A method based on tensor decomposition and L P Seismic Denoising Method with Pseudonorm Mixed Domain Constraints

Abstract

The present invention provides a method based on tensor decomposition and L P A seismic denoising method based on pseudo-norm mixed domain constraints relates to the fields of oil and gas exploration and seismic data processing, which comprises the following steps: 1: preprocessing seismic data and obtaining seismic records S in the spatiotemporal domain; 2: extracting non-local related information and boundary information of seismic records in the spatiotemporal domain by using CP tensor decomposition and anisotropic total variation and constructing spatiotemporal domain constraints; 3: using L P Pseudo-norm and short-time Fourier transform mine the sparse information of seismic records in the time-frequency domain and construct time-frequency domain constraints; Step 4: Construct an objective function in combination with the seismic records and the constraints, and use the alternating direction multiplier method to iteratively calculate the objective function to obtain the seismic record X after denoising in the mixed domain. The present invention can eliminate random noise in seismic records, reduce the loss of effective signals, and improve the signal-to-noise ratio of seismic records.

Description

Technical Field

[0001] The invention relates to the field of oil and gas exploration and seismic data processing, and proposes a seismic denoising method based on tensor decomposition and pseudo-norm mixed domain constraints. Background Art

[0002] Seismic exploration technology plays a vital role in the exploration and development of oil, natural gas and mineral resources. However, the original seismic data obtained during seismic exploration are often affected by various noises. Therefore, how to effectively reduce the noise in seismic data and improve the signal-to-noise ratio of seismic records has become one of the important research directions in the field of seismic processing.

[0003] There is a problem of large edge errors in seismic records after CP tensor decomposition, and total variation constraints can effectively deal with the problem of large edge errors. Chen Hui et al. used tensor decomposition combined with isotropic total variation to perform time domain denoising on seismic data, and achieved certain results, proving the effectiveness of this method. However, total variation only solves the problem of large errors in seismic records after CP decomposition, resulting in residual noise in the denoising results and loss of effective information. Therefore, a denoising method is needed to overcome the above problems. Summary of the invention

[0004] The purpose of the present invention is to provide a seismic denoising method based on tensor decomposition and pseudo-norm mixed domain constraint, which solves the problem that the use of CP tensor decomposition leads to large edge errors of seismic records, and the noise in the denoising results is still residual and effective information is lost. Based on tensor decomposition, the method mines the sparse information of seismic records in the time-frequency domain through pseudo-norm and short-time Fourier transform, reduces the loss of effective information, and introduces boundary information through anisotropic total variation to improve the boundary continuity of seismic records.

[0005] In order to achieve the above-mentioned purpose, the present invention adopts the following technical means:

[0006] The present invention provides a method based on tensor decomposition and The seismic denoising method in pseudo-norm mixed domain includes the following steps:

[0007] Step 1: Preprocess the seismic data and obtain seismic records in the time and space domains ;

[0008] Step 2: Use CP tensor decomposition and anisotropic total variation to extract non-local related information and boundary information of seismic records in the time and space domains and construct constraints in the time and space domains;

[0009] Step 3: Exploitation Pseudo-norm and short-time Fourier transform are used to mine the sparse information of seismic records in time-frequency domain and construct constraints in time-frequency domain;

[0010] Step 4: Construct the objective function by combining the seismic records and the constraints, and use the alternating direction multiplier method to iteratively calculate the objective function to obtain the seismic records after hybrid domain denoising. The constraints are space-time domain constraints and time-frequency domain constraints.

