a random number, taking values in [0,1], used to control the non-linear degree. For example, amplifies the change far from the origin, reduces the change far from the origin, making the synthetic data more in line with the distribution pattern of the real data.

[0092] Among them, other smooth noise profile waveforms such as single pulse waves, square wave-like waves, etc. can all execute the above steps 1.1 - 1.4 to generate a large number of noise profile samples.

[0093] Step 2: Model training. Using the constructed dataset, input the noisy samples into the CLR-MLP AE neural network for training to obtain the signal-to-noise mapping model.

[0094] Step 3: Measured signal denoising. Input the measured magnetotelluric signal to be denoised into the signal-to-noise mapping model to obtain the noise profile or the denoised magnetotelluric signal. The denoised magnetotelluric signal is the measured signal minus the noise profile.

[0095] In this embodiment, preferably, before inputting into the network, the idea of delay embedding is introduced to enhance the temporal features of the noisy signal, that is, the information of the past time points of the time series is embedded into the representation of the current time point to capture historical dependencies, specifically as follows:

[0096] First, divide the original noisy signal according to the patch length k to obtain the initial noisy signal matrix. The noisy signal matrix is composed of the divided patch sequences and is expressed as: , where each row corresponds to a patch sequence, is the signal at the k-th sampling point in the noisy signal;

[0097] Secondly, define the delay sequence length and the value range of . Traverse the values of within the value range and calculate the autocorrelation function for each delay sequence length ;

[0098]

[0099] In the formula, represents the row label in matrix X, represents the element in the -th row and -th column of matrix X, is the average value of the -th row;

[0100] Then, normalize all the results and find the minimum value of the delay sequence length , regarded as the optimal value :

[0101] ,

[0102] In the formula, is the autocorrelation function when the delay sequence length is 0, is the normalized result;

[0103] Finally, based on the optimal value Perform delay embedding on the patch sequence in the original noisy signal matrix to obtain a new patch sequence, and reconstruct the noisy signal matrix X as: .

[0104] Furthermore, it is preferably to perform anomaly detection and marking on the patch sequence of the noisy signal, that is, mark the abnormal patch sequence, and the unmarked patch sequence is not used as a subsequence to input the spatial mixture coding;

[0105] Among them, the anomaly detection process is as follows:

[0106] First, calculate the distance between each patch sequence and other patch sequences; then extract the nearest neighbor distance corresponding to each patch sequence based on the distance, and then calculate the average distance of the neighbor distances;

[0107]

[0108]

[0109] In the formula, is the neighbor distance between two patch sequences , is the patch sequence and its nearest neighbor average distance, is the length of the patch sequence, is the patch sequence the l-th sequence value in, is the patch sequence the nearest neighbor set composed of neighbors;

[0110] Then, determine the anomaly point judgment threshold as follows:

[0111]

[0112] In the formula, is a preset coefficient, define the variable , exists: , , T is the length of the noisy signal matrix X;

[0113] Finally, if the average distance , consider the th window abnormal, that is, mark the patch sequence .

[0114] It should be understood that the above two optimizations are preferred and feasible ways in the embodiments of the present invention. In other feasible embodiments, one of the improvement points can be selected for technical optimization, or on the basis of not departing from the above technical idea of the present invention, the above two technical points may not be optimized.

[0115] Regarding the CLR-MLP AE neural network, in this embodiment, the noise profile samples are used as labels, that is, the model output; in other feasible embodiments, high-quality signal samples can also be used as training labels, that is, the denoised signal is used as the model output.

[0116] In this embodiment, all noisy samples are set as the training input of the network, and the noise profile samples are set as the training output of the network. 10% of the training samples are extracted as the test set to verify the performance of the CLR-MLP AE network; set the training parameters of the CLR-MLP AE neural network, such as network layer design, initial learning rate, learning rate decay factor, maximum number of training times, training function, transfer function, etc.; among them, the network layer includes an input layer, an encoder, a decoder, and an output layer, the initial learning rate is 0.001, the learning rate decay factor is 0.005, the maximum number of training times is 5000, the number of encoding layers is 4, the number of decoding layers is 4, and the number of neurons in each layer of the encoding layer is 512, 256, 128, 64 in sequence, and the number of neurons in each layer of the decoding layer is 64, 128, 256, 512 in sequence.

