A seismic data denoising method and device based on fusion of enhanced low rank and gradient smoothness

Abstract

This invention discloses a seismic data denoising method based on fusion enhancement of low-rank and gradient smoothness, belonging to the field of seismic data processing technology. The method includes the following steps: dividing the noisy seismic data into multiple data blocks; calculating the similarity value between each data block and the remaining data blocks to obtain a nonlocal self-similarity value; taking the smallest nonlocal self-similarity value among all data blocks containing the data point to obtain a nonlocal self-similarity matrix; stacking all nonlocal self-similarity matrices to construct multiple first three-dimensional similarity block groups; performing second-order gradient transformations along the three directions of the first three-dimensional similarity block groups to obtain three second-order gradient tensors; applying low-rank constraints to the three second-order gradient tensors of the first three-dimensional similarity block groups to obtain a second three-dimensional similarity block group; reconstructing and restoring the denoised seismic data. This invention can accurately represent the curved geological structures appearing in seismic data and effectively improve the denoising performance of seismic data.

Description

Technical Field

[0001] This invention relates to the field of seismic data processing technology, and in particular to a method and apparatus for denoising seismic data based on fusion enhancement of low rank and gradient smoothness. Background Technology

[0002] Seismic data is a crucial tool in geophysics for studying geological structures. However, due to various factors such as environmental influences, human activities, and equipment limitations, seismic data is frequently affected by significant noise. Random noise in seismic data can impair amplitude information and reduce the signal-to-noise ratio. Furthermore, noise can hinder subsequent applications, such as seismic imaging, inversion results, velocity analysis, and fault detection. Therefore, effectively removing noise and reducing signal leakage to improve the reliability of seismic data has become a critical issue in seismic data preprocessing.

[0003] Currently, many traditional seismic data noise reduction techniques have been developed, which can be broadly categorized into three types: transform-based methods, filter-based methods, and data feature exploration-based methods. The first type, transform-based methods, involves transferring seismic data from the time or spatial domain to the transform domain and then utilizing the different characteristics of signal and noise within the transform domain to attenuate noise. Typical transform-based methods include Fourier transform, wavelet transform, curvelet transform, and Radon transform. These methods rely heavily on threshold selection; inappropriate threshold selection can lead to residual noise or signal attenuation. Furthermore, the effectiveness of these methods decreases if seismic data and noise overlap in the transform domain and cannot be sufficiently distinguished. The second type, filter-based methods, involves designing specific filters to eliminate noise while preserving useful seismic signals. Although filter-based methods such as fx predictive filters, diffusion filters, grayscale filters, and fission particle filters have been widely used and have good denoising effects, their performance largely depends on the design of the filters used. The third category is based on exploring data features, including decomposition-based methods, low-rank matrix constraint-based methods, methods that use total variation to explore local smoothness, dictionary learning-based methods, and sparse coding-based methods. These methods improve denoising performance by capturing the inherent prior information in seismic data, but they are difficult to effectively improve the denoising performance of seismic data. Summary of the Invention

[0004] To address the aforementioned shortcomings in existing technologies, this invention provides a seismic data denoising method and apparatus based on fusion enhancement of low-rank and gradient smoothness. By introducing a second-order gradient tensor for low-rank modeling, it effectively captures geometric features related to curvature, thereby accurately representing the curved geological structures appearing in seismic data and effectively improving the denoising performance of seismic data.

[0005] In a first aspect, the present invention provides a seismic data denoising method based on fusion enhancement of low rank and gradient smoothness, comprising the following steps:

[0006] S10: Add Gaussian white noise of the same standard deviation to the clean seismic data X to obtain noisy seismic data Y;

[0007] S20: Divide the noisy seismic data Y into multiple p*p data blocks of equal size according to a certain step size L. Calculate the similarity value between each data block and the remaining data blocks in turn. Superimpose the first a smallest similarity values ​​to obtain the nonlocal self-similarity value of the data block. Take the smallest nonlocal self-similarity value among all data blocks containing the data point as the value at the corresponding position in the nonlocal self-similarity matrix to obtain the nonlocal self-similarity matrix S. Stack all nonlocal self-similarity matrices S to construct multiple first three-dimensional similarity block groups. The value of i is [1, N], where N is the number of three-dimensional similar block groups;

[0008] S30: Along each first three-dimensional similar block group Perform second-order gradient transformations in the three directions respectively to obtain three second-order gradient tensors. The value of k is [1, 3], and the value of i is [1, N].

