A Mamba-based super-resolution reconstruction method for seismic images

Abstract

This invention relates to a Mamba-based super-resolution reconstruction method for seismic images, comprising a local feature extraction module, a global feature extraction module, and a high-quality seismic profile reconstruction module to address the insufficient resolution caused by high-frequency attenuation and sparse acquisition. This invention introduces the Mamba model to construct a novel super-resolution reconstruction network. The local feature extraction module extracts shallow feature information through convolutional layers; the global feature extraction module obtains global features through multi-level residual state space blocks; and the high-quality seismic image reconstruction module reconstructs high-resolution seismic images through pixel recombination and convolutional operations. Furthermore, this invention employs the Charbonnier loss function to effectively avoid the gradient vanishing problem and improves upon the traditional Mamba loss function. This invention can significantly reduce computational complexity and time cost while improving seismic image resolution.

Description

Technical Field

[0001] This invention belongs to the fields of geophysical exploration and artificial intelligence technology, specifically relating to a super-resolution reconstruction method for seismic images based on Mamba. Background Technology

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

[0003] The goal of seismic image super-resolution reconstruction is to improve the spatial resolution of seismic images while restoring the amplitude of the effective signal, enhancing its dominant frequency, and expanding its bandwidth. Traditional methods include deconvolution, inverse Q-filtering, spectral whitening, and broadband constrained inversion. These methods rely on certain prior assumptions, and discrepancies between actual conditions and these assumptions can degrade the super-resolution reconstruction performance of traditional methods.

[0004] In recent years, with the rapid development of artificial intelligence technology, researchers have proposed seismic image super-resolution reconstruction methods based on deep learning. Deep learning methods establish a nonlinear mapping relationship between low-resolution and high-resolution seismic images, automatically adjusting network parameters to achieve super-resolution reconstruction. Because deep learning-based methods do not rely on specific prior information, they often exhibit superior performance compared to traditional methods. Li et al. used a deep convolutional neural network (CNN) for both seismic image super-resolution and denoising, employing a composite loss function combining L1 loss and multi-scale structural similarity loss to effectively recover stratigraphic features. Min et al. proposed a dual-decoder U-Net (D2UNet) for seismic image super-resolution, improving the resolution and fidelity of noisy data. Generative Adversarial Networks (GANs) are deep learning networks based on game theory, primarily improving model performance through adversarial training between the generator and discriminator. In recent years, GANs have also been applied to seismic image super-resolution reconstruction. Sun et al. proposed a novel GAN ​​that uses residual learning and iterative backprojection for random noise suppression and high-resolution reconstruction, improving the visibility of geological features. Oliveira et al. used Conditional GAN ​​(CGAN) for seismic data interpolation, significantly improving resolution and seismic image reconstruction quality. Transformer is an encoder-decoder network based on a self-attention mechanism that effectively captures global information by transforming images into labels and calculating cross-correlation between these labels. This approach differs from the convolutional operations used by CNNs and GANs. Because Transformer can capture long-range dependencies, it outperforms CNNs and GANs in certain tasks, such as denoising, interpolation, and velocity inversion. Park et al. were the first to apply Transformer to seismic image resolution enhancement. Their method utilizes efficient multi-head attention to capture long-range dependencies and combines mean squared error and structural similarity loss functions to improve the model's learning ability; this method effectively enhances the structural features of seismic images, improves image resolution, and achieves denoising.

[0005] Although the Transformer is considered a more promising method than CNNs and GANs for super-resolution reconstruction, the computational burden caused by its self-attention operation is significant, especially during network training. This is particularly detrimental when dealing with large-scale seismic data. Therefore, there is an urgent need 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 this invention is to provide a Mamba-based method for super-resolution reconstruction of seismic images, in order 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 this invention is achieved through the following technical solution:

[0008] A Mamba-based super-resolution reconstruction method for seismic images includes the following steps:

[0009] S1. Construct the dataset required for training, validating, and predicting the earthquake image super-resolution reconstruction model;

[0010] S2. Construct a local feature extraction module for a Mamba-based seismic image super-resolution reconstruction network: The local feature extraction module extracts local stratigraphic feature information through cascaded convolutional layers.

