Seismic data interpolation method and system based on CBAM-Res2Unet network

Abstract

The present application belongs to the technical field of oil and gas exploration and seismic data processing, and discloses a seismic data interpolation method and system based on CBAM-Res2Unet network. The method solves the problems of limited receptive field caused by fixed convolution kernel in traditional ResUNet network and non-selective transmission of low-level features in skip connection. The method comprises: generating seismic records through wave equation forward modeling and constructing a training set containing random missing data; designing CBAM-Res2Unet network, wherein the encoder and the decoder adopt Res2Net modules containing compression excitation modules, and the multi-scale feature extraction capability is enhanced through grouped convolution and hierarchical residual connection; introducing CBAM modules in the skip connection to adaptively weight the features by using channel and spatial attention mechanisms; and adding a spectral normalization layer in the deep network to stabilize the training. The system comprises data acquisition, network generation, training and interpolation modules. Through multi-scale feature fusion, attention mechanism and stability optimization, the present application realizes high-precision interpolation of complex missing seismic data.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of oil and gas exploration and seismic data processing, and provides a seismic data interpolation method and system based on a CBAM-Res2Unet network. BACKGROUND

[0002] Complex acquisition conditions often result in missing seismic traces, which will affect subsequent steps such as AVO analysis, delay analysis and fluid detection. Therefore, interpolation is necessary for better understanding of the reservoir. In order to obtain reliable interpretation results, interpolation must be performed on the missing seismic traces. Therefore, interpolation is of great significance.

[0003] The seismic data interpolation method based on the CBAM-Res2Unet network is one of the important methods for deep learning seismic data interpolation. The method uses missing seismic data to make a training set to train the network, and uses the trained network to perform interpolation processing on the missing seismic data. The CBAM-Res2Unet network not only helps to prevent overfitting, but also can more effectively perform interpolation. However, the fixed size of the convolution kernel of the traditional ResUnet network limits the receptive field and the low-level features in the skip connection have no selective transmission, which makes it difficult for the network to capture long-distance related information. This will affect the training effect of the network, and further affect the interpolation result, resulting in discontinuity of the interpolated seismic data.

[0004] Therefore, in the prior art, the seismic data interpolation method based on the ResUnet network has the following technical problems:

[0005] The fixed size of the convolution kernel of the ResUnet network limits the receptive field and the low-level features in the skip connection have no selective transmission, which makes it difficult for the network to capture long-distance related information. This will affect the training effect of the network, and further affect the interpolation result, resulting in discontinuity of the interpolated seismic data, i.e. the quality of the processing result is difficult to guarantee. SUMMARY

[0006] In view of the above problems, the purpose of the present application is to provide a seismic data interpolation method and system based on a CBAM-Res2Unet network, which solves the problem of the fixed size of the convolution kernel of the ResUnet network limiting the receptive field and the low-level features in the skip connection having no selective transmission.

[0007] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0008] The present application provides a seismic data interpolation method based on CBAM-Res2Unet, comprising the following steps:

[0009] Step 1: Obtain seismic data and form a training set and a validation set, wherein the seismic data is a seismic shot record;

[0010] Step 2: Obtain a preset CBAM-Res2Unet network based on the CBAM-Res2Unet network, the network comprising an encoder module, a decoder module, and a skip connection layer, wherein:

[0011] The encoder module comprises five layers, each layer comprising a convolutional layer, a Res2Net module comprising a compressed excitation module, and a down-sampling layer in sequence, wherein a spectral normalization layer is added outside the convolutional layer of the fifth layer;

[0012] The decoder module comprises five layers, each layer comprising a convolutional layer, a Res2Net module comprising a compressed excitation module, and an up-sampling layer in sequence;

[0013] The skip connection layer is provided with a CBAM module between the corresponding layers of the encoder and the decoder, and each CBAM module enhances the feature expression capability by adaptively learning the channel and spatial attention weights;

[0014] Step 3: Train and verify the CBAM-Res2Unet network based on the training set and the verification set:

[0015] Step 4: Based on the trained CBAM-Res2Unet network, interpolate the seismic data to be interpolated.

[0016] In the above technical solution, the step 1 comprises the following steps:

[0017] Step 1.1: Perform wave equation-based forward numerical simulation to obtain seismic records;

[0018] Step 1.2: Merge all the seismic records obtained in step 1.1 to obtain a large seismic data collection, and then generate two copies, wherein copy 1 is randomly missing 30%, 50%, and 70% of the seismic records, and copy 2 is the corresponding complete data, i.e., the target data;

[0019] Step 1.3: Randomly select multiple pairs of data from copy 1 and copy 2 using a preset size grid to form a training pair set A, and finally use the training pair set A as the final training set and verification set.

[0020] In the above technical solution, the preset CBAM-Res2Unet network in step 2 comprises an input layer, an encoder module, a decoder module, and an output layer connected in sequence, and a skip connection layer for connecting the encoder and the decoder;

[0021] The encoder module comprises a 5-layer connected encoder structure, each layer of the encoder comprises a convolutional layer, a Res2Net module comprising a compression excitation module and a down-sampling layer in sequence, each layer comprises a residual connection for directly adding an output of a convolutional layer of the layer to an input feature map, the residual connection comprises a convolutional layer for capturing the feature map, two convolutional layers of the fifth layer (one convolutional layer before and after the fifth layer Res2Net module) are respectively added with a spectral normalization layer,

[0022] The convolutional layer performs convolutional operation on the input feature map to reserve detailed features and information, and gradually reduces the size of the feature map while reserving important information through feature extraction and residual connection;

[0023] The Res2Net module performs grouped convolutional operation on the input feature map, improves the multi-scale representation capability at a finer granularity, and increases the receptive field of each network layer;

[0024] The compression excitation module is added after the second convolutional layer in the Res2Net module and before the residual connection in the module, and is used for weighting the features of different channels to enhance the key features;

[0025] The two convolutional layers of the fifth layer are respectively added with a spectral normalization layer, which is used to enhance the stability of the network;

[0026] The skip connection layer comprises: four CBAM modules are included in the skip connection, each skip connection comprises a CBAM module,

[0027] The CBAM module learns the channel and spatial attention weights adaptively to improve the feature expression capability of the network, and can capture the correlation between features in different dimensions;

[0028] The decoder module comprises: a decoder comprising five convolutional layers and up-sampling layers connected to each other, each decoder comprises a convolutional layer, a Res2Net module comprising a compression excitation module and an up-sampling layer.

