A method for seismic noise suppression using variational mode decomposition and schrodinger equation

Abstract

The present application belongs to the technical field of oil and gas exploration seismic data processing. The present application discloses a method for suppressing seismic noise by using variational mode decomposition and Schrodinger equation. The method decomposes the seismic data of the target layer by using the variational mode decomposition algorithm to obtain the intrinsic mode function data body, then constructs an adaptive denoising operator by using the Schrodinger equation for each trace of the intrinsic mode function data body, calculates the projection coefficient of the noisy seismic signal projected onto the adaptive basis, then performs soft threshold processing on the projection coefficient, reconstructs each intrinsic mode function data body after processing, and generates denoised seismic data. The method first decomposes the seismic signal into a series of intrinsic mode functions by using the variational mode decomposition, then denoises the intrinsic mode functions by using the adaptive denoising operator constructed by the Schrodinger equation, which is beneficial to removing high-frequency and low-frequency noise at the same time and has the characteristics of better protecting high-frequency information.

Description

Technical Field

[0001] This invention relates to the field of geophysical processing methods for oil and gas exploration, specifically to a method for suppressing seismic noise using variational mode decomposition and the Schrödinger equation. Background Technology

[0002] Seismic data is subject to various noises during acquisition due to environmental factors, instrumentation, and data source influences, significantly reducing the signal-to-noise ratio. Therefore, seismic data denoising is a crucial step in seismic data processing, impacting subsequent seismic imaging, inversion, and interpretation. Current seismic data denoising methods primarily include predictive filtering, sparse transform methods, low-rank-based methods, decomposition-based methods, and machine learning methods. Predictive filtering methods, such as fx deconvolution and non-stationary predictive filtering, often suffer from performance limitations due to filter length and the smoothing radius of the shaping operator. Sparse transform methods include dictionary learning methods with adaptive learning bases and analytical transform methods with fixed bases, such as wavelet transforms. These methods transform noisy seismic data into a sparse domain, allowing the signal to be represented using parameters. For denoising complex seismic signals, dictionary learning methods with adaptive learning bases outperform analytical transform methods with fixed bases; however, the construction and updating of dictionary atoms are critical, directly determining denoising performance. Low-rank-based methods assume that the pure seismic signal is low-rank, and noise increases the rank of the pure seismic signal. However, this assumption leads to the processing method obtaining an approximation of the true situation. Decomposition-based methods separate noise using methods such as empirical mode decomposition and singular value decomposition. However, these methods often result in some separated noise containing useful signals, while the retained signals contain residual noise. Machine learning methods, such as convolutional neural networks, can achieve good denoising results, but they often require a large amount of training data.

[0003] The purpose of this invention is to overcome the shortcomings of traditional seismic data denoising methods and provide a new method for seismic noise suppression using variational mode decomposition and the Schrödinger equation. This method is beneficial for protecting the high-frequency weak signals of seismic signals. Summary of the Invention

[0004] A method for suppressing seismic noise using variational mode decomposition and the Schrödinger equation includes the following steps:

[0005] (1) The seismic data of the target segment is decomposed using the variational mode decomposition algorithm to obtain the intrinsic mode function data volume of the seismic data of the target segment;

[0006] (2) For the intrinsic mode function data volume of the target section seismic data, an adaptive denoising operator is constructed for each channel using the Schrödinger equation, and the projection coefficients of the noisy seismic signal onto the adaptive basis are calculated.

[0007] (3) The projection coefficients of the noisy seismic signal onto the adaptive basis are subjected to soft thresholding, and the processed intrinsic mode function data volumes are reconstructed to generate denoised seismic data.

[0008] The present invention provides a method for suppressing seismic noise using variational mode decomposition and the Schrödinger equation. The core issue is to generate eigenmode function data volumes from seismic data through variational mode decomposition, construct an adaptive denoising operator for the eigenmode function data volumes using the Schrödinger equation, and reconstruct the processed eigenmode function data volumes to generate denoised seismic data.

[0009] The specific implementation principle of this invention is as follows:

[0010] 1. The seismic data of the target segment is decomposed using a variational mode decomposition algorithm to obtain the intrinsic mode function data volume of the seismic data of the target segment.