[0011] S3. Constructing a global feature extraction module for a Mamba-based seismic image super-resolution reconstruction network: The global feature extraction module consists of two state space groups and a convolutional layer cascaded together. The state space groups are used to extract global information from the seismic image, and the convolutional layer is used to further extract feature information and adjust the number of channels. Each state space group consists of four multi-level state space blocks and a convolutional layer cascaded together. The multi-level residual state space blocks are used to capture long-distance dependencies in the feature map, and the convolutional layer is used to further improve the global feature representation. Finally, the input and output of the global feature extraction module are fused through a skip connection operation to achieve the fusion of local and global feature information.

[0012] S4. Construct a high-quality seismic image reconstruction module based on the Mamba-based seismic image super-resolution reconstruction network: The high-quality seismic image reconstruction module consists of two convolutional layers and a pixel reconstruction layer cascaded together; 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 reconstruction layer improves the spatial resolution of the seismic image by rearranging the pixels in the seismic image, thereby preserving detailed 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 the local feature extraction module, the global feature extraction module, and the high-quality seismic image reconstruction module cascaded together; the input seismic image is first processed by the local feature extraction module to extract local stratigraphic features, then by the global feature extraction module to obtain global stratigraphic features, and finally by the high-quality seismic image reconstruction module to reconstruct a high-quality seismic image;

[0014] S6. Construct a loss function to test the performance of the Mamba-based seismic image super-resolution reconstruction constructed in step S5.

[0015] S7. Network Model Training: Initialize the parameters of the Mamba-based seismic image super-resolution reconstruction network composed in step S5, determine the learning rate, optimization function and number of iterations, optimize the loss function constructed in step S6 based on the verification results output by the Mamba-based seismic image super-resolution reconstruction network composed in step S5, and finally obtain the optimal network model parameters. Training ends.

[0016] S8. Network Model Validation: Validate the Mamba-based seismic image super-resolution reconstruction network model obtained after training in step S7. If the evaluation index of the validation result meets the set threshold, the Mamba-based seismic image super-resolution reconstruction network model obtained after training in step S7 is taken as the optimal super-resolution reconstruction model; otherwise, return to step S7 and retrain the network model by modifying the training hyperparameters.

[0017] S9. Application of Network Model: Input the low-resolution seismic images of the actual survey area into the optimal super-resolution reconstruction network model obtained in step S7 to obtain high-resolution seismic images.

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

[0019] S11. Generate a one-dimensional reflectance model with reflectance values ​​ranging from [-1, 1].

[0020] S12. Construct folded structures and folds, and construct fault structures through vertical and planar shearing;

[0021] S13. Use the high-frequency Ricker wavelet convolutional reflectivity model to obtain high-frequency seismic profiles; then, extract multiple two-dimensional high-resolution seismic profiles from the high-frequency seismic profiles as high-resolution seismic images by center cropping.

[0022] S14. Use the low-frequency Ricker wavelet convolutional reflectivity model to obtain low-frequency seismic profiles; then, extract multiple two-dimensional low-resolution seismic profiles from the low-frequency seismic profiles by center clipping; finally, add random color noise with a frequency range of 5 to 80 Hz to the two-dimensional low-resolution seismic profiles.

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

[0024] Further, step S2 specifically involves the following: the local feature extraction module of the Mamba network used for seismic image super-resolution reconstruction 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 width and height of the output feature map of this module remain unchanged, while the number of channels increases from 1 to 64.

[0025] Further, step S3 specifically involves the following: The global feature extraction module of the Mamba network used for seismic image super-resolution reconstruction consists of two state space groups and one convolutional layer. Each state space group comprises four multi-level residual state space blocks and one cascaded convolutional layer, which allows for better extraction of global features from the seismic image. The input and output feature maps of the global feature extraction module are fused through residual connections.