[0029] In the above technical solution, the Res2Net module performs grouped convolutional operation on the input feature map, improves the multi-scale representation capability at a finer granularity, and increases the receptive field of each network layer, and the operation of the Res2Net module comprises:

[0030] The input feature map is divided into four groups, the convolutional output of the previous group is concatenated with the input feature map of the next group, the convolutional operation is used for feature extraction, and the hierarchical residual connection is used to expand the receptive field;

[0031] Finally, all group outputs are fused through a 1*1 convolution, and the mathematical expression is:

[0032]

[0033] wherein x represents an input feature map, F(x) represents an output feature map of the previous convolution, G i (x) represents a feature transformation operation of the i-th branch, W i represents the weight of the i-th branch, and F(y) represents the final output.

[0034] A CBAM module is added in each skip connection layer to improve the feature expression ability of the network by adaptively learning channel and spatial attention weights, and the correlation between features in different dimensions can be captured, and the operation of the CBAM module includes:

[0035] Channel attention stage: global maximum pooling and average pooling are performed on the input feature map respectively, and channel weights are generated by sharing MLP, and the calculation formula is:

[0036]

[0037] wherein M c (F) is a channel attention function, δ represents an activation function Sigmoid, F is a feature input, represents an average pooling operation of a channel c, represents a maximum pooling operation of c channels, W0 and W1 are network parameters in a multi-layer perceptron MLP respectively, AvgPool(F) represents global average pooling of each channel of the feature map F, and MaxPool(F) represents global maximum pooling of each channel of the feature map F;

[0038] Spatial attention stage: maximum and average pooling are performed on the channel weighted feature map, and spatial weights are generated by 7x7 convolution, and the calculation formula is:

[0039]

[0040] The final output is a channel and spatial attention double weighted feature map, F″ is:

[0041]

[0042] wherein M s (F) is a spatial attention function, f 7×7 represents a 7x7 convolution kernel, wherein F' is a feature after spatial attention mechanism, F" is a refined feature map, represents a global average pooling result of the input feature map F, represents a global maximum pooling result of the input feature map F.

[0043] The compression excitation module is used to weight the features of different channels, and the operation of the compression excitation module comprises the following steps:

[0044] Step A: performing a convolution operation on the input feature map X to generate a feature map U, denoted as:

[0045] F tr : X→U, X∈R W″*H″*C″ , U∈R W′*H′*C′

[0046] Wherein, F tr is a convolution transformation, wherein R represents a real number set, W', W" represents a width, H', H" represents a height, C', C" represents a channel number, and the cth channel of the feature map U is as follows:

[0047]

[0048] Wherein v c represents the cth convolution kernel, x s represents the s th input covered by the current convolution kernel, u c represents the s th output, and K represents the number of convolution kernels.

[0049] Step B: performing a squeezing operation on the intermediate feature map U to obtain global information, and generating a channel description vector z∈R C by global average pooling, and the specific calculation is as follows:

[0050] Wherein z c represents the average value of the c channels of the layer, and u c (i, j) represents the feature value of the c th channel at position (i, j).

[0051] Step C: performing an excitation operation on the channel description vector z c , and generating a channel weight vector s c ∈R C by two-level fully connected layers, and the calculation process is as follows:

[0052] s c =sigmoid(W2·ReLU(W1·z c )) wherein W1 and W2 represent linear layers, and z represents the channel average value of each layer.

[0053] Step D: performing a channel-by-channel multiplication of the channel weight vector s and the intermediate feature map U to output a refined feature map The calculation is as follows:

[0054] Wherein s c represents the weight value of the c th channel, and u cTo correspond to the channel feature map.

[0055] A spectral normalization layer is added outside each convolutional layer in the fifth layer to limit the spectral norm of the weight matrix of the fifth layer. The specific steps of the spectral normalization process are as follows:

[0056] Step A: Apply Lipschitz constraint to the weight matrix of the fifth layer convolutional layer

[0057] The mapping relationship of the convolutional layer is represented as g: h in → h out , where h in represents the input data, and h out represents the output data. The Lipschitz constant is defined as:

[0058]

[0059] where h is the input feature map, ||·|| represents the L2 norm, representing the calculation of all non-zero input vectors h. The network mapping relationship is represented by the weight W as:

[0060] g(h) = Wh

[0061] According to the above formula, the Lipschitz constant is determined by the maximum singular value σ max (W) of the matrix W:

[0062] |g|Lip = σ max (W)

[0063] Step B: Calculate the spectral norm (maximum singular value of the matrix) of the weight matrix using the power iteration method

[0064] Initialize a random vector and Update the approximate maximum singular value through iteration:

[0065]

[0066] where represents the left singular vector, represents the right singular vector, and T represents the transpose;

[0067] Calculate the spectral norm approximation value after iteration:

[0068]

[0069] Step C: Normalize the weight matrix

[0070] Based on the approximate spectral norm of step B, normalize the weight matrix W:

[0071]

[0072] The normalized weight matrix is substituted for the original weight W, ensuring that the Lipschitz constant of the network layer is 1. The normalized weight matrix is substituted for the original weight W, ensuring that the Lipschitz constant of the network layer is 1.

[0073] The application provides a CBAM-Res2Unet network-based seismic data interpolation system, comprising:

[0074] The acquisition module acquires seismic data and forms a training set and a verification set, wherein the seismic data is a seismic shot record;

[0075] The network generation module acquires a preset CBAM-Res2Unet network;

[0076] The training module trains and verifies the CBAM-Res2Unet network based on the training set and the verification set;

[0077] The interpolation module interpolates the seismic data to be interpolated based on the trained CBAM-Res2Unet network.

[0078] In the above system, the acquisition module specifically implements the following steps:

[0079] Step 1.1: Obtain seismic records based on wave equation forward numerical simulation;

[0080] Step 1.2: Merge all the seismic records obtained in step 1.1 to obtain a large seismic data collection, and generate two copies therefrom, wherein copy 1 is randomly missing 30%, 50%, and 70% of the seismic records, and copy 2 is the corresponding complete data, i.e., the target data;

[0081] Step 1.3: Randomly select multiple pairs of data from copy 1 and copy 2 using a preset size grid to form a training pair set A, and finally use the training pair set A as the final training set and verification set.