[0011] In the above scheme, step 1 comprises the following steps:

[0012] Step 1.1: Input noisy earthquake records in time and space ;

[0013] Step 1.2: Based on earthquake records in time and space domains Construct the fidelity term in the objective function, as shown in Formula 1:

[0014] Formula 1

[0015] in, represents the noisy seismic records in the time and space domain, represents the denoised seismic record, represents the Frobenius norm, represents the minimization operator;

[0016] In the above scheme, step 2 comprises the following steps:

[0017] Step 2.1: Adoption The size of the matrix for earthquake records Perform segmentation processing to obtain segmented seismic record blocks. ;

[0018] Step 2.2: For each small block, use cosine similarity to calculate the similarity between blocks, and select the first 10,000 blocks from large to small in terms of similarity, and stack them into a three-dimensional tensor ;

[0019] Step 2.3: Use CP decomposition to decompose the tensor Decompose to obtain the sum of multiple rank 1 tensors. If the three-dimensional tensor , then its decomposition form is as follows:

[0020] Formula 2

[0021] in represents the outer product, represents its CP rank and , ,in Represents the factor matrix on the first dimension space, Represents the factor matrix on the second dimension space, Represents the factor matrix on the third dimension space;

[0022] Step 2.4: According to the rank of the input Before selection The new tensor is obtained by superimposing the groups as the seismic record after the CP tensor decomposition. , and construct the CP tensor decomposition constraint term

[0023] Formula 3

[0024] in Represents the weight coefficient of the low-rank constraint of CP decomposition;

[0025] Step 2.5: Based on Formula 3, the boundary information of the seismic records in the time and space domain is extracted using the anisotropic total variation method, and the time and space domain constraint terms are constructed, as shown in Formula 4:

[0026] Formula 4

[0027] in express The weight coefficient of the constraint, represents the anisotropic total variation, and its expression is shown in Formula 5:

[0028] Formula 5

[0029] in express norm, represents the longitudinal difference operator, represents the horizontal difference operator, and the definition of the vertical difference operator is shown in Formula 6:

[0030] Formula 6

[0031] The definition of the lateral difference operator is shown in Formula 7:

[0032] Formula 7

[0033] In the above scheme, step 3 comprises the following steps:

[0034] Step 3.1: Use short-time Fourier transform to solve the matrix The time-frequency domain seismic record is obtained from the seismic record, as shown in Formula 8:

[0035] Formula 8

[0036] Among them, the short-time Fourier transform positive solution matrix As shown in Formula 9:

[0037] Formula 9

[0038] in, represents a column vector, Control window length, Control frequency range, represents the Fourier transform factor;

[0039] Simplified form of short-time Fourier transform positive solution matrix As shown in formula 10:

[0040] Formula 10

[0041] Step 3.2: Exploitation The pseudo-norm mines the sparse information of seismic records in the time-frequency domain, as shown in Formula 11:

[0042] Formula 11

[0043] in, yes The weight coefficient of the pseudo-norm sparsity constraint, express Pseudo-norm, its expression is shown in formula 12:

[0044] Formula 12

[0045] in , , and Represents the first Row, No. columns, total number of rows and total number of columns, Representation Elements of P Power;

[0046] In the above scheme, step 4 includes the following steps:

[0047] Step 4.1: Construct the objective function by combining the seismic records and constraints as shown in Formula 13:

[0048] Formula 13

[0049] Step 4.2: Based on formula 13, introduce the Lagrange multiplier term , and , the dual term , and , we get the seismic denoising objective function based on hybrid domain constraints, as shown in Formula 14:

[0050] Formula 14

[0051] in and represents the weight coefficient of the dual term;

[0052] Step 4.3: Set low-rank constraint, sparse constraint, Weight coefficients for constraints and dual terms , , , and The value of Pseudo-norm The value of

[0053] Step 4.4: Set the initial value of the Lagrange multiplier , , and its dual initial value , , ;

[0054] Step 4.5: Update the seismic records to be denoised in the time domain according to the alternating direction multiplier algorithm and the Sylvester equation algorithm , the sub-objective function is shown in Formula 15:

[0055] Formula 15

[0056] The calculation formula is shown in Formula 16:

[0057] Formula 16

[0058] in represents the Kronecker product, the matrix and As shown in formula 17:

[0059] Formula 17

[0060] in represents the identity matrix, represents transpose, express The unit matrix, express The unit matrix, Represents vectorization;

[0061] Step 4.6: Update the Lagrange multiplier terms according to the alternating direction multiplier algorithm and the soft threshold shrinkage algorithm , and , as shown in formulas 18, 19, and 20:

[0062] Formula 18

[0063] Formula 19

[0064] Formula 20

[0065] in is a given parameter, the value is less than 1, Represents the dual term No. The data of the iteration, Indicates earthquake records No. The data of the iteration, Represents the dual term No. The data of the iteration;

[0066] Step 4.7: Update the dual term using the alternating direction multiplier algorithm and Fermat’s lemma , and , as shown in Formulas 21, 22, and 23:

[0067] Formula 21

[0068] Formula 22

[0069] Formula 23

[0070] Step 4.8: Judgement If yes, return to step 4.5 to loop; if no, end the loop.