[0026] 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 long-range dependencies in the seismic image. Then, the output feature map of the visual state space module is layer normalized and combined with a convolutional layer to compensate for local feature information. In addition, a novel channel attention module is constructed to further improve feature extraction capabilities by assigning greater weights to important features to enhance feature representation and prevent interference from redundant features. Finally, the introduction of multi-layer residual connections effectively promotes 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 scan 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 scan module is used to model long-range dependencies through discrete state space equations. Layer normalization is applied to normalize features to stabilize the training process. The second branch consists of a linear layer and a SiLU activation function, used to expand the channels and enhance the nonlinearity of the network. The second branch complements the features extracted by the first branch, enabling the network to learn more comprehensive information about the input features. Finally, the output features of the two branches are fused by a Hadamard product, and then the number of channels is adjusted back to C by a linear layer.

[0028] Furthermore, the channel attention module consists of a global max pooling layer, a global average pooling layer, a 1×1 convolutional layer, and a sigmoid activation function. First, the input feature map is fed into the global max pooling layer and the global average pooling layer, respectively. The output feature maps of these two pooling layers are fused by element-wise addition, reducing the spatial dimension of the feature map to 1 while keeping the number of channels unchanged. Next, two 1×1 convolutional layers are used to further extract features from the fused feature map. Subsequently, the sigmoid activation function generates 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.

[0029] Furthermore, the two-dimensional selective scanning module first flattens the two-dimensional 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. Then, it captures the long-distance dependencies in each scanning sequence through 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 specifically involves the following: the high-quality seismic image reconstruction module of the Mamba network used for super-resolution reconstruction of seismic images consists of two convolutional layers and a pixel reconstruction 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 reconstruction layer improves the spatial resolution of seismic images by rearranging the pixels in the seismic images, thereby preserving detailed stratigraphic feature information.

[0031] Further, step S6 specifically involves: replacing the conventional Mamba loss function with the Charbonnier loss function for the Mamba network used for seismic image super-resolution reconstruction, and its mathematical expression is as follows:

[0032]

[0033] Among them, I SR Representing reconstructed high-resolution seismic images, I HR This represents high-resolution seismic images from the training set. ε is a constant set to maintain numerical stability; ε is set to 1 × 10⁻⁶. -3 .

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

[0035] S81. Input the paired low-resolution-high-resolution seismic images from 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 results, such as structural similarity and peak signal-to-noise ratio, do not meet the set thresholds, return to step S7, adjust and optimize the network model parameters, and retrain the Mamba-based earthquake image super-resolution reconstruction network.

[0037] S83. When the evaluation indicators of the verification results, namely 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 beneficial effects of the present invention are:

[0039] 1. This invention uses the Mamba framework to achieve super-resolution reconstruction of seismic images, demonstrating Mamba's advantages in global modeling;

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

[0041] 3. This invention designs a channel attention module to reduce channel redundancy in the visual state space module and enhances the ability to extract effective information by increasing the weight of important features.

[0042] 4. This invention uses the Charbonnier loss function as the loss function for the Mamba-based seismic image super-resolution reconstruction network, aiming to eliminate the gradient vanishing problem, improve detail preservation, and reduce artifacts in the reconstructed seismic images. Attached Figure Description

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

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

[0045] Figure 2 Flowchart of the super-resolution reconstruction method for post-stack seismic profiles;

[0046] Figure 3 The test set includes paired low-to-high-resolution seismic images and high-resolution seismic images reconstructed using a Mamba-based seismic image super-resolution reconstruction method;

[0047] Figure 4 The test set shows the single-channel waveform comparison curves of paired low-to-high-resolution seismic images and high-resolution seismic images reconstructed by 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 Comparison curves of single-channel waveforms between actual seismic images of the Netherlands survey area and high-resolution seismic images reconstructed using the Mamba-based seismic image super-resolution reconstruction method. Detailed Implementation

[0050] The present invention will be further described below with reference to embodiments:

[0051] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0052] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0053] This invention was implemented on the Anaconda platform using the Python compiler, with Ubuntu 20.04 as the operating system, an NVIDIA GeForce RTX 3090 GPU, and PyTorch as the deep learning framework. Its core is the proposal of a Mamba-based super-resolution reconstruction method for seismic images. Seismic exploration demands high resolution from seismic images, particularly for identifying oil and gas reservoirs and mineral deposits, as well as for monitoring seismic activity. However, due to factors such as high-frequency attenuation, noise interference, and sparse acquisition, seismic images typically exhibit low resolution and low signal-to-noise ratio, limiting their application effectiveness. 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 CNNs and GANs, which have significantly improved the resolution and signal quality of seismic images. However, while Transformer, as an emerging technology, excels in capturing global information with its self-attention mechanism, its computational burden becomes a challenge when processing large-scale seismic data. Therefore, this invention designs a Mamba-based seismic image super-resolution reconstruction method that improves seismic image resolution while avoiding a secondary increase in training time and computational complexity. The invented network is trained, validated, and applied by constructing pairs of low-resolution and high-resolution seismic images. When the evaluation index of the validation results meets the set threshold, the trained Mamba-based seismic image super-resolution reconstruction network is selected as the optimal super-resolution reconstruction network.

[0054] This invention relates to a seismic image super-resolution reconstruction method based on Mamba, comprising the following steps:

[0055] S1. Construct the dataset required for training, validating, and predicting the super-resolution reconstruction model of seismic images.

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

[0057] Secondly, construct folded structures and folds, and construct fault structures through vertical and planar shearing.

[0058] Then, a high-frequency seismic profile was obtained using a high-frequency Ricker wavelet convolutional reflectivity model; subsequently, multiple two-dimensional high-resolution seismic profiles were extracted from the high-frequency seismic profiles by center cropping, which were then used as high-resolution seismic images.

[0059] Next, a low-frequency Recker wavelet convolutional reflectivity model is used to obtain low-frequency seismic profiles. Then, multiple two-dimensional low-resolution seismic profiles are extracted from the low-frequency seismic profiles by center clipping, and random color noise with a frequency range of 5 to 80 Hz is added to the two-dimensional low-resolution seismic profiles.

[0060] Finally, a 2x downsampling operation is performed on the two-dimensional low-frequency seismic profile with random color noise to reduce its spatial resolution, and the downsampled seismic profile is used as a low-resolution seismic image to complete the seismic image generation process.

[0061] In this way, the present invention generated 2,720 pairs of low-resolution and high-resolution seismic images, of which 70% (1,904 pairs) were used for training, 10% (272 pairs) for validation, and 20% (544 pairs) for testing.

[0062] S2. Construct a local feature extraction module for a Mamba-based earthquake image super-resolution reconstruction network, mainly used for extracting local feature information.

[0063] The local feature extraction module of the Mamba network used 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, such as... Figure 1 As shown. In this process, 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 a Mamba-based seismic image super-resolution reconstruction network, which is mainly used for extracting global feature information.

[0065] The global feature extraction module of the Mamba network used for super-resolution reconstruction of seismic images consists of two state space groups and one convolutional layer. Each state space group consists of four multi-level residual state space blocks and one convolutional layer cascaded together, which can better extract 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 seismic image super-resolution reconstruction 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 long-range dependencies in the seismic image. Then, the output feature map of the visual state space module is 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 feature extraction capabilities by assigning greater weights to important features to enhance feature representation and prevent interference from redundant features. Finally, multi-layer residual connections are introduced to effectively promote the interaction between feature information.

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

[0069] The visual state space module within the multi-level residual state space block of the global feature extraction module of the Mamba network for super-resolution reconstruction of seismic images consists of two main branches. The first branch includes a linear layer, a depthwise separable convolutional layer, a SiLU activation function, a 2D selective scan module, and layer normalization. The linear layer expands the number of channels of the input normalized features to λC (where λ is the channel expansion factor). The depthwise separable convolutional layer extracts local features while maintaining computational efficiency. The SiLU activation function enhances the network's nonlinearity. The 2D selective scan module models long-range dependencies through discrete state space equations. Layer normalization is applied to normalize the features to stabilize the training process. The second branch, composed of a linear layer and a SiLU activation function, expands the channels and enhances the network's nonlinearity. The second branch complements the features extracted by the first branch, enabling the network to learn more comprehensive information about the input features. Finally, the output features of the two branches are fused through a Hadamard product, and then the number of channels is adjusted back to C through a linear layer. The output of the visual state space module can be represented as:

[0070] Y = Linear(V1 e V1)

[0071] Here, 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 represented as:

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

[0073] Here, X represents the input to the visual state space module. The second branch V2 can be represented 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 of the global feature extraction module of the Mamba network for super-resolution reconstruction of seismic images consists of a global max pooling layer, a global average pooling layer, a 1×1 convolutional layer, and a sigmoid activation function. First, the input feature map is fed into the global max pooling layer and the global average pooling layer respectively. The output feature maps of these two pooling layers are fused by element-wise addition and Euclidean algorithm to reduce the spatial dimension of the feature map to 1 while maintaining the number of channels. Next, two 1×1 convolutional layers are used to further extract features from the fused feature map. Subsequently, the sigmoid activation function generates 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. The output of the channel attention module can be expressed as:

[0077]

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

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

[0080] The Mamba network used for super-resolution reconstruction of seismic images employs a global feature extraction module, which uses a multi-level residual state space block within a visual state space module. The two-dimensional selective scanning module first flattens the two-dimensional seismic feature map into a one-dimensional sequence and scans it in four directions: from top left to bottom right, from bottom right to top left, from top right to bottom left, and from bottom left to top right. Then, it captures long-range dependencies in each scan sequence using discrete state space equations. Finally, by summing and reconstructing the results of all scan sequences, the original two-dimensional structure is effectively restored, thus achieving accurate reconstruction of the two-dimensional seismic feature map.

[0081] S4. Construct a high-quality seismic image reconstruction module based on the Mamba-based seismic image super-resolution reconstruction network, mainly used for reconstructing 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 reconstruction layer cascaded together. 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 reconstruction layer improves the spatial resolution of seismic images by rearranging the pixels in the seismic image, thereby preserving detailed information.

[0083] S5. Construct a Mamba-based super-resolution reconstruction network for seismic images.

[0084] The Mamba network used for super-resolution reconstruction of seismic images is composed of a cascaded local feature extraction module described in step S2, a global feature extraction module described in step S3, and a high-quality seismic image reconstruction module described in step S4. The input seismic image is first processed by the local feature extraction module to extract local stratigraphic features, then by the global feature extraction module to obtain global stratigraphic features, and finally by the high-quality seismic image reconstruction module to reconstruct a high-quality seismic image.

[0085] S6. Construct a loss function for the Mamba-based seismic image super-resolution reconstruction network, 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 used for seismic image super-resolution reconstruction adopts the Charbonnier loss function instead of the conventional Mamba loss function, and its mathematical expression is as follows:

[0087]

[0088] Among them, I SR Representing reconstructed high-resolution seismic images, I HR This represents high-resolution seismic images from the training set. ε is a constant set to maintain numerical stability; ε is set to 1 × 10⁻⁶. -3 .

[0089] S7. Network Model Training: Initialize the parameters of the Mamba-based seismic image super-resolution reconstruction network composed in step S5, determine the learning rate, optimization function and number of iterations, optimize the loss function constructed in step S6 based on the verification results output by the Mamba-based seismic image super-resolution reconstruction network composed in step S5, and finally obtain the optimal network model parameters. Training ends.

[0090] S8. Network Model Validation: Validate the Mamba-based seismic image super-resolution reconstruction network model obtained after training in step S7. If the evaluation index of the validation result meets the set threshold, the Mamba-based seismic image super-resolution reconstruction network model obtained after training in step S7 is taken as the optimal super-resolution reconstruction model; otherwise, return to step S7 and retrain the network model by modifying the training hyperparameters.

[0091] Specifically, firstly, paired low / high-resolution seismic images from the test set are input into the trained Mamba-based seismic image super-resolution reconstruction network for validation. If the validation results' evaluation metrics—structural similarity (SSIM) and peak signal-to-noise ratio (PSNR)—do not meet the set thresholds, the process returns to step S5, where the training hyperparameters are adjusted and optimized before retraining the Mamba-based seismic image super-resolution reconstruction network. When the validation results' evaluation metrics—SSIM and PSNR—meet the set thresholds, training stops. Then, the trained Mamba-based seismic image super-resolution reconstruction network is applied to seismic images in the actual survey area, such as... Figure 2 As shown.