[0082] In the above system, the CBAM-Res2Unet network comprises an input layer, an encoder module, a decoder module, and an output layer connected in sequence, and a skip connection layer for connecting the encoder and the decoder;

[0083] The encoder module comprises 5 layers of connected encoder structures, each layer of the encoder comprising a convolution layer, a Res2Net module comprising a compression excitation module, and a down-sampling layer in sequence, each layer comprising a residual connection for directly adding an input feature map to the output of the convolution layer of the layer, the residual connection comprising a convolution layer for capturing the feature map, and a spectral normalization layer is added to the two convolution layers of the fifth layer,

[0084] The convolutional layer performs convolution operation on the input feature map to reserve detailed features and information, and gradually reduces the size of the feature map while preserving important information through feature extraction and residual connection;

[0085] The Res2Net module performs grouped convolution operation on the input feature map, improves multi-scale representation capability at a finer granularity, and increases the receptive field of each network layer;

[0086] The compression excitation module is added after the second convolution layer in the Res2Net module and before the residual connection in the module, which is used to weight the features of different channels to enhance key features;

[0087] In the fifth layer, two convolutional layers are added: two convolutional layers are added respectively, and a spectral normalization layer is added to enhance the stability of the network;

[0088] The skip connection layer includes: four CBAM modules are included in the skip connection, and each skip connection includes a CBAM module,

[0089] The CBAM module learns the channel and spatial attention weights adaptively to improve the feature expression capability of the network, and can capture the correlation between features in different dimensions;

[0090] The decoder module includes: five convolutional layers and up-sampling layers are connected to form a decoder, and each decoder includes a convolutional layer, a Res2Net module with a compression excitation module, and an up-sampling layer.

[0091] In the above system, the Res2Net module performs grouped convolution operation on the input feature map, improves multi-scale representation capability at a finer granularity, and increases the receptive field of each network layer, and the operation of the Res2Net module includes:

[0092] The input feature map is divided into four groups, the convolution output of the previous group is concatenated with the input feature map of the next group, the convolution operation is used for feature extraction, and the hierarchical residual connection is used to expand the receptive field;

[0093] Finally, all group outputs are fused through 1x1 convolution, and the mathematical expression is:

[0094]

[0095] Where x represents the input feature map, F(x) represents the output feature map of the previous convolution, G i (x) represents the feature transformation operation of the i-th branch, W i represents the weight of the i-th branch, and F(y) represents the final output.

[0096] The CBAM module is added in each jump connection layer to improve the feature expression capability of the network by adaptively learning channel and spatial attention weights, and the operation of the CBAM module includes:

[0097] The channel attention stage: global maximum pooling and average pooling are respectively performed on the input feature map, and channel weights are generated by a shared MLP, and the calculation formula is:

[0098]

[0099] Where M c (F) is a channel attention function, δ represents an activation function Sigmoid, F is a feature input, represents an average pooling operation of c channels, represents a maximum pooling operation of c channels, W0 and W1 are network parameters in a multi-layer perceptron MLP, AvgPool(F) represents global average pooling on each channel of the feature map F, and MaxPool(F) represents global maximum pooling on each channel of the feature map F.

[0100] The spatial attention stage: maximum and average pooling are performed on the channel weighted feature map, and spatial weights are generated by 7x7 convolution, and the calculation formula is:

[0101]

[0102] The final output is a channel and spatial attention double weighted feature map, F″ is:

[0103]

[0104] Where M s (F) is a spatial attention function, f 7×7 represents a 7x7 convolution kernel, where F′ is a feature after spatial attention mechanism, and F″ is a refined feature map, represents a global average pooling result of the input feature map F, represents a global maximum pooling result of the input feature map F.

[0105] The compression excitation module is used to weight the features of different channels, and the operation of the compression excitation module includes the following steps:

[0106] Step A: perform convolution operation on the input feature map X to generate feature map U, represented as:

[0107] F tr : X→U, X∈R W″*H″*C″ , U∈R W′*H′*C′

[0108] where F tr is a convolutional transformation, where R represents the real set, W', W" represents the width, H', H" represents the height, C', C" represents the number of channels, and the c-th channel of the feature map U is convoluted as follows:

[0109]

[0110] where v c represents the c-th convolution kernel, x s represents the s-th input covered by the current convolution kernel, u c represents the s-th output, and K represents the number of convolution kernels.

[0111] Step B: Perform a squeezing operation on the intermediate feature map U to obtain global information, and generate a channel description vector z C ∈ R

[0112] where z c represents the average value of the c channels of this layer, and u c (i, j) represents the feature value of the c-th channel at position (i, j).

[0113] Step C: Perform an excitation operation on the channel description vector z c , and generate a channel weight vector s c ∈ R C through two fully connected layers, with the calculation process being:

[0114] s c = sigmoid(W2·ReLU(W1·z c )) where W1, W2 represent linear layers, and z represents the channel average value of each layer.

[0115] Step D: Perform a channel-by-channel multiplication of the channel weight vector s and the intermediate feature map U to output a refined feature map with the calculation being:

[0116]

[0117] where s c represents the weight value of the c-th channel, and u c is the corresponding channel feature map.

[0118] A spectral normalization layer is added outside each convolutional layer of the fifth layer to limit the spectral norm of the weight matrix of the fifth layer. The specific steps of spectral normalization processing are as follows:

[0119] Step A: Apply Lipschitz constraint to the weight matrix of the fifth layer convolutional layer

[0120] The mapping relationship of the convolution layer is represented as g: h in → h out Wherein, h in represents input data, h out represents output data, and the Lipschitz constant is defined as:

[0121]

[0122] Wherein, h represents an input feature map, and ||·|| represents an L2 norm, representing the calculation of all non-zero input vectors h. The network mapping relationship is represented by weights W as:

[0123] g(h) = Wh

[0124] According to the above formula, the Lipschitz constant is determined by the maximum singular value σ max (W) of the matrix W:

[0125] |g|Lip = σ max (W)

[0126] Step B: Calculate the spectral norm (the maximum singular value of the matrix) of the weight matrix by using the power iteration method

[0127] Initialize a random vector and Update the approximate maximum singular value by iteration:

[0128]

[0129] Wherein, represents a left singular vector, represents a right singular vector, and T represents transposition;

[0130] Calculate the spectral norm approximation value after iteration:

[0131]

[0132] Step C: Normalize the weight matrix

[0133] Based on the approximate spectral norm of step B, the normalization operation is performed on the weight matrix W:

[0134]

[0135] Replace the normalized weight matrix with the original weight W, so as to ensure that the Lipschitz constant of the network layer is 1.

