Seismic image super-resolution reconstruction method based on Mama

Abstract

The invention relates to a Mama-based seismic image super-resolution reconstruction method, which comprises the step of constructing a local feature extraction module, a global feature extraction module and a high-quality seismic section reconstruction module so as to solve the problem of insufficient resolution caused by high-frequency attenuation and sparse acquisition. According to the invention, a Mama model is introduced, and a novel super-resolution reconstruction network is constructed. The local feature extraction module extracts shallow feature information through a convolutional layer; the global feature extraction module obtains global features through the multi-stage residual state space block; and the high-quality seismic image reconstruction module realizes reconstruction of a high-resolution seismic image through pixel recombination and convolution operation. In addition, a Charbonnier loss function is adopted, the gradient disappearance problem is effectively avoided, and the loss function of traditional Mamba is improved. According to the method, the seismic image resolution can be improved, and meanwhile, the calculation complexity and the time cost are remarkably reduced.

Description

Technical Field

[0001] The invention belongs to the technical field of geophysical exploration and artificial intelligence, and in particular relates to a Mamba-based seismic image super-resolution reconstruction method. Background Art

[0002] Seismic images can identify oil and gas reservoirs, mineral deposits, and potential seismic activity areas, thus providing an important basis for resource exploration and natural disaster prevention. However, due to factors such as high-frequency attenuation, noise interference, and sparse acquisition of observation systems, seismic images often exhibit the disadvantages of low resolution and low signal-to-noise ratio. Therefore, improving the resolution of seismic images has become an important research hotspot in seismic exploration.

[0003] The goal of super-resolution reconstruction of seismic images is to improve the spatial resolution of seismic images, while restoring the amplitude of effective signals, enhancing their main frequencies and expanding bandwidth. Traditional methods include deconvolution, inverse Q filtering, spectral whitening and broadband constrained inversion. The above methods rely on certain prior assumptions, and the contradiction between the actual situation and the prior assumptions may reduce the super-resolution reconstruction performance of traditional methods.

[0004] In recent years, with the rapid development of artificial intelligence technology, researchers have proposed a super-resolution reconstruction method for seismic images based on deep learning. The deep learning method establishes a nonlinear mapping relationship between low-resolution and high-resolution seismic images, and automatically adjusts network parameters to achieve super-resolution reconstruction of seismic images. Since the deep learning-based method does not rely on specific prior information, it often performs better than traditional methods. Li et al. used a deep convolutional neural network (CNN) to simultaneously perform super-resolution and denoising of seismic images, and adopted a composite loss function combining L1 loss and multi-scale structural similarity loss to effectively restore stratigraphic features. Min et al. proposed a dual decoder U-Net (D2UNet) for seismic image super-resolution, which improved the resolution and fidelity of noisy data. Generative adversarial network (GAN) is a deep learning network based on game theory, which mainly improves model performance through adversarial training between generator and discriminator. In recent years, GAN has also been applied to super-resolution reconstruction of seismic images. Sun et al. proposed a new type of GAN that performs random noise suppression and high-resolution reconstruction through residual learning and iterative back projection, improving the visibility of geological features. Oliveira et al. used conditional GAN ​​(CGAN) for seismic data interpolation, significantly improving the resolution and quality of seismic image reconstruction. Transformer is an encoder-decoder network based on the self-attention mechanism, which effectively captures global information by converting images into tags and calculating the cross-correlation between these tags. This method is different from the convolution operation used by CNN and GAN. Because Transformer can capture long-range dependencies, it outperforms CNN and GAN in certain tasks such as denoising, interpolation, and velocity inversion. Park et al. first attempted to apply Transformer to resolution enhancement of seismic images. Their method uses efficient multi-head attention to capture long-range dependencies, and combines the mean square error and structural similarity loss functions to improve the learning ability of the model; this method effectively enhances the structural features of seismic images, improves image resolution, and achieves denoising.

[0005] Although Transformer is regarded as a more promising method than CNN and GAN in super-resolution reconstruction, the self-attention operation leads to a heavy computational burden, especially in the network training stage. This phenomenon is particularly disadvantageous when processing large-scale seismic data. Based on this, it is urgent to develop a method that strikes a balance between super-resolution reconstruction performance and training time cost. Summary of the invention

[0006] The purpose of the present invention is to provide a seismic image super-resolution reconstruction method based on Mamba to solve the problems of long-distance dependency modeling in super-resolution reconstruction and the sharp increase in computational complexity and training time of traditional deep learning methods such as Transformer.