[0011] For each seismic data point in the target segment The variational mode decomposition algorithm is used for decomposition. The calculation formula for the variational mode decomposition algorithm is as follows:

[0012] (1)

[0013]

[0014] in, Indicates the first One eigenmode function It is the center frequency. For time, Let be the impulse function. This indicates taking the minimum value;

[0015] Eigenmode functions generated by variational mode decomposition ,in, , The decomposition series of the intrinsic mode functions is shown in the following equation:

[0016] (2)

[0017] in, and These are signals and intrinsic mode functions Fourier transform, These are Lagrange multipliers, equilibrium parameters. Used for data fidelity constraints This indicates taking the real part of the signal. Indicates the inverse Fourier transform;

[0018] Decomposition series of intrinsic mode functions Using kurtosis in intervals The selection is made within the options provided, and the calculation formula is as follows:

[0019] (3)

[0020] in, Indicates the calculation of kurtosis. This indicates taking the maximum value;

[0021] When the decomposition series of the eigenmode function Once determined, then within the interval Using kurtosis to select equilibrium parameters within a range The calculation formula is as follows:

[0022] (4)

[0023] 2. For the intrinsic mode function data volume of the seismic data of the target section, an adaptive denoising operator is constructed for each trace using the Schrödinger equation, and the projection coefficients of the noisy seismic signal onto the adaptive basis are calculated.

[0024] 2.1 For the intrinsic mode function data volume of the seismic data of the target section, an adaptive denoising operator is constructed for each trace using the Schrödinger equation;

[0025] For each seismic data point in the target segment Eigenmode functions obtained using variational mode decomposition algorithm Perform Gaussian filtering, and the filtered signal is denoted as... The input potential energy of the Schrödinger equation is ,in, For spatial location, Let be the wave function. The Schrödinger equation can be expressed as:

[0026] (5)

[0027] Among them, Hamiltonian operator , It is Planck's constant. It is the mass of a quantum particle. It is a gradient operator;

[0028] The Hamiltonian matrix is ​​constructed using the Schrödinger equation, as shown in the following formula:

[0029] (6)

[0030] in, Represents the Hamiltonian matrix in which the first... The Hamiltonian matrix has the following form: elements.

[0031] (7)

[0032] The eigenpairs of the Hamiltonian matrix, i.e., eigenvalues ​​and eigenvectors, are calculated. The eigenvectors in the eigenpairs of the Hamiltonian matrix constitute the quantum field adaptive denoising operator. ;

[0033] 2.2 Calculate the projection coefficients of the noisy seismic signal onto the adaptive basis;

[0034] The following formula is used to calculate each noisy seismic data point in the target segment. eigenmode functions Projection coefficients projected onto the adaptive basis :

[0035] (8)

[0036] in, Eigenmode functions The normalized non-conjugate transpose matrix.

[0037] 3. The projection coefficients of the noisy seismic signal onto the adaptive basis are subjected to soft thresholding, and the processed intrinsic mode function data volumes are reconstructed to generate denoised seismic data.

[0038] For each noisy seismic data in the target segment eigenmode functions Projection coefficients projected onto the adaptive basis The following formula is used for soft thresholding:

[0039] (9)

[0040] in, The denoised intrinsic mode functions are... The number of data points for the intrinsic mode function, and the soft thresholding factor. for

[0041] (10)

[0042] in, and These are the hyperparameters used to determine the threshold function;

[0043] Denoising the seismic signal Reconstruct using the following formula:

[0044] (11).

[0045] The present invention provides a method for suppressing seismic noise using variational mode decomposition and the Schrödinger equation, which has the following characteristics, mainly manifested as follows:

[0046] (1) This technology uses the Schrödinger equation to transform seismic data into the quantum domain for processing to improve the accuracy of seismic data denoising.

[0047] (2) This technique first uses variational mode decomposition to decompose the seismic signal into a series of intrinsic mode functions, and then uses an adaptive denoising operator constructed by the Schrödinger equation to denoise the intrinsic mode functions, which is beneficial to remove high-frequency and low-frequency noise at the same time.

[0048] (3) The Schrödinger equation adaptive soft threshold denoising algorithm used in this algorithm has the feature of better protecting high-frequency information.

[0049] (4) This algorithm runs fast and is suitable for processing large batches of seismic signals. Attached Figure Description

[0050] Figure 1 This is a flowchart of a method for suppressing seismic noise using variational mode decomposition and the Schrödinger equation.

[0051] Figure 2 Post-stack migration seismic profile of a location in the Ordos Basin

[0052] Figure 3 Seismic profiles and residual profiles after denoising using conventional wavelet transform.

[0053] Figure 4 Seismic profiles and residual profiles denoised directly using the Schrödinger equation adaptive denoising algorithm.

[0054] Figure 5 These are the seismic profiles and residual profiles after processing using this technique. Detailed Implementation

[0055] (1) Figure 1 This is a flowchart of a method for suppressing seismic noise using variational mode decomposition and the Schrödinger equation. Here, IMF represents the intrinsic mode functions.