[0136] Compared with the prior art, the present application has the following beneficial effects:

[0137] The CBAM-Res2Unet network is used for interpolation of seismic data. On the basis of ResUnet, the Res2Net module containing the compression excitation module, the CBAM module and the spectral normalization layer are added. The CBAM module learns the channel and spatial attention weights adaptively to improve the feature expression ability of the network, and can capture the correlation between features in different dimensions, thereby improving the interpolation ability. The Res2Net module improves the multi-scale representation ability at a finer granularity and increases the receptive field of each network layer to improve the interpolation ability. The compression excitation module learns the importance of each channel to explicitly simulate the interdependence between feature channels. It weights each feature according to its importance, then highlights the key features, and achieves the effect of improving the signal-to-noise ratio of seismic data interpolation. The spectral normalization layer decomposes the eigenvalues of the weight matrix and then normalizes it. In the process of optimizing the neural network, the parameter change is also more stable and is not prone to gradient explosion, which improves the interpolation performance of the network. That is, the CBAM-Res2Unet network technology obtained after improvement realizes the maximum preservation of weight matrix information; the compression excitation module is used to realize the segmentation image extraction function while preserving the detail information of the image. Through the improvement of the network performance, the application finally achieves the effect of improving the signal-to-noise ratio of seismic data interpolation. BRIEF DESCRIPTION OF DRAWINGS

[0138] Figure 1 A flowchart of a CBAM-Res2Unet network-based seismic data interpolation method according to the application is shown in the figure;

[0139] Figure 2 The CBAM-Res2Unet network architecture according to the application is shown in the figure;

[0140] Figure 3 The target data seismic profile of the test data according to the application is shown in the figure;

[0141] Figure 4 The missing seismic data seismic profile of the test data according to the application is shown in the figure;

[0142] Figure 5 The interpolation result according to the application is shown in the figure. DETAILED DESCRIPTION

[0143] The embodiments of the application will be described in detail below. Although the application will be described and illustrated by means of some specific embodiments, it is to be understood that the application is not restricted to just these embodiments. Rather, any modification or equivalent replacement in keeping with the principle of the application shall fall within the scope of the claims of the application.

[0144] Also, for a better understanding of the present application, numerous specific details are given in the following detailed description. The skilled person will understand that the application can be practiced without these specific details.

[0145] The technical problem solved by the present application is to solve the problem of limited receptive field caused by fixed convolution kernel size of ResUnet network in the prior art and non-selective transmission of low-level features in the skip connection, and to improve the signal-to-noise ratio of seismic data interpolation.

[0146] A seismic data interpolation method based on a CBAM-Res2Unet network, comprising the following steps:

[0147] Step 1: Obtain seismic data and form a training set and a validation set, wherein the seismic data is a seismic shot record; comprising the following steps:

[0148] Step 1.1: Perform wave equation-based forward numerical simulation to obtain seismic records;

[0149] Step 1.2: Merge all seismic records obtained in step 1.1 to obtain a large seismic data collection, and generate two copies therefrom, wherein copy 1 is a random 30%, 50%, and 70% missing seismic record, and copy 2 is the corresponding complete data, i.e. the target data;

[0150] Step 1.3: Randomly select multiple pairs of data from copy 1 and copy 2 using a pre-set size grid to form a training pair set A, and finally use the training pair set A as the final training set and validation set.

[0151] Step 2: Obtain a pre-set CBAM-Res2Unet network; the main structure of the pre-set CBAM-Res2Unet network is a ResUnet network, which includes an encoder and a decoder and a skip connection layer. Residual connection is used in the encoder and the decoder, Res2Net module containing compression excitation module, and a spectral normalization layer is added outside the two convolution layers of the fifth layer of the network, and a CBAM module is added in each layer of the skip connection.

[0152] The specific steps are as follows:

[0153] The main network structure is constructed by using a ResUnet network, and includes five encoders and five decoders, that is, four down-sampling connected encoders and four up-sampling connected decoders, an input layer connected with the first encoder and an output layer connected with the fifth decoder, the first encoder to the fifth encoder are jump connected with the first decoder to the fifth decoder, each encoder includes a convolution layer and a Res2Net module including a compression excitation module, each decoder includes an up-sampling layer and a Res2Net module including a compression excitation module, the convolution kernel size of each is 3*3, a CBAM module is included in the jump connection layer, the channel numbers of the five encoders are 32, 64, 128, 256, 256, 512 in turn respectively, and the channel numbers of the five decoders are 512, 256, 128, 64, 32 in turn respectively. A Res2Net module including a compression excitation module is added after the convolution layer in each layer of the encoder and the decoder, and grouping convolution operation is performed on the input feature map, and the specific steps of the grouping convolution are:

[0154] We divide the input features into 4 groups. A group of filters first extracts elements from a group of input feature maps, and then sends the output feature maps of the previous group to another group of input feature Figure 1 maps to the next group of filters. This process is repeated several times until all input feature maps are processed. Finally, the feature maps of all groups are concatenated and sent to another 1*1 filter to fully fuse the information. Along any path from the input feature map to the output feature map, the equivalent receptive field increases when passing through the 3*3 filter, and due to the combination effect, many equivalent feature scales are obtained, that is,

[0155]

[0156] where x represents the input feature map, F(x) represents the output feature map of the previous group of convolutions, G i (x) represents the feature transformation operation of the i-th branch, W i represents the weight of the i-th branch, and F(y) represents the final output.

