Irregular grid seismic data reconstruction method based on deep learning

Abstract

The invention discloses an irregular grid seismic data reconstruction method based on deep learning, and belongs to the technical field of compressed sensing irregular grid seismic data reconstruction. In order to improve the quality of seismic data reconstruction, the method comprises the steps that a seismic data training set is generated, and each group of data in the seismic data training set comprises complete seismic data and two interpolation matrixes; an irregular convex set projection convolutional neural network is constructed, and the irregular convex set projection convolutional neural network is obtained by unfolding a loop structure of an irregular convex set projection method into a cascade structure and replacing original sparse transformation with a convolutional layer and an activation function; training the irregular convex set projection convolutional neural network by using the seismic data training set to obtain a trained irregular convex set projection convolutional neural network; and inputting acquired missing irregular grid seismic data and two interpolation matrixes calculated according to the irregular grid information into the trained irregular convex set projection convolutional neural network, and outputting reconstructed seismic data.

Description

Technical Field

[0001] The present invention belongs to the technical field of compressed sensing irregular grid seismic data reconstruction, and specifically relates to an irregular grid seismic data reconstruction method based on deep learning. Background Art

[0002] Reconstructing seismic data from irregular grids to regular grids is a long-standing problem in seismic data processing. Due to environmental factors during the acquisition process or irregular acquisition design based on compressed sensing theory, the sources or detectors are usually irregularly distributed. The goal of seismic reconstruction is to regularize the acquired irregular grid data onto a regular grid and provide a higher density of coverage for subsequent seismic data processing, thereby improving imaging accuracy.

[0003] In essence, the irregularities generated by field seismic data acquisition can be summarized into two categories. One is objective irregularities, which are caused by natural obstacles in the acquisition process and are inevitable. For example, there are obstacles such as buildings in the acquisition area, which cause large gaps in the observed data, resulting in discontinuity or even distortion of the seismic image, affecting subsequent imaging. In order to solve this problem, many scholars have proposed many seismic data reconstruction methods, such as minimum weighted norm interpolation (MWNI), anti-leakage Fourier transform (ALFT), prediction error filter, sparse Fourier inversion and improved minimum weighted norm interpolation (MWNI); the other is subjective irregularities. Regularity and subjective irregularity are irregular sampling observation systems pre-defined based on compressed sensing theory. Through subjective design, the irregularity of pseudo-random distribution is used to reduce the number of field acquisition points, thereby shortening the field acquisition time. Through subsequent data reconstruction, seismic data with the same accuracy as conventional acquisition is obtained. By utilizing the spatial coherence of seismic signals in the transformed domain, seismic records compressed below the Nyquist frequency can be perfectly restored through sparse inversion. Related problems of subjective irregularity can usually be solved by the following algorithms: interpolation compressed sensing method, non-uniform optimal sampling method (NUOS), irregular convex set projection method (EPOCS), etc. for data reconstruction.

[0004] Although traditional methods have made significant progress in data reconstruction, they still face limitations such as reliance on prior information, low computational efficiency, and difficulty in parameter selection. With the rapid development of artificial intelligence (AI) in recent years, AI deep learning methods have demonstrated unique advantages in seismic data reconstruction, lacking the need for specific prior assumptions and offering high computational efficiency. Numerous researchers have applied network structures such as generative adversarial networks (GANs) and U-Net to seismic data reconstruction, achieving promising results.

[0005] While deep learning holds considerable potential for seismic data reconstruction, it also has limitations. Reconstruction is effective when the test data shares similar characteristics with the training data. However, when the differences are significant, the results are often unsatisfactory. Consequently, numerous researchers have proposed novel approaches that combine traditional methods with deep learning to improve generalization, such as the Iterative Shrinkage Soft Thresholding Network (ISTA-Net) and the Projection on Convex Sets Network (POCS-Net). However, these approaches rarely address the impact of irregular grids on reconstruction. Therefore, a data reconstruction method that combines traditional methods with deep learning is needed, taking into account irregular grids. Summary of the Invention

[0006] The problem to be solved by the present invention is to improve the quality of seismic data reconstruction and propose an irregular grid seismic data reconstruction method based on deep learning.

