Method for removing random interference in coal field seismic data
The seismic data is denoised by the singular value decomposition algorithm, which solves the problem of poor random interference denoising effect in coalfield seismic exploration data processing, and achieves the effect of improving signal-to-noise ratio and data quality.
Patent Information
- Application Number
- CN202411568427.1
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-11-05
- Publication Date
- 2025-02-21
Smart Images
Figure CN119493168A_ABST
Abstract
Description
Technical Field
[0001] The invention relates to a seismic data denoising method, belongs to the field of coalfield seismic exploration data processing, and specifically relates to a method for removing random interference in seismic data based on a singular value decomposition algorithm.
[0002] Background technology introduction
[0003] The singular value decomposition filtering method is based on the characteristic of correlation of seismic data. It uses singular values as orthogonal basis to decompose signals in space. On this basis, it uses the correlation difference of seismic waves to realize wave field separation and denoising. If a larger eigenvalue is used to reconstruct the data, the elimination of weak signals and random noise is realized. According to the relevant theory of singular value decomposition, the decomposed singular value subspace is composed of horizontal events. After the data is reconstructed, the horizontal events of different energies are superimposed, and visually curved events appear. Therefore, singular value decomposition is more suitable for data processing with linear events, and there will be large errors in theory when reconstructing inclined or curved strata through singular value decomposition. For the reflection wave events of seismic data, the correlation of each channel data is very good, while the noise is randomly distributed in the channel gather, and the correlation is poor. Therefore, removing random noise interference is very suitable for signal-noise separation and denoising using the theory of singular value decomposition. Based on the characteristic that the reflection wave of seismic data has well-correlated aligned events, the present invention performs singular value decomposition on seismic data, and determines the noise reduction order by the weighted ratio method, thereby realizing the separation and denoising of seismic wave fields.
[0004] Technical issues solved
[0005] The embodiment of the present invention provides a method for removing random interference in seismic data, which solves the problems of poor random interference denoising effect and low signal-to-noise ratio of seismic data in existing coalfield seismic exploration data processing.
[0006] Detailed technical solution
[0007] To solve the above problems, the solution of the present invention is:
[0008] The singular value decomposition step of the seismic data determines the singular values that characterize the reflected waves and random interference;
[0009] Singular value sorting step, sorting the singular values in a non-increasing sequence to determine relatively large singular values;
[0010] The weighted ratio calculation step is to sequentially substitute all singular values into the formula to calculate the weighted ratio of each singular value, and select the k value corresponding to when the weighted ratio reaches 80% to 90%, which is determined as the noise reduction order;
[0011] The seismic data reconstruction step uses the previous k singular values to reconstruct the seismic data and determine the seismic data after removing random interference.
[0012] Preferably, in the above method for removing random interference from seismic data, in the seismic data singular value decomposition step, any m×n-order matrix X can be decomposed into the product of an m×m orthogonal matrix U, an m×n-order diagonal matrix Σ and an n×n-order orthogonal matrix V.
[0013] X=U∑V T (1)
[0014] Where U is XX T The eigenvectors of T The eigenvectors of X, ∑ is composed of singular values, that is, ∑ = diag(σ1,σ2,···,σ r )(r≤min{m,n}), where σ i (i=1,2,···,r) are the singular values of the matrix X, and are arranged in non-increasing order. The square root of the eigenvalue is generally defined as the singular value of the matrix. The above formula is called the singular value decomposition of the matrix X.
[0015] From (1), another expression of singular value decomposition can be derived:
[0016]
[0017] Where u i , v i are the i-th eigenvectors of U and V respectively, represents the eigenimage of the i-th singular value. The singular value decomposition formula can be regarded as the orthogonal decomposition of X from left to right. When the matrix has r singular values, the matrix X can be decomposed into the algebraic sum of r subspaces. That is,
[0018] X N×M =(X N×M )1+(X N×M )2+···+(X N×M ) r (3)
[0019] In the formula is the subspace corresponding to the ith singular value. Since equation (3) is a decomposition process from left to right, it is a reconstruction process from right to left. After the seismic signal X undergoes singular value decomposition, its total energy can be expressed as Explain the strength of seismic trace energy and σ i Therefore, the larger the singular value component, the greater the contribution to the seismic signal. When all seismic traces are correlated, r = 1, then E X=σ1. Therefore, for seismic profiles, aligned events have the best correlation, corresponding to the first or first few eigenvalues, unaligned events have poor correlation, corresponding to some of the later eigenvalues, and pure random noise has even worse correlation or close to zero, corresponding to some of the last small singular values.
[0020] Preferably, in the above-mentioned method for removing random interference in seismic data, the weighted ratio calculation step, in order to improve the effect of the singular value decomposition denoising method, the present invention first corrects the singular value data
[0021]
[0022] The modified singular value weighted ratio η is calculated by the following formula:
[0023]
[0024] Define k singular value decomposition denoising parameters, so that the parameters can be determined by weighted ratio rate. Statistics show that by taking the first k singular values corresponding to the weighted ratio η reaching 80% to 90% for data reconstruction, denoised data with better signal-to-noise ratio can be obtained.