[0157] The CBAM module can adaptively learn the channel and spatial attention weights, and the specific steps are:

[0158] The first input feature map is processed by the channel attention module. For the input feature map, first, global max pooling and global average pooling operations are performed on each channel to calculate the maximum feature value and the average feature value on each channel. Two vectors containing the number of channels are generated, representing the global maximum feature and the average feature of each channel, respectively. The feature vectors after global max pooling and average pooling are input into a shared fully connected layer. The fully connected layer is used to learn the attention weight of each channel. The global maximum feature vector and the average feature vector are intersected to obtain the final attention weight vector. In order to ensure that the attention weight is between 0 and 1, a Sigmoid activation function is applied to generate the channel attention weight. These weights will be applied to each channel of the original feature map. Using the obtained attention weight, multiply it with each channel of the original feature map to obtain the channel feature map after attention weighting. c (F) is:

[0159]

[0160] where M c (F) is the channel attention function, δ represents the activation function Sigmoid, F is the feature input, represents the average pooling operation of c channels, represents the maximum pooling operation of c channels, W0 and W1 are network parameters in the multi-layer perceptron (MLP), AvgPool(F) represents global average pooling on each channel of the feature map F, and MaxPool(F) represents global maximum pooling on each channel of the feature map F;

[0161] The spatial attention stage: maximum and average pooling are performed on the channel-weighted feature map, and spatial weights are generated through a 7x7 convolution, with the calculation formula being:

[0162]

[0163] The final output is a channel and spatial attention double-weighted feature map, F″ is:

[0164]

[0165] where M s (F) is the spatial attention function, f 7×7 represents a 7x7 convolution kernel, where F′ is the feature after the spatial attention mechanism, and F″ is the refined feature map, represents the global average pooling result of the input feature map F, represents the global maximum pooling result of the input feature map F.

[0166] The compression excitation module processes the weight information of different channels. The specific steps of compression excitation processing are:

[0167] Step A: Convolution operation is performed on the input feature map X to generate a feature map U, denoted as:

[0168] F tr : X→U, X∈R W″*H″*C″ , U∈R W′*H′*C′

[0169] where F tr is a convolutional transformation, where R represents the set of real numbers, W', W" represents the width, H', H" represents the height, C', C" represents the number of channels, and the c-th channel of the feature map U is convolved as follows:

[0170]

[0171] where v c represents the c-th convolution kernel, x s represents the s-th input covered by the current convolution kernel, u c represents the s-th output, and K represents the number of convolution kernels.

[0172] Step B: Squeeze operation is performed on the intermediate feature map U to obtain global information, and a channel description vector z∈R C is generated by global average pooling, which is calculated as:

[0173] where z c represents the average value of the c channels of this layer, and u c (i, j) represents the feature value of the c-th channel at position (i, j).

[0174] Step C: Excitation operation is performed on the channel description vector z c , and a channel weight vector s c ∈R C is generated by two fully connected layers, with the calculation process being:

[0175] s c = sigmoid(W2·ReLU(W1·z c )) where W1, W2 represent linear layers, and z represents the channel average value of each layer.

[0176] Step D: The channel weight vector s is multiplied with the intermediate feature map U channel by channel, and the refined feature map is output, which is calculated as:

[0177]

[0178] where s c represents the weight value of the c-th channel, and u c is the corresponding channel feature map.

[0179] Spectral Normalization Layer, limiting the spectral norm of the weight matrix of the fifth layer of convolutional layer, the specific steps of spectral normalization processing are:

[0180] Step A: Apply Lipschitz constraint to the weight matrix of the fifth layer of convolutional layer

[0181] The mapping relationship of the convolutional layer is represented as g: h in → h out , where h in represents the input data, and h out represents the output data. The Lipschitz constant is defined as:

[0182]

[0183] where h is the input feature map, ||·|| represents the L2 norm, representing the calculation of all non-zero input vectors h. The network mapping relationship is represented by the weight W as:

[0184] g(h) = Wh

[0185] According to the above formula, the Lipschitz constant is determined by the maximum singular value σ max (W) of the matrix W:

[0186] |g|Lip = σ max (W)

[0187] Step B: Calculate the spectral norm (maximum singular value of the matrix) of the weight matrix using the power iteration method

[0188] Initialize a random vector and Update the approximate maximum singular value by iteration:

[0189]

[0190] where represents the left singular vector, represents the right singular vector, and T represents the transpose;

[0191] Calculate the approximate spectral norm after iteration:

[0192]

[0193] Step C: Normalize the weight matrix

[0194] Based on the approximate spectral norm of step B, normalize the weight matrix W:

[0195]

[0196] The normalized weight matrix is replaced with the original weight W, ensuring that the Lipschitz constant of the network layer is 1. The normalized weight matrix is replaced with the original weight W, ensuring that the Lipschitz constant of the network layer is 1.

[0197] Step 3: Train and validate the network based on the training set and the validation set;

[0198] Step 4: Based on the trained CBAM-Res2Unet network, interpolate the seismic data to be interpolated.

[0199] Step 4.1: Select part of the seismic record of the model and make a test data for missing;

[0200] Step 4.2: Input the seismic data to be interpolated into the optimal model selected in step 3.2 for testing.

[0201] Embodiment 1

[0202] The present application provides a CBAM-Res2Unet network-based seismic data interpolation system, comprising:

[0203] The acquisition module acquires seismic data and forms a training set and a validation set, wherein the seismic data is a seismic shot record;

[0204] The network generation module acquires a preset CBAM-Res2Unet network;

[0205] The training module trains and validates the CBAM-Res2Unet network based on the training set and the validation set;

[0206] The interpolation module interpolates the seismic data to be interpolated based on the trained CBAM-Res2Unet network.

[0207] In the above system, the acquisition module specifically implements the following steps:

[0208] Step 1.1: Perform wave equation-based forward numerical simulation to obtain seismic records;

[0209] Step 1.2: Combine all the seismic records obtained in step 1.1 to obtain a large seismic data collection, and generate two copies, wherein copy 1 is randomly missing 30%, 50% and 70% of the seismic records, and copy 2 is the corresponding complete data, i.e. the target data;

[0210] Step 1.3: Randomly select multiple pairs of data from copy 1 and copy 2 with a preset size grid to form a training pair set A, and finally use the training pair set A as the final training set and validation set.