[0007] To achieve the above object, the present invention is implemented through the following technical solutions:

[0008] A method for reconstructing irregular grid seismic data based on deep learning, comprising the following steps:

[0009] S1. Collect seismic data to generate a seismic data training set, where each set of data in the seismic data training set includes complete seismic data and two interpolation matrices W, is the interpolation matrix of seismic data from irregular to regular grid, and W is the interpolation matrix of seismic data from regular to irregular grid;

[0010] S2. Constructing an irregular convex set projection convolutional neural network, wherein the irregular convex set projection convolutional neural network is obtained by expanding the cyclic structure of the irregular convex set projection method into a cascade structure and replacing the original sparse transformation with a convolutional layer and an activation function;

[0011] S3. Using the seismic data training set obtained in step S1 to train the irregular convex set projection convolutional neural network obtained in step S2, to obtain a trained irregular convex set projection convolutional neural network;

[0012] S4. Collect missing irregular grid seismic data and calculate two interpolation matrices based on irregular grid information W is input into the trained irregular convex set projection convolutional neural network, and the reconstructed seismic data is output.

[0013] Furthermore, in step S1, W is multiplied by the regular grid seismic data matrix to obtain irregular grid data. The regular grid seismic data is obtained by multiplying the irregular grid seismic data matrix. The interpolation matrix is ​​calculated by the set regular grid coordinates and the irregular grid missing coordinates. The calculation formula is:

[0014]

[0015] Where w(t) is the interpolation weight between a regular grid point and an adjacent irregular grid point, t represents the distance between the regular grid point and the irregular grid point, a is a constant, which can be 10 or 3π, and N represents the interpolation range. I0 is the first kind of 0th order modified Bessel function, the formula is as follows:

[0016]

[0017] Here, i is the index of the summation function.

[0018] Furthermore, the specific implementation method of step S2 includes the following steps:

[0019] S2.1. Expand the loop structure of the convex set projection method into a cascade structure. Set the cascade structure to have 20 layers of modules with the same structure. The output of each module is the input of the next module. The expression of the kth module is:

[0020]

[0021] Among them, D obs represents the observed irregular grid missing data, D k-1 represents the output of the k-1th module, D k represents the output of the kth module, and They represent the interpolation operators from irregular grid data to regular grid data and from regular grid data to irregular grid data, respectively. I is the unit matrix. is the inverse transformation module of the k-1th module, G k-1 is the forward transformation module of the k-1th module, represents the kth module threshold constraint operator, λ k is the threshold of the kth module, Θ k-1 is the trainable parameter in the forward transformation module of the k-1th module, is the trainable parameter in the inverse transformation module of the k-1th module, and N is the number of modules;

[0022] S2.2. Use the two interpolation matrices obtained in step S1 W replaces the interpolation operator in the expression of the kth module in step S2.1 and The expression for the output of the kth module of the irregular convex set projection convolutional neural network is:

[0023]

[0024] Furthermore, in step S2.1, each module is divided into a neural network part and a back-embedding part;

[0025] The specific structure of the neural network part is the first convolution layer → activation function layer → second convolution layer → threshold constraint → third convolution layer → activation function layer → fourth convolution layer. The number of convolution kernels in each convolution layer is one, the size is 3×3, the step size is 1, and the padding is 1 to ensure that the data size remains unchanged. The activation function is the ReLU function. The first convolution layer → activation function layer → second convolution layer is the forward transformation, and the third convolution layer → activation function layer → fourth convolution layer is the reverse transformation. The threshold constraint part returns the elements in the data that are less than the threshold to zero, that is:

[0026]

[0027] Among them, λ k is the threshold of the kth module, which is a learnable parameter, and N is the number of modules;

[0028] The specific structure of the back embedding part is to multiply the output of the neural network part by and with The output of the back-embedded module is obtained by adding:

[0029]

[0030] in, Represents the output of the neural network part of the kth module.

[0031] Furthermore, the specific implementation method of step S3 is to use the seismic data training set obtained in step S1 to train the irregular convex set projection convolutional neural network obtained in step S2, and use the gradient descent method to update the parameters of the irregular convex set projection convolutional neural network to obtain a trained convolutional neural network;

[0032] The expression for the loss function L(Θ) during training is defined as:

[0033] L(Θ)=L1(Θ)+0.01L2(Θ)

[0034] Among them, L1(Θ) is the loss function used to control the reconstruction quality, and L2(Θ) is the loss function used to control the similarity between the convolution layer and the sparse transformation;

[0035] The expression of L1(Θ) is:

[0036]

[0037] in, is a batch of training sets, Θ represents the network parameters, D c iis the complete data, N b is the size of a batch of training sets, N p Is the complete data D c i The number of elements in ||·|| F represents the Frobenius norm;

[0038] The expression of L2(Θ) is:

[0039]

[0040] Among them, Θ k-1 is the trainable parameter in the forward transformation module of the k-1th module, is the trainable parameter in the inverse transformation module of the k-1th module.