[0025] Preferably, in the method and device for removing random interference from seismic data, in the seismic data reconstruction step, the first k larger singular values in the singular value sequence are contributed by effective signals, and the latter smaller singular values are completely composed of random interference, so the subspace of the effective signal is reconstructed by the first k singular values. The reconstructed seismic data is the result after removing random noise.
[0026] From the above description, it can be seen that the present invention has the following advantages: the method of the present invention is based on the characteristic that seismic data has correlation, uses singular values as an orthogonal basis to decompose signals in space, and on this basis uses the correlation differences of seismic waves to achieve wave field separation and denoising, which can effectively remove random interference in seismic data. BRIEF DESCRIPTION OF THE DRAWINGS
[0027] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.
[0028] Figure 1 A schematic diagram of a process for removing random interference provided by an embodiment of the present invention;
[0029] Figure 2The noisy seismic data and the subspace data reconstructed by selecting different singular values after singular value decomposition, including (a) noisy ADCIGs; (b) subspace corresponding to σ1; (c) subspace corresponding to σ2; (d) subspace corresponding to σ3; (e) subspace corresponding to σ4; (f) subspace corresponding to the 20th and subsequent singular values;
[0030] Figure 3 A weighted ratio curve provided by an embodiment of the present invention;
[0031] Figure 4 This is a diagram showing the effect of random interference removal provided by an embodiment of the present invention, wherein Figure a is an angle gather containing noise, Figure b is a gather after denoising, and Figure c is the removed random noise. DETAILED DESCRIPTION
[0032] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.
[0033] Figure 1 A schematic flow chart of a method for removing random interference from seismic data provided by an embodiment of the present invention is shown in FIG. Figure 1 As shown, the method mainly includes the following steps:
[0034] Step 101, determining singular values characterizing reflected waves and random interference;
[0035] Step 102, sorting the singular values in a non-increasing sequence to determine relatively large singular values;
[0036] Step 103, all singular values are sequentially substituted into a formula to calculate a weighted ratio of each singular value, and a k value corresponding to when the weighted ratio reaches 85% is selected and determined as a noise reduction parameter;
[0037] Step 104, using the first k singular values to reconstruct the seismic data, and determine the seismic data after removing random interference.
[0038] In step 101, the main purpose of this step is to perform singular value decomposition on the original seismic data to determine the singular values that characterize the reflection wave and the random interference wave. For any m×n-order matrix X, it can be decomposed into the product of an m×m orthogonal matrix U, an m×n-order diagonal matrix Σ, and an n×n-order orthogonal matrix V.
[0039] X=U∑V T (1)
[0040] Where U is XX T The eigenvectors of T The eigenvectors of X, ∑ is composed of singular values, that is, ∑ = diag(σ1,σ2,···,σ r )(r≤min{m,n}), where σ i (i=1,2,···,r) are the singular values of the matrix X, and are arranged in non-increasing order. The square root of the eigenvalue is generally defined as the singular value of the matrix. The above formula is called the singular value decomposition of the matrix X.
[0041] From (1), another expression of singular value decomposition can be derived:
[0042]
[0043] Where u i , v i are the i-th eigenvectors of U and V respectively, represents the eigenimage of the i-th singular value. The singular value decomposition formula can be regarded as the orthogonal decomposition of X from left to right. When the matrix has r singular values, the matrix X can be decomposed into the algebraic sum of r subspaces. That is,
[0044] X N×M =(X N×M )1+(X N×M )2+···+(X N×M ) r (3)
[0045] In the formula is the subspace corresponding to the ith singular value. Since equation (3) is a decomposition process from left to right, it is a reconstruction process from right to left.
[0046] After the singular value decomposition of the seismic signal X, its total energy can be expressed as Explain the strength of seismic trace energy and σ i Therefore, the larger the singular value component, the greater the contribution to the seismic signal. When all seismic traces are correlated, r = 1, then E X =σ1. Therefore, for seismic profiles, aligned events have the best correlation, corresponding to the first or first few eigenvalues, unaligned events have poor correlation, corresponding to some of the later eigenvalues, and pure random noise has even worse correlation or close to zero, corresponding to some of the last small singular values. Figure 2 is the noisy seismic data and the subspace data reconstructed by selecting different singular values after singular value decomposition, where Figure 2(a) is the original seismic data with noise, and there is waveform stretching at high angles. (b) is the subspace reconstructed by the first singular value feature image, which reflects the neatly arranged coherent event axes. (c) is the subspace reconstructed by the second singular value, which reflects the interrupted event axes. (d) and (e) are the signal images reconstructed by the third and fourth singular values, respectively, with more interrupted event axes. (f) is the data reconstructed by the singular value images after the 20th, and only noise is seen in the signal. In addition, it can be seen that the event axes in Figures (c) and (d) have phase differences while being interrupted, which is a reflection of the waveform stretching in the original data. When reconstructing data, if the subspace corresponding to the first k singular values is selected, a signal with good correlation is obtained. If the last few small eigenvalues are used to reconstruct the data, the main thing obtained is noise. Therefore, the purpose of signal-to-noise separation and denoising can be achieved through data reconstruction.
