Seismic data denoising method based on fuzzy rules and mutual information spatial-frequency domain decoupling

Abstract

This invention discloses a seismic data denoising method based on fuzzy rules and spatial-frequency domain decoupling of mutual information, belonging to the field of seismic data denoising technology. The method involves downsampling a noisy image, inputting it into a first fuzzy convolutional layer, performing further downsampling, inputting it into a second fuzzy convolutional layer and an activation function layer, performing further downsampling, inputting it into a third fuzzy convolutional layer and a batch normalization layer, and performing further downsampling. The downsampling result is then sequentially input into a fourth fuzzy convolutional layer, a spatial-frequency attention interaction module, a decoupled mutual information constraint module, and a first anti-fuzzy convolutional layer. Then, it is sequentially upsampled, input into a second anti-fuzzy convolutional layer and a batch normalization layer, performing further upsampling, inputting it into a third anti-fuzzy convolutional layer and an activation function layer, performing further upsampling, and inputting it into a fourth anti-fuzzy convolutional layer, finally obtaining the denoised image. This invention preserves the effective signal to the greatest extent while suppressing noise, maintaining the integrity of the low-frequency structure while retaining the high-frequency details of the seismic signal.

Description

Technical Field

[0001] This invention discloses a seismic data denoising method based on fuzzy rules and mutual information spatial-frequency domain decoupling, belonging to the field of seismic data denoising technology. Background Technology

[0002] The basic principle of seismic exploration is to establish a signal observation system by setting up detectors on the Earth's surface. Seismic waves are generated using artificially excited seismic sources. These waves propagate through the strata using the elasticity and density differences of the subsurface medium, interacting with different media to produce reflection and refraction. The seismic waves are then received by the observation system, completing the process of seismic data acquisition. This process provides rich information about subsurface structures, including reservoir structure and stratigraphic properties. However, due to limitations such as the complex surface environment, the cost of acquisition equipment, and operating conditions, the seismic data acquired during actual monitoring often suffers from problems such as irregular spatial sampling, signal distortion, and noise interference, directly affecting the accuracy of subsequent data processing and interpretation. In the field of seismic monitoring, accurate acquisition and analysis of seismic signals are crucial. Traditional seismic data denoising methods mainly include three categories: mathematical transformation, compressed sensing, and matrix factorization. However, traditional methods require extensive human-computer interaction and have a low degree of automation, especially for large datasets. Furthermore, they are difficult to process irregularly sampled data, making it difficult to effectively restore data integrity and potentially introducing additional errors or artifacts, especially in areas with developed faults or strong anisotropy, where over-smoothing is prone to occur.

[0003] With the development of deep learning, denoising methods based on deep learning have significantly improved the effectiveness of seismic data processing. Convolutional Neural Networks (CNNs) extract features through multi-level convolutions and perform excellently in suppressing random noise such as Gaussian noise. However, the fixed convolutional kernels of CNNs limit their ability to perceive global contextual information, making it difficult to model long-range dependencies. In addition, noise and signals in seismic data often overlap in the time-frequency domain, and traditional networks reconstruct losses pixel by pixel. For example, L1 / L2 loss constrains the output, which cannot explicitly decouple the signal and noise components in the features, resulting in deep networks easily retaining high-frequency noise or over-smoothing details. Transformers have shown potential in global modeling with their self-attention mechanism, but their computational complexity increases with the square of the input size, making the computational cost for high-resolution seismic data such as 3D pre-stack data extremely high, and they lack fine-grained capture of some local transient features such as fault edges. Although frequency domain methods can separate the frequency band components of the signal, traditional thresholding is prone to causing frequency band truncation artifacts, and they do not form a dynamic interaction with spatial domain features, limiting the joint suppression capability of multi-scale noise.

[0004] Fuzzy rules are a fuzzy logic-based processing method for seismic signal denoising. Their core is to use fuzzy sets and membership functions to describe the fuzzy characteristics of grayscale values ​​or features in seismic signals. Fuzzy rules define fuzzy sets to describe the features of seismic signal pixels, such as "close to the average grayscale value" or "significantly deviating from the average grayscale value." Membership functions quantify the degree to which a pixel belongs to these fuzzy sets. Based on these fuzzy sets and membership functions, a fuzzy rule library can be constructed, for example, "If the grayscale value of a pixel is close to the average grayscale value of its neighborhood, then the pixel belongs to the valid signal; if the grayscale value of a pixel significantly deviates from the average grayscale value of its neighborhood, then the pixel may belong to noise." The fuzzy inference system classifies and processes each pixel in the seismic signal according to these rules, thereby achieving noise suppression and signal preservation. Existing deep learning models typically model noise as implicit priors, relying on end-to-end training to implicitly learn the noise distribution, which still has limitations in balancing interpretability and model complexity, as well as in handling noise. Noise intensity in seismic data exhibits significant spatial non-uniformity due to factors such as formation absorption and attenuation, and near-surface scattering. Traditional fixed threshold or uniform noise assumptions fail in such scenarios, leading to poor regional adaptability of denoising results. Fuzzy rule control can map noise intensity to a continuous probability distribution through fuzzy membership functions, achieving soft thresholding. Compared to hard thresholding methods, this mechanism avoids edge oscillations or amplitude distortion caused by binarization truncation. Furthermore, it dynamically adjusts noise suppression intensity through learnable threshold parameters and smoothing factors, adapting to complex noise distributions. Its membership graph also intuitively interprets the spatial distribution characteristics of noise, significantly enhancing model interpretability. Summary of the Invention

