Seismic Data Processing Method Based on Underfitting and Adaptive Leakage Compensation

Abstract

This invention belongs to the field of seismic data processing technology and relates to a seismic data processing method based on underfitting and adaptive leakage compensation. Addressing the problems of parameter optimization difficulties, signal leakage, and noise residue in traditional low-rank denoising methods for non-stationary data, it proposes a problem reconstruction-type processing mechanism. Through underfitting, the effective signal is controllably allocated to the residual domain, constructing a residual signal space with structural differences. Based on this, a multi-domain consistency discrimination mechanism is used to independently identify the leakage signal in the residual, and selective reconstruction is performed based on the identification results, achieving decoupling between noise suppression and signal recovery. This invention transforms the optimization problem, which relies on precise parameter estimation, into a recovery problem based on structural discrimination, providing a parameter fault-tolerant mechanism that makes the signal recovery performance insensitive to parameter changes. While ensuring the stability of noise suppression, it achieves high-fidelity recovery of the effective signal, significantly improving the stability and applicability of complex seismic data processing.

Description

Technical Field

[0001] This invention belongs to the field of seismic data processing technology, specifically relating to a method for suppressing random noise in seismic data based on underfitting and adaptive leakage compensation, which is suitable for high-fidelity seismic signal recovery. Background Technology

[0002] Random noise suppression in seismic data is a crucial step in seismic data processing, and its results directly affect the reliability of subsequent quantitative interpretations such as amplitude variation with offset (AVO) analysis and pre-stack inversion. Multi-channel Singular Spectrum Analysis (MSSA) is a widely used low-rank denoising method. It constructs a Hankel matrix in the frequency-space domain and performs singular value decomposition (SVD) to project the signal into a low-rank subspace, thereby separating the signal from random noise.

[0003] However, the effectiveness of the above methods is highly dependent on the selection of key parameters, especially parameters such as the signal subspace dimension (rank) and spectral contraction intensity. In actual seismic data, due to the significant spatial non-stationarity of the statistical characteristics of signals and noise, the optimal parameters differ significantly between different data blocks, making it difficult to determine a uniform and stable parameter configuration globally. If parameter optimization is performed separately for each data block, a large number of repetitive parameter search and adjustment processes are required. This process not only significantly increases computational costs but also relies on manual experience or complex strategies, making it difficult to implement stably in large-scale data processing, thus lacking scalability and operability in engineering applications.

[0004] In this situation, selecting parameters that are too high can lead to residual noise, while selecting parameters that are too low can cause signal leakage and damage to weak signals. Additionally, it may introduce ringing artifacts. To address this, existing technologies propose damped MSSA methods, which achieve smooth attenuation by applying soft thresholding or spectral shrinkage to singular values. However, these methods typically introduce systematic amplitude attenuation, making it difficult to balance noise suppression with amplitude fidelity.

[0005] Meanwhile, existing technologies are generally based on the following technical assumption: that optimal parameters can be estimated through local data features, and that effective separation of signal and noise can be achieved through fine-tuning. However, under complex seismic data conditions, this assumption often fails to hold, making the parameter selection problem inherently uncertain and difficult to solve stably. Consequently, although existing methods can achieve good processing results under specific parameter configurations, they remain at the theoretically feasible stage due to their sensitivity to parameters, and are difficult to stably apply to large-scale data processing without requiring block-by-block parameter tuning.

[0006] Furthermore, existing methods typically treat signal leakage as an adverse consequence of improper parameter selection and try to avoid it by optimizing parameters or strengthening constraints. This fails to fully utilize the effective information contained in the leaked signal, further exacerbating the reliance on precise parameter selection. Consequently, traditional methods suffer from an inherent contradiction between noise suppression effectiveness, parameter stability, and amplitude fidelity, which limits their efficiency and stability in practical engineering environments.

[0007] Therefore, how to break through the dependence on accurate estimation of optimal parameters, achieve stable signal recovery without the need for independent parameter optimization for each data block, and transform the original parameter adjustment-dependent processing into a data structure discrimination and recovery process, thereby improving the applicability and scalability of the method under complex non-stationary conditions, has become a key technical problem that urgently needs to be solved in the field of random noise suppression of seismic data. Summary of the Invention

[0008] The purpose of this invention is to provide a random noise suppression method for seismic data based on underfitting and adaptive leakage compensation. This method addresses the problem that existing low-rank seismic data denoising methods are highly dependent on optimal parameters and difficult to apply stably under non-stationary data conditions. This method no longer relies on precise estimation of the optimal parameters for each data block. Instead, it reconstructs the signal processing structure, transforming the signal recovery problem, which originally depended on parameter optimization, into a recovery problem based on data structure discrimination, thereby achieving stable and high-fidelity seismic signal reconstruction.