[0007] The objective of the present invention is achieved through the following technical solutions:

[0008] A method for super-resolution reconstruction of seismic images based on Mamba, comprising the following steps:

[0009] S1. Construct the dataset required for training, verification and prediction of seismic image super-resolution reconstruction model;

[0010] S2. Constructing a local feature extraction module of a seismic image super-resolution reconstruction network based on Mamba: the local feature extraction module realizes the extraction of local stratigraphic feature information through cascaded convolutional layers;

[0011] S3. Construct a global feature extraction module of the Mamba-based seismic image super-resolution reconstruction network: the global feature extraction module is composed of two state space groups and a convolution layer cascade, the state space group is used to extract global information in the seismic image, and the convolution layer is used to further extract feature information and adjust the number of channels; each state space group is composed of four multi-level state space blocks and a convolution layer cascade, the multi-level residual state space block is used to capture the long-distance dependency in the feature map, and the convolution layer is used to further improve the global feature representation; finally, the input and output of the global feature extraction module are fused through the jump connection operation to achieve the fusion of local feature information and global feature information;

[0012] S4. Construct a high-quality seismic image reconstruction module based on the Mamba seismic image super-resolution reconstruction network: the high-quality seismic image reconstruction module is composed of two convolutional layers and a pixel reorganization layer in cascade; the first convolutional layer is used to enhance the extracted global and local features, and the second convolutional layer is used to reconstruct high-quality seismic images; the pixel reorganization layer improves the spatial resolution of the seismic image by rearranging the pixels in the seismic image, thereby retaining the detail information;

[0013] S5. Constructing a Mamba-based seismic image super-resolution reconstruction network: the Mamba-based seismic image super-resolution reconstruction network is composed of a cascade of the local feature extraction module, the global feature extraction module and the high-quality seismic image reconstruction module; the local feature extraction module first extracts local stratigraphic features from the input seismic image, then the global feature extraction module obtains global stratigraphic features, and finally the high-quality seismic image reconstruction module reconstructs a high-quality seismic image;

[0014] S6, constructing a loss function for testing the performance of the Mamba-based seismic image super-resolution reconstruction constructed in step S5;

[0015] S7, network model training: initializing the parameters of the Mamba-based seismic image super-resolution reconstruction network formed in step S5, determining the learning rate, optimization function and number of iterations, optimizing the loss function constructed in step S6 according to the verification result of the Mamba-based seismic image super-resolution reconstruction network output formed in step S5, and finally obtaining the optimal network model parameters, and the training ends;

[0016] S8, network model verification: verifying the Mamba-based seismic image super-resolution reconstruction network model obtained after the training in step S7, and if the evaluation index of the verification result meets the set threshold, the Mamba-based seismic image super-resolution reconstruction network model obtained after the training in step S7 is used as the optimal super-resolution reconstruction model; otherwise, returning to step S7, retraining the network model by modifying the training hyperparameters;

[0017] S9. Network model application: input the low-resolution seismic image of the actual survey area into the optimal super-resolution reconstruction network model obtained in step S7 to obtain a high-resolution seismic image.

[0018] Furthermore, step S1 specifically includes the following steps:

[0019] S11, generating a one-dimensional reflectance model, where the reflectance value range is between [-1, 1];

[0020] S12, construct fold structures and folds, and construct fault structures through vertical and planar shear;

[0021] S13, convolving the reflectivity model with a high-frequency Ricker wavelet to obtain a high-frequency seismic profile; then, extracting a plurality of two-dimensional high-resolution seismic profiles from the high-frequency seismic profile as a high-resolution seismic image by center cropping;

[0022] S14, convolving the reflectivity model with a low-frequency Ricker wavelet to obtain a low-frequency seismic profile; then, extracting multiple two-dimensional low-resolution seismic profiles from the low-frequency seismic profile by center cropping; finally, adding random colored noise with a frequency range of 5 to 80 Hz to the two-dimensional low-resolution seismic profile;

[0023] S15. Perform a two-fold downsampling operation on the two-dimensional low-frequency seismic profile with random colored noise to reduce its spatial resolution, and use the downsampled seismic profile as a low-resolution seismic image to complete the process of generating a seismic image.

[0024] Further, step S2 is specifically as follows: the local feature extraction module of the Mamba network for super-resolution reconstruction of seismic images consists of cascaded 3×3 and 5×5 convolutional layers, and uses the LeakyReLU activation function to enhance the nonlinearity of the network model. In this process, the low-resolution seismic image is first input into the local feature extraction module to extract shallow and local features. The output feature map width and height of the module remain unchanged, while the number of channels increases from 1 to 64.

[0025] Further, step S3 is specifically as follows: the global feature extraction module of the Mamba network for super-resolution reconstruction of seismic images is composed of two state space groups and a convolution layer, each state space group is composed of four multi-level residual state space blocks and a convolution layer cascade, so that the global features of the seismic image can be better extracted. The input feature map and the output feature map of the global feature extraction module are fused through residual connection;

[0026] The multi-level residual state space block first applies layer normalization to the output feature map of the local feature extraction module; next, the visual state space module is introduced to capture the long-range dependencies of the seismic image. Then, the output feature map of the visual state space module is layer normalized and combined with the convolution layer to compensate for the local feature information; in addition, a new channel attention module is constructed to further improve the feature extraction capability, and the feature representation is enhanced by assigning greater weights to important features, thereby preventing the interference of redundant features. Finally, the introduction of multi-layer residual connections can effectively promote the interaction between feature information.