[0071] Because the present invention adopts the above technical means, it has the following beneficial effects:

[0072] The present invention provides a seismic denoising method based on tensor decomposition and Lp pseudo-norm mixed domain constraint, which mines sparse information of seismic records in the time-frequency domain through Lp pseudo-norm and short-time Fourier transform, and mines boundary information of seismic records in the time-space domain through ATV, thereby solving the problem that the use of CP tensor decomposition leads to large edge errors of seismic records, and the denoising result still has residual noise and loss of effective information. The effect of improving the signal-to-noise ratio and continuity of seismic records is achieved. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 is a flowchart of the method of the present invention;

[0074] Figure 2 A noise-free seismic profile of the present invention;

[0075] Figure 3 A noisy seismic profile according to the present invention;

[0076] Figure 4 This is a schematic diagram of the denoising result of combining CP tensor decomposition with ATV;

[0077] Figure 5 It is a schematic diagram of the denoising result of the present invention. DETAILED DESCRIPTION

[0078] The following is a detailed description of the embodiments of the present invention. Although the present invention will be described and illustrated in conjunction with some specific embodiments, it should be noted that the present invention is not limited to these embodiments. On the contrary, modifications or equivalent substitutions made to the present invention should all be included in the scope of the claims of the present invention.

[0079] In addition, in order to better illustrate the present invention, numerous specific details are given in the following specific embodiments. It will be understood by those skilled in the art that the present invention can also be implemented without these specific details.

[0080] Combine the following Figure 1-5 The present invention is described in detail.

[0081] The technical problem solved by the present invention is as follows: the problem that the use of CP tensor decomposition leads to large edge errors in seismic records and that noise in denoising results is still residual and effective information is lost is solved, thereby improving the denoising effect.

[0082] Technical means: A method based on tensor decomposition and The seismic denoising method based on pseudo-norm mixed domain constraint includes the following steps:

[0083] Step 1: Preprocess the seismic data and obtain seismic records in the time and space domains ;

[0084] Step 2: Use CP tensor decomposition and anisotropic total variation to extract non-local related information and boundary information of seismic records in the time and space domains and construct constraints in the time and space domains;

[0085] Step 3: Exploitation Pseudo-norm mines sparse information of seismic records in time-frequency domain and constructs constraints in time-frequency domain;

[0086] Step 4: Use the alternating direction multiplier method to iteratively calculate the objective function to obtain the seismic record after hybrid domain denoising The constraints are space-time domain constraints and time-frequency domain constraints.

[0087] Step 1 includes the following steps:

[0088] Step 1.1: Input noisy seismic records in time and space domain;

[0089] Step 1.2: Based on earthquake records in time and space domains Construct the fidelity term in the objective function, as shown in Formula 1:

[0090] Formula 1

[0091] in, represents the noisy seismic records in the time and space domain, represents the denoised seismic record, represents the Frobenius norm, Indicates that the objective function is minimized The value of

[0092] Step 2 includes the following steps:

[0093] Step 2.1: Use a matrix of different sizes to segment the seismic records to obtain segmented small blocks of seismic records. ;

[0094] Step 2.2: For each small block, use cosine similarity to calculate the similarity between blocks, and select the first 10,000 blocks from large to small in terms of similarity, and stack them into a three-dimensional tensor ;

[0095] Step 2.3: Use CP decomposition to decompose the tensor Decompose to obtain the sum of multiple rank 1 tensors. If the three-dimensional tensor , then its decomposition form is as follows:

[0096] Formula 2

[0097] in represents the outer product, represents its CP rank and , ,in Represents the factor matrix on the first dimension space, Represents the factor matrix on the second dimension space, Represents the factor matrix on the third dimension space;

[0098] Step 2.4: According to the rank of the input Before selection The new tensor is obtained by superimposing the groups as the seismic record after the CP tensor decomposition. , and construct the CP tensor decomposition constraint term

[0099] Formula 3

[0100] in Represents the weight coefficient of the low-rank constraint of CP decomposition;

[0101] Step 2.5: Based on Formula 3, the boundary information of the seismic records in the time and space domain is extracted using the anisotropic total variation method, and the time and space domain constraint terms are constructed, as shown in Formula 4:

[0102] Formula 4

[0103] where represents the weight coefficient of the constraint, represents the anisotropic total variation, and its expression is shown in Formula 5:

[0104] Formula 5

[0105] in represents the norm, represents the longitudinal difference operator, represents the horizontal difference operator, and the definition of the vertical difference operator is shown in Formula 6:

[0106] Formula 6

[0107] The definition of the lateral difference operator is shown in Formula 7:

[0108] Formula 7

[0109] Step 3 includes the following steps:

[0110] Step 3.1: Use the short-time Fourier transform forward solution matrix to obtain the time-frequency domain seismic record from the seismic record, as shown in Formula 8:

[0111] Formula 8

[0112] Among them, the short-time Fourier transform positive solution matrix is ​​shown in formula 9:

[0113] Formula 9

[0114] in, represents a column vector, Control window length, Control frequency range, represents the Fourier transform factor;

[0115] The simplified short-time Fourier transform forward solution matrix is ​​shown in formula 10:

[0116] Formula 10

[0117] Step 3.2: Use the pseudo-norm to mine the sparse information of seismic records in the time-frequency domain, as shown in Formula 11:

[0118] Formula 11

[0119] in, yes The weight coefficient of the pseudo-norm sparsity constraint, express Pseudo-norm, its expression is shown in formula 12:

[0120] Formula 12

[0121] in , , and Represents the first Row, No. columns, total number of rows and total number of columns, Representation Elements The Pth power;

[0122] Step 4 includes the following steps:

[0123] Step 4.1: Construct the objective function by combining the seismic records and constraints as shown in Formula 13:

[0124] Formula 13

[0125] Step 4.2: Based on formula 13, introduce the Lagrange multiplier term , and , the dual term , and , we get the seismic denoising objective function based on hybrid domain constraints, as shown in Formula 14:

[0126] Formula 14

[0127] in and represents the weight coefficient of the dual term;

[0128] Step 4.3: Set the weight coefficients of low-rank constraint, sparse constraint, constraint and dual terms respectively , , , and The value of Pseudo-norm The value of

[0129] Step 4.4: Set the initial value of the Lagrange multiplier , , and its dual initial value , , ;

[0130] Step 4.5: Update the seismic records to be denoised in the time domain according to the alternating direction multiplier algorithm and the Sylvester equation algorithm , the sub-objective function is shown in Formula 15:

[0131] Formula 15

[0132] The calculation formula is shown in Formula 16:

[0133] Formula 16

[0134] The matrices and are given by formula 17:

[0135] Formula 17

[0136] in represents the identity matrix, represents transpose, express The unit matrix, express The unit matrix, Represents vectorization;

[0137] Step 4.6: Update the Lagrange multiplier terms according to the alternating direction multiplier algorithm and the soft threshold shrinkage algorithm , and , as shown in formulas 18, 19, and 20:

[0138] Formula 18

[0139] Formula 19

[0140] Formula 20

[0141] in is a given parameter, the value is less than 1, Represents the dual term No. The data of the iteration, Indicates earthquake records No. The data of the iteration, Represents the dual term No. The data of the iteration;

[0142] Step 4.7: Update the dual term using the alternating direction multiplier algorithm and Fermat’s lemma , and , as shown in Formulas 21, 22, and 23:

[0143] Formula 21

[0144] Formula 22

[0145] Formula 23

[0146] Step 4.8: Judgement If yes, return to step 4.5 to loop; if no, end the loop.