[0117] Among them, the training rule of the CLR-MLP AE neural network includes the CLR-MLP AE network output error determination rule (least squares method), and the specific formula is as follows:

[0118]

[0119] In the formula, represents the error between the expected output and the actual output of the network, represents that the CLR-MLP AE network has output nodes, represents the expected output value of the th node, the th node's actual output value of the network.

[0120] Since the training process is a process that can be implemented by the prior art, the present invention does not provide a detailed description of this. The core improvement of the present invention is to optimize the neural network structure, as follows: The CLR-MLP AE neural network is a network that is provided with a CLR-MLP-Mixer encoder and decoder based on low-rank transformation to achieve feature contraction and expansion. The CLR-MLP-Mixer encoder introduces an SVD matrix-fully connected layer that implements low-rank transformation in the parallel spatial hybrid encoder and temporal hybrid encoder to replace the corresponding first fully connected layer in the original MLP-Mixer encoder and introduces a convolutional layer. The SVD matrix-fully connected layer is to embed the fully connected layer between the sequence dimensionality reduction and sequence dimensionality increase operations of the SVD matrix decomposition algorithm.

[0121] It should be understood that the spatial mixing encoder is a feature representation for the spatial dimension within the subsequence. The input is the multidimensional spatial feature of the subsequence. The encoder fuses different spatial features through multi-layer SVD decomposition and fully connected layers to explore the correlation and spatial distribution characteristics between the spatial points within the subsequence. For subsequences with abnormal labels, the spatial mixing encoder is used to encode and learn their features to fully extract the spatial structure information within the abnormal subsequence; subsequences that are not marked as abnormal do not go through the encoding process of the spatial mixing encoder. The temporal encoder CMLP is a multi-layer perception structure for the time dimension. The input is the time dimension vector composed of all elements in the same column position in the time delay embedding matrix. The encoder extracts the dynamic change trend and long-term and short-term dependency characteristics of each subsequence in the time dimension through multi-layer SVD decomposition and fully connected layers. For the column direction of the time delay embedding matrix, that is, the temporal characteristics of each subsequence in the same dimension, the temporal mixing encoder is used to encode and learn it to explore the global dependency and dynamic change pattern between subsequences in the time dimension.

[0122] Therefore, the technical solution of the present invention inputs the patch sequence in the noisy signal matrix X as a subsequence into the spatial hybrid encoder in the CLR-MLP-Mixer encoder, and inputs the time dimension vector composed of the elements at the same position in each patch sequence in the noisy signal matrix X as a subsequence, and inputs it into the time hybrid encoder in the CLR-MLP-Mixer encoder.

[0123] SVD matrix-fully connected layer for each subsequence The following processing is performed:

[0124] First, for each subsequence Perform SVD matrix decomposition to obtain a left singular matrix, a diagonal matrix, and a right singular matrix;

[0125]

[0126] In the formula, respectively represent the left singular matrix, the diagonal matrix, and the right singular matrix. T is the matrix transpose symbol. The left singular matrix corresponds to the principal component direction of the data, achieving dimensionality reduction between different patches; the diagonal matrix contains singular values, representing the importance of features and achieving feature screening between different patches; the right singular matrix corresponds to the orthogonal basis of the feature direction, achieving dimensionality increase between different patches.

[0127] The fully connected layer is used to perform non-linear transformations on the left singular matrix and the diagonal matrix respectively (using the left singular matrix and the diagonal matrix for low-rank transformation and retaining the main information. This process compresses the redundant information between different subsequences, achieving dimensionality reduction and feature screening in the time dimension), specifically:

[0128]

[0129]

[0130] In the formula, is the left singular matrix obtained through the fully connected layer, is the diagonal matrix obtained through the fully connected layer, are respectively learnable weight matrices, is the bias term, and sigmoid is the non-linear transformation function corresponding to the fully connected layer;

[0131] Finally, the left singular matrix and the diagonal matrix obtained through the fully connected layer are combined with the right singular matrix to obtain the feature map corresponding to the subsequence , and then they are sequentially concatenated to obtain the output feature map in the SVD matrix - fully connected layer, specifically:

[0132] .

[0133] After completing the low-rank transformation of SVD, a linear transformation is then performed to map the feature dimension C to a hidden dimension H, represents the weight matrix, represents the bias vector, and the formula of the linear expression is as follows:

[0134]

[0135] In the formula, is the result after the linear transformation, represents the ReLU activation function.