[0027] Furthermore, the state space module consists of two main branches. The first branch includes a linear layer, a depthwise separable convolutional layer, a SiLU activation function, a two-dimensional selective scanning module, and layer normalization; the linear layer is used to expand the number of channels of the input standardized features to λC (where λ is the channel expansion factor); the depthwise separable convolutional layer is used to extract local features while maintaining computational efficiency; the SiLU activation function is used to enhance the nonlinearity of the network; the two-dimensional selective scanning module is used to model long-distance dependencies through discrete state space equations; layer normalization is applied to the standardized features to stabilize the training process; the second branch consists of a linear layer and a SiLU activation function, which are used to expand the channels and enhance the nonlinearity of the network; the second branch supplements the features extracted by the first branch, enabling the network to learn the important information of the input features more comprehensively; finally, the output features of the two branches are fused through the Hadamard product, and then the number of channels is adjusted back to C through the linear layer.

[0028] Furthermore, the channel attention module consists of a global maximum pooling layer, a global average pooling layer, a 1×1 convolution layer and a Sigmoid activation function; first, the input feature map is input into the global maximum pooling layer and the global average pooling layer respectively; the output feature maps of the two pooling layers are fused by element-wise addition to reduce the spatial dimension of the feature map to 1 while keeping the number of channels unchanged; then, two 1×1 convolution layers are used to further extract features from the fused feature map; then, the Sigmoid activation function generates the channel attention weight; finally, the generated channel attention weight is multiplied element-by-element with the input feature map of the channel attention module to output the channel attention feature map.

[0029] Furthermore, the two-dimensional selective scanning module first flattens the two-dimensional seismic feature map into a one-dimensional sequence and scans in four directions: from the upper left corner to the lower right corner, from the lower right corner to the upper left corner, from the upper right corner to the lower left corner, and from the lower left corner to the upper right corner; then, the long-distance dependencies in each scanning sequence are captured by discrete state space equations; finally, by summing and reconstructing the results of all scanning sequences, the original two-dimensional structure is effectively restored, thereby achieving accurate reconstruction of the two-dimensional seismic feature map.

[0030] Further, step S4 is specifically as follows: the high-quality seismic image reconstruction module of the Mamba network for super-resolution reconstruction of seismic images is composed of two convolutional layers and a pixel reorganization layer cascaded together; the first convolutional layer is used to further enhance the fused global and local features, and the second convolutional layer is used to reconstruct high-resolution seismic images; the pixel reorganization layer improves the spatial resolution of the seismic image by rearranging pixels in the seismic image, thereby retaining detailed stratigraphic feature information.

[0031] Further, step S6 is specifically as follows: the loss function of the Mamba network for super-resolution reconstruction of seismic images is replaced by the Charbonnier loss function instead of the conventional loss function of Mamba, and its mathematical expression is:

[0032]

[0033] Among them, I SR Represents the reconstructed high-resolution seismic image, I HR represents the high-resolution seismic image in the training set. ε is a constant set to maintain numerical stability and is set to 1×10 -3 .

[0034] Furthermore, in step S8, the network model verification specifically includes the following steps:

[0035] S81, inputting the paired low-resolution and high-resolution seismic images in the validation set into the trained Mamba-based seismic image super-resolution reconstruction network for validation;

[0036] S82, when the evaluation indicators of the verification result: structural similarity and peak signal-to-noise ratio do not meet the set thresholds, continue to return to step S7, adjust and optimize the network model parameters and retrain the Mamba-based seismic image super-resolution reconstruction network;

[0037] S83. When the evaluation indicators of the verification results: structural similarity and peak signal-to-noise ratio meet the set thresholds, the network model training is stopped, and then the trained Mamba-based seismic image super-resolution reconstruction network is applied to the seismic images of the actual survey area.

[0038] Compared with the prior art, the present invention has the following beneficial effects:

[0039] 1. The present invention adopts the Mamba framework to achieve super-resolution reconstruction of seismic images, demonstrating the advantages of Mamba in global modeling;

[0040] 2. The present invention designs a multi-level residual state space module and introduces a visual state space module to effectively extract the global features of seismic images and capture the stratigraphic structure and long-distance dependencies;

[0041] 3. The present invention designs a channel attention module to reduce channel redundancy in the visual state space module and improve the ability to extract effective information by enhancing the weights of important features;

[0042] 4. The present invention adopts the Charbonnier loss function as the loss function of the Mamba-based seismic image super-resolution reconstruction network, aiming to eliminate the gradient vanishing problem, improve detail retention, and reduce artifacts in the reconstructed seismic image. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for use in the embodiments are briefly introduced below. It should be understood that the following drawings only show certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other related drawings can be obtained based on these drawings without creative work.