[0005] The purpose of this invention is to provide a seismic data denoising method based on fuzzy rules and mutual information spatial-frequency domain decoupling, so as to solve the problem of unsatisfactory seismic data denoising accuracy in the prior art.

[0006] A seismic data denoising method based on fuzzy rules and mutual information spatial-frequency domain decoupling includes downsampling the noisy image, inputting it into a first fuzzy convolutional layer, downsampling, inputting it into a second fuzzy convolutional layer and a ReLU activation function layer, downsampling, inputting it into a third fuzzy convolutional layer and a batch normalization layer, and downsampling.

[0007] The downsampling result is sequentially input into the fourth fuzzy convolutional layer, the spatial frequency attention interaction module, the decoupling mutual information constraint module, and the first defuzzy convolutional layer. Then, it is sequentially upsampled, input into the second defuzzy convolutional layer and the batch normalization layer, upsampled again, input into the third defuzzy convolutional layer and the ReLU activation function layer, upsampled again, input into the fourth defuzzy convolutional layer, and finally the denoised image is obtained.

[0008] There is a skip connection between the first blurred convolutional layer and the fourth deblurred convolutional layer;

[0009] There is a skip connection between the second blurred convolutional layer and the third deblurred convolutional layer;

[0010] There is a skip connection between the third blurred convolutional layer and the second deblurred convolutional layer;

[0011] There is a skip connection between the first blurred convolutional layer and the fourth deblurred convolutional layer.

[0012] The fuzzy convolutional layer consists of two branches. One branch calculates the local variance and the dynamic membership weights based on Gaussian membership in sequence. The other branch takes the input of a 3×3 convolution and performs feature addition on the results of the two branches to finally obtain the weighted output features.

[0013] The spatial-frequency attention interaction module inputs the input features to the spatial domain feature extraction branch and the frequency domain feature extraction branch, respectively. The frequency domain feature extraction branch outputs frequency domain features and frequency domain weights. Frequency domain weights The input is fed into the Sigmoid activation function layer, and then combined with spatial weights. Performing characteristic multiplication yields the empty pilot term. The empty pilot term is multiplied by the frequency domain features;

[0014] The spatial feature extraction branch outputs spatial features and spatial weights. Spatial weight The input is fed into the Sigmoid activation function layer, and then combined with the frequency domain weights. Performing characteristic multiplication yields the frequency guide empty term. The frequency-guided spatial term is multiplied with the spatial domain features;

[0015] The result of multiplying the two features is then added to obtain the output of the spatial frequency attention interaction module.

[0016] The spatial feature extraction branch includes inputting the input features into three paths: a 3×3 depthwise convolution, a 5×5 depthwise convolution, and a 7×7 depthwise convolution. The processing result of the 3×3 depthwise convolution is then sent to a channel-weighted convolution. The result of the 5×5 depthwise convolution layer is fed into the channel-weighted layer. The result of the 7×7 depthwise convolution layer is fed into the channel-weighted layer. The layer performs feature addition on the processing results of the three channel weighted layers and then inputs them into the ReLU activation function layer;

[0017] The output of the ReLU activation function layer is divided into three paths. The first path is input to the global average pooling layer and the multilayer perceptron. The second path is input to the global max pooling layer and the multilayer perceptron. Then, the outputs of the first and second paths of the multilayer perceptron are multiplied by features. The result of the feature multiplication is input to the Sigmoid activation function layer for topological masking and hyperbolic tangent transformation. Then, it is multiplied by the third path to form spatial features. The spatial features are input to a 1×1 convolutional layer and a softmax activation function layer to obtain spatial weights.

[0018] The frequency domain feature extraction branch includes sending the input features to the FFT transform module, outputting the amplitude spectrum and phase spectrum. The amplitude spectrum is processed in three lines: one line is input to the horizontal Sobel operator layer, the second line is input to the vertical Sobel operator layer, and then both the first and second lines are input to the four-quadrant tangent-inverse transform layer and the eight-direction binary mask layer. Then, the output of the amplitude spectrum is multiplied by the feature and output to the 1×1 convolutional layer and the IFFT transform layer.