[0136] Then, it passes through the convolutional layer, that is, one-dimensional convolution is applied in the feature dimension. represents the size of the convolutional kernel, stride represents the stride size, and c represents the number of output channels. The mathematical model of the convolutional layer is expressed as:

[0137]

[0138] In the formula, represents the result after convolution processing. represents the one-dimensional convolutional layer. Especially in the time channel, the convolutional layer further extracts local temporal patterns in the output, especially the dependencies between adjacent time segments. This helps to enhance the model's perception of local patterns in time series, thereby improving the recognition of signals with strong time dependence.

[0139] Finally, the fully connected layer is used to map the output of the hidden layer back to the original feature dimension C again, and the formula is as follows:

[0140]

[0141] In the formula, is the final output of the spatial encoder CMLP.

[0142] After fusing the feature maps of the time channel and the spatial channel through the Concat layer, that is, the Concat layer aggregates the outputs of each patch together. Subsequently, the decoder needs to reconstruct the original data through the latent representation. Specifically, the decoder consists of an adaptive transposed convolutional layer, a batch normalization layer, and an activation function. The transposed convolutional layer performs deconvolution operations on the input features. Different from ordinary convolution, the transposed convolution expands and restores the input features in a "reverse" way, thereby generating more complete signal features. When operating, the convolutional kernel performs weighted summation on the local area of the input sequence, and then "unfolds" in the "reverse" direction and places the result at the corresponding position in the output sequence. The batch normalization layer normalizes the output of each time step. Specifically, it calculates the feature mean and standard deviation of each time step in the current batch, and then normalizes these features to zero mean and unit variance. Then, trainable scaling and offset parameters are applied, allowing the model to readjust the features after normalization. Batch normalization can help the model speed up the training process, prevent the problem of gradient disappearance or explosion during training, and improve the robustness of the model to changes in input data. Among them, common activation functions include ReLU, Leaky ReLU, Sigmoid, Tanh, etc. The activation function performs a non-linear transformation on the normalized output, enabling the model to express and capture complex patterns and features in the time series. After being processed by the activation function, the values of the time series features are restricted within a specific range, which helps to enhance the non-linear expression ability of the model and enables it to better fit complex time series patterns.

[0143] In this embodiment, the size of the transposed convolution kernel is preferably adaptively adjusted according to the following rules:

[0144]

[0145] In the formula, is the adjustment step size of the convolution kernel size, with a default value of 1, is the threshold of the loss change, used to determine whether to continue the adjustment.

[0146] Among them, the denoising effect of processing the simulated noise data, that is, the noisy sample data, using the CLR-MLP AE denoising model is as Figure 4 shown. It can be seen from the figure that the CLR-MLP AE denoising model can generate a smooth noise profile according to the noisy data, and the restored denoised data basically coincides with the real denoised data.

[0147] Application example:

[0148] First, the magnetotelluric signal is de-meaned, and then the de-meaned magnetotelluric signal is evenly segmented according to the training sample length; assume the measured magnetotelluric data M is as follows:

[0149]

[0150] In the formula, is the th element in this section of data, and also represents the total length of the magnetotelluric signal; evenly segment according to the sample length of 50, assume is an integer, j represents that the measured data can be evenly divided into j segments, then the data matrix is as follows:

[0151]

[0152] In the formula, the elements in all come from , represents the th element in, and also represents the th element in;

[0153] Input the data matrix into the CLR-MLP AE denoising model, and the noise profile matrix W output by the model is:

[0154]

[0155]

[0155] In the formula, represents the th element, and corresponding to the element position in the matrix ;

[0156] The measured magnetotelluric data with uniform segmentation minus the noise profile output by the CLR-MLP AE denoising model to obtain the denoised matrix as follows:

[0157]

[0158] where the denoised data in the above formula can be understood as the original measured magnetotelluric data subtracting each data element in the noise profile output by the CLR-MLP AE model . Finally, the denoised data matrix is converted into one-dimensional data to complete the denoising process of the measured magnetotelluric data . As Figure 5 shown, the denoising effect of two segments of measured magnetotelluric data processed by the CLR-MLP AE model is shown. As Figure 6 shown in (a) and (b), the apparent resistivity curves before and after processing of the measured points are shown, Figure 6 and (c) and (d) are the phase curves before and after processing of the measured points. By comparing the apparent resistivity phase curves before and after processing, it can be seen that the method of the present invention can effectively suppress strong interference in the magnetotelluric signal, the near-source effect presented by the original apparent resistivity curve is alleviated, and the phase tends to be normal, indicating that the method of the present invention can not only quickly process magnetotelluric data, but also effectively remove strong interference in the magnetotelluric signal. The present invention has broad application prospects for the processing of magnetotelluric signal data.