[0044] Figure 1 Seismic image super-resolution reconstruction network based on Mamba;

[0045] Figure 2 Flow chart of the post-stack seismic profile super-resolution reconstruction method;

[0046] Figure 3 Paired low-resolution seismic images in the test set and high-resolution seismic images reconstructed using the Mamba-based seismic image super-resolution reconstruction method;

[0047] Figure 4 Single-channel waveform comparison curves of paired low-resolution seismic images in the test set and high-resolution seismic images reconstructed using the Mamba-based seismic image super-resolution reconstruction method;

[0048] Figure 5 Actual seismic images of the Netherlands survey area and high-resolution seismic images reconstructed using the Mamba-based seismic image super-resolution reconstruction method;

[0049] Figure 6 Single-channel waveform comparison curves of the actual seismic image of the Netherlands survey area and the high-resolution seismic image reconstructed by the Mamba-based seismic image super-resolution reconstruction method. DETAILED DESCRIPTION

[0050] The present invention will be further described below in conjunction with embodiments:

[0051] The present invention will be further described in detail below in conjunction with the accompanying drawings and embodiments. It is to be understood that the specific embodiments described herein are only used to explain the present invention, rather than to limit the present invention. It should also be noted that, for ease of description, only parts related to the present invention, rather than all structures, are shown in the accompanying drawings.

[0052] It should be noted that similar reference numerals and letters represent similar items in the following drawings, so once an item is defined in one drawing, it does not need to be further defined and explained in the subsequent drawings. At the same time, in the description of the present invention, the terms "first", "second", etc. are only used to distinguish the description and cannot be understood as indicating or implying relative importance.

[0053] The present invention is implemented on the Python language compiler Anaconda platform, the operating system is Ubuntu20.04, the GPU is NVIDIA GeForce RTX 3090, and the deep learning framework is Pytorch. The core is to propose a super-resolution reconstruction method for seismic images based on Mamba. Seismic exploration has a high demand for the resolution of seismic images, especially in the identification of oil and gas reservoirs and mineral deposits and the monitoring of seismic activity. However, due to factors such as high-frequency attenuation, noise interference and sparse acquisition, seismic images usually show low resolution and low signal-to-noise ratio, which limits their application effect. Traditional reconstruction methods such as deconvolution and inverse Q filtering rely on specific prior assumptions and are often limited. In recent years, the rapid development of deep learning technology has provided new solutions for super-resolution reconstruction, especially through methods such as CNN and GAN, which have significantly improved the resolution and signal quality of seismic images. However, as an emerging technology, Transformer performs well in capturing global information with its self-attention mechanism, but its computational burden becomes a challenge when processing large-scale seismic data. Therefore, the present invention designs a super-resolution reconstruction of seismic images based on Mamba, which improves the resolution of seismic images while avoiding the problem of quadratic increase in training time and computational complexity. The invented network is trained, verified and applied by constructing paired low-resolution and high-resolution seismic images. When the evaluation index of the verification result meets the set threshold, the trained super-resolution reconstruction network of seismic images based on Mamba is used as the optimal super-resolution reconstruction network.

[0054] The present invention provides a super-resolution reconstruction method for seismic images based on Mamba, comprising the following steps:

[0055] S1. Construct the dataset required for training, validation and prediction of seismic image super-resolution reconstruction models.

[0056] First, a one-dimensional reflectance model is generated with reflectance values ​​ranging from [-1, 1].

[0057] Secondly, construct fold structures and folds, and construct fault structures through vertical and planar shear.

[0058] Then, the reflectivity model is convolved with a high-frequency Ricker wavelet to obtain a high-frequency seismic profile; subsequently, multiple two-dimensional high-resolution seismic profiles are extracted from the high-frequency seismic profile by center cropping as high-resolution seismic images.

[0059] Next, the reflectivity model is convolved with a low-frequency Ricker wavelet to obtain a low-frequency seismic profile; next, multiple two-dimensional low-resolution seismic profiles are extracted from the low-frequency seismic profile by center cropping, and random colored noise with a frequency range of 5 to 80 Hz is added to the two-dimensional low-resolution seismic profile.

[0060] Finally, a two-fold downsampling operation is performed on the two-dimensional low-frequency seismic profile with random colored noise to reduce its spatial resolution, and the downsampled seismic profile is used as a low-resolution seismic image to complete the process of seismic image generation.

[0061] In this way, the present invention generates 2720 pairs of low-resolution and high-resolution seismic images, of which 70% (1904 pairs) are used for training, 10% (272 pairs) are used for validation, and 20% (544 pairs) are used for testing.

[0062] S2. Construct a local feature extraction module of the Mamba-based seismic image super-resolution reconstruction network, which is mainly used to extract local feature information.