[0019] The three lines are sequentially input into a logarithmic transform layer, a 1×1 convolutional layer, a sigmoid activation function layer, and a hyperbolic tangent transform layer. Then, they are multiplied with the output of the phase spectrum, and an IFFT transform is performed. The results of the two IFFT transforms are added together to output the frequency domain features. The output of the sigmoid activation function layer is then subjected to an IFFT transform to obtain the frequency domain weights.

[0020] The decoupling mutual information constraint module includes a feature decoupling module and a mutual information constraint module;

[0021] The feature decoupling module includes dividing the input features of the decoupling mutual information constraint module into two lines. One line inputs a 3×3 depthwise separable convolutional layer, a global average pooling layer, and a fully connected layer. The other line inputs a 3×3 convolutional layer, a LeakyReLU activation function layer, a 1×1 convolutional layer, and a Sigmoid activation function layer.

[0022] The mutual information constraint module includes a fully connected layer to obtain noise features, which are then combined with the input features of the decoupled mutual information constraint module to minimize KL divergence. A sigmoid activation function layer to obtain content features is then combined with the input features of the decoupled mutual information constraint module to maximize JSD divergence. Finally, the two divergence processing results are added together to output the mutual information constraint loss.

[0023] Calculate local variance include:

[0024] ;

[0025] In the formula, Given the input feature map, , For position offset index, and They are respectively , The three possible values, , The three possible values ​​are -1, 0, and 1. This is the position offset constant. For input position Feature map, For input position Feature map;

[0026] Calculate dynamic membership weights based on Gaussian membership. include:

[0027] ;

[0028] In the formula, The learnable attenuation coefficient;

[0029] Fuzzy convolutional layer include:

[0030] ;

[0031] In the formula, To learn convolution kernels, Represents the feature dot product. This is the bias value.

[0032] The loss function for decoupling the mutual information constraint module is:

[0033] ;

[0034] To decouple the loss function of the mutual information constraint module, To maximize the loss function between the input and content features, To minimize the loss function between the input and noise features, To balance the mutual information constraint weights;

[0035] The loss function that maximizes the mutual information between the input and content features is:

[0036] ;

[0037] In the formula, Indicates in joint distribution The expected score of the discriminator on positive samples. Represents the product of marginal distributions Calculation The expected value is used as a penalty term for negative samples. For content discriminator function, Indicates input features, Indicates content characteristics, Other content features besides the current input. It is a natural constant;

[0038] The loss function that minimizes the mutual information between the input and noise features is:

[0039] ;

[0040] In the formula, Indicates in joint distribution The expected score of the discriminator on positive samples. It is a parameterized discriminator composed of two MLP layers. Represents the product of marginal distributions Calculation The expected value is used as the penalty term for negative samples. It is a noise characteristic. Other noise features that are not part of the current input.

[0041] Total loss function for:

[0042] ;

[0043] ;

[0044] ;

[0045] In the formula, It refers to the amount of data processed in a batch. It is clean, noise-free seismic data. yes and Mutual information between them yes and Mutual information between them It is the content discriminator weight. It is the weight of the noise discriminator. , , yes The three weights, yes Divergence calculation, yes Divergence calculation.

[0046] Compared with the prior art, the present invention has the following advantages: the present invention retains the effective signal to the greatest extent while suppressing noise, and maintains the integrity of the low-frequency structure while preserving the high-frequency details of the seismic signal. Attached Figure Description

[0047] Figure 1 This is a schematic diagram of the overall deep learning architecture of the present invention;

[0048] Figure 2 This is a schematic diagram of the spatial frequency attention interaction module structure;

[0049] Figure 3 This is a schematic diagram of the branch structure for spatial feature extraction.

[0050] Figure 4 This is a schematic diagram of the branch structure for frequency domain feature extraction;

[0051] Figure 5 A schematic diagram of the decoupling mutual information constraint module structure;

[0052] Figure 6 Flowchart of a method for denoising earthquake data test sets;

[0053] Figure 7 This is a flowchart of the training steps of the present invention;

[0054] Figure 8 Flowchart of methods for denoising actual seismic data. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. All other embodiments obtained by those skilled in the art based on the embodiments of this invention without creative effort are within the scope of protection of this invention.

[0056] Seismic data denoising methods based on fuzzy rules and mutual information spatial-frequency domain decoupling, such as Figure 1 The process includes downsampling the noisy image, inputting it into a first fuzzy convolutional layer, downsampling it, inputting it into a second fuzzy convolutional layer and a ReLU activation function layer, downsampling it, inputting it into a third fuzzy convolutional layer and a batch normalization layer, and downsampling it.