[0211] The CBAM-Res2Unet network in the system comprises an input layer, an encoder module, a decoder module and an output layer connected in sequence, and a skip connection layer for connecting the encoder and the decoder;

[0212] The encoder module comprises five layers of connected encoder structures, each layer of the encoder comprising a convolutional layer, a Res2Net module comprising a compression excitation module and a down-sampling layer in sequence, each layer comprising a residual connection for directly adding an output of a convolutional layer of the layer to an input feature map, the residual connection comprising a convolutional layer for capturing the feature map, and a spectral normalization layer being added to each of the two convolutional layers of the fifth layer,

[0213] The convolutional layer performs convolutional operation on the input feature map to reserve detailed features and information, and gradually reduces the size of the feature map while reserving important information through feature extraction and residual connection;

[0214] The Res2Net module performs grouped convolutional operation on the input feature map, improves multi-scale representation capability at a finer granularity, and increases the receptive field of each network layer;

[0215] The compression excitation module is added after the second convolutional layer in the Res2Net module and before the residual connection in the module, and is used for weighting features of different channels to enhance key features;

[0216] The two convolutional layers of the fifth layer each have a spectral normalization layer added thereto, for enhancing the stability of the network;

[0217] The skip connection layer comprises four skip connections each comprising a CBAM module,

[0218] The CBAM module adaptively learns channel and spatial attention weights to improve the feature expression capability of the network, and can capture the correlation between features in different dimensions;

[0219] The decoder module comprises five decoders each comprising a convolutional layer, a Res2Net module comprising a compression excitation module and an up-sampling layer connected in sequence.

[0220] The Res2Net module performs grouped convolutional operation on the input feature map, improves multi-scale representation capability at a finer granularity, and increases the receptive field of each network layer, and the operation of the Res2Net module comprises:

[0221] The input feature map is divided into four groups, the convolutional output of a previous group is concatenated with the input feature map of a subsequent group, convolutional operation is used for feature extraction, and the receptive field is expanded through hierarchical residual connection.

[0222] Finally, all group outputs are fused by 1x1 convolution, and the mathematical expression is:

[0223]

[0224] where x represents the input feature map, F(x) represents the output feature map of the previous convolution, G i (x) represents the feature transformation operation of the i-th branch, W i represents the weight of the i-th branch, and F(y) represents the final output.

[0225] In each skip connection layer, a CBAM module is added to improve the feature expression ability of the network by adaptively learning channel and spatial attention weights, which can capture the correlation between features in different dimensions. The operation of the CBAM module includes:

[0226] Channel attention stage: global maximum pooling and average pooling are performed on the input feature map respectively, and channel weights are generated by shared MLP, and the calculation formula is:

[0227]

[0228] where M c (F) is the channel attention function, δ represents the activation function Sigmoid, F is the feature input, represents the average pooling operation of the c channels, represents the maximum pooling operation of the c channels, W0 and W1 are network parameters in the multi-layer perceptron MLP, AvgPool(F) represents global average pooling on each channel of the feature map F, and MaxPool(F) represents global maximum pooling on each channel of the feature map F.

[0229] Spatial attention stage: maximum and average pooling are performed on the channel weighted feature map, and spatial weights are generated by 7x7 convolution, and the calculation formula is:

[0230]

[0231] The final output is the channel and spatial attention double weighted feature map, F″ is:

[0232]

[0233] where M s (F) is the spatial attention function, f 7×7 represents a 7x7 convolution kernel, where F' is the feature after spatial attention mechanism, F" is the refined feature map, represents the global average pooling result of the input feature map F, represents the global max-pooling result of the input feature map F.

[0234] The compression excitation module is used to weight the features of different channels, and the operation of the compression excitation module includes the following steps:

[0235] Step A: Convolution operation is performed on the input feature map X to generate a feature map U, which is represented as:

[0236] F tr : X→U, X∈R W″*H″*C″ , U∈R W′*H′*C′

[0237] Where F tr is a convolutional transformation, where R represents the set of real numbers, W', W" represents the width, H', H" represents the height, C, C represents the number of channels, and the cth channel of the feature map U is convolved as follows:

[0238]

[0239] Where v c represents the cth convolution kernel, x s represents the s-th input covered by the current convolution kernel, u c represents the s-th output, and K represents the number of convolution kernels.

[0240] Step B: Perform squeezing operation on the intermediate feature map U to obtain global information, and generate a channel description vector z∈R C by global average pooling, which is calculated as:

[0241] Where z c represents the average value of the c channels of this layer, and u c (i, j) represents the feature value of the cth channel at position (i, j).

[0242] Step C: Perform excitation operation on the channel description vector z c , and generate a channel weight vector s c ∈R C by two-level fully connected layer, the calculation process is:

[0243] s c = sigmoid(W2·ReLU(W1·z c )) where W1, W2 represent linear layers, and z represents the channel average value of each layer.

[0244] Step D: Perform channel-by-channel multiplication of the channel weight vector s and the intermediate feature map U to output the refined feature map , which is calculated as:

[0245]

[0246] where s c represents the weight value of the cth channel, u c is the corresponding channel feature map.

[0247] A spectral normalization layer is added outside each convolutional layer in the fifth layer to limit the spectral norm of the weight matrix of the fifth layer. The specific steps of the spectral normalization process are as follows:

[0248] Step A: Apply Lipschitz constraint to the weight matrix of the fifth layer convolutional layer

[0249] The mapping relationship of the convolutional layer is represented as g: h in → h out , where h in represents the input data, h out represents the output data. The Lipschitz constant is defined as:

[0250]

[0251] where h is the input feature map, ||·|| represents the L2 norm, representing the calculation of all non-zero input vectors h. The network mapping relationship is represented by the weight W as:

[0252] g(h) = Wh

[0253] According to the above formula, the Lipschitz constant is determined by the maximum singular value σ max (W) of the matrix W:

[0254] |g|Lip = σ max (W)

[0255] Step B: Calculate the spectral norm (maximum singular value of the matrix) of the weight matrix using the power iteration method

[0256] Initialize a random vector and Update the approximate maximum singular value through iteration:

[0257]

[0258] where, represents the left singular vector, represents the right singular vector, and T represents the transpose;

[0259] Calculate the spectral norm approximation value after iteration:

[0260]

[0261] Step C: Normalize the weight matrix

[0262] Based on the approximate spectral norm of step B, the weight matrix W is normalized:

[0263]

[0264] The normalized weight matrix is replaced with the original weight W, ensuring that the Lipschitz constant of the network layer is 1.

