Seismic data denoising method and device based on fusion enhancement of low rank and gradient smoothness

Abstract

The invention discloses a seismic data denoising method based on fusion enhancement of low rank and gradient smoothness, and relates to the technical field of seismic data processing. The method comprises the following steps: dividing noisy seismic data into a plurality of data blocks, and calculating similarity values of each data block and other data blocks to obtain non-local self-similarity values; taking minimum non-local self-similarity values in all data blocks where the data points are located to obtain non-local self-similarity matrixes, and stacking all the non-local self-similarity matrixes and constructing a plurality of first three-dimensional similar block groups; performing second-order gradient transformation along three directions of the first three-dimensional similar block group to obtain three second-order gradient tensors; applying low-rank constraint to the three second-order gradient tensors of the first three-dimensional similar block group to obtain a second three-dimensional similar block group; and reconstructing, restoring and obtaining de-noised seismic data. The method can accurately represent the bending geologic structure appearing in the seismic data, and effectively improves the denoising performance of the seismic data.

Description

Technical Field

[0001] The present invention relates to the technical field of seismic data processing, and in particular to a seismic data denoising method and device based on fusion-enhanced low-rank and gradient smoothness. Background Art

[0002] Seismic data is an important tool for studying geological structures in geophysics. However, due to a variety of factors such as environmental factors, human activities, and equipment limitations, seismic data are often affected by a large amount of noise. Random noise in seismic data affects the amplitude information and reduces the signal-to-noise ratio. In addition, noise can also hinder subsequent applications such as seismic imaging, inversion results, velocity analysis, and fault detection. Therefore, improving the reliability of seismic data by effectively removing noise and reducing signal leakage has become a key issue in seismic data preprocessing.

[0003] At present, many traditional seismic data noise removal techniques have been developed, which can be roughly divided into three categories: transform-based methods, filter-based methods, and methods based on data feature exploration. Among them, the first category is transform-based methods, which transfer seismic data from the time or space domain to the transform domain, and then use the different characteristics of the signal and noise in the transform domain to achieve noise attenuation. Typical transform-based methods include Fourier transform, wavelet transform, curvelet transform, and Radon transform. These methods rely on the selection of thresholds, and improper threshold selection will lead to residual noise or signal attenuation. In addition, if the seismic data and noise overlap in the transform domain and cannot be fully distinguished, the effectiveness of these methods will be reduced. The second category is filter-based methods, which design specific filters to remove noise while retaining useful seismic signals. Although filter-based methods such as fx prediction filters, diffusion filters, grayscale filters, and fission particle filters have been widely used and have good denoising effects, their performance depends largely on the design of the filters used. The third category is methods based on exploring data features, including decomposition-based methods, low-rank matrix constraint-based methods, methods using total variation to explore local smoothness, dictionary learning-based methods, and sparse coding-based methods. The above methods improve the denoising performance by capturing the inherent prior information in seismic data, but it is difficult to effectively improve the denoising performance of seismic data. Summary of the invention

[0004] In view of the above-mentioned deficiencies in the prior art, the present invention provides a seismic data denoising method and device based on the fusion of enhanced low-rank and gradient smoothness. By introducing the second-order gradient tensor for low-rank modeling, it is possible to effectively capture the geometric features related to curvature, thereby accurately representing the curved geological structures appearing in the seismic data and effectively improving the denoising performance of the seismic data.

[0005] In a first aspect, an embodiment of 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 with the same standard deviation to the clean seismic data X to obtain noisy seismic data Y;

[0007] S20: According to a certain step length L, the noisy seismic data Y is divided into multiple p*p data blocks of the same size, and the similarity value between each data block and the remaining data blocks is calculated in turn, and the first n smallest similarity values ​​are superimposed as the non-local self-similarity value of the data block; the smallest non-local self-similarity value among all data blocks where the data point is located is taken as the value of the corresponding position of the non-local self-similarity matrix to obtain the non-local self-similarity matrix S, and all non-local self-similarity matrices S are stacked and constructed into 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 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 of Apply low-rank constraints to obtain the second three-dimensional similar block group The value of i is [1, N];

[0010] S50: Group the second three-dimensional similar blocks Reconstruct and restore the seismic data to obtain the de-noised seismic data

[0011] Furthermore, along each first three-dimensional similar block group Perform second-order gradient transformations in the three directions to obtain three second-order gradient tensors The steps include:

[0012] For each first three-dimensional similar block group According to formula (1):

[0013]

[0014] Get the first three-dimensional similar block group Second-order gradient tensor along three directions

[0015] Among them, l, m and n are the first three-dimensional similar block groups three dimensions.