[0147] Technical effect: The present invention adopts CP tensor decomposition with anisotropic total variation constraints and introduces frequency domain information through pseudo-norm, which solves the problems of large edge errors of seismic records caused by using CP tensor decomposition and residual noise in denoising results and loss of effective information, thereby improving the denoising effect.

[0148] Example 1

[0149] like Figure 1-5 As shown, the mixed domain constrained denoising is as follows:

[0150] Step 1.1: Input noisy seismic records in time and space domain;

[0151] Step 1.2: Based on earthquake records in time and space domains Construct the fidelity term in the objective function, as shown in Formula 1:

[0152] Formula 1

[0153] in, represents the noisy seismic records in the time and space domain, represents the denoised seismic record, represents the Frobenius norm, Indicates that the objective function is minimized The value of .

[0154] Step 2.1: Adoption The size of the matrix for earthquake records Perform segmentation processing to obtain segmented seismic record blocks. ;

[0155] Step 2.2: For each small block, use cosine similarity to calculate the similarity between blocks, and select the first 10,000 blocks from large to small in terms of similarity, and stack them into a three-dimensional tensor ;

[0156] Step 2.3: Use CP decomposition to decompose the tensor Decompose to obtain the sum of multiple rank 1 tensors. If the third-order tensor , then its decomposition form is as follows:

[0157] Formula 2

[0158] in represents the outer product, represents its CP rank and , ,in Represents the factor matrix on the first dimension space, Represents the factor matrix on the second dimension space, Represents the factor matrix on the third dimension space;

[0159] Step 2.4: According to the rank of the input Before selection The new tensor is obtained by superimposing the groups as the seismic record after the CP tensor decomposition. , and construct the CP tensor decomposition constraint term

[0160] Formula 3

[0161] in Represents the weight coefficient of the low-rank constraint of CP decomposition;

[0162] Step 2.5: Based on Formula 3, the boundary information of the seismic records in the time and space domain is extracted using the anisotropic total variation method, and the time and space domain constraint terms are constructed, as shown in Formula 4:

[0163] Formula 4

[0164] in express The weight coefficient of the constraint, represents the anisotropic total variation, and its expression is shown in Formula 5:

[0165] Formula 5

[0166] in express norm, represents the longitudinal difference operator, represents the horizontal difference operator, and the definition of the vertical difference operator is shown in Formula 6:

[0167] Formula 6

[0168] The definition of the lateral difference operator is shown in Formula 7:

[0169] Formula 7

[0170] Step 3.1: Use the short-time Fourier transform forward solution matrix to obtain the time-frequency domain seismic record from the seismic record, as shown in Formula 8:

[0171] Formula 8

[0172] Among them, the short-time Fourier transform positive solution matrix is ​​shown in formula 9:

[0173] Formula 9

[0174] in, represents a column vector, Control window length, Control frequency range, represents the Fourier transform factor;

[0175] Simplified form of short-time Fourier transform positive solution matrix As shown in formula 10:

[0176] Formula 10

[0177] Step 3.2: Use the pseudo-norm to mine the sparse information of seismic records in the time-frequency domain, as shown in Formula 11:

[0178] Formula 11

[0179] in, yes The weight coefficient of the pseudo-norm sparsity constraint, express Pseudo-norm, its expression is shown in formula 12:

[0180] Formula 12

[0181] in , , and Represents the first Row, No. columns, total number of rows and total number of columns, Representation Elements The Pth power;

[0182] Step 4.1: Construct the objective function by combining the seismic records and constraints as shown in Formula 13:

[0183] Formula 13

[0184] Step 4.2: Based on formula 13, introduce the Lagrange multiplier term , and , the dual term , and , we get the seismic denoising objective function based on hybrid domain constraints, as shown in Formula 14:

[0185] Formula 14

[0186] in and represents the weight coefficient of the dual term;

[0187] Step 4.3: Set low-rank constraint, sparse constraint, Weight coefficients for constraints and dual terms , , , and The value of Pseudo-norm The value of