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

[0093] Example 1

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

[0095] This invention inputs low-resolution seismic images from the generated test set into the trained Mamba-based seismic image super-resolution reconstruction network, and outputs the following results: Figure 3 As shown, the output reconstructed high-resolution seismic image retains richer stratigraphic structure, better continuity of phase axes, and clearer fault structure. Figure 4 As shown, the single-channel waveforms of the reconstructed high-resolution seismic images are very similar to those of the high-resolution seismic images in the test set, proving that the present invention has effective seismic image super-resolution reconstruction performance. The trained Mamba-based seismic image super-resolution reconstruction network of the present invention was applied to real seismic images from the Netherlands survey area, as shown... Figure 5 As shown, the high-resolution post-stack seismic profile reconstructed using this invention effectively recovers weak signals, and the detailed features of the reconstructed high-resolution image are clearer. Figure 6As shown, the high-resolution seismic image reconstructed by this invention has the same amplitude value of a single-channel waveform as the seismic image of the Netherlands survey area. Furthermore, this invention effectively broadens the signal bandwidth, further demonstrating that this invention has superior seismic image super-resolution reconstruction performance.

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

Claims

1. A method for super-resolution reconstruction of seismic images based on Mamba, characterized in that, Includes the following steps: S1. Construct the dataset required for training, validating, and predicting the earthquake image super-resolution reconstruction model; S2. Construct a local feature extraction module for a Mamba-based seismic image super-resolution reconstruction network: The local feature extraction module extracts local stratigraphic feature information through cascaded convolutional layers. S3. Constructing a global feature extraction module for a Mamba-based seismic image super-resolution reconstruction network: The global feature extraction module consists of two state space groups and a convolutional layer cascaded together. The state space groups are used to extract global information from the seismic image, and the convolutional layer is used to further extract feature information and adjust the number of channels. Each state space group consists of four multi-level state space blocks and a convolutional layer cascaded together. The multi-level residual state space blocks are used to capture long-distance dependencies in the feature map, and the convolutional layer is used to further improve the global feature representation. Finally, the input and output of the global feature extraction module are fused through a skip connection operation to achieve the fusion of local and global feature information. S4. Construct a high-quality seismic image reconstruction module based on the Mamba-based seismic image super-resolution reconstruction network: The high-quality seismic image reconstruction module consists of two convolutional layers and a pixel reconstruction layer cascaded together; 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 reconstruction layer improves the spatial resolution of the seismic image by rearranging the pixels in the seismic image, thereby preserving detailed information. S5. Constructing a Mamba-based seismic image super-resolution reconstruction network: The Mamba-based seismic image super-resolution reconstruction network is composed 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, cascaded together; the input seismic image is first processed by the local feature extraction module to extract local stratigraphic features, then by the global feature extraction module to obtain global stratigraphic features, and finally by the high-quality seismic image reconstruction module to reconstruct a high-quality seismic image; S6. Construct a loss function to test the performance of the Mamba-based seismic image super-resolution reconstruction constructed in step S5. S7. Network Model Training: Initialize the parameters of the Mamba-based seismic image super-resolution reconstruction network composed in step S5, determine the learning rate, optimization function and number of iterations, optimize the loss function constructed in step S6 based on the verification results output by the Mamba-based seismic image super-resolution reconstruction network composed in step S5, and finally obtain the optimal network model parameters. Training ends. S8. Network Model Validation: Validate the Mamba-based seismic image super-resolution reconstruction network model obtained after training in step S7. If the evaluation index of the validation result meets the set threshold, the Mamba-based seismic image super-resolution reconstruction network model obtained after training in step S7 is taken as the optimal super-resolution reconstruction model; otherwise, return to step S7 and retrain the network model by modifying the training hyperparameters. S9. Application of Network Model: Input the low-resolution seismic images of the actual survey area into the optimal super-resolution reconstruction network model obtained in step S7 to obtain high-resolution seismic images.