[0009] This invention is achieved through the following technical solution:

[0010] A seismic data processing method based on underfitting and adaptive leakage compensation includes the following steps:

[0011] S1. The original seismic data is divided into blocks and frequency domain transformation is performed. An underfitting driving mechanism is introduced to estimate the signal of the processed seismic data. By limiting the dimension of the signal subspace and the spectral attenuation intensity, some effective signal energy is transferred from the signal subspace to the residual domain in a controllable manner, thereby constructing a residual signal space with structural differences.

[0012] S2. In the residual signal space, establish a correlation characterization model between the residual and the signal estimation results, and independently identify the leakage signal components in the residual based on the multi-domain consistency discrimination mechanism.

[0013] S3. Based on the identification results of step S2, reconstruction is performed only on the windows where leakage signals exist to obtain the estimated leakage signals within the windows. The estimation results of all windows are combined to obtain the complete leakage signal estimate.

[0014] S4. The leakage signal estimation results from step S3 and the signal estimation results from step S1 are fused to obtain the final seismic signal output.

[0015] Furthermore, in step S1, the original seismic data is divided into blocks and subjected to frequency domain transformation, specifically including the following steps:

[0016] S11, Transfer the original seismic data volume The data is divided into several spatiotemporal blocks using overlapping windows, and its expression is as follows:

[0017] ;

[0018] In the formula, For window operators, t is the time coordinate and x is the spatial coordinate;

[0019] S12. Perform a Fast Fourier Transform on each data block along the time direction to convert it into a frequency-spatial domain data slice, expressed as:

[0020] ;

[0021] In the formula, The frequency is used to decouple the time dimension into independently processable frequency components through this transformation.

[0022] Furthermore, in step S1, an underfitting driving mechanism is introduced to estimate the signal of the processed seismic data, specifically including the following steps:

[0023] S13. For each frequency slice obtained in step S12 Extract the spatial vector of the current data block. ;

[0024] In the formula, The number of spatial channels within the current window. , Let be the complex amplitude of the i-th channel on the frequency slice;

[0025] S14. Select the embedding dimension L, where L takes the value of... Construct the Hankel matrix ;

[0026] Among them, the number of columns The matrix elements are arranged according to the following rules:

[0027] ;

[0028] In the formula, i is the row index. j is the column index ,Right now It has the following form:

[0029] ;

[0030] S15. Perform singular value decomposition on the Hankel matrix:

[0031] ;

[0032] In the formula, and Let be unitary matrices formed by the left and right singular vectors, respectively. It is a diagonal matrix of singular values, with the singular values ​​arranged in descending order. ;

[0033] S16. Employ an underfitting driving mechanism, setting the number of singular values ​​N to be retained; the damping power K; and defining the noise threshold. The first N singular values ​​are weighted using a damped spectrum shrinkage operator. The weighting formula is as follows:

[0034] ;

[0035] In the formula, These are the weighted singular values. It is the small regularization constant;

[0036] S17. Reconstruct the filtered Hankel matrix using the weighted singular values:

[0037] ;

[0038] In the formula, and These are the j-th left and right singular vectors, respectively;

[0039] S18. Recover the filtered spatial vector using inverse Hankel diagonal mean. ;

[0040] S19. Repeat steps S13 to S18 for all frequency slices. After processing all frequency slices for each data block, transform the data back to the time domain using an inverse fast Fourier transform. Then, stitch the data blocks together using an overlapping and adding method to obtain the damped MSSA estimation result. .

[0041] Furthermore, in step S16, the number of singular values ​​N to be retained is set to 2-4; the damping power K is set to 2-4. The value is 10 -6 Magnitude.

[0042] Furthermore, in step S18, the filtered spatial vector is recovered by inverse Hankel diagonal averaging. Specifically: for The reconstructed spatial sequence is obtained by averaging the elements on all anti-diagonal lines.

[0043] Furthermore, step S2 specifically includes the following steps:

[0044] S21. Calculate the residual data volume :

[0045] ;

[0046] In the formula, The original earthquake data, The damping MSSA estimation result obtained in step S19;

[0047] S22, transfer the residual data volume Compared with damped MSSA estimation results Divided into overlapping spatiotemporal windows The window size is consistent with the windowing parameters in step S11;

[0048] S23. Establish a correlation characterization model between the residual signal and the estimation result, and use at least two discrimination criteria to pre-judge whether there is a leakage signal within the window.

[0049] Furthermore, in step S23, the discrimination criteria include at least two of the following: local correlation coefficient criterion, energy consistency criterion, phase consistency criterion, and matched filter response energy criterion. When at least two criteria determine that a leakage signal exists, it is confirmed that a leakage signal exists in the window; otherwise, it is determined that there is no leakage signal.