[0057] The downsampling result is sequentially input into the fourth fuzzy convolutional layer, the spatial frequency attention interaction module, the decoupling mutual information constraint module, and the first defuzzy convolutional layer. Then, it is sequentially upsampled, input into the second defuzzy convolutional layer and the batch normalization layer, upsampled again, input into the third defuzzy convolutional layer and the ReLU activation function layer, upsampled again, input into the fourth defuzzy convolutional layer, and finally the denoised image is obtained.

[0058] There is a skip connection between the first blurred convolutional layer and the fourth deblurred convolutional layer;

[0059] There is a skip connection between the second blurred convolutional layer and the third deblurred convolutional layer;

[0060] There is a skip connection between the third blurred convolutional layer and the second deblurred convolutional layer;

[0061] There is a skip connection between the first blurred convolutional layer and the fourth deblurred convolutional layer.

[0062] The fuzzy convolutional layer consists of two branches. One branch calculates the local variance and the dynamic membership weights based on Gaussian membership in sequence. The other branch takes the input of a 3×3 convolution and performs feature addition on the results of the two branches to finally obtain the weighted output features.

[0063] The space frequency attention interaction module, such as Figure 2 The input features are fed into the spatial domain feature extraction branch and the frequency domain feature extraction branch, respectively. The frequency domain feature extraction branch outputs the frequency domain features and frequency domain weights. Frequency domain weights The input is fed into the Sigmoid activation function layer, and then combined with spatial weights. Performing characteristic multiplication yields the empty pilot term. The empty pilot term is multiplied by the frequency domain features;

[0064] The spatial feature extraction branch outputs spatial features and spatial weights. Spatial weight The input is fed into the Sigmoid activation function layer, and then combined with the frequency domain weights. Performing characteristic multiplication yields the frequency guide empty term. The frequency-guided spatial term is multiplied with the spatial domain features;

[0065] The result of multiplying the two features is then added to obtain the output of the spatial frequency attention interaction module.

[0066] The spatial feature extraction branch is as follows: Figure 3 This involves splitting the input features into three paths and feeding them into a 3×3 depthwise convolution, a 5×5 depthwise convolution, and a 7×7 depthwise convolution, respectively. The result of the 3×3 depthwise convolution is then fed into a channel-weighted convolution. The result of the 5×5 depthwise convolution layer is fed into the channel-weighted layer. The result of the 7×7 depthwise convolution layer is fed into the channel-weighted layer. The layer performs feature addition on the processing results of the three channel weighted layers and then inputs them into the ReLU activation function layer;

[0067] The output of the ReLU activation function layer is divided into three paths. The first path is input to the global average pooling layer and the multilayer perceptron. The second path is input to the global max pooling layer and the multilayer perceptron. Then, the outputs of the first and second paths of the multilayer perceptron are multiplied by features. The result of the feature multiplication is input to the Sigmoid activation function layer for topological masking and hyperbolic tangent transformation. Then, it is multiplied by the third path to form spatial features. The spatial features are input to a 1×1 convolutional layer and a softmax activation function layer to obtain spatial weights.

[0068] The frequency domain feature extraction branch is as follows Figure 4 The process includes sending the input features to the FFT transformation module, outputting the amplitude spectrum and phase spectrum. The amplitude spectrum is processed in three lines: one line is input to the horizontal Sobel operator layer, the second line is input to the vertical Sobel operator layer, and then both the first and second lines are input to the four-quadrant tangent-inverse transform layer and the eight-direction binary mask layer. Finally, the output of the amplitude spectrum is multiplied by the feature and output to the 1×1 convolutional layer and the IFFT transformation layer.

[0069] The three lines are sequentially input into a logarithmic transform layer, a 1×1 convolutional layer, a sigmoid activation function layer, and a hyperbolic tangent transform layer. Then, they are multiplied with the output of the phase spectrum, and an IFFT transform is performed. The results of the two IFFT transforms are added together to output the frequency domain features. The output of the sigmoid activation function layer is then subjected to an IFFT transform to obtain the frequency domain weights.

[0070] The decoupling mutual information constraint module, as shown in the example Figure 5 It includes a feature decoupling module and a mutual information constraint module;

[0071] The feature decoupling module includes dividing the input features of the decoupling mutual information constraint module into two lines. One line inputs a 3×3 depthwise separable convolutional layer, a global average pooling layer, and a fully connected layer. The other line inputs a 3×3 convolutional layer, a LeakyReLU activation function layer, a 1×1 convolutional layer, and a Sigmoid activation function layer.