[0159] Based on the above method, an embodiment of the present invention further provides a system based on the above method, including: a sample library construction module, a CLR-MLP AE denoising model construction module, and a denoising module.

[0160] Among them, the sample library construction module: is used to construct the noisy samples and training labels of the magnetotelluric signal, and the training labels are defined as the noise profile or the denoised magnetotelluric signal; the CLR-MLP AE denoising model construction module: uses the constructed data set, inputs the noisy samples into the CLR-MLP AE neural network for training to obtain a signal-to-noise mapping model; the denoising module: inputs the measured magnetotelluric signal to be denoised into the signal-to-noise mapping model to obtain the noise profile or the denoised magnetotelluric signal, and the measured signal minus the noise profile is the denoised magnetotelluric signal.

[0161] It should be understood that the functional unit modules in the embodiments of the present invention can be concentrated in one processing unit, or each unit module exists physically alone, or two or more unit modules are integrated in one unit module, and can be implemented in the form of hardware or software.

[0162] Based on the above method, an embodiment of the present invention further provides a computer-readable storage medium storing a computer program, which is called by a processor to implement the steps of a magnetotelluric signal denoising method based on feature fusion. The specific implementation is as follows:

[0163] Dataset construction: constructing a noisy sample of magnetotelluric signals and training labels, where the training labels are defined as noise profiles or denoised magnetotelluric signals;

[0164] Model training: using the constructed dataset, inputting the noisy samples into the CLR-MLP AE neural network for training to obtain a signal-to-noise mapping model;

[0165] Measured signal denoising: inputting the measured magnetotelluric signal to be denoised into the signal-to-noise mapping model to obtain a noise profile or a denoised magnetotelluric signal, and subtracting the noise profile from the measured signal to obtain the denoised magnetotelluric signal.

[0166] For the specific implementation process of each step, please refer to the description of the foregoing method.

[0167] It should be understood that in the embodiments of the present invention, the so-called processor may be a central processing unit (CPU), and the processor may also be other general-purpose processors, digital signal processors (DSPs), application specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. The general-purpose processor may be a microprocessor or the processor may also be any conventional processor, etc. The memory may include a read-only memory and a random access memory, and provide instructions and data to the processor. A part of the memory may also include a non-volatile random access memory. For example, the memory may also store information about the device type.

[0168] Based on such understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in various embodiments of the present invention. The aforementioned readable storage medium includes: USB flash drives, mobile hard disks, read-only memories (ROMs), random access memories (RAMs), magnetic disks, or optical discs, etc., all kinds of media that can store program codes.

[0169] Those skilled in the art should understand that the embodiments of the present application can be provided as methods, systems, or computer program products. Therefore, the present application can adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present application can adopt the form of a computer program product implemented on one or more computer-readable storage media (including but not limited to disk memories, CD-ROMs, optical memories, etc.) that contain computer-usable program codes. The present application refers to the flowchart of the method, device (system), and computer program product according to the embodiments of the present application, and / or the instructions executed by the processor to generate a device for realizing the functions specified in one or more processes of the flowchart and / or one or more boxes of the block diagram. These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer-readable memory generate a manufactured product including an instruction device, and the instruction device realizes the functions specified in one or more processes of the flowchart and / or one or more boxes of the block diagram. These computer program instructions can also be loaded onto a computer or other programmable data processing device, so that a series of operation steps are executed on the computer or other programmable device to generate computer-implemented processing, and thus the instructions executed on the computer or other programmable device provide steps for realizing the functions specified in one or more processes of the flowchart and / or one or more boxes of the block diagram.

[0170] It should be emphasized that the examples described in the present invention are illustrative rather than restrictive. Therefore, the present invention is not limited to the examples described in the specific embodiments. Any other embodiments obtained by those skilled in the art based on the technical solution of the present invention, without departing from the purpose and scope of the present invention, whether modified or replaced, also belong to the protection scope of the present invention.