[0009] S40: For each first three-dimensional similar block group The three second-order gradient tensors By applying low-rank constraints, a second set of three-dimensional similar blocks is obtained. The value of i is [1, N];

[0010] S50: Group the second three-dimensional similar blocks Reconstructing and restoring the seismic data to obtain denoised seismic data.

[0011] Furthermore, the first three-dimensional similar block group The three second-order gradient tensors By applying low-rank constraints, a second set of three-dimensional similar blocks is obtained. The steps specifically include:

[0012] For each first three-dimensional similar block group According to formula (2):

[0013]

[0014] Obtain the second three-dimensional similar block group

[0015] Among them, y iThis represents the three-dimensional similar block group obtained in step S20; λ is the equilibrium parameter; ||·|| F The Frobenius norm; k represents three directions, with values ​​[1, 3]; ||·|| ★ It is a low-rank constraint term.

[0016] Furthermore, based on the ADMM algorithm, auxiliary variables are introduced. Solving this equation, we choose the tensor nuclear norm as the low-rank representation, and obtain the closed-form solution of equation (2):

[0017]

[0018] in, and Let represent the Fast Fourier Transform (FFT) operator and the Inverse Fast Fourier Transform (IFT) operator, 1 represent a tensor of all 1s, and (·) represent the tensor of all 1s. H Represents the complex conjugate operator. Λ <i，k> Let μ be the Lagrange operator and μ be the penalty parameter.

[0019] Furthermore, along each first three-dimensional similar block group Perform second-order gradient transformations in the three directions respectively to obtain three second-order gradient tensors. The steps specifically include:

[0020] For each first three-dimensional similar block group According to formula (1):

[0021]

[0022] The first three-dimensional similar block group χ is obtained i Second-order gradient tensor along three directions

[0023] Where l, m, and n are the first three-dimensional similar block groups, respectively. The three dimensions.

[0024] Further, the second three-dimensional similar block group Reconstructing and restoring the seismic data to obtain denoised seismic data. The steps specifically include:

[0025] The processed second three-dimensional similar block group The obtained nonlocal self-similarity matrix corresponds to the locations that can be reconstructed from the seismic data to obtain the denoised seismic data.

[0026] Secondly, an embodiment of the present invention provides a seismic data denoising device based on fusion enhancement of low rank and gradient smoothness, comprising:

[0027] The Gaussian white noise addition module is used to add Gaussian white noise of the same standard deviation to clean seismic data X to obtain noisy seismic data Y.

[0028] The similarity block group construction module is used to divide the noisy seismic data Y into multiple p*p data blocks of the same size according to a certain step size L. It then calculates the similarity value between each data block and the remaining data blocks, and superimposes the first a smallest similarity values ​​as the non-local self-similarity value of the data block. Finally, it takes the smallest non-local self-similarity value among all data blocks containing the data point as the value at the corresponding position in the non-local self-similarity matrix, obtaining the non-local self-similarity matrix S. All non-local self-similarity matrices S are stacked to construct multiple first three-dimensional similarity block groups. The value of i is [1, N], where N is the number of three-dimensional similar block groups;

[0029] The second-order gradient transformation module is used to transform along each first three-dimensional similar block group. Perform second-order gradient transformations in the three directions respectively to obtain three second-order gradient tensors. The value of k is [1, 3], and the value of i is [1, N].

[0030] The low-rank constraint application module is used for applying constraints to each first 3D similar block group. The three second-order gradient tensors By applying low-rank constraints, a second set of three-dimensional similar blocks is obtained. The value of i is [1, N];

[0031] The reconstruction and restoration module is used to group the second three-dimensional similar blocks. Reconstructing and restoring the seismic data to obtain denoised seismic data.