[0063] The local feature extraction module of the Mamba network for super-resolution reconstruction of seismic images consists of cascaded 3×3 and 5×5 convolutional layers, and uses the LeakyReLU activation function to enhance the nonlinearity of the network model, as shown in Figure 1 As shown in Figure 2, the low-resolution seismic image is first input into the local feature extraction module to extract shallow and local features. The width and height of the output feature map of this module remain unchanged, while the number of channels increases from 1 to 64.

[0064] S3. Construct a global feature extraction module for the Mamba-based seismic image super-resolution reconstruction network, which is mainly used to extract global feature information.

[0065] The global feature extraction module of the Mamba network for super-resolution reconstruction of seismic images consists of two state space groups and a convolutional layer. Each state space group consists of four multi-level residual state space blocks and a cascade of convolutional layers, which can better extract the global features of seismic images; the input feature map and output feature map of the global feature extraction module are fused through residual connections.

[0066] The multi-level residual state space block in the global feature extraction module specifically includes:

[0067] The multi-level residual state space block in the global feature extraction module of the Mamba network for super-resolution reconstruction of seismic images first applies layer normalization to the output feature map of the local feature extraction module; next, the visual state space module is introduced to capture the long-range dependencies of the seismic image. Then, the output feature map of the visual state space module is layer normalized and combined with the convolution layer to compensate for the local feature information; in addition, a new channel attention module is constructed to further improve the feature extraction ability, and the feature representation is enhanced by assigning larger weights to important features, thereby preventing the interference of redundant features. Finally, the introduction of multi-layer residual connections can effectively promote the interaction between feature information.

[0068] The visual state space module in the multi-level residual state space block specifically includes:

[0069] Visual state space module in multi-level residual state space block in global feature extraction module of Mamba network for super-resolution reconstruction of seismic images The visual state space module consists of two main branches. The first branch includes a linear layer, a depthwise separable convolutional layer, a SiLU activation function, a two-dimensional selective scanning module, and layer normalization; the linear layer is used to expand the number of channels of the input normalized features to λC (where λ is the channel expansion factor); the depthwise separable convolutional layer is used to extract local features while maintaining computational efficiency; the SiLU activation function is used to enhance the nonlinearity of the network; the two-dimensional selective scanning module is used to model long-range dependencies through discrete state space equations; layer normalization is applied to the normalized features to stabilize the training process; the second branch consists of a linear layer and a SiLU activation function to expand the channels and enhance the nonlinearity of the network; the second branch supplements the features extracted by the first branch, enabling the network to learn the important information of the input features more comprehensively; finally, the output features of the two branches are fused through the Hadamard product, and then the number of channels is adjusted back to C through the linear layer; the output of the visual state space module can be expressed as:

[0070] Y=Linear(V1 e V1)

[0071] Among them, V1 and V2 represent the outputs of the two branches, e represents the Hadamard product operation, and Linear represents the linear layer. The first branch V1 can be expressed as:

[0072] V1=LN(2DSSM(SiLU(DWConv(Linear(X)))))

[0073] Where X represents the input of the visual state space module. The second branch V2 can be expressed as:

[0074] V2=SiLU(Linear(X))

[0075] The channel attention module in the multi-level residual state space block specifically includes:

[0076] The channel attention module in the multi-level residual state space block in the global feature extraction module of the Mamba network for super-resolution reconstruction of seismic images consists of a global maximum pooling layer, a global average pooling layer, a 1×1 convolutional layer and a Sigmoid activation function. First, the input feature map is input into the global maximum pooling layer and the global average pooling layer respectively. The output feature maps of the two pooling layers are fused by element-wise addition to reduce the spatial dimension of the feature map to 1 while keeping the number of channels unchanged. Then, two 1×1 convolutional layers are used to further extract features from the fused feature map. Subsequently, the Sigmoid activation function generates the channel attention weight. Finally, the generated channel attention weight is element-wise multiplied with the input feature map of the channel attention module to output the channel attention feature map. The output of the channel attention module can be expressed as:

[0077]

[0078] Among them, Y CAM and X CAM Represent the output and input of the channel attention module respectively; Conv1 represents a 1×1 convolutional layer, GMP and GAP represent the global maximum pooling layer and the global average pooling layer respectively; represents the element-wise multiplication operation, Represents an element-wise addition operation.

[0079] The two-dimensional selective scanning module in the visual state space module in the multi-level residual state space block in the global feature extraction module specifically includes:

[0080] The 2D selective scanning module of the visual state space module in the multi-level residual state space block in the global feature extraction module of the Mamba network for super-resolution reconstruction of seismic images first flattens the 2D seismic feature map into a one-dimensional sequence and scans it in four directions: from the upper left corner to the lower right corner, from the lower right corner to the upper left corner, from the upper right corner to the lower left corner, and from the lower left corner to the upper right corner; subsequently, the long-range dependencies in each scanning sequence are captured by discrete state space equations; finally, by summing and reconstructing the results of all scanning sequences, the original 2D structure is effectively restored, thereby achieving accurate reconstruction of the 2D seismic feature map.