[0016] Furthermore, for each first three-dimensional similar block group The three second-order gradient tensors of Apply low-rank constraints to obtain the second three-dimensional similar block group The steps include:

[0017] For each first three-dimensional similar block group According to formula (2):

[0018]

[0019] Get the second three-dimensional similar block group

[0020] Among them, y i represents the three-dimensional similar block group obtained by step S20; λ is the balance parameter; ||·||F is the Frobenius norm; k is three directions, and the value is [1, 3]; ||·|| ★ is a low-rank constraint.

[0021] Furthermore, based on the ADMM algorithm, an auxiliary variable is introduced Solve it and choose the tensor nuclear norm as the low-rank representation, and get the closed solution of formula (2):

[0022]

[0023] in, and represents the fast Fourier transform operator and the inverse fast Fourier transform operator, 1 represents a full 1 tensor, (·) H represents the complex conjugate operator, Λ <i，k> is the Lagrangian operator, and μ is the penalty parameter.

[0024] Furthermore, the second three-dimensional similar block group Reconstruct and restore the seismic data to obtain the de-noised seismic data The steps include:

[0025] The processed second three-dimensional similar block group The corresponding position of the obtained non-local self-similarity matrix is ​​restored back to the seismic data to obtain the de-noised seismic data

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

[0027] A Gaussian white noise adding module is used to add Gaussian white noise with the same standard deviation to the clean seismic data X to obtain the 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 length L, calculate the similarity value of each data block with the remaining data blocks in turn, and superimpose the first n smallest similarity values ​​as the non-local self-similarity value of the data block; take the smallest non-local self-similarity value of 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;

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

[0030] A low-rank constraint imposing module is used to impose a low-rank constraint on each first three-dimensional similar block group. The three second-order gradient tensors of Apply low-rank constraints to obtain the second three-dimensional similar block group The value of i is [1, N];

[0031] A reconstruction and restoration module is used to group the second three-dimensional similar blocks Reconstruct and restore the seismic data to obtain the de-noised seismic data

[0032] The beneficial effects of the present invention are:

[0033] The present invention first adds Gaussian white noise with the same standard deviation to the clean seismic data X to obtain noisy seismic data Y; then divides the noisy seismic data Y into multiple data blocks of the same size, and constructs them into a first three-dimensional similar block group by calculation, stacking and For the first three-dimensional similar block group Perform second-order gradient transformations in three directions to obtain three second-order gradient tensors Then for the three second-order gradient tensors Apply low-rank constraints to obtain the second three-dimensional similar block group Finally, the second three-dimensional similar block group Reconstruct and restore the seismic data to obtain the de-noised seismic data The present invention uses a similar block matching framework to map low-dimensional seismic data to high-dimensional structural data, which can simultaneously encode non-local self-similarity, global low rank and gradient smoothness, reduce the number of introduced equilibrium parameters, and more comprehensively represent the seismic data; by introducing a second-order gradient tensor for low-rank modeling, it can effectively capture geometric features related to curvature and accurately represent the curved geological structures that often appear in seismic data, thereby effectively removing noise from the seismic data; in addition, by combining the three types of data prior information of non-local self-similarity, global low rank and gradient smoothness of seismic data, the denoised seismic data can be accurately restored. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 It is a flow chart of a seismic data denoising method based on fusion enhancement of low rank and gradient smoothness provided by an embodiment of the present invention;

[0035] Figure 2 is a quantitative comparison result diagram of the method proposed in the embodiment of the present invention and the comparative method in three seismic data;

[0036] Figure 3 It is a functional module block diagram of a seismic data denoising device based on fusion enhancement of low rank and gradient smoothness provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0037] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0038] Example 1

[0039] like Figure 1 As shown, the embodiment of the present invention provides a seismic data denoising method based on fusion enhancement of low rank and gradient smoothness, and the seismic data denoising method mainly includes the following steps:

[0040] Step S10: Add Gaussian white noise with the same standard deviation to the clean seismic data X to obtain noisy seismic data Y.