[0072] The mutual information constraint module includes a fully connected layer to obtain noise features, which are then combined with the input features of the decoupled mutual information constraint module to minimize KL divergence. A sigmoid activation function layer to obtain content features is then combined with the input features of the decoupled mutual information constraint module to maximize JSD divergence. Finally, the two divergence processing results are added together to output the mutual information constraint loss.

[0073] Calculate local variance include:

[0074] ;

[0075] In the formula, Given the input feature map, , For position offset index, and They are respectively , The three possible values, , The three possible values ​​are -1, 0, and 1. This is the position offset constant. For input position Feature map, For input position Feature map;

[0076] Calculate dynamic membership weights based on Gaussian membership. include:

[0077] ;

[0078] In the formula, The learnable attenuation coefficient;

[0079] Fuzzy convolutional layer include:

[0080] ;

[0081] In the formula, To learn convolution kernels, Represents the feature dot product. This is the bias value.

[0082] The loss function for decoupling the mutual information constraint module is:

[0083] ;

[0084] To decouple the loss function of the mutual information constraint module, To maximize the loss function between the input and content features, To minimize the loss function between the input and noise features, To balance the mutual information constraint weights;

[0085] The loss function that maximizes the mutual information between the input and content features is:

[0086] ;

[0087] In the formula, Indicates in joint distribution The expected score of the discriminator on positive samples. Represents the product of marginal distributions Calculation The expected value is used as a penalty term for negative samples. For content discriminator function, Indicates input features, Indicates content characteristics, Other content features besides the current input. It is a natural constant;

[0088] The loss function that minimizes the mutual information between the input and noise features is:

[0089] ;

[0090] In the formula, Indicates in joint distribution The expected score of the discriminator on positive samples. It is a parameterized discriminator composed of two MLP layers. Represents the product of marginal distributions Calculation The expected value is used as the penalty term for negative samples. It is a noise characteristic. Other noise features that are not part of the current input.

[0091] Total loss function for:

[0092] ;

[0093] ;

[0094] ;

[0095] In the formula, It refers to the amount of data processed in a batch. It is clean, noise-free seismic data. yes and Mutual information between them yes and Mutual information between them It is the content discriminator weight. It is the weight of the noise discriminator. , , yes The three weights, yes Divergence calculation, yes Divergence calculation.

[0096] Information bottleneck theory is an influential theory in representation learning that provides a formula to balance the trade-off between prediction accuracy and information capacity to achieve representations that reduce task-irrelevant information. Information bottleneck theory aims to retain task-relevant information while discarding as much task-irrelevant information as possible. Mutual information measures the amount of information shared between two random variables, i.e., how much uncertainty one variable reduces through the other. In seismic signal denoising, mutual information can be used to quantify the dependency between seismic signal features and the effective signal and noise. Through the concept of mutual information, it measures how much information is shared between two random variables, i.e., how much uncertainty one variable reduces through the other. Traditional deep learning denoising methods typically use reconstruction loss to constrain the similarity between the output and the clean signal, but this method struggles to explicitly separate the information dependency between signal and noise, and may also filter out some effective signal. In contrast, mutual information constraints based on information theory maximize the statistical dependency between features and the clean signal, ensuring the integrity of the effective signal, while minimizing the mutual information between features and noise, suppressing the deep penetration of noise components. This mechanism breaks through the implicit constraints of traditional end-to-end training, theoretically guaranteeing the explicit separation of signal and noise in the feature space, and avoiding the coupling of high-frequency noise and effective signal during convolution. Mutual information measurement not only optimizes the independence of feature channels, but also provides a quantitative evaluation basis for network decision logic, enhancing the interpretability and cross-regional generalization ability of the model.

[0097] The frequency domain is a representation of a signal derived from the spatial domain through a transformation (such as the Fourier transform). It describes the energy distribution of the signal, that is, an indicator of the drastic changes in the numerical values ​​of the seismic signal, reflecting the rate of change. As a complex two-dimensional signal, the spatial domain representation of a seismic signal often fails to directly reveal its inherent structure and characteristics. Seismic signals exhibit strong coupling characteristics in the spatial and frequency domains; low-frequency components correspond to the continuous structure of strata, while high-frequency components contain detailed information such as faults and fractures. Frequency domain analysis provides a novel perspective. By decomposing the frequency of the seismic signal, it is possible to deeply mine various information within the signal, providing a powerful tool for seismic signal processing tasks. The combination of spatial and frequency domains, through multi-dimensional joint optimization, can provide prior guidance for problems such as the insensitivity of spatial interpolation to periodicity or frequency band characteristics, avoiding the introduction of spurious frequency components by spatial extrapolation. The interaction of spatial and frequency domain information is of great significance in seismic signal reconstruction. By protecting the edges of details in the spatial domain and enhancing weak signal bands in the frequency domain, the combination significantly improves the imaging resolution of micro-geological targets such as thin interbedded layers and small faults.