[0188] Step 4.4: Set the initial value of the Lagrange multiplier , , and its dual initial value , , ;

[0189] Step 4.5: Update the seismic records to be denoised in the time domain according to the alternating direction multiplier algorithm and the Sylvester equation algorithm , the sub-objective function is shown in Formula 15:

[0190]

[0191] Formula 15

[0192] The calculation formula is shown in Formula 16:

[0193] Formula 16

[0194] The matrices and are given by formula 17:

[0195] Formula 17

[0196] in represents the identity matrix, represents transpose, express The unit matrix, express The unit matrix, Represents vectorization;

[0197] Step 4.6: Update the Lagrange multiplier terms according to the alternating direction multiplier algorithm and the soft threshold shrinkage algorithm , and , as shown in Formulas 18, 19, and 20:

[0198] Formula 18

[0199] Formula 19

[0200] Formula 20

[0201] in is a given parameter, the value is less than 1, Represents the dual term No. The data of the iteration, Indicates earthquake records No. The data of the iteration, Represents the dual term No. The data of the iteration;

[0202] Step 4.7: Update the dual term using the alternating direction multiplier algorithm and Fermat’s lemma , and , as shown in Formulas 21, 22, and 23:

[0203] Formula 21

[0204] Formula 22

[0205] Formula 23

[0206] Step 4.8: Judgement If yes, return to step 4.5 to loop; if no, end the loop.

[0207] Effect analysis: Figure 2-5 As shown in the figure, the denoised seismic record profile can more clearly reflect the underground layer and structure than the noisy seismic record profile, which proves the correctness of this method. Figure 2 and Figure 5 , we can find that the denoised earthquake record is very close to the real noise-free earthquake record. Figure 4 and Figure 5 It can be found that this method is more effective in suppressing noise, and effective information is better preserved, which further proves the correctness of the method. The present invention adopts CP tensor decomposition with anisotropic total variation constraints, and introduces frequency domain information through pseudo-norm, and proposes a seismic denoising method based on mixed domain constraints in combination with the alternating direction multiplier method. The noisy seismic records are denoised using the denoising method mentioned above, and the optimal denoising results are output through repeated iterations. The problem of large edge errors of seismic records caused by the use of CP tensor decomposition and residual noise in the denoising results and loss of effective information is solved, thereby improving the denoising effect.

Claims

1. A method based on tensor decomposition and The seismic denoising method based on pseudo-norm mixed domain constraint is characterized by: The steps include: Step 1: Preprocess the seismic data and obtain seismic records in the time and space domains ; Step 2: Use CP tensor decomposition and anisotropic total variation to extract non-local related information and boundary information of seismic records in the time and space domains and construct constraints in the time and space domains; Step 3: Exploitation Pseudo-norm and short-time Fourier transform are used to mine the sparse information of seismic records in time-frequency domain and construct constraints in time-frequency domain; Step 4: Construct the objective function by combining the seismic records and the constraints, and use the alternating direction multiplier method to iteratively calculate the objective function to obtain the seismic records after hybrid domain denoising. , where the constraints refer to the space-time domain constraints and the time-frequency domain constraints.

2. A method according to claim 1 based on tensor decomposition and The seismic denoising method based on pseudo-norm mixed domain constraint is characterized by: The step 1 comprises the following steps: Step 1.1: Input noisy earthquake records in time and space ; Step 1.2: Based on earthquake records in time and space domains Construct the fidelity term in the objective function, as shown in Formula 1: Formula 1 in, represents the noisy seismic records in the time and space domain, represents the denoised seismic record, represents the Frobenius norm, Represents the minimization operator.