[0047] In step 102, this step mainly performs singular value sorting, wherein the sorting needs to be in non-increasing order, which is conducive to quickly selecting relatively large singular values.
[0048] In step 103, all singular values are weighted according to the formula to calculate the noise reduction order. In order to reduce the influence of weak noise on the noise reduction order estimation, the singular value sequence is first modified as follows:
[0049]
[0050] The modified singular value weighted ratio η is calculated by the following formula:
[0051]
[0052] Define k as the noise reduction order, so that the noise reduction order can be determined by the cumulative contribution rate. Statistics show that the k value corresponding to η reaching 80% to 90% is taken as the noise reduction order ( Figure 3 ), a better denoising effect can be obtained.
[0053] In step 104, the first k singular values are used to reconstruct the seismic data to determine the seismic data after random interference is removed. Figure 4 a is the Marmousi model data after angle domain migration and random noise addition. It can be seen that the seismic data has obvious waveform stretching and random noise. In denoising, the denoising order is estimated by the weighted ratio method, and the characteristic image of the first 8 singular values is taken for data reconstruction. The denoising results show that the random noise in the original data is well removed, the high-angle frequency stretching is also suppressed, and the signal-to-noise ratio of the profile is significantly improved ( Figure 4 b), Figure 4c is the noise removed by singular value decomposition. It can be seen that the noise data does not contain signals with horizontal event axes, indicating that the effective information is protected after denoising.
[0054] Note that references in the specification to "one embodiment," "an embodiment," "an example embodiment," "some embodiments," etc. indicate that the described embodiments may include a particular feature, structure, or characteristic, but each embodiment may not necessarily include the particular feature, structure, or characteristic. Moreover, such phrases do not necessarily refer to the same embodiment. In addition, when a particular feature, structure, or characteristic is described in conjunction with an embodiment, whether or not explicitly described, it would be within the knowledge of a person skilled in the art to implement such feature, structure, or characteristic in conjunction with other embodiments.
Claims
1. A method for removing random interference in coalfield seismic data, characterized in that: include: The seismic data singular value decomposition step is to perform singular value decomposition on the post-stack seismic data to determine the singular values representing the reflection wave and the random interference; Singular value sorting step, sorting the singular values in non-increasing order to determine relatively large singular values; Denoising parameter determination step: all singular values are sequentially substituted into the formula to calculate the weighted ratio of each singular value. When the weighted ratio reaches 80% to 90%, the corresponding k value is determined as a reasonable denoising parameter. In the seismic data reconstruction step, the first k singular values are used to perform inverse singular value decomposition to determine the seismic data after random interference is removed.
2. The method according to claim 1, characterized in that In the seismic data singular value decomposition step, the singular value decomposition process is as follows: Any m×n matrix X can be decomposed into the product of an m×m orthogonal matrix U, an m×n diagonal matrix Σ, and an n×n orthogonal matrix V. X=U∑V T (1) Where U is XX T The eigenvectors of T The eigenvectors of X, ∑ is composed of singular values, that is, ∑ = diag(σ1,σ2,···,σ r )(r≤min{m,n}), where σ i (i=1,2,···,r) are the singular values of the matrix X, and are arranged in non-increasing order. The square root of the eigenvalue is generally defined as the singular value of the matrix. The above formula is called the singular value decomposition of the matrix X. From (1), another expression of singular value decomposition can be derived: Where u i , v i are the i-th eigenvectors of U and V respectively, represents the eigenimage of the i-th singular value. The singular value decomposition formula can be regarded as the orthogonal decomposition of X from left to right. When the matrix has r singular values, the matrix X can be decomposed into the algebraic sum of r subspaces. That is, X N×M =(X N×M )1+(X N×M )2+···+(X N×M ) r (3) In the formula is the subspace corresponding to the ith singular value. Since equation (3) is a decomposition process from left to right, it is a reconstruction process from right to left. After the singular value decomposition of the seismic signal X, its total energy can be expressed as Explain the strength of seismic trace energy and σ i Therefore, the larger the singular value, the greater the overall ratio of the seismic signal energy strength. When all the seismic traces are correlated, r = 1, then E X =σ1.
3. The method according to claim 1, characterized in that Weighted ratio calculation steps: In order to reduce the impact of weak noise on the noise reduction order estimation, the present invention first corrects the singular values after the seismic data is decomposed. The modified singular value to seismic data energy weighted ratio η is calculated by the following formula: k is defined as the singular value decomposition denoising parameter, which can be determined by the energy weighting ratio. Statistics show that taking the first k singular values corresponding to a weighting ratio η of 80% to 90% for data reconstruction can achieve better singular value decomposition denoising effect.
4. The method according to claim 1, characterized in that In the seismic data reconstruction step, the first k larger singular values in the singular value sequence are contributed by the effective signal, and the later smaller singular values are contributed by the random interference wave. Therefore, the subspace of the effective signal can be reconstructed by the first k singular values. The reconstructed seismic data is the result after removing the random noise.