[0041] In this embodiment, the mathematical relationship between the noisy seismic data Y and the seismic data X is as follows:

[0042] Y = X + N;

[0043] N~NN(μ,σ 2 );

[0044] Where N is random noise, which means it obeys the standard normal distribution with mean μ and standard deviation σ.

[0045] Step S20: According to a certain step length L, the noisy seismic data Y is divided into multiple p*p data blocks of the same size, and the similarity value between each data block and the remaining data blocks is calculated in turn, and the first n smallest similarity values ​​are superimposed as the non-local self-similarity value of the data block; the smallest non-local self-similarity value in all data blocks where the data point is located is taken as the value of the corresponding position of the non-local self-similarity matrix to obtain the non-local self-similarity matrix S, and all non-local self-similarity matrices S are stacked and constructed into multiple first three-dimensional similarity block groups.

[0046] Specifically, the step length L is preferably an integer between 2 and 20; in the size of the data block p*p, the value of p is preferably an integer between 30 and 100; the first three-dimensional similar block group In , i is an integer between 1 and N, and N is the number of three-dimensional similar block groups.

[0047] This embodiment uses a similar block matching framework to map low-dimensional seismic data to high-dimensional structural data, which can simultaneously encode non-local self-similarity, global low rank and gradient smoothness, reduce the number of introduced balance parameters, and more comprehensively represent the seismic data.

[0048] Step S30: along each first three-dimensional similar block group Perform second-order gradient transformations in the three directions to obtain three second-order gradient tensors

[0049] Among them, the value of k is [1, 3], and the value of i is [1, N].

[0050] In one embodiment, the first three-dimensional similar block group Perform second-order gradient transformations in the three directions to obtain three second-order gradient tensors The steps include:

[0051] For each first three-dimensional similar block group According to formula (1):

[0052]

[0053] Get the first three-dimensional similar block group Second-order gradient tensor along three directions

[0054] Among them, l, m and n are the first three-dimensional similar block groups The three dimensions of l, m and n have the same value range as the first three-dimensional similar block group to match the size.

[0055] Step S40: for each first three-dimensional similar block group The three second-order gradient tensors of Apply low-rank constraints to obtain the second three-dimensional similar block group

[0056] Among them, the value of i is [1, N].

[0057] In one embodiment, for each first three-dimensional similar block group The three second-order gradient tensors of Apply low-rank constraints to obtain the second three-dimensional similar block group The steps include:

[0058] For each first three-dimensional similar block group According to formula (2):

[0059]

[0060] Get the second three-dimensional similar block group

[0061] Among them, y i represents the three-dimensional similar block group obtained by step S20; λ is the balance parameter; ||·||F is the Frobenius norm; k is three directions, and the value is [1, 3]; ||·|| ★ is a low-rank constraint.

[0062] Furthermore, this embodiment introduces auxiliary variables based on the ADMM algorithm Solve it and choose the tensor nuclear norm as the low-rank representation, and get the closed solution of formula (2):

[0063]

[0064] in, and represents the fast Fourier transform operator and the inverse fast Fourier transform operator, 1 represents a full 1 tensor, (·) H represents the complex conjugate operator, Λ <i，k> is the Lagrangian operator, and μ is the penalty parameter.

[0065] Specifically, the optimization problem of the above formula (2) can be equivalently transformed into the following formula:

[0066]

[0067] The augmented Lagrangian function of the above formula can be expressed as

[0068]

[0069] for Sub-problem

[0070]

[0071] Among them, ||·|| ＊ As a low-rank constraint term, the present invention selects the tensor nuclear norm as a low-rank representation, and the closed-form solution of the above formula is:

[0072]

[0073] Where τ = λ / μ, Represents the tensor singular value decomposition operator.

[0074] for Sub-questions:

[0075]

[0076] By taking the derivative, we can get the equivalent form of the above equation:

[0077]

[0078] Through fast Fourier transform, we can get the closed form solution as:

[0079]

[0080] in, and represents the fast Fourier transform operator and the inverse fast Fourier transform operator, 1 represents a full 1 tensor, (·) H represents the complex conjugate operator, Λ <i，k> is the Lagrangian operator, and μ is the penalty parameter.