[0032] The low-rank constraint application module is specifically used for:

[0033] For each first three-dimensional similar block group According to formula (2):

[0034]

[0035] Obtain the second three-dimensional similar block group

[0036] Among them, y i This represents the three-dimensional similar block group obtained in step S20; λ is the equilibrium parameter; ||·|| F The Frobenius norm; k represents three directions, with values ​​[1, 3]; ||·|| ＊ It is a low-rank constraint term;

[0037] Based on the ADMM algorithm, auxiliary variables are introduced. Solving this equation, we choose the tensor nuclear norm as the low-rank representation, and obtain the closed-form solution of equation (2):

[0038]

[0039] in, and Let represent the Fast Fourier Transform (FFT) operator and the Inverse Fast Fourier Transform (IFT) operator, 1 represent a tensor of all 1s, and (·) represent the tensor of all 1s. H Represents the complex conjugate operator. Λ <i，k> Let μ be the Lagrange operator and μ be the penalty parameter.

[0040] The beneficial effects of this invention are as follows:

[0041] This invention first adds Gaussian white noise of the same standard deviation to clean seismic data X to obtain noisy seismic data Y; then, the noisy seismic data Y is divided into multiple data blocks of the same size, which are calculated, stacked, and constructed into a first three-dimensional similar block group. For the first three-dimensional similar block group Perform second-order gradient transformations in each of the three directions to obtain three second-order gradient tensors. Then apply the three second-order gradient tensors By applying low-rank constraints, a second set of three-dimensional similar blocks is obtained. Finally, the second three-dimensional similar block group Reconstructing and restoring the seismic data to obtain denoised seismic data. This invention uses a similar block matching framework to map low-dimensional seismic data to high-dimensional structural data. It can simultaneously encode nonlocal self-similarity, global low-rank, and gradient smoothness, reducing the number of introduced balance parameters and representing seismic data more comprehensively. By introducing a second-order gradient tensor for low-rank modeling, it can effectively capture curvature-related geometric features and accurately represent the curved geological structures that frequently appear in seismic data, thereby effectively removing noise from seismic data. In addition, by combining the three prior information of seismic data—nonlocal self-similarity, global low-rank, and gradient smoothness—the denoised seismic data can be accurately recovered. Attached Figure Description

[0042] Figure 1 This is a flowchart illustrating a seismic data denoising method based on fusion enhancement of low rank and gradient smoothness provided in an embodiment of the present invention.

[0043] Figure 2 This is a graph showing the quantitative comparison results of the method proposed in this embodiment of the invention and the comparative method in three seismic datasets;

[0044] Figure 3 This is a functional block diagram of a seismic data denoising device based on fusion enhancement of low rank and gradient smoothness provided in an embodiment of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are merely illustrative of the present invention and are not intended to limit the present invention.

[0046] Example 1

[0047] like Figure 1 As shown, this embodiment of the invention provides a seismic data denoising method based on fusion enhancement of low rank and gradient smoothness. This seismic data denoising method mainly includes the following steps:

[0048] Step S10: Add Gaussian white noise of the same standard deviation to the clean seismic data X to obtain noisy seismic data Y.

[0049] In this embodiment, the mathematical relationship between noisy seismic data Y and seismic data X is as follows:

[0050] Y = X + N;

[0051] N~N(μ,σ) 2 );

[0052] Where N is random noise, representing a standard normal distribution with mean μ and standard deviation σ.

[0053] Step S20: Divide the noisy seismic data Y into multiple p*p data blocks of the same size according to a certain step size L. Calculate the similarity value between each data block and the other data blocks in turn. Stack the first a smallest similarity values ​​to obtain the nonlocal self-similarity value of the data block. Take the smallest nonlocal self-similarity value among all data blocks containing the data point as the value at the corresponding position in the nonlocal self-similarity matrix to obtain the nonlocal self-similarity matrix S. Stack all nonlocal self-similarity matrices S to construct multiple first three-dimensional similarity block groups.