[0081] S4. Build a high-quality seismic image reconstruction module based on the Mamba seismic image super-resolution reconstruction network, which is mainly used to reconstruct high-resolution seismic images.

[0082] The high-quality seismic image reconstruction module of the Mamba network for super-resolution reconstruction of seismic images consists of two convolutional layers and a pixel reorganization layer in cascade; the first convolutional layer is used to enhance the extracted global and local features, and the second convolutional layer is used to reconstruct high-quality seismic images; the pixel reorganization layer improves the spatial resolution of the seismic image by rearranging the pixels in the seismic image, thereby retaining the detail information.

[0083] S5. Construct a seismic image super-resolution reconstruction network based on Mamba.

[0084] The Mamba network for super-resolution reconstruction of seismic images is composed of a cascade of the local feature extraction module described in step S2, the global feature extraction module described in step S3, and the high-quality seismic image reconstruction module described in step S4; the local stratigraphic features of the input seismic image are first extracted by the local feature extraction module, the global stratigraphic features are then obtained by the global feature extraction module, and finally the high-quality seismic image is reconstructed by the high-quality seismic image reconstruction module.

[0085] S6. Construct a loss function of the Mamba-based seismic image super-resolution reconstruction network, which is mainly used to test the super-resolution reconstruction performance of the invented Mamba-based seismic image super-resolution reconstruction network.

[0086] Specifically, the loss function of the Mamba network for super-resolution reconstruction of seismic images adopts the Charbonnier loss function to replace the conventional loss function of Mamba, and its mathematical expression is:

[0087]

[0088] Among them, I SR Represents the reconstructed high-resolution seismic image, I HR represents the high-resolution seismic image in the training set. ε is a constant set to maintain numerical stability and is set to 1×10 -3 .

[0089] S7, network model training: initializing the parameters of the Mamba-based seismic image super-resolution reconstruction network formed in step S5, determining the learning rate, optimization function and number of iterations, optimizing the loss function constructed in step S6 according to the verification result of the Mamba-based seismic image super-resolution reconstruction network output formed in step S5, and finally obtaining the optimal network model parameters, and the training ends;

[0090] S8, network model verification: verifying the Mamba-based seismic image super-resolution reconstruction network model obtained after the training in step S7, and if the evaluation index of the verification result meets the set threshold, the Mamba-based seismic image super-resolution reconstruction network model obtained after the training in step S7 is used as the optimal super-resolution reconstruction model; otherwise, returning to step S7, retraining the network model by modifying the training hyperparameters;

[0091] Specifically, first, the paired low / high resolution seismic images in the test set are input into the trained Mamba-based seismic image super-resolution reconstruction network for verification. When the evaluation indicators of the verification results: structural similarity (SSIM) and peak signal-to-noise ratio (PSNR) do not meet the set thresholds, the process returns to step S5, and the Mamba-based seismic image super-resolution reconstruction network is retrained after adjusting and optimizing the training hyperparameters. When the evaluation indicators of the verification results: SSIM and PSNR meet the set thresholds, the training is stopped, and then the trained Mamba-based seismic image super-resolution reconstruction network is applied to the seismic images of the actual survey area, such as Figure 2 shown.

[0092] S9. Network model application: Input the seismic image of the actual survey area into the optimal Mamba-based seismic image super-resolution reconstruction network obtained in step S7 to obtain a high-resolution seismic image.

[0093] Example 1

[0094] This embodiment provides an application of super-resolution reconstruction of low-resolution seismic images using a Mamba-based seismic image super-resolution reconstruction method, as follows:

[0095] The present invention inputs the low-resolution seismic images in the generated test set into the trained seismic image super-resolution reconstruction network based on Mamba, and the output result is as follows: Figure 3 As shown in Figure 1, the reconstructed high-resolution seismic image output retains a richer stratigraphic structure, with better continuity of the event axis and clearer fault structure. Figure 4 As shown in FIG. 1 , the single-channel waveform of the high-resolution seismic image reconstructed by the present invention is very similar to that of the high-resolution seismic image in the test set, which proves that the present invention has effective super-resolution reconstruction performance of seismic images. The trained Mamba-based seismic image super-resolution reconstruction network of the present invention is applied to the real seismic images of the Netherlands survey area, as shown in FIG. Figure 5 As shown in FIG. 1 , the high-resolution post-stack seismic profile reconstructed by the present invention can well restore weak signals, and the detailed features of the reconstructed high-resolution image are clearer. Figure 6As shown, the high-resolution seismic image reconstructed by the present invention has the same amplitude value as the single-channel waveform of the seismic image of the Netherlands survey area, and the present invention effectively broadens the frequency band of the signal, further proving that the present invention has superior seismic image super-resolution reconstruction performance.