[0081] This embodiment introduces the second-order gradient tensor to perform low-rank modeling, which can effectively capture the geometric features related to curvature and accurately represent the curved geological structures that often appear in seismic data, thereby effectively removing noise from seismic data.

[0082] Step S50: Group the second three-dimensional similar blocks Reconstruct and restore the seismic data to obtain the de-noised seismic data

[0083] This embodiment can accurately restore the denoised seismic data by combining three types of data prior information: non-local self-similarity, global low rank and gradient smoothness of seismic data.

[0084] In order to verify the seismic data denoising effect of this embodiment, the seismic data denoising method (ELGS) based on fusion enhanced low rank and gradient smoothness provided in this embodiment is compared with the weighted nuclear norm minimization denoising method (WNNM), multi-channel singular spectrum analysis denoising method (MSSA), local dictionary regularized regression denoising method (LDRR), deep denoising autoencoder denoising method (DDAE) and block-based UNET network denoising method (PATCHUNET).

[0085] In order to evaluate the excellent performance of the ELGS provided in this embodiment and the comparison methods, this embodiment provides three test data sets and three noise scenes, wherein the noise intensities represented by scenes 1, 2 and 3 are 0.1, 0.2 and 0.3 respectively.

[0086] like Figure 2 As shown, the best indicators are highlighted in bold. The observation results show that the ELGS method proposed in this embodiment achieves more competitive noise recovery performance. This is attributed to the ELGS method encoding the multidimensional characteristics of seismic data, including time evolution characteristics, geological spatial structure and non-local self-similarity. The other comparative methods are attributed to the occurrence of varying degrees of signal leakage or failure to completely remove noise. In short, the ELGS method proposed in this embodiment achieves the best evaluation indicators, which is attributed to the effective representation of the non-local self-similarity, gradient smoothness and low rank of high-dimensional structural data obtained from low-dimensional seismic data.

[0087] Example 2

[0088] like Figure 3 As shown, an embodiment of the present 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 adding module 100, a similar block group building module 200, a second-order gradient transformation module 300, a low rank constraint applying module 400 and a reconstruction and restoration module 500.

[0089] In this embodiment, the Gaussian white noise adding module 100 is specifically used to add Gaussian white noise with the same standard deviation to the clean seismic data X to obtain the noisy seismic data Y.

[0090] 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 length L, calculate the similarity value of each data block with the remaining data blocks in turn, and superimpose the first n 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.

[0091] The second-order gradient transformation module 300 is specifically used to transform the first three-dimensional similar block group along each Perform second-order gradient transformations in the three directions to obtain three second-order gradient tensors The value of k is [1, 3], and the value of i is [1, N].

[0092] The low-rank constraint imposing module 400 is specifically used to apply a low-rank constraint to each first three-dimensional similar block group. The three second-order gradient tensors of Apply low-rank constraints to obtain the second three-dimensional similar block group The value of i is [1, N].

[0093] The reconstruction and restoration module 500 is used to group the second three-dimensional similar blocks Reconstruct and restore the seismic data to obtain the de-noised seismic data

[0094] In detail, each module in the seismic data denoising device based on fusion enhancement of low rank and gradient smoothness provided in an embodiment of the present invention adopts the same technical means as the seismic data denoising method based on fusion enhancement of low rank and gradient smoothness provided in the above-mentioned Example 1 when used, and can produce the same technical effects, which will not be repeated here.

[0095] In summary, the embodiment of the present invention first adds Gaussian white noise with the same standard deviation to the clean seismic data X to obtain noisy seismic data Y; then divides the noisy seismic data Y into multiple data blocks of the same size, and constructs the first three-dimensional similar block group by calculation, stacking and construction For the first three-dimensional similar block group Perform second-order gradient transformations in three directions to obtain three second-order gradient tensors Then for the three second-order gradient tensors Apply low-rank constraints to obtain the second three-dimensional similar block group Finally, the second three-dimensional similar block group Reconstruct and restore the seismic data to obtain the de-noised seismic data

[0096] The embodiment of the present invention uses a similar block matching framework to map low-dimensional seismic data to high-dimensional structural data, which can simultaneously encode non-local self-similarity, global low rank and gradient smoothness, reduce the number of introduced equilibrium parameters, and more comprehensively represent the seismic data; by introducing a second-order gradient tensor for low-rank modeling, it can effectively capture geometric features related to curvature and accurately represent the curved geological structures that often appear in seismic data, thereby effectively removing noise from the seismic data; in addition, by combining the three types of data prior information of non-local self-similarity, global low rank and gradient smoothness of seismic data, the denoised seismic data can be accurately restored.