[0054] Specifically, the step size L is preferably an integer between 2 and 20; in the size p*p of the data block, the value of p is preferably an integer between 30 and 100; the first three-dimensional similar block group In this context, i takes the value of an integer between 1 and N, where N is the number of three-dimensional similar block groups.

[0055] This embodiment uses a similar block matching framework to map low-dimensional seismic data to high-dimensional structural data. It can simultaneously encode nonlocal self-similarity, global low rank, and gradient smoothness, reducing the number of introduced balance parameters and representing seismic data more comprehensively.

[0056] Step S30: Along each first three-dimensional similar block group Perform second-order gradient transformations in the three directions respectively to obtain three second-order gradient tensors.

[0057] Where k takes the value [1, 3] and i takes the value [1, N].

[0058] In one implementation, the [section] along each first three-dimensional similar block group Perform second-order gradient transformations in the three directions respectively to obtain three second-order gradient tensors. The steps specifically include:

[0059] For each first three-dimensional similar block group According to formula (1):

[0060]

[0061] Obtain the first three-dimensional similar block group Second-order gradient tensor along three directions

[0062] Where l, m, and n are the first three-dimensional similar block groups, respectively. The range of values ​​for the three dimensions, l, m, and n, is the same as that of the first three-dimensional similar block group. The sizes match.

[0063] Step S40: For each first three-dimensional similar block group The three second-order gradient tensors By applying low-rank constraints, a second set of three-dimensional similar blocks is obtained.

[0064] Where i takes the value [1, N].

[0065] In one implementation, the first three-dimensional similarity block group The three second-order gradient tensors By applying low-rank constraints, a second set of three-dimensional similar blocks is obtained. The steps specifically include:

[0066] For each first three-dimensional similar block group x i According to formula (2):

[0067]

[0068] Obtain the second three-dimensional similar block group

[0069] Among them, y i This represents the three-dimensional similar block group obtained in step S20; λ is the equilibrium parameter; ||·|| F The Frobenius norm; k represents three directions, with values ​​[1, 3]; ||·|| ＊ It is a low-rank constraint term.

[0070] Furthermore, this embodiment introduces auxiliary variables based on the ADMM algorithm. Solving this equation, we choose the tensor nuclear norm as the low-rank representation, and obtain the closed-form solution of equation (2):

[0071]

[0072] in, and Let represent the Fast Fourier Transform (FFT) operator and the Inverse Fast Fourier Transform (IFT) operator, 1 represent a tensor of all 1s, and (·) represent the tensor of all 1s. H Represents the complex conjugate operator. Λ <i，k> Let μ be the Lagrange operator and μ be the penalty parameter.

[0073] Specifically, the optimization problem of the above formula (2) can be equivalently transformed into the following formula:

[0074]

[0075] The augmented Lagrangian function in the above equation can be expressed as:

[0076]

[0077] for subproblems

[0078]

[0079] Among them, ||·|| ★ As a low-rank constraint term, this invention chooses the tensor nuclear norm as the low-rank representation, and the closed-form solution of the above equation is:

[0080]

[0081] Where τ=λ / μ, This represents the singular value decomposition operator for tensors.

[0082] for Subproblems:

[0083]

[0084] By taking the derivative, we can obtain the equivalent form of the above expression:

[0085]

[0086] Through the Fast Fourier Transform, we can obtain the closed-form solution as follows:

[0087]

[0088] in, and Let represent the Fast Fourier Transform (FFT) operator and the Inverse Fast Fourier Transform (IFT) operator, 1 represent a tensor of all 1s, and (·) represent the tensor of all 1s. H Represents the complex conjugate operator. Λ <i，k> Let μ be the Lagrange operator and μ be the penalty parameter.

[0089] This embodiment introduces a second-order gradient tensor for low-rank modeling, which can effectively capture geometric features related to curvature, accurately represent the curved geological structures that frequently appear in seismic data, and thus effectively remove noise from seismic data.