[0098] This invention combines fuzzy control theory with information theory-based mutual information constraints and a two-way space-frequency interaction architecture. It utilizes fuzzy rule design to fuzzify seismic signals for downsampling. By quantifying the dependencies between features and signal / noise, it maximizes the mutual information between the feature map and the clean seismic signal while minimizing its mutual information with noise, thus achieving decoupling constraints and preserving effective signals to the greatest extent possible while suppressing noise. Furthermore, through the design of a two-way space-frequency attention mechanism, it collaboratively utilizes spatial domain structural information and frequency domain spectral features to maintain the integrity of low-frequency structures while preserving high-frequency details of the seismic signal. Finally, a fuzzy decoder performs inverse rule weight generation and defuzzification convolution operations to complete the seismic signal reconstruction.

[0099] This invention requires three datasets: a training set, a validation set, and a test set, in a ratio of 3:1:1. The training set is used to train the denoising model, the validation set to fine-tune the model, and the test set to evaluate the model's denoising performance. The training set is constructed by arbitrarily extracting multiple seismic data blocks of the same dimension from the seismic data of a specific work area, where each data block contains a certain number of rows. The number of columns is ,suggestion and The value is greater than 256. Using conventional denoising methods, the noisy seismic data blocks extracted above are denoised to obtain denoised seismic data blocks. Each noisy data block corresponds to a denoised data block. The dataset consisting of multiple noisy seismic data blocks and their corresponding denoised seismic data blocks constitutes the training set. The validation set is constructed in the same way as the training set, except that the data blocks in the validation set must be different from those in the training set. The test set consists of missing data blocks extracted from this work area, excluding those in the training and validation sets.

[0100] Noisy seismic data from the training set is input into the constructed network model. The network output is seismic data with noise removed using the network of this invention. This denoised seismic data is compared with clean seismic data, and the error between the two is calculated. If the error is greater than a set threshold (the threshold size is set according to the actual situation), backpropagation is performed to update the parameters. This process is repeated until the error is less than the set threshold, at which point parameter updates are stopped and the network parameters are saved. This invention uses the Adam optimization algorithm to solve for the parameters, and updates the parameters based on the error gradient information during error backpropagation.

[0101] Noisy seismic data blocks from the validation set are input into the constructed network model. The network output is the noise-removed seismic data from the network of this invention. The denoised data is compared with clean seismic data, and the error between the two is calculated. If the error is less than a set threshold (the threshold size is set according to the actual situation), it proves that the trained network parameters have reached the optimum, and the test set seismic data can be denoised. If the error is greater than the set threshold, it proves that the trained network parameters have not reached the optimum, and the network is retrained until a good denoising effect is achieved in the validation stage. Noisy seismic data from the test set is input into the pre-trained and validated network of this invention, and the network output is the noise-removed seismic data from the network of this invention.

[0102] The process of the seismic data test set denoising method of this invention is as follows: Figure 6 As shown, the process includes preparing the dataset for forward noise addition, initializing the network model, calculating the loss function, performing gradient backpropagation, and if the error is not less than a threshold, returning to calculate the loss function; if the error is less than the threshold, the denoised test set data is obtained. The training steps of this invention are as follows: Figure 7 As shown, after initializing the network model parameters, the clean data from traditional noise denoising and the training set with added noise are input into the network for iteration, and the network model parameters are saved. The actual seismic data denoising method flow is as follows: Figure 8 As shown, noisy data is input, a trained network model is used, and the denoising result is output.

[0103] This invention integrates fuzzy control theory, mutual information constraints, and a two-way space-frequency attention interaction mechanism to explicitly decouple the dependence of seismic signals and noise, achieving high-fidelity reconstruction in noisy seismic scenarios. By constructing a dynamic noise prior model guided by fuzzy rules, a fuzzy membership function is introduced to dynamically estimate the noise intensity distribution, guiding bidirectional attention in the spatial and frequency domains to focus on non-uniform noise regions, enhancing feature interpretability while suppressing the weight of noise regions. Furthermore, mutual information quantifies the dependence between features and signals and noise, forcing the network to maximize the mutual information between constrained features and clean signals, and minimize the mutual information between features and noise, ensuring the integrity of effective signals. Finally, a cross-domain attention interaction module is designed, constructing a space-frequency domain feature fusion system through a two-way space-frequency attention collaborative mechanism. Based on a dual-branch collaborative strategy of spatial topology enhancement and frequency spectral analysis, a dynamic closed-loop optimization link is established between the two domains to achieve boundary artifact suppression and improved computational efficiency. This invention's fusion architecture based on fuzzy control theory, mutual information constraints, and a two-way space-frequency attention interaction mechanism is an end-to-end network model, with noisy seismic data as input and denoised seismic data as output.