Claims

1. A method for suppressing noise of magnetotelluric signals based on feature contraction and expansion, characterized in that: A signal-to-noise mapping model based on a CLR-MLP AE neural network is constructed to suppress noise on magnetotelluric signals. The method comprises the following steps: Data set construction, constructing noisy samples of magnetotelluric signals and training labels, wherein the training labels are defined as noise profiles or denoised magnetotelluric signals; Model training, using the constructed data set, the noisy samples are input into the CLR-MLP AE neural network for training to obtain the signal-to-noise mapping model; Denoising the measured signal, inputting the magnetotelluric measured signal to be de-noised into the signal-to-noise mapping model to obtain a noise profile or a de-noised magnetotelluric signal, wherein the measured signal minus the noise profile is the de-noised magnetotelluric signal; Among them, the CLR-MLP AE neural network is a network equipped with a CLR-MLP-Mixer encoder and decoder based on low-rank transformation to achieve feature contraction and expansion. The CLR-MLP-Mixer encoder introduces an SVD matrix-fully connected layer for achieving low-rank transformation in the parallel spatial hybrid encoder and temporal hybrid encoder to replace the fully connected layer in the original MLP-Mixer encoder and add a convolutional layer. The SVD matrix-fully connected layer embeds the fully connected layer between the sequence dimensionality reduction and sequence dimensionality increase operations of the SVD matrix decomposition algorithm.

2. The method for suppressing noise of magnetotelluric signals based on feature contraction and expansion according to claim 1, characterized in that: When constructing noisy samples of magnetotelluric signals, the Nonlinear SMOTE algorithm and nonlinear interpolation are introduced to expand the noisy samples; Among them, the noise part with non-zero amplitude in the noise profile is extracted, and then Nonlinear SMOTE is introduced to find its K nearest neighbor samples in the feature space; Then, a new noisy sample is generated by nonlinear interpolation according to the K nearest neighbor samples. The formula of nonlinear interpolation is: , where is the vector of noise parts with non-zero amplitude in the noise profile, yes The K-nearest neighbor samples of is a random number with a value in [0,1]. It is a parameter that controls the degree of nonlinearity.

3. The method for suppressing noise of magnetotelluric signals based on feature contraction and expansion according to claim 1, characterized in that: The noisy signal input into the CLR-MLP-Mixer encoder is divided into a plurality of patch sequences according to the patch length k, and a noisy signal matrix X is constructed, and then the patch sequence in the noisy signal matrix X is input as a subsequence into the spatial hybrid encoder in the CLR-MLP-Mixer encoder, and the time dimension vector composed of the elements at the same position in each patch sequence in the noisy signal matrix X is input as a subsequence into the time hybrid encoder in the CLR-MLP-Mixer encoder; The SVD matrix-fully connected layer is used for each subsequence The following processing is performed: First, for each subsequence Perform SVD matrix decomposition to obtain a left singular matrix, a diagonal matrix, and a right singular matrix; , where They represent left singular matrix, diagonal matrix, right singular matrix respectively, and T is the matrix transpose symbol; The fully connected layer is used to perform nonlinear transformations on the left singular matrix and the diagonal matrix, respectively, as follows: , , where is the left singular matrix obtained by the fully connected layer, is the diagonal matrix obtained by the fully connected layer, are the learnable weight matrices, is the bias term, and sigmoid is the nonlinear transformation function corresponding to the fully connected layer; Finally, the left singular matrix obtained by the fully connected layer and the diagonal matrix With right singular matrix Combine to get the feature map corresponding to the subsequence , and then concatenate them in order to get the output feature map of the SVD matrix-fully connected layer, specifically: 。 4. The method for suppressing noise of magnetotelluric signals based on feature contraction and expansion according to claim 2, characterized in that: The method further includes: before inputting into the CLR-MLP-Mixer encoder, introducing a delay embedding idea to enhance the timing characteristics of the noisy signal, as follows: First, the original noisy signal is segmented according to the patch length k to obtain the initial noisy signal matrix. The noisy signal matrix is ​​composed of the segmented patch sequence. The noisy signal matrix is ​​expressed as: , each row corresponds to a patch sequence, is the kth sampling point signal in the noisy signal; Second, define the delay sequence length and The value range of , within the value range Traverse the values ​​and calculate the length of each delayed sequence The autocorrelation function of ; , where represents the row number label in matrix X, Represents the first Line The elements of the column, For the The average value of the row; Then, all the results are normalized and the delay sequence length is found based on the normalized results. The minimum value of is considered as the optimal value : , , where is the delay sequence length When the autocorrelation function is 0, is the normalized result; Finally, based on the optimal value The patch sequence in the original noisy signal matrix is ​​delayed and embedded to obtain a new patch sequence, and the noisy signal matrix X is reconstructed as: .