[0090] Step S50: Group the second three-dimensional similar blocks Reconstructing and restoring the seismic data to obtain denoised seismic data.

[0091] This embodiment combines three prior information about seismic data: nonlocal self-similarity, global low rank, and gradient smoothness, to accurately recover denoised seismic data.

[0092] To verify the seismic data denoising effect of this embodiment, the seismic data denoising method (ELGS) based on fusion enhancement of low rank and gradient smoothness provided in this embodiment is compared with the weighted nuclear norm minimization denoising method (WNNM), the multi-channel singular spectrum analysis denoising method (MSSA), the local dictionary regularized regression denoising method (LDRR), the deep denoising autoencoder denoising method (DDAE), and the block-based UNET network denoising method (PATCHUNET).

[0093] To evaluate the superior performance of ELGS and other comparison methods provided in this embodiment, three test datasets and three noise scenarios are presented. Scenario 1, Scenario 2, and Scenario 3 represent noise intensities of 0.1, 0.2, and 0.3, respectively.

[0094] like Figure 2As shown, the best performance metrics are highlighted in bold. Observations indicate that the ELGS method proposed in this embodiment achieves more competitive noise recovery performance. This is attributed to the ELGS method's encoding of multidimensional features of seismic data, including temporal evolution characteristics, geological spatial structure, and nonlocal self-similarity. Other comparative methods, however, suffer from varying degrees of signal leakage or incomplete noise removal. In summary, the ELGS method proposed in this embodiment achieves the best evaluation metrics by effectively representing the nonlocal self-similarity, gradient smoothness, and low rank of high-dimensional structural data obtained from low-dimensional seismic data.

[0095] Example 2

[0096] like Figure 3 As shown, this embodiment of the invention also provides a seismic data denoising device based on fusion enhancement of low rank and gradient smoothness. The seismic data denoising device includes a Gaussian white noise addition module 100, a similar block group construction module 200, a second-order gradient transformation module 300, a low-rank constraint application module 400, and a reconstruction and restoration module 500.

[0097] In this embodiment, the Gaussian white noise addition module 100 is specifically used to add Gaussian white noise of the same standard deviation to clean seismic data X to obtain noisy seismic data Y.

[0098] The similarity block group construction module 200 is specifically used to divide the noisy seismic data Y into multiple p*p data blocks of the same size according to a certain step size L, calculate the similarity value between each data block and the other data blocks in turn, and superimpose the first a smallest similarity values ​​as the non-local self-similarity value of the data block; take the smallest non-local self-similarity value among all data blocks where the data point is located as the value of the corresponding position of the non-local self-similarity matrix to obtain the non-local self-similarity matrix S, and stack all the non-local self-similarity matrices S to construct multiple first three-dimensional similarity block groups. The value of i is [1, N], where N is the number of three-dimensional similar block groups.

[0099] The second-order gradient transformation module 300 is specifically used to transform along each first three-dimensional similar block group. Perform second-order gradient transformations in the three directions respectively to obtain three second-order gradient tensors. The value of k is [1, 3], and the value of i is [1, N].

[0100] The low-rank constraint application module 400 is specifically used to apply constraints to each first three-dimensional similar block group. The three second-order gradient tensors By applying low-rank constraints, a second set of three-dimensional similar blocks is obtained. The value of i is [1, N].

[0101] The reconstruction and restoration module 500 is used to group the second three-dimensional similar blocks. Reconstructing and restoring the seismic data to obtain denoised seismic data.

[0102] The low-rank constraint application module 400 is also specifically used for:

[0103] For each first three-dimensional similar block group According to formula (2):

[0104]

[0105] Obtain the second three-dimensional similar block group

[0106] Among them, y i This represents the three-dimensional similar block group obtained in step S20; λ is the equilibrium parameter; ||·|| F The Frobenius norm; k represents three directions, with values ​​[1, 3]; ||·|| ★ It is a low-rank constraint term;

[0107] Based on the ADMM algorithm, auxiliary variables are introduced. Solving this equation, we choose the tensor nuclear norm as the low-rank representation, and obtain the closed-form solution of equation (2):

[0108]

[0109] in, and Let represent the Fast Fourier Transform (FFT) operator and the Inverse Fast Fourier Transform (IFT) operator, 1 represent a tensor of all 1s, and (·) represent the tensor of all 1s. H Represents the complex conjugate operator. Λ <i，k> Let μ be the Lagrange operator and μ be the penalty parameter.