[0050] Among them, the local correlation coefficient criterion is used to calculate the residual. and Pearson correlation coefficient :

[0051] ;

[0052] when When this happens, it is determined that a leak signal exists within the window;

[0053] The energy consistency criterion is the ratio of the calculated residual energy to the energy of the first-stage result:

[0054] ;

[0055] like Within the preset range If the ratio is stable relative to the neighborhood window, then a leakage signal is determined to exist.

[0056] The phase consistency criterion is the phase difference between the calculated residual and the result:

[0057] ;

[0058] If the phase difference is concentrated near zero, the phase consistency index is: If so, it is determined that a leakage signal exists;

[0059] The matched filter response energy criterion is obtained by solving the non-stationary least squares matched filter problem. Its objective function is:

[0060] ;

[0061] In the formula, This represents the convolution operation. For short convolutional filters, This is the Tikhonov regularization parameter, which takes the value of a positive real number;

[0062] Calculate filter energy:

[0063] ;

[0064] when Greater than the preset threshold When, it serves as an auxiliary basis for judgment.

[0065] Furthermore, step S3 specifically involves: only identifying the markers. Reconstruction is performed in the window with a value of 1, and the matched filter is applied. Acting on ,calculate The estimated leakage signal within this window is obtained. ; Set the window identified as having no leakage signal to zero directly.

[0066] Furthermore, in step S11, the data blocks are divided using overlapping windows with the same window size. In steps S19 and S24, the data blocks are spliced ​​using overlapping addition or weighted splicing.

[0067] Compared with the prior art, the beneficial effects of the present invention are:

[0068] 1. Strong parameter tolerance and independence from optimal parameter estimation: This invention transforms the signal recovery process, which relies on precise parameter selection in traditional methods, into a recovery process based on residual structure discrimination through a synergistic mechanism of underfitting-driven and selective reconstruction. This significantly reduces the sensitivity to parameters such as rank and window size. Stable signal recovery performance is maintained even when parameters deviate from optimal values. Experiments show that when the window size increases from 20×20 to 80×80, the signal-to-noise ratio of this method remains between 7.7 and 10.6 dB, while the performance of traditional methods significantly decreases.

[0069] 2. High amplitude fidelity and clear recovery mechanism: Through the decoupling strategy of "independent identification first and selective reconstruction later", the signal leakage caused by the underfitting in the first stage is transformed into identifiable structural information and targeted recovery is carried out, thereby effectively compensating for the amplitude attenuation caused by damped MSSA, ensuring the amplitude fidelity of weak reflection signal, and meeting the quantitative interpretation requirements of AVO analysis and pre-stack inversion.

[0070] 3. Decoupling of noise suppression and signal recovery to avoid erroneous noise recovery: This invention uses a multi-domain consistency discrimination mechanism to selectively reconstruct only the leakage signals with structural characteristics in the residuals, making the noise suppression and signal recovery processes independent of each other. This avoids the problem of erroneous noise recovery caused by the blind application of traditional matched filtering to the entire data. The processed residuals exhibit statistical randomness with no obvious coherent structural residues.

[0071] 4. The processing is transformed from parameter optimization to structural discrimination, which has good scalability and stability: This invention no longer relies on parameter optimization for different data blocks, but achieves stable processing under unified parameter conditions by constructing residual structures and performing discriminative recovery. This reduces the dependence on local statistical characteristics and human experience, and improves the stability and applicability of the method in large-scale non-stationary data processing.

[0072] 5. Achieving a shift from parameter-driven processing to structure-driven processing: This invention introduces an underfitting driving mechanism, transforming the parameter problem that requires precise control in traditional methods into a usable signal structure problem. This changes the processing paradigm of low-rank denoising methods, enabling seismic data denoising to shift from a theoretical processing method that relies on fine parameter adjustment to a stable processing method based on structure discrimination. Attached Figure Description

[0073] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0074] Figure 1 Here are examples of synthetic data, where (a) is the real signal, (b) is random noise, and (c) is noisy data;

[0075] Figure 2 For the comparison of random noise suppression results of synthetic data, (a) is the signal estimated by standard MSSA, (b) is the noise removed by standard MSSA, (c) is the signal estimated by the method of the present invention, and (d) is the noise removed by the method of the present invention.

[0076] Figure 3 Here is an example of noisy data from the field;

[0077] Figure 4 Comparison of random noise suppression results for field data: (a) is the signal estimated by standard MSSA, (b) is the noise removed by standard MSSA, (c) is the signal estimated by the method of the present invention, and (d) is the noise removed by the method of the present invention.

[0078] Figure 5 The signal-to-noise ratio comparison curves are shown for different spatial window sizes.

[0079] Figure 6 This is a flowchart illustrating the steps of the seismic