[0265] Because of the above-mentioned embodiments, the following key technical effects are summarized:

[0266] 1. Improve interpolation performance: The technical solution introduces Res2Net modules, CBAM modules, spectral normalization and compression excitation modules into the ResUnet network, which improves the performance of seismic data interpolation. The CBAM module learns the channel and spatial attention weights adaptively to improve the feature expression ability of the network, which can capture the correlation between features in different dimensions, thereby improving the interpolation ability. The Res2Net module improves the multi-scale representation ability at a finer granularity and increases the receptive field of each network layer to improve the interpolation ability. The spectral normalization layer enhances the stability of the network by constraining the spectral norm of the weight matrix, and the compression excitation module enhances the key features by weighting different channel features, thereby improving the interpolation effect.

[0267] 2. Improve network training stability: The traditional ResUnet network may have unstable training problems during training. By adding compression excitation modules and spectral normalization layers to the network, the technical solution enhances the training stability of the network, reduces the risk of gradient explosion, and enables the network to more stably learn the features of seismic data.

[0268] 3. Preserve detail information: The CBAM module, Res2Net module and compression excitation module increase the receptive field when processing feature maps, not only enhancing key features but also preserving image detail information. This makes the interpolated seismic data not only complete but also restores more original data details, which is beneficial for subsequent seismic data analysis and interpretation.

[0269] 4. Effectively handle complex data missing: The present invention uses seismic records generated by wave equation-based forward numerical simulation, combined with seismic records with random missing and complete seismic data, to construct a training set. This method can effectively handle complex missing situations that may occur during actual acquisition, improving the adaptability and practicality of the interpolation method.

[0270] 5.Systematic processing flow: The present application not only includes the design of network structure, but also covers the whole flow from seismic data acquisition, training set construction to network training and interpolation processing. This systematic processing flow guarantees the coherence and consistency from data preparation to the final interpolation result.

[0271] Compared with the prior art, the technical solution has the advantages of realizing more stable and efficient seismic data interpolation through the improved network structure and training flow, while retaining more data details, which is of great significance for improving the accuracy and efficiency of seismic data processing.

[0272] As shown in Figures 4-5 , the interpolated nodes are close to the target data, proving the correctness of the method. The present application uses the improved CBAM-Res2Unet network to perform interpolation processing on seismic data. Based on the CBAM-Res2Unet network, more information can be extracted from the data, avoiding the problem of unstable network training. The interpolation performance of the traditional ResUnet network is significantly improved, achieving the effect of improving the signal-to-noise ratio of seismic data interpolation.

[0273] The above is only a representative embodiment in the many specific application ranges of the present application, and does not constitute any limitation on the protection scope of the present application. Any technical solution formed by transformation or equivalent replacement falls within the scope of protection of the present application.

Claims

1. A CBAM-Res2Unet network-based seismic data interpolation method, characterized in that, The method comprises the following steps: Step 1: obtaining seismic data and constructing a training set and a verification set, wherein the seismic data is a seismic shot record; Step 2: obtaining a preset CBAM-Res2Unet network based on the CBAM-Res2Unet network, the network comprising an encoder module, a decoder module and a jump connection layer, wherein: The encoder module comprises five layers, each layer comprising a convolutional layer, a Res2Net module comprising a compression excitation module and a down-sampling layer in sequence, and a spectral normalization layer is added outside the convolutional layer of the fifth layer; The decoder module comprises five layers, each layer comprising a convolutional layer, a Res2Net module comprising a compression excitation module and an up-sampling layer in sequence; The jump connection layer is provided with a CBAM module between the corresponding layers of the encoder and the decoder, and each CBAM module learns the channel and spatial attention weights adaptively to enhance the feature expression capability; Step 3: training and verifying the CBAM-Res2Unet network based on the training set and the verification set; Step 4: interpolating the seismic data to be interpolated based on the trained CBAM-Res2Unet network; The preset CBAM-Res2Unet network in step 2 comprises an input layer, an encoder module, a decoder module and an output layer connected in sequence, and a jump connection layer for connecting the encoder and the decoder; The encoder module comprises five layers of connected encoder structures, each encoder comprising a convolutional layer, a Res2Net module comprising a compression excitation module and a down-sampling layer in sequence, and a residual connection for directly adding the output of the convolutional layer of each layer to the output of the convolutional layer of the layer, the residual connection comprising a convolutional layer for capturing the feature image, and a spectral normalization layer is added outside the two convolutional layers of the fifth layer, The convolutional layer performs convolutional operation on the input feature map to preserve the detail features and information, and gradually reduces the size of the feature map while preserving important information through feature extraction and residual connection; The Res2Net module performs grouped convolutional operation on the input feature map, improves the multi-scale representation capability at a finer granularity, and increases the receptive field of each network layer; The compression excitation module is added after the second convolutional layer in the Res2Net module and before the residual connection in the module, and is used for weighting the features of different channels to enhance the key features; In the fifth layer, two convolutional layers are added with a spectral normalization layer outside each convolutional layer to enhance the stability of the network; The jump connection layer comprises four CBAM modules, each jump connection comprising a CBAM module, The CBAM module adaptively learns the channel and spatial attention weights to improve the feature expression capability of the network and capture the correlation between features in different dimensions; The decoder module comprises five convolutional layers and up-sampling layers connected in sequence, each decoder comprising a convolutional layer, a Res2Net module comprising a compression excitation module and an up-sampling layer.

2. The CBAM-Res2Unet network-based seismic data interpolation method according to claim 1, characterized in that: The step 1 comprises the following steps: Step 1.1: performing wave equation-based forward numerical simulation to obtain seismic records; Step 1.2: Merge all the seismic records obtained in step 1.1 to obtain a large seismic data set, and generate two copies, wherein copy 1 is randomly missing 30%, 50%, and 70% of the seismic records, and copy 2 is the corresponding complete data, i.e. the target data; Step 1.3: Randomly select multiple pairs of data from copy 1 and copy 2 using a preset size grid to form a training pair set A, and finally use training pair set A as the final training set and validation set.