[0110] In detail, each module in the seismic data denoising device based on fusion enhancement of low rank and gradient smoothness provided in this embodiment of the invention adopts the same technical means as the seismic data denoising method based on fusion enhancement of low rank and gradient smoothness provided in Embodiment 1 above, and can produce the same technical effect, which will not be repeated here.

[0111] In summary, the embodiments of the present invention first add Gaussian white noise of the same standard deviation to clean seismic data X to obtain noisy seismic data Y; then, the noisy seismic data Y is divided into multiple data blocks of the same size, which are calculated, stacked, and constructed into a first three-dimensional similar block group. For the first three-dimensional similar block group Perform second-order gradient transformations in each of the three directions to obtain three second-order gradient tensors. Then apply the three second-order gradient tensors By applying low-rank constraints, a second set of three-dimensional similar blocks is obtained. Finally, the second three-dimensional similar block group Reconstructing and restoring the seismic data to obtain denoised seismic data.

[0112] This invention employs a similar block matching framework to map low-dimensional seismic data to high-dimensional structural data. This framework can simultaneously encode nonlocal self-similarity, global low-rank, and gradient smoothness, reducing the number of introduced balance parameters and providing a more comprehensive representation of seismic data. By introducing a second-order gradient tensor for low-rank modeling, it can effectively capture curvature-related geometric features, accurately representing the curved geological structures frequently found in seismic data, thereby effectively removing noise from the seismic data. Furthermore, by combining the three prior information of seismic data—nonlocal self-similarity, global low-rank, and gradient smoothness—the denoised seismic data can be accurately recovered.

[0113] In the embodiments provided by this invention, it should be understood that the disclosed devices, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and other division methods may exist in actual implementation. The modules described as separate components may or may not be physically separate, and the components shown as modules may or may not be physical units, i.e., they may be located in one place or distributed across multiple network units. Some or all of the modules can be selected to achieve the purpose of this embodiment according to actual needs. In addition, the functional modules in the various embodiments of this invention can be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The integrated unit described above can be implemented in hardware or in the form of hardware plus software functional modules.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A seismic data denoising method based on fusion enhancement of low-rank and gradient smoothness, characterized in that, Includes the following steps: S10: Add Gaussian white noise of the same standard deviation to the clean seismic data X to obtain noisy seismic data Y; S20: Divide the noisy seismic data Y into multiple p*p data blocks of equal size according to a certain step size L. Calculate the similarity value between each data block and the remaining data blocks in turn. Superimpose the first a smallest similarity values ​​to obtain the nonlocal self-similarity value of the data block. Take the smallest nonlocal self-similarity value among all data blocks containing the data point as the value at the corresponding position in the nonlocal self-similarity matrix to obtain the nonlocal self-similarity matrix S. Stack all nonlocal self-similarity matrices S to construct multiple first three-dimensional similarity block groups. The value of i is [1, N], where N is the number of three-dimensional similar block groups; S30: Along each first three-dimensional similar block group Perform second-order gradient transformations in the three directions respectively to obtain three second-order gradient tensors. The value of k is [1, 3], and the value of i is [1, N]. S40: For each first three-dimensional similar block group The three second-order gradient tensors By applying low-rank constraints, a second set of three-dimensional similar blocks is obtained. The value of i is [1, N]; S50: Group the second three-dimensional similar blocks Reconstructing and restoring the seismic data to obtain denoised seismic data. The first three-dimensional similar block group The three second-order gradient tensors By applying low-rank constraints, a second set of three-dimensional similar blocks is obtained. The steps specifically include: For each first three-dimensional similar block group According to formula (2): Obtain the second three-dimensional similar block group Among them, y i This represents the three-dimensional similar block group obtained in step S20; λ is the equilibrium parameter; ||·|| F The Frobenius norm; k represents three directions, with values ​​[1, 3]; ||·|| ＊ It is a low-rank constraint term; Based on the ADMM algorithm, auxiliary variables are introduced. Solving this equation, we choose the tensor nuclear norm as the low-rank representation, and obtain the closed-form solution of equation (2): in, and Let represent the Fast Fourier Transform (FFT) operator and the Inverse Fast Fourier Transform (IFT) operator, 1 represent a tensor of all 1s, and (·) represent the tensor of all 1s. H Represents the complex conjugate operator. Λ <i，k> Let μ be the Lagrange operator and μ be the penalty parameter.