[0041] Beneficial effects of the present invention:

[0042] The present invention describes a method for reconstructing irregular grid seismic data based on deep learning, which combines a deep learning method with an EPOCS method and applies it to seismic data reconstruction. By performing reconstruction tests on a variety of seismic data, it can be found that this method has the ability to reconstruct different types of missing data. It can not only process missing data of regular grids, but also achieve good reconstruction effects on missing data of irregular grids. The proposed method fully integrates the advantages of deep learning such as fast computational efficiency and high precision. This method is not limited by the traditional method based on the linear event assumption, and is more effective in processing complex nonlinear seismic data. At the same time, the method takes into account the real coordinate information in the field and avoids approximate errors. Compared with most seismic data reconstruction methods, this method has better reconstruction quality, and the reconstructed seismic data event continuity is better. BRIEF DESCRIPTION OF THE DRAWINGS

[0043] Figure 1 This is a flowchart of the method for reconstructing irregular grid seismic data based on deep learning according to the present invention;

[0044] Figure 2 Schematic diagram of the neural network structure of the present invention;

[0045] Figure 3Figure 1 is a reconstruction diagram of simple synthetic data for test 1, where (a) is the complete regular grid seismic data, (b) is the irregular grid seismic data with 50% missing data, (c) is the regular grid seismic data after binning of (b), (d) is the reconstruction result of simple synthetic data obtained by the EPOCS method, (e) is the reconstruction result of simple synthetic data obtained by the POCS-Net method, (f) is the reconstruction result of simple synthetic data obtained by the EPOCS-Net method, (g) is the difference between (a) and (d), (h) is the difference between (a) and (e), and (i) is the difference between (a) and (f);

[0046] Figure 4 Figure 2 is the reconstruction diagram of the complex synthetic data for test 2, where (a) is the complete regular grid seismic data, (b) is the irregular grid seismic data with 50% missing data, (c) is the regular grid seismic data after binning of (b), (d) is the reconstruction result of the complex synthetic data obtained by the EPOCS method, (e) is the reconstruction result of the complex synthetic data obtained by the POCS-Net method, (f) is the reconstruction result of the complex synthetic data obtained by the EPOCS-Net method, (g) is the difference between (a) and (d), (h) is the difference between (a) and (e), and (i) is the difference between (a) and (f);

[0047] Figure 5 Figure 3 is the reconstruction diagram of the actual data of test three, where (a) is the complete regular grid actual seismic data, (b) is the irregular grid seismic data with 50% missing data, (c) is the regular grid seismic data after binning of (b), (d) is the reconstruction result of the actual seismic data obtained by the EPOCS method, (e) is the reconstruction result of the actual seismic data obtained by the POCS-Net method, (f) is the reconstruction result of the actual seismic data obtained by the EPOCS-Net method, (g) is the difference between (a) and (d), (h) is the difference between (a) and (e), and (i) is the difference between (a) and (f). DETAILED DESCRIPTION

[0048] In order to make the objectives, technical solutions, and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are only intended to explain the present invention and are not intended to limit the present invention. That is, the specific embodiments described herein are only some embodiments of the present invention, not all embodiments. Generally, the components of the specific embodiments of the present invention described and illustrated in the drawings herein can be arranged and designed in various different configurations, and the present invention can also have other embodiments.

[0049] Therefore, the following detailed description of the specific embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the invention as claimed, but is merely representative of selected specific embodiments of the present invention. All other specific embodiments obtained by those skilled in the art based on the specific embodiments of the present invention without making any creative efforts shall fall within the scope of protection of the present invention.

[0050] In order to further understand the content, features and effects of the present invention, the following specific embodiments are given as examples, and the attached Figure 1 -Attached Figure 5 The detailed instructions are as follows:

[0051] Example 1:

[0052] A method for reconstructing irregular grid seismic data based on deep learning, comprising the following steps:

[0053] S1. Collect seismic data to generate a seismic data training set, where each set of data in the seismic data training set includes complete seismic data and two interpolation matrices W, is the interpolation matrix of seismic data from irregular to regular grid, and W is the interpolation matrix of seismic data from regular to irregular grid;

[0054] Furthermore, in step S1, W is multiplied by the regular grid seismic data matrix to obtain irregular grid data. The regular grid seismic data is obtained by multiplying the irregular grid seismic data matrix. The interpolation matrix is ​​calculated by the set regular grid coordinates and the irregular grid missing coordinates. The calculation formula is:

[0055]

[0056] Where w(t) is the interpolation weight between a regular grid point and an adjacent irregular grid point, t represents the distance between the regular grid point and the irregular grid point, a is a constant, which can be 10 or 3π, and N represents the interpolation range. I0 is the first kind of 0th order modified Bessel function, the formula is as follows:

[0057]

[0058] Here, i is the index of the summation function.