[0096] Note that the above are only preferred embodiments of the present invention and the technical principles used. Those skilled in the art will understand that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in more detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A super-resolution reconstruction method for seismic images based on Mamba, characterized in that: The following steps are involved: S1. Construct the dataset required for training, verification and prediction of seismic image super-resolution reconstruction model; S2. Constructing a local feature extraction module of a seismic image super-resolution reconstruction network based on Mamba: the local feature extraction module realizes the extraction of local stratigraphic feature information through cascaded convolutional layers; S3. Construct a global feature extraction module of the Mamba-based seismic image super-resolution reconstruction network: the global feature extraction module is composed of two state space groups and a convolution layer cascade, the state space group is used to extract global information in the seismic image, and the convolution layer is used to further extract feature information and adjust the number of channels; each state space group is composed of four multi-level state space blocks and a convolution layer cascade, the multi-level residual state space block is used to capture the long-distance dependency in the feature map, and the convolution layer is used to further improve the global feature representation; finally, the input and output of the global feature extraction module are fused through the jump connection operation to achieve the fusion of local feature information and global feature information; S4. Construct a high-quality seismic image reconstruction module based on the Mamba seismic image super-resolution reconstruction network: the high-quality seismic image reconstruction module is composed of two convolutional layers and a pixel reorganization layer in cascade; the first convolutional layer is used to enhance the extracted global and local features, and the second convolutional layer is used to reconstruct high-quality seismic images; the pixel reorganization layer improves the spatial resolution of the seismic image by rearranging the pixels in the seismic image, thereby retaining the detail information; S5, constructing a Mamba-based seismic image super-resolution reconstruction network: the Mamba-based seismic image super-resolution reconstruction network is composed of a cascade of the local feature extraction module in step S2, the global feature extraction module in step S3, and the high-quality seismic image reconstruction module in step S4; the local feature extraction module first extracts local stratigraphic features from the input seismic image, and then the global feature extraction module obtains global stratigraphic features, and finally, the high-quality seismic image reconstruction module reconstructs a high-quality seismic image; S6, constructing a loss function for testing the performance of the Mamba-based seismic image super-resolution reconstruction constructed in step S5; S7, network model training: initializing the parameters of the Mamba-based seismic image super-resolution reconstruction network formed in step S5, determining the learning rate, optimization function and number of iterations, optimizing the loss function constructed in step S6 according to the verification result of the Mamba-based seismic image super-resolution reconstruction network output formed in step S5, and finally obtaining the optimal network model parameters, and the training ends; S8, network model verification: verifying the Mamba-based seismic image super-resolution reconstruction network model obtained after the training in step S7, and if the evaluation index of the verification result meets the set threshold, the Mamba-based seismic image super-resolution reconstruction network model obtained after the training in step S7 is used as the optimal super-resolution reconstruction model; otherwise, returning to step S7, retraining the network model by modifying the training hyperparameters; S9. Network model application: input the low-resolution seismic image of the actual survey area into the optimal super-resolution reconstruction network model obtained in step S7 to obtain a high-resolution seismic image.

2. The method for super-resolution reconstruction of seismic images based on Mamba according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11, generating a one-dimensional reflectance model, where the reflectance value range is between [-1, 1]; S12, construct fold structures and folds, and construct fault structures through vertical and planar shear; S13, convolving the reflectivity model with a high-frequency Ricker wavelet to obtain a high-frequency seismic profile; then, extracting a plurality of two-dimensional high-resolution seismic profiles from the high-frequency seismic profile as a high-resolution seismic image by center cropping; S14, convolving the reflectivity model with a low-frequency Ricker wavelet to obtain a low-frequency seismic profile; then, extracting multiple two-dimensional low-resolution seismic profiles from the low-frequency seismic profile by center cropping; finally, adding random colored noise with a frequency range of 5 to 80 Hz to the two-dimensional low-resolution seismic profile; S15. Perform a two-fold downsampling operation on the two-dimensional low-frequency seismic profile with random colored noise to reduce its spatial resolution, and use the downsampled seismic profile as a low-resolution seismic image to complete the process of generating a seismic image.

3. The method for super-resolution reconstruction of seismic images based on Mamba according to claim 1, characterized in that: Step S2, specifically: the local feature extraction module of the Mamba network for super-resolution reconstruction of seismic images consists of cascaded 3×3 and 5×5 convolutional layers, and uses the LeakyReLU activation function to enhance the nonlinearity of the network model; in this process, the low-resolution seismic image is first input into the local feature extraction module to extract shallow and local features; the output feature map width and height of the module remain unchanged, while the number of channels increases from 1 to 64.