2. The seismic data denoising method based on fusion enhancement of low rank and gradient smoothness according to claim 1, characterized in that, Along each first three-dimensional similar block group Perform second-order gradient transformations in the three directions respectively to obtain three second-order gradient tensors. The steps specifically include: For each first three-dimensional similar block group According to formula (1): Obtain the first three-dimensional similar block group Second-order gradient tensor along three directions Where l, m, and n are the first three-dimensional similar block groups, respectively. The three dimensions.

3. The seismic data denoising method based on fusion enhancement of low rank and gradient smoothness according to claim 1, characterized in that, The second three-dimensional similar block group Reconstructing and restoring the seismic data to obtain denoised seismic data. The steps specifically include: The processed second three-dimensional similar block group The obtained nonlocal self-similarity matrix corresponds to the locations that can be reconstructed from the seismic data to obtain the denoised seismic data.

4. A seismic data denoising device based on fusion enhancement of low-rank and gradient smoothness, applied to the seismic data denoising method based on fusion enhancement of low-rank and gradient smoothness as described in claim 1, characterized in that, The seismic data denoising device includes: The Gaussian white noise addition module is used to add Gaussian white noise of the same standard deviation to clean seismic data X to obtain noisy seismic data Y. The similarity block group construction module is used to divide the noisy seismic data Y into multiple p*p data blocks of the same size according to a certain step size L. It then calculates the similarity value between each data block and the remaining data blocks, and superimposes the first a smallest similarity values ​​as the non-local self-similarity value of the data block. Finally, it takes the smallest non-local self-similarity value among all data blocks containing the data point as the value at the corresponding position in the non-local self-similarity matrix, obtaining the non-local self-similarity matrix S. All non-local self-similarity matrices S are stacked to construct multiple first three-dimensional similarity block groups. The value of i is [1, N], where N is the number of three-dimensional similar block groups; The second-order gradient transformation module is used to transform along each first three-dimensional similar block group. Perform second-order gradient transformations in the three directions respectively to obtain three second-order gradient tensors. The value of k is [1, 3], and the value of i is [1, N]. The low-rank constraint application module is used for applying constraints to each first 3D similar block group. The three second-order gradient tensors By applying low-rank constraints, a second set of three-dimensional similar blocks is obtained. The value of i is [1, N]; The reconstruction and restoration module is used to group the second three-dimensional similar blocks. Reconstructing and restoring the seismic data to obtain denoised seismic data. The low-rank constraint application module is specifically used for: For each first three-dimensional similar block group According to formula (2): Obtain the second three-dimensional similar block group Among them, y i This represents the three-dimensional similar block group obtained in step S20; λ is the equilibrium parameter; ||·|| F is the Frobenius norm; k represents three directions, taking values ​​[1, 3]; ||·||* is a low-rank constraint term; Based on the ADMM algorithm, auxiliary variables are introduced. Solving this equation, we choose the tensor nuclear norm as the low-rank representation, and obtain the closed-form solution of equation (2): in, and Let represent the Fast Fourier Transform (FFT) operator and the Inverse Fast Fourier Transform (IFT) operator, 1 represent a tensor of all 1s, and (·) represent the tensor of all 1s. H Represents the complex conjugate operator. Λ <i，k> Let μ be the Lagrange operator and μ be the penalty parameter.

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