[0059] Furthermore, the seismic data training set consists of 249,234 sets of data, each set of data contains complete seismic data of size 128×128 and two interpolation matrices W;

[0060] S2. Constructing an irregular convex set projection convolutional neural network, wherein the irregular convex set projection convolutional neural network is obtained by expanding the cyclic structure of the irregular convex set projection method into a cascade structure and replacing the original sparse transformation with a convolutional layer and an activation function;

[0061] Furthermore, the specific implementation method of step S2 includes the following steps:

[0062] S2.1. Expand the loop structure of the convex set projection method into a cascade structure. Set the cascade structure to have 20 layers of modules with the same structure. The output of each module is the input of the next module. The expression of the kth module is:

[0063]

[0064] Among them, D obs represents the observed irregular grid missing data, D k-1 represents the output of the k-1th module, D k represents the output of the kth module, and They represent the interpolation operators from irregular grid data to regular grid data and from regular grid data to irregular grid data, respectively. I is the unit matrix. is the inverse transformation module of the k-1th module, G k-1 is the forward transformation module of the k-1th module, represents the kth module threshold constraint operator, λ k is the threshold of the kth module, Θ k-1 is the trainable parameter in the forward transformation module of the k-1th module, is the trainable parameter in the inverse transformation module of the k-1th module, and N is the number of modules;

[0065] Furthermore, N takes the value of 20;

[0066] Furthermore, in step S2.1, each module is divided into a neural network part and a back-embedding part;

[0067] The specific structure of the neural network part is the first convolution layer → activation function layer → second convolution layer → threshold constraint → third convolution layer → activation function layer → fourth convolution layer. The number of convolution kernels in each convolution layer is one, the size is 3×3, the step size is 1, and the padding is 1 to ensure that the data size remains unchanged. The activation function is the ReLU function. The first convolution layer → activation function layer → second convolution layer is the forward transformation, and the third convolution layer → activation function layer → fourth convolution layer is the reverse transformation. The threshold constraint part returns the elements in the data that are less than the threshold to zero, that is:

[0068]

[0069] Among them, λ k is the threshold of the kth module, which is a learnable parameter, and N is the number of modules;

[0070] The specific structure of the back embedding part is to multiply the output of the neural network part by and with The output of the back-embedded module is obtained by adding:

[0071]

[0072] in, Represents the output of the neural network part of the kth module.

[0073] S2.2. Use the two interpolation matrices obtained in step S1 W replaces the interpolation operator in the expression of the kth module in step S2.1 and The expression for the output of the kth module of the irregular convex set projection convolutional neural network is:

[0074]

[0075] S3. Using the seismic data training set obtained in step S1 to train the irregular convex set projection convolutional neural network obtained in step S2, to obtain a trained irregular convex set projection convolutional neural network;

[0076] Furthermore, the specific implementation method of step S3 is to use the seismic data training set obtained in step S1 to train the irregular convex set projection convolutional neural network obtained in step S2, and use the gradient descent method to update the parameters of the irregular convex set projection convolutional neural network to obtain a trained convolutional neural network;

[0077] The expression for the loss function L(Θ) during training is defined as:

[0078] L(Θ)=L1(Θ)+0.01L2(Θ)

[0079] Among them, L1(Θ) is the loss function used to control the reconstruction quality, and L2(Θ) is the loss function used to control the similarity between the convolution layer and the sparse transformation;

[0080] The expression of L1(Θ) is:

[0081]

[0082] in, is a batch of training sets, Θ represents the network parameters, D c i is the complete data, N bis the size of a batch of training sets, N p Is the complete data D c i The number of elements in ||·|| F represents the Frobenius norm;

[0083] The expression of L2(Θ) is:

[0084]

[0085] Among them, Θ k-1 is the trainable parameter in the forward transformation module of the k-1th module, is the trainable parameter in the inverse transformation module of the k-1th module.