[0097] In the embodiments provided by the present invention, it should be understood that the disclosed equipment, devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of the modules is only a logical function division, and there may be other division methods in actual implementation. The modules described as separate components may or may not be physically separated, and the components displayed as modules may or may not be physical units, that is, they may be located in one place, or they may be distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the scheme of this embodiment. In addition, the functional modules in the various embodiments of the present invention may be integrated in a processing unit, or each unit may exist physically separately, or two or more units may be integrated in one unit. The above-mentioned integrated units may be implemented in the form of hardware or in the form of hardware plus software functional modules.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements 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: The following steps are involved: S10: Add Gaussian white noise with the same standard deviation to the clean seismic data X to obtain noisy seismic data Y; S20: According to a certain step length L, the noisy seismic data Y is divided into multiple p*p data blocks of the same size, and the similarity value between each data block and the remaining data blocks is calculated in turn, and the first n smallest similarity values ​​are superimposed as the non-local self-similarity value of the data block; the smallest non-local self-similarity value among all data blocks where the data point is located is taken as the value of the corresponding position of the non-local self-similarity matrix to obtain the non-local self-similarity matrix S, and all non-local self-similarity matrices S are stacked and constructed into 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 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 of Apply low-rank constraints to obtain the second three-dimensional similar block group The value of i is [1, N]; S50: Group the second three-dimensional similar blocks Reconstruct and restore the seismic data to obtain the de-noised seismic data 2. The seismic data denoising method based on fusion enhancement of low rank and gradient smoothness according to claim 1, characterized in that: The similar block group along each first three-dimensional Perform second-order gradient transformations in the three directions to obtain three second-order gradient tensors The steps include: For each first three-dimensional similar block group According to formula (1): Get the first three-dimensional similar block group Second-order gradient tensor along three directions Among them, l, m and n are the first three-dimensional similar block groups 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: For each first three-dimensional similar block group The three second-order gradient tensors of Apply low-rank constraints to obtain the second three-dimensional similar block group The steps include: For each first three-dimensional similar block group According to formula (2): Get the second three-dimensional similar block group Among them, y i represents the three-dimensional similar block group obtained by step S20; λ is the balance parameter; ||·||F is the Frobenius norm; k is three directions, and the value is [1, 3]; ||·|| ＊ is a low-rank constraint.

4. The seismic data denoising method based on fusion enhancement of low rank and gradient smoothness according to claim 3 is characterized in that: Based on the ADMM algorithm, auxiliary variables are introduced Solve it and choose the tensor nuclear norm as the low-rank representation, and get the closed solution of formula (2): in, and represents the fast Fourier transform operator and the inverse fast Fourier transform operator, 1 represents a full 1 tensor, (·) H represents the complex conjugate operator, Λ <i，k> is the Lagrangian operator, and μ is the penalty parameter.

5. 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 Reconstruct and restore the seismic data to obtain the de-noised seismic data The steps include: The processed second three-dimensional similar block group The corresponding position of the obtained non-local self-similarity matrix is ​​restored back to the seismic data to obtain the de-noised seismic data 6. A seismic data denoising device based on fusion enhancement of low rank and gradient smoothness, characterized in that: include: A Gaussian white noise adding module is used to add Gaussian white noise with the same standard deviation to the clean seismic data X to obtain the 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 length L, calculate the similarity value of each data block with the remaining data blocks in turn, and superimpose the first n smallest similarity values ​​as the non-local self-similarity value of the data block; take the smallest non-local self-similarity value of 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; A second-order gradient transformation module is used to transform the first three-dimensional similarity block group along each Perform second-order gradient transformations in the three directions to obtain three second-order gradient tensors The value of k is [1, 3], and the value of i is [1, N]; A low-rank constraint imposing module is used to impose a low-rank constraint on each first three-dimensional similar block group. The three second-order gradient tensors of Apply low-rank constraints to obtain the second three-dimensional similar block group The value of i is [1, N]; A reconstruction and restoration module is used to group the second three-dimensional similar blocks Reconstruct and restore the seismic data to obtain the de-noised seismic data

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