[0104] The backbone network designed in this invention, based on fuzzy control theory and decoupled from mutual information constraints and bidirectional space-frequency attention interaction fusion architecture, is an improved U-Net network. The U-Net has a symmetrical encoder-decoder structure. The encoder progressively extracts multi-scale features of the seismic signal through convolution and pooling operations, reducing the spatial resolution of the seismic signal while increasing the abstraction of features, effectively capturing noise information at different levels in the seismic signal. Simultaneously, skip connections directly connect the feature maps in the encoder to corresponding positions in the decoder, allowing the decoder to directly obtain feature information from each layer of the encoder, enhancing the network's ability to preserve edge and texture features. To improve the extraction and utilization of local, global, and frequency information of the seismic signal, enhance the network's interpretability, and better address the problem of non-uniform noise distribution and feature coupling in seismic data, this invention replaces the traditional convolutional module of the conventional U-Net with a fuzzy rule-guided noise modeling module. A multi-scale fuzzy inference layer is embedded at the front end of the encoder. The noise intensity distribution of the seismic data is estimated through a dynamic membership function, and a four-level feature pyramid is designed to calculate local variance layer by layer and generate a spatially adaptive noise mask, guiding the network to focus on high-noise regions. Subsequently, a dual-path discriminator structure for the content path and noise path is constructed. A variational contrastive learning framework is used to maximize the mutual information between content features and the input signal, while minimizing the mutual information between noise features and the input signal. This explicitly decouples the statistical dependence of the effective seismic signal and noise, and quantifies the degree of feature separation. Finally, a cross-domain attention interaction module is designed to achieve dynamic joint modulation of spatial and frequency domain features through a bidirectional gating mechanism. Based on a complementary enhancement strategy of the spatial pilot term and the frequency pilot spatial term, a closed-loop interaction link is established between the frequency and spatial domains.

[0105] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A seismic data denoising method based on fuzzy rules and mutual information spatial-frequency domain decoupling, characterized in that, This includes downsampling the noisy image, inputting it into a first blurred convolutional layer, downsampling it, inputting it into a second blurred convolutional layer and a ReLU activation function layer, downsampling it, inputting it into a third blurred convolutional layer and a batch normalization layer, and downsampling it. The downsampling result is sequentially input into the fourth fuzzy convolutional layer, the space-frequency attention interaction module, the decoupling mutual information constraint module, and the first defuzzy convolutional layer. Then, it is sequentially upsampled, input into the second defuzzy convolutional layer and the batch normalization layer, upsampled again, input into the third defuzzy convolutional layer and the ReLU activation function layer, upsampled again, and input into the fourth defuzzy convolutional layer to finally obtain the denoised image. The fuzzy convolutional layer consists of two branches. One branch calculates the local variance and the dynamic membership weights based on Gaussian membership in sequence. The other branch is input to a 3×3 convolution. The results of the two branches are added together to obtain the weighted output features. The spatial-frequency attention interaction module inputs the input features to the spatial domain feature extraction branch and the frequency domain feature extraction branch, respectively. The frequency domain feature extraction branch outputs frequency domain features and frequency domain weights. Frequency domain weights The input is fed into the Sigmoid activation function layer, and then combined with spatial weights. Performing characteristic multiplication yields the empty pilot term. The empty pilot term is multiplied by the frequency domain features; The spatial feature extraction branch outputs spatial features and spatial weights. Spatial weight The input is fed into the Sigmoid activation function layer, and then combined with the frequency domain weights. Performing characteristic multiplication yields the frequency guide empty term. The frequency-guided spatial term is multiplied with the spatial domain features; The result of multiplying the two features is then added to obtain the output of the space-frequency attention interaction module; The decoupling mutual information constraint module includes a feature decoupling module and a mutual information constraint module; The feature decoupling module includes dividing the input features of the decoupling mutual information constraint module into two lines. One line inputs a 3×3 depthwise separable convolutional layer, a global average pooling layer, and a fully connected layer. The other line inputs a 3×3 convolutional layer, a LeakyReLU activation function layer, a 1×1 convolutional layer, and a Sigmoid activation function layer. The mutual information constraint module includes: a fully connected layer to obtain noise features, which are then combined with the input features of the decoupled mutual information constraint module to minimize KL divergence; a sigmoid activation function layer to obtain content features, which are then combined with the input features of the decoupled mutual information constraint module to maximize JSD divergence; and finally, the two divergence processing results are added together to output the mutual information constraint loss. The loss function for decoupling the mutual information constraint module is: ； To decouple the loss function of the mutual information constraint module, To maximize the loss function between the input and content features, To minimize the loss function between the input and noise features, To balance the mutual information constraint weights.