[0086] Furthermore, the training parameters are as follows: batch size is set to 32, Adam optimizer is selected as the optimizer, learning rate is set to 0.0001, and training rounds are set to 100;

[0087] S4. Collect missing irregular grid seismic data and calculate two interpolation matrices based on irregular grid information W is input into the trained irregular convex set projection convolutional neural network, and the reconstructed seismic data is output.

[0088] Specifically, in this embodiment, three groups of tests are performed to analyze and compare the reconstruction effects of the present invention using the irregular convex set projection method (EPOCS), the convex set projection network method (POCS-Net), and the irregular convex set projection convolutional neural network method (EPOCS-Net) proposed in the present invention. The reconstruction quality is quantified according to the signal-to-noise ratio, and the signal-to-noise ratio formula is expressed as:

[0089]

[0090] Among them, d true is the complete earthquake data, d r To reconstruct earthquake data.

[0091] Test 1: Using the EPOCS method, POCS-Net method, and EPOCS-Net method to operate on 50% missing simple synthetic data of irregular grids, reconstructed seismic data were obtained. The signal-to-noise ratio of the reconstructed data is shown in Table 1:

[0092] Table 1

[0093]

[0094] From Table 1 , it can be observed that the EPOCS-Net method has a higher signal-to-noise ratio than the EPOCS method and the POCS-Net method, that is, the seismic data reconstruction quality is better;

[0095] refer to Figure 3 ,Observation shows that the EPOCS-Net method has a better reconstruction effect;

[0096] Test 2: Using the EPOCS method, POCS-Net method, and EPOCS-Net method to operate on 50% missing irregular grid complex synthetic data, reconstructed seismic data were obtained. The signal-to-noise ratio of the reconstructed data is shown in Table 2:

[0097] Table 2

[0098]

[0099] From Table 2 , we can observe that the EPOCS-Net method has a higher signal-to-noise ratio than the EPOCS method and the POCS-Net method, that is, the seismic data reconstruction quality is better;

[0100] refer to Figure 4 , we can see that the EPOCS-Net method has a better reconstruction effect. Figure 3 (g) with Figure 4 In (g), we can see that the EPOCS method reconstructs many artifacts in the area outside the phase axis. This is a common problem of the reconstruction method of the POCS framework using Fourier transform. Figure 3 (h) with Figure 4 In (h), the POCS-Net reconstruction results show significant signal leakage, indicating that the event amplitudes of the reconstructed results differ significantly from those of the complete data. This is because the POCS-Net method reconstructs binned sampled data, which can introduce errors in the amplitude and phase of the data. The EPOCS-Net method, on the other hand, can avoid these two issues to a certain extent, resulting in higher-quality reconstruction results.

[0101] Test 3: Using the EPOCS method, POCS-Net method, and EPOCS-Net method to operate on the 50% missing irregular grid real data, reconstructed seismic data were obtained. The signal-to-noise ratio of the reconstructed data is shown in Table 3:

[0102] Table 3

[0103]

[0104] From Table 3 , we can observe that the EPOCS-Net method has a higher signal-to-noise ratio and better seismic data reconstruction quality than the EPOCS method and the POCS-Net method;

[0105] refer to Figure 5,For actual seismic data, the reconstruction effects of various ,reconstruction methods have declined, but the EPOCS-Net method still has ,certain advantages over the other two methods.

[0106] It should be noted that relational terms such as "first" and "second" are used only to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any actual relationship or order between these entities or operations. Moreover, the terms "comprises," "comprising," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus comprising a series of elements includes not only those elements, but also other elements not explicitly listed, or elements inherent to such process, method, article, or apparatus. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of additional identical elements in the process, method, article, or apparatus comprising the element.

[0107] Although the present application has been described above with reference to specific embodiments, various modifications may be made thereto and components may be substituted with equivalents without departing from the scope of the present application. In particular, as long as there are no structural conflicts, the various features of the embodiments disclosed herein may be combined with each other in any manner, and the omission of an exhaustive description of these combinations in this specification is solely for the sake of space and resource conservation. Therefore, the present application is not limited to the specific embodiments disclosed herein, but includes all technical solutions within the scope of the claims.