3. A method according to claim 2 based on tensor decomposition and The seismic denoising method based on pseudo-norm mixed domain constraint is characterized by: The step 2 comprises the following steps: Step 2.1: Adoption The size of the matrix for earthquake records Perform segmentation processing to obtain segmented seismic record blocks. ; Step 2.2: For each small block, use cosine similarity to calculate the similarity between blocks, and select the first 10,000 blocks from large to small in terms of similarity, and stack them into a three-dimensional tensor ; Step 2.3: Use CP decomposition to decompose the tensor Decompose to obtain the sum of multiple rank 1 tensors. If the three-dimensional tensor , then its decomposition form is as follows: Formula 2 in represents the outer product, represents its CP rank and , ,in Represents the factor matrix on the first dimension space, Represents the factor matrix on the second dimension space, Represents the factor matrix on the third dimension space; Step 2.4: According to the rank of the input Before selection The new tensor is obtained by superimposing the groups as the seismic record after the CP tensor decomposition. , and construct the CP tensor decomposition constraint term Formula 3 in Represents the weight coefficient of the low-rank constraint of CP decomposition; Step 2.5: Based on Formula 3, the boundary information of the seismic records in the time and space domain is extracted using the anisotropic total variation method, and the time and space domain constraint terms are constructed, as shown in Formula 4: Equation 4 in express The weight coefficient of the constraint, represents the anisotropic total variation, and its expression is shown in Formula 5: Formula 5 in express norm, represents the longitudinal difference operator, represents the horizontal difference operator, and the definition of the vertical difference operator is shown in Formula 6: Formula 6 The definition of the lateral difference operator is shown in Formula 7: Formula 7.

4. A method according to claim 3 based on tensor decomposition and The seismic denoising method based on pseudo-norm mixed domain constraint is characterized by: The step 3 comprises the following steps: Step 3.1: Use short-time Fourier transform to solve the matrix The time-frequency domain seismic record is obtained from the seismic record, as shown in Formula 8: Formula 8 Among them, the short-time Fourier transform positive solution matrix As shown in Formula 9: Formula 9 in, represents a column vector, Control window length, Control frequency range, represents the Fourier transform factor; Simplified form of short-time Fourier transform positive solution matrix As shown in formula 10: Formula 10 Step 3.2: Exploitation The pseudo-norm mines the sparse information of seismic records in the time-frequency domain, as shown in Formula 11: Formula 11 in, yes The weight coefficient of the pseudo-norm sparsity constraint, express Pseudo-norm, its expression is shown in formula 12: Formula 12 in , , and Represents the first Row, No. columns, total number of rows and total number of columns, Representation elements of P Power.

5. A method according to claim 4 based on tensor decomposition and The seismic denoising method based on pseudo-norm mixed domain constraint is characterized by: The step 4 comprises the following steps: Step 4.1: Construct the objective function by combining the seismic records and constraints as shown in Formula 13: Formula 13 Step 4.2: Based on formula 13, introduce the Lagrange multiplier term , and , the dual term , and , we get the seismic denoising objective function based on hybrid domain constraints, as shown in Formula 14: Formula 14 in and represents the weight coefficient of the dual term; Step 4.3: Set low-rank constraint, sparse constraint, Weight coefficients for constraints and dual terms , , , and The value of Pseudo-norm The value of Step 4.4: Set the initial value of the Lagrange multiplier , , and its dual initial value , , ; Step 4.5: Update the seismic records to be denoised in the time domain according to the alternating direction multiplier algorithm and the Sylvester equation algorithm , the sub-objective function is shown in Formula 15: Formula 15 The calculation formula is shown in Formula 16: Formula 16 in represents the Kronecker product, the matrix and As shown in formula 17: Formula 17 in represents the identity matrix, represents transpose, express The unit matrix, express The unit matrix, Represents vectorization; Step 4.6: Update the Lagrange multiplier terms according to the alternating direction multiplier algorithm and the soft threshold shrinkage algorithm , and , as shown in formulas 18, 19, and 20: Formula 18 Formula 19 Formula 20 in Represents the dual term No. The data of the iteration, Indicates earthquake records No. The data of the iteration, Represents the dual term No. The data of the iteration; Step 4.7: Update the dual term using the alternating direction multiplier algorithm and Fermat’s lemma , and , as shown in Formulas 21, 22, and 23: Official 21 Formula 22 Formula 23 Step 4.8: Judgement If yes, return to step 4.5 to loop; if no, end the loop.

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