4. The method for super-resolution reconstruction of seismic images based on Mamba according to claim 1, characterized in that: Step S3, specifically: the global feature extraction module of the Mamba network for super-resolution reconstruction of seismic images consists of two state space groups and a convolution layer, and each state space group consists of four multi-level residual state space blocks and a convolution layer cascaded; The input feature map and output feature map of the global feature extraction module are fused through residual connection; The multi-level residual state space block first applies layer normalization to the output feature map of the local feature extraction module; Next, a visual state space module is introduced to capture the long-range dependencies of seismic images. Then, the output feature maps of the visual state space module are layer-normalized and combined with convolutional layers to compensate for local feature information. In addition, a novel channel attention module is constructed to further improve the feature extraction capability and enhance the feature representation by assigning larger weights to important features, thereby preventing the interference of redundant features. Finally, the introduction of multi-layer residual connections can effectively promote the interaction between feature information.

5. The method for super-resolution reconstruction of seismic images based on Mamba according to claim 4, characterized in that: The visual state space module consists of two main branches; the first branch includes a linear layer, a depth-separable convolution layer, a SiLU activation function, a two-dimensional selective scanning module and layer normalization; the linear layer is used to expand the number of channels of the input standardized features to λC (where λ is the channel expansion factor); the depth-separable convolution layer is used to extract local features while maintaining computational efficiency; the SiLU activation function is used to enhance the nonlinearity of the network; the two-dimensional selective scanning module is used to model long-distance dependencies through discrete state space equations; layer normalization is applied to standardized features to stabilize the training process; The second branch consists of a linear layer and a SiLU activation function, which is used to expand the channels and enhance the nonlinearity of the network. The second branch supplements the features extracted by the first branch, enabling the network to learn the important information of the input features more comprehensively. Finally, the output features of the two branches are fused through the Hadamard product, and then the number of channels is adjusted back to C through a linear layer.

6. The method for super-resolution reconstruction of seismic images based on Mamba according to claim 4, characterized in that: The channel attention module consists of a global maximum pooling layer, a global average pooling layer, a 1×1 convolution layer and a sigmoid activation function; first, the input feature map is input into the global maximum pooling layer and the global average pooling layer respectively; the output feature maps of the two pooling layers are fused by element-wise addition to reduce the spatial dimension of the feature map to 1 while keeping the number of channels unchanged; then, two 1×1 convolution layers are used to further extract features from the fused feature map; Subsequently, the Sigmoid activation function generates the channel attention weights; finally, the generated channel attention weights are multiplied element-wise with the input feature map of the channel attention module to output the channel attention feature map.

7. The method for super-resolution reconstruction of seismic images based on Mamba according to claim 5, characterized in that: The two-dimensional selective scanning module first flattens the two-dimensional seismic characteristic map into a one-dimensional sequence, and scans in four directions: from the upper left corner to the lower right corner, from the lower right corner to the upper left corner, from the upper right corner to the lower left corner, and from the lower left corner to the upper right corner; Subsequently, the long-range dependencies in each scanning sequence are captured by discrete state-space equations; finally, the original two-dimensional structure is effectively restored by summing and reconstructing the results of all scanning sequences, thereby achieving accurate reconstruction of the two-dimensional seismic feature map.

8. The method for super-resolution reconstruction of seismic images based on Mamba according to claim 1, characterized in that: Step S4, specifically: the high-quality seismic image reconstruction module of the Mamba network for super-resolution reconstruction of seismic images is composed of two convolutional layers and a pixel reorganization layer cascaded; the first convolutional layer is used to further enhance the fused global and local features, and the second convolutional layer is used to reconstruct high-resolution seismic images; the pixel reorganization layer improves the spatial resolution of the seismic image by rearranging the pixels in the seismic image, thereby retaining the detailed stratigraphic feature information.

9. The method for super-resolution reconstruction of seismic images based on Mamba according to claim 1, characterized in that: In step S6, the loss function uses the Charbonnier loss function to replace the conventional loss function of Mamba, and its mathematical expression is: Among them, I SR Represents the reconstructed high-resolution seismic image, I HR represents the high-resolution seismic image in the training set. ε is a constant set to maintain numerical stability and is set to 1×10 -3 .

10. The method for super-resolution reconstruction of seismic images based on Mamba according to claim 1, characterized in that: In step S8, the network model verification specifically includes the following steps: S81, inputting the paired low-resolution and high-resolution seismic images in the validation set into the trained Mamba-based seismic image super-resolution reconstruction network for validation; S82, when the evaluation indicators of the verification result: structural similarity and peak signal-to-noise ratio do not meet the set thresholds, continue to return to step S7, adjust and optimize the network model parameters and retrain the Mamba-based seismic image super-resolution reconstruction network; S83. When the evaluation indicators of the verification results: structural similarity and peak signal-to-noise ratio meet the set thresholds, the network model training is stopped, and then the trained Mamba-based seismic image super-resolution reconstruction network is applied to the seismic images of the actual survey area.

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