Claims

1. A method for reconstructing irregular grid seismic data based on deep learning, characterized in that: The steps include: S1. Collect seismic data to generate a seismic data training set, where each set of data in the seismic data training set includes complete seismic data and two interpolation matrices W, is the interpolation matrix of seismic data from irregular to regular grid, and W is the interpolation matrix of seismic data from regular to irregular grid; S2. Constructing an irregular convex set projection convolutional neural network, wherein the irregular convex set projection convolutional neural network is obtained by expanding the cyclic structure of the irregular convex set projection method into a cascade structure and replacing the original sparse transformation with a convolutional layer and an activation function; S3. Using the seismic data training set obtained in step S1 to train the irregular convex set projection convolutional neural network obtained in step S2, to obtain a trained irregular convex set projection convolutional neural network; S4. Collect missing irregular grid seismic data and calculate two interpolation matrices based on irregular grid information W is input into the trained irregular convex set projection convolutional neural network, and the reconstructed seismic data is output.

2. The method for reconstructing irregular grid seismic data based on deep learning according to claim 1, characterized in that: In step S1, W is multiplied by the regular grid seismic data matrix to obtain irregular grid data. The regular grid seismic data is obtained by multiplying the irregular grid seismic data matrix. The interpolation matrix is ​​calculated by the set regular grid coordinates and the irregular grid missing coordinates. The calculation formula is: Where w(t) is the interpolation weight between a regular grid point and an adjacent irregular grid point, t represents the distance between the regular grid point and the irregular grid point, a is a constant, which can be 10 or 3π, and N represents the interpolation range. I0 is the first kind of 0th order modified Bessel function, the formula is as follows: Here, i is the index of the summation function.

3. A method for reconstructing irregular grid seismic data based on deep learning according to claim 1 or 2, characterized in that: The specific implementation method of step S2 includes the following steps: S2.

1. Expand the loop structure of the convex set projection method into a cascade structure. Set the cascade structure to have 20 layers of modules with the same structure. The output of each module is the input of the next module. The expression of the kth module is: Among them, D obs represents the observed irregular grid missing data, D k-1 represents the output of the k-1th module, D k represents the output of the kth module, and They represent the interpolation operators from irregular grid data to regular grid data and from regular grid data to irregular grid data, respectively. I is the unit matrix. is the inverse transformation module of the k-1th module, G k-1 is the forward transformation module of the k-1th module, represents the kth module threshold constraint operator, λ k is the threshold of the kth module, Θ k-1 is the trainable parameter in the forward transformation module of the k-1th module, is the trainable parameter in the inverse transformation module of the k-1th module, and N is the number of modules; S2.

2. Use the two interpolation matrices obtained in step S1 W replaces the interpolation operator in the expression of the kth module in step S2.1 and The expression for the output of the kth module of the irregular convex set projection convolutional neural network is:

4. The method for reconstructing irregular grid seismic data based on deep learning according to claim 3, characterized in that: In step S2.1, each module is divided into a neural network part and a back-embedding part; The specific structure of the neural network part is the first convolution layer → activation function layer → second convolution layer → threshold constraint → third convolution layer → activation function layer → fourth convolution layer. The number of convolution kernels in each convolution layer is one, the size is 3×3, the step size is 1, and the padding is 1 to ensure that the data size remains unchanged. The activation function is the ReLU function. The first convolution layer → activation function layer → second convolution layer is the forward transformation, and the third convolution layer → activation function layer → fourth convolution layer is the reverse transformation. The threshold constraint part returns the elements in the data that are less than the threshold to zero, that is: Among them, λ k is the threshold of the kth module, which is a learnable parameter, and N is the number of modules; The specific structure of the back embedding part is to multiply the output of the neural network part by and with The output of the back-embedded module is obtained by adding: in, Represents the output of the neural network part of the kth module.

5. The method for reconstructing irregular grid seismic data based on deep learning according to claim 4, characterized in that: The specific implementation method of step S3 is to use the seismic data training set obtained in step S1 to train the irregular convex set projection convolutional neural network obtained in step S2, and use the gradient descent method to update the parameters of the irregular convex set projection convolutional neural network to obtain a trained convolutional neural network; The expression for the loss function L(Θ) during training is defined as: L(Θ)=L1(Θ)+0.01L2(Θ) Among them, L1(Θ) is the loss function used to control the reconstruction quality, and L2(Θ) is the loss function used to control the similarity between the convolution layer and the sparse transformation; The expression of L1(Θ) is: in, is a batch of training sets, Θ represents the network parameters, D c i is the complete data, N b is the size of a batch of training sets, N p Is the complete data D c i The number of elements in ||·|| F represents the Frobenius norm; The expression of L2(Θ) is: Among them, Θ k-1 is the trainable parameter in the forward transformation module of the k-1th module, is the trainable parameter in the inverse transformation module of the k-1th module.

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