[0056] (2) Figure 2 This is a post-stack migrated seismic profile of a location in the Ordos Basin. The sampling frequency is 500Hz.

[0057] (3) Figure 3 This shows the seismic profile and residual profile after denoising using conventional wavelet transform. The residual plot shows that much useful information has still been removed.

[0058] (4) Figure 4The image shows the seismic profile and residual profile after direct denoising using the Schrödinger equation adaptive denoising algorithm. The residual plot shows that although this method is more effective than wavelet transform denoising, some useful information is still removed between 4500 ms and 4600 ms.

[0059] (5) The seismic profile and residual profile after processing by this technique are shown. As can be seen from the residual plot, the residual plot mainly contains noise information, which is better than the denoising effect of conventional wavelet transform and direct Schrödinger equation adaptive algorithm.

Claims

1. A method for suppressing seismic noise using variational mode decomposition and the Schrödinger equation, characterized in that... The following steps are adopted: (1) The seismic data of the target segment is decomposed using the variational mode decomposition algorithm to obtain the intrinsic mode function data volume of the seismic data of the target segment; the calculation formula of the variational mode decomposition algorithm is as follows: (1) in, Indicates the first One eigenmode function It is the center frequency. For time, Let be the impulse function. This indicates taking the minimum value; Eigenmode functions generated by variational mode decomposition ,in, , Let be the series decomposition of the intrinsic mode functions, as shown in the following equation: (2) in, and These are signals and intrinsic mode functions Fourier transform, These are Lagrange multipliers, equilibrium parameters. Used for data fidelity constraints This indicates taking the real part of the signal. Indicates the inverse Fourier transform; Decomposition series of intrinsic mode functions Using kurtosis in intervals The selection is made within the options provided, and the calculation formula is as follows: (3) in, Indicates the calculation of kurtosis. This indicates taking the maximum value; When the decomposition series of the intrinsic mode functions Once determined, then within the interval Using kurtosis to select equilibrium parameters within a range The calculation formula is as follows: (4) (2) For the intrinsic mode function data volume of the seismic data of the target section, Gaussian filtering is performed channel by channel. A Hamiltonian matrix is ​​constructed using the Schrödinger equation, and the eigenpairs of the Hamiltonian matrix are calculated. The eigenvectors in the eigenpairs of the Hamiltonian matrix are used to construct a quantum domain adaptive denoising operator, and the projection coefficients of the noisy seismic signal onto the adaptive basis are calculated. The input potential energy of the Schrödinger equation is: ,in, For spatial location, For wave function, Here are the filtered intrinsic mode functions; the Schrödinger equation is: (5) Among them, Hamiltonian operator , It is Planck's constant. It is the mass of a quantum particle. It is the gradient operator. The formula for constructing the Hamiltonian matrix using the Schrödinger equation is as follows: (6) in, Represents the Hamiltonian matrix in which the first... With n elements, the Hamiltonian matrix has the following form: (7) The following formula is used to calculate each noisy seismic data point in the target segment. eigenmode functions Projection coefficients projected onto the adaptive basis : (8) in, Eigenmode functions The normalized non-conjugate transpose matrix, A quantum field adaptive denoising operator is constructed from the eigenvectors of the eigenpairs of the Hamiltonian matrix. (3) Soft thresholding is applied to the projection coefficients of the noisy seismic signal onto the adaptive basis, and the processed intrinsic mode function data volumes are reconstructed to generate denoised seismic data. The soft thresholding formula is as follows: (9) in, The denoised intrinsic mode functions are... The number of data points for the intrinsic mode function, and the soft thresholding factor. for (10) in, and These are the hyperparameters used to determine the threshold function; Denoising the seismic signal Reconstruct using the following formula: (11)。 2. The method for suppressing seismic noise using variational mode decomposition and the Schrödinger equation according to claim 1, characterized in that: Accurate calculation of the intrinsic mode function data volume of the seismic data of the target layer in step 1.

3. The method for suppressing seismic noise using variational mode decomposition and the Schrödinger equation according to claim 2, characterized in that: For the intrinsic mode function data volume of the seismic data of the target section, an adaptive denoising operator is constructed for each trace using the Schrödinger equation, and the projection coefficients of the noisy seismic signal onto the adaptive basis are calculated.

4. The method for suppressing seismic noise using variational mode decomposition and the Schrödinger equation according to claim 3, characterized in that: The projection coefficients of the noisy seismic signal projected onto the adaptive basis are subjected to soft thresholding, and the processed intrinsic mode function data volumes are reconstructed to generate denoised seismic data.

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