3. The CBAM-Res2Unet network-based seismic data interpolation method according to claim 1, characterized in that: The operation of the Res2Net module includes: The input feature map is divided into four groups, the convolution output of the previous group is concatenated with the input feature map of the next group, the convolution operation is used for feature extraction, and the receptive field is expanded through hierarchical residual connection; Finally, all group outputs are fused through 1x1 convolution, and the mathematical expression is: wherein, represents the input feature map, represents the output feature map of the previous group of convolutions, represents the feature transformation operation of the branch, represents the weights of the branch, represents the final output.

4. The CBAM-Res2Unet network-based seismic data interpolation method according to claim 1, characterized in that: The operation of the CBAM module includes: Channel attention stage: global maximum pooling and average pooling are performed on the input feature map respectively, and channel weights are generated through shared MLP, and the calculation formula is: in For channel attention function, The activation function is Sigmoid. As feature input, Represents a channel Average pooling operation for each channel represent Maximum pooling operation for each channel. and These are the network parameters in a multilayer perceptron (MLP). Indicates the feature map Global average pooling is performed on each channel. Indicates the feature map Perform global max pooling on each channel; Spatial attention stage: maximum and average pooling are performed on the channel weighted feature map, and spatial weights are generated through 7x7 convolution, and the calculation formula is: The final output is a channel and spatial attention double weighted feature map, is: in, Let be the spatial attention function. Represents a 7x7 convolution kernel, where Features obtained through spatial attention mechanisms For a refined feature map, Represents the input feature map The global average pooling result, Represents the input feature map The result of global max pooling.

5. The CBAM-Res2Unet network-based seismic data interpolation method according to claim 1, characterized in that: The operation of the compression excitation module includes the following steps: Step A: Convolution operation on input feature map to generate a feature map denoted as: wherein, is a convolution transform, wherein denotes the set of real numbers, , denotes the width, denotes the height, , denotes the number of channels, the feature map of the th channel is given by the convolution formula wherein represents the i-th convolution kernel, represents the i-th input covered by the current convolution kernel, represents the i-th output, represents the number of convolution kernels; Step B: middle feature map The global information is obtained by the squeeze operation, and the channel description vector is generated by the global average pooling The specific calculation is as follows: Wherein represents the average value of the channels of the layer, represents the feature value of the channel at position ; Step C: Channel description vector The channel weight vector s is generated by two fully connected layers with the calculation process as follows: wherein , represents a linear layer, represents the channel average value of each layer; Step D: Channel weight vector s is multiplied with the intermediate feature map U channel by channel, and the output is the refined feature map with the calculation as follows: wherein represents the weight value of the cth channel, is the corresponding channel feature map.

6. The CBAM-Res2Unet network-based seismic data interpolation method according to claim 1, characterized in that: A spectral normalization layer is added outside each convolution layer of the fifth layer to limit the spectral norm of the weight matrix of the fifth layer, and the specific steps of spectral normalization processing are as follows: Step 7-1: Apply Lipschitz constraint to the weight matrix of the fifth layer convolution layer The mapping relationship of the convolution layer is represented as wherein represents the input data, represents the output data L The Lipschitz constant is defined as: wherein, is an input feature map, denotes norm representing the calculation of all non-zero input vectors h, the network mapping relationship is represented by weights W: According to the above formula, the Lipschitz constant is determined by the largest singular value of the matrix ​​ Step 7-2: Calculate the spectral norm (maximum singular value) of the weight matrix using power iteration method Initialize random vector and Update the approximation of the largest singular value by iteration: wherein denotes a left singular vector, denotes a right singular vector, denotes a transpose; Calculate the spectral norm approximation after iteration: Step 7-3: Normalize the weight matrix Based on the approximate spectral norm of step 7-2, the weight matrix is normalized as follows: The normalized weight matrix Replacing the original weights , ensuring that the Lipschitz constant of the network layer is 1.

7. A CBAM-Res2Unet network-based seismic data interpolation system, characterized in that, It includes: Acquisition module: obtain seismic data and form a training set and a validation set, wherein the seismic data is a seismic shot record; Network generation module: obtain a preset CBAM-Res2Unet network; Training module: train and validate the CBAM-Res2Unet network based on the training set and the validation set; Interpolation module: interpolate the seismic data to be interpolated based on the trained CBAM-Res2Unet network; The CBAM-Res2Unet network includes an input layer, an encoder module, a decoder module and an output layer connected in turn, and a skip connection layer for connecting the encoder and the decoder; The encoder module includes 5 layers of connected encoder structures, each layer of the encoder includes a convolution layer, a Res2Net module including a compression excitation module, and a down-sampling layer in turn, each layer includes a residual connection for directly adding the input feature map to the output of the convolution layer of the current layer, the residual connection includes a convolution layer for capturing the feature image, and a spectral normalization layer is added outside the two convolution layers of the fifth layer, The convolution layer performs convolution operation on the input feature map to preserve detailed features and information, and gradually reduces the size of the feature map while preserving important information through feature extraction and residual connection; The Res2Net module performs group convolution operation on the input feature map, improves the multi-scale representation capability at a finer granularity, and increases the receptive field of each network layer; The compression excitation module is arranged after the second convolutional layer in the Res2Net module and before the residual connection in the module, and is used for weighting the features of different channels to enhance the key features. In the fifth layer, two convolutional layers are added with a spectral normalization layer respectively, so as to enhance the stability of the network. The skip connection layer comprises: four CBAM modules are included in the skip connection, and each skip connection comprises a CBAM module, The CBAM module learns the channel and spatial attention weights adaptively, so as to improve the feature expression capability of the network, and the correlation between the features in different dimensions can be captured. The decoder module comprises: five convolutional layers and up-sampling layers are connected to form a decoder, and each decoder comprises a convolutional layer, a Res2Net module comprising a compression excitation module and an up-sampling layer.

8. The CBAM-Res2Unet network-based seismic data interpolation system according to claim 7, wherein, The acquisition module specifically implements the following steps: Step 1.1: forward numerical simulation based on wave equation to obtain seismic records; Step 1.2: all seismic records obtained in step 1.1 are combined to obtain a large seismic data set, and two copies are generated, wherein copy 1 is randomly missing 30%, 50% and 70% of the seismic records, and copy 2 is the corresponding complete data, that is, the target data; Step 1.3: copy 1 and copy 2 are randomly selected with a grid of a preset size to form a plurality of pairs of data to form a training pair set A, and finally the training pair set A is used as the final training set and the verification set.

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