2. The seismic data denoising method based on fuzzy rules and mutual information spatial-frequency domain decoupling as described in claim 1, characterized in that, There is a skip connection between the first blurred convolutional layer and the fourth deblurred convolutional layer; There is a skip connection between the second blurred convolutional layer and the third deblurred convolutional layer; There is a skip connection between the third blurred convolutional layer and the second deblurred convolutional layer; There is a skip connection between the first blurred convolutional layer and the fourth unblurred convolutional layer.

3. The seismic data denoising method based on fuzzy rules and mutual information spatial-frequency domain decoupling according to claim 2, characterized in that, The spatial feature extraction branch includes inputting the input features into three paths: a 3×3 depthwise convolution, a 5×5 depthwise convolution, and a 7×7 depthwise convolution. The processing result of the 3×3 depthwise convolution is then sent to a channel-weighted convolution. The result of the 5×5 depthwise convolution layer is fed into the channel-weighted layer. The result of the 7×7 depthwise convolution layer is fed into the channel-weighted layer. The layer performs feature addition on the processing results of the three channel weighted layers and then inputs them into the ReLU activation function layer; The output of the ReLU activation function layer is divided into three paths. The first path is input to the global average pooling layer and the multilayer perceptron. The second path is input to the global max pooling layer and the multilayer perceptron. Then, the outputs of the first and second paths of the multilayer perceptron are multiplied by features. The result of the feature multiplication is input to the Sigmoid activation function layer for topological masking and hyperbolic tangent transformation. Then, it is multiplied by the third path to form spatial features. The spatial features are input to a 1×1 convolutional layer and a softmax activation function layer to obtain spatial weights.

4. The seismic data denoising method based on fuzzy rules and mutual information spatial-frequency domain decoupling according to claim 3, characterized in that, The frequency domain feature extraction branch includes sending the input features to the FFT transform module, outputting the amplitude spectrum and phase spectrum. The amplitude spectrum is processed in three lines: one line is input to the horizontal Sobel operator layer, the second line is input to the vertical Sobel operator layer, and then both the first and second lines are input to the four-quadrant tangent-inverse transform layer and the eight-direction binary mask layer. Then, the output of the amplitude spectrum is multiplied by the feature and output to the 1×1 convolutional layer and the IFFT transform layer. The three lines are sequentially input into a logarithmic transform layer, a 1×1 convolutional layer, a sigmoid activation function layer, and a hyperbolic tangent transform layer. Then, they are multiplied with the output of the phase spectrum, and an IFFT transform is performed. The results of the two IFFT transforms are added together to output the frequency domain features. The output of the sigmoid activation function layer is then subjected to an IFFT transform to obtain the frequency domain weights.

5. The seismic data denoising method based on fuzzy rules and mutual information spatial-frequency domain decoupling according to claim 4, characterized in that, Calculate local variance include: ； In the formula, Given the input feature map, , For position offset index, and They are respectively , The three possible values, , The three possible values ​​are -1, 0, and 1. This is the position offset constant. For input position Feature map, For input position Feature map; Calculate dynamic membership weights based on Gaussian membership. include: ； In the formula, The learnable attenuation coefficient; Fuzzy convolutional layer include: ； In the formula, To learn convolution kernels, Represents the feature dot product. This is the bias value.

6. The seismic data denoising method based on fuzzy rules and mutual information spatial-frequency domain decoupling according to claim 5, characterized in that, The loss function that maximizes the mutual information between the input and content features is: ； In the formula, Indicates in joint distribution The expected score of the discriminator on positive samples. Represents the product of marginal distributions Calculation The expected value is used as a penalty term for negative samples. For content discriminator function, Indicates input features, Indicates content characteristics, Other content features besides the current input. It is a natural constant; The loss function that minimizes the mutual information between the input and noise features is: ； In the formula, Indicates in joint distribution The expected score of the discriminator on positive samples. It is a parameterized discriminator composed of two MLP layers. Represents the product of marginal distributions Calculation The expected value is used as the penalty term for negative samples. It is a noise characteristic. Other noise features that are not part of the current input.

7. The seismic data denoising method based on fuzzy rules and mutual information spatial-frequency domain decoupling according to claim 6, characterized in that, Total loss function for: ； ； ； In the formula, It refers to the amount of data processed in a batch. It is clean, noise-free seismic data. yes and Mutual information between them yes and Mutual information between them It is the content discriminator weight. It is the weight of the noise discriminator. , , yes The three weights, yes Divergence calculation, yes Divergence calculation.

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