5. The method for suppressing noise of magnetotelluric signals based on feature contraction and expansion according to claim 4, characterized in that: The method further comprises: before inputting into the CLR-MLP-Mixer encoder, performing abnormal detection and marking on the patch sequence of the noisy signal, that is, marking the abnormal patch sequence, and not inputting the unmarked patch sequence as a subsequence into the spatial hybrid coding; The anomaly detection process is as follows: First, calculate the distance between each patch sequence and other patch sequences; then extract the nearest corresponding patch sequence of each patch sequence based on the distance. Neighbor distances, and then calculate the The average distance of the neighbor distances; , , where For two patch sequences The neighbor distance, Patch sequence Its closest The average distance between neighbors, is the length of the patch sequence, Patch sequence The lth sequence value in Patch sequence The most recent A neighbor set consisting of neighbors; Then, determine the outlier judgment threshold ,as follows: , where To preset coefficients, define variables , exist: , , T is the length of the noisy signal matrix X; Finally, if the distance from the average , see The window is abnormal, that is, the patch sequence is marked .

6. The method for suppressing noise of magnetotelluric signals based on feature contraction and expansion according to claim 1, characterized in that: The decoder is a decoder based on adaptive transposed convolution, which is composed of an adaptive transposed convolution layer, a batch normalization layer, and an activation function. The mathematical model is expressed as: , where Represents the result after transposed convolution operation; represents the transposed convolution operation; stride represents the stride size, Representing the output of the concat layer of the CLR-MLP-Mixer encoder, the definition formula of the transposed convolution is as follows: , in the above formula, Representative Input values, is the first in the output sequence after transposed convolution calculation output values, Represents the weight of the transposed convolution kernel, represents the step size, and N represents the total length of the output sequence of the concat layer; Among them, the size of the transposed convolution kernel is adaptively adjusted according to the following rules: , where It is The size of the convolution kernel after one round of training, Representative The mean square error between the output and the true value after one round of training, is the adjustment step of the convolution kernel size, It is the threshold of loss change, which is used to determine whether to continue adjustment.

7. The method for suppressing noise of magnetotelluric signals based on feature contraction and expansion according to claim 3, characterized in that: After integrating the features of the spatial encoder and the temporal encoder's channel outputs, a learnable weight coefficient is introduced After integration, the features Focusing is expressed as: , where is the weight coefficient Adjusted output result, weight coefficient Adaptive tuning during network training.

8. A system based on the method for suppressing noise of magnetotelluric signals based on feature contraction and expansion according to any one of claims 1 to 7, characterized in that: These include: Sample library construction module: used to construct noisy samples and training labels of magnetotelluric signals, wherein the training labels are defined as noise profiles or noise-reduced magnetotelluric signals; CLR-MLP AE denoising model construction module: Using the constructed data set, the noisy samples are input into the CLR-MLP AE neural network for training to obtain the signal-to-noise mapping model; The CLR-MLP AE neural network is a network provided with a CLR-MLP-Mixer encoder and decoder based on low-rank transformation to realize feature contraction and expansion. The CLR-MLP-Mixer encoder introduces an SVD matrix-fully connected layer for realizing low-rank transformation in parallel spatial hybrid encoders and temporal hybrid encoders to replace the corresponding first fully connected layer in the original MLP-Mixer encoder. The SVD matrix-fully connected layer embeds the fully connected layer between the sequence dimensionality reduction and sequence dimensionality increase operations of the SVD matrix decomposition algorithm. Denoising module: inputting the magnetotelluric measured signal to be de-noised into the signal-to-noise mapping model to obtain a noise profile or a de-noised magnetotelluric signal, and the de-noised magnetotelluric signal is obtained by subtracting the noise profile from the measured signal.

9. A computer-readable storage medium, characterized in that: A computer program is stored, and the computer program is called by a processor to implement: the steps of the method for suppressing noise of magnetotelluric signals based on feature contraction and expansion as described in any one of claims 1 to 7.

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