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. Generate a one-dimensional reflectance model with reflectance values ​​ranging from [-1, 1]. S12. Construct folded structures and folds, and construct fault structures through vertical and planar shearing; S13. Use the high-frequency Ricker wavelet convolutional reflectivity model to obtain high-frequency seismic profiles; then, extract multiple two-dimensional high-resolution seismic profiles from the high-frequency seismic profiles as high-resolution seismic images by center cropping. S14. Use the low-frequency Ricker wavelet convolutional reflectivity model to obtain low-frequency seismic profiles; then, extract multiple two-dimensional low-resolution seismic profiles from the low-frequency seismic profiles by center clipping; finally, add random color noise with a frequency range of 5 to 80 Hz to the two-dimensional low-resolution seismic profiles. S15. Perform a double downsampling operation on the two-dimensional low-frequency seismic profile with random color noise to reduce its spatial resolution, and use the downsampled seismic profile as a low-resolution seismic image to complete the process of generating seismic images.

3. The method for super-resolution reconstruction of seismic images based on Mamba according to claim 1, characterized in that, Step S2 is as follows: The local feature extraction module of the Mamba network used 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 width and height of the output feature map of this 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 is as follows: The global feature extraction module of the Mamba network used for super-resolution reconstruction of seismic images consists of two state space groups and one convolutional layer. Each state space group consists of four multi-level residual state space blocks and one cascaded convolutional layer. The input and output feature maps of the global feature extraction module are fused through residual connections; 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 long-range dependencies in seismic images. Then, the output feature map of the visual state space module is layer-normalized and combined with a convolutional layer to compensate for local feature information. In addition, a novel channel attention module is constructed to further improve feature extraction capabilities by assigning greater weights to important features to enhance feature representation and prevent interference from redundant features. Finally, multi-layer residual connections are introduced to 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 depthwise separable convolutional layer, a SiLU activation function, a two-dimensional selective scan 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 scan module is used to model long-range dependencies through discrete state space equations. Layer normalization is applied to normalize features to stabilize the training process. The second branch consists of a linear layer and a SiLU activation function, used to expand the channels and enhance the non-linearity of the network; the second branch complements the features extracted by the first branch, enabling the network to learn more comprehensive information about the input features; finally, the output features of the two branches are fused by a Hadamard product, and then the number of channels is adjusted back to C by 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 max pooling layer, a global average pooling layer, a 1×1 convolutional layer, and a sigmoid activation function. First, the input feature map is fed into the global max pooling layer and the global average pooling layer, respectively. The output feature maps of these two pooling layers are fused by element-wise addition and Euclidean algorithm 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 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 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, long-range dependencies in each scan sequence are captured through discrete state-space equations; finally, the original two-dimensional structure is effectively recovered by summing and reconstructing the results of all scan 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 is as follows: The high-quality seismic image reconstruction module of the Mamba network used for super-resolution reconstruction of seismic images consists of two convolutional layers and a pixel reconstruction 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 reconstruction layer improves the spatial resolution of seismic images by rearranging the pixels in the seismic images, thereby preserving detailed stratigraphic features.

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 is changed from the Mamba standard loss function to the Charbonnier loss function, and its mathematical expression is as follows: in, I SR High-resolution seismic images representing reconstruction, I HR Representing high-resolution seismic images in the training set, ε It is a constant set to maintain numerical stability. ε 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, network model validation specifically includes the following steps: S81. Input the paired low-resolution-high-resolution seismic images from the validation set into the trained Mamba-based seismic image super-resolution reconstruction network for validation. S82. When the evaluation indicators of the verification results, such as structural similarity and peak signal-to-noise ratio, do not meet the set thresholds, return to step S7, adjust and optimize the network model parameters, and retrain the Mamba-based earthquake image super-resolution reconstruction network. S83. When the evaluation indicators of the verification results, namely structural similarity and peak signal-to-noise ratio, meet the set thresholds, the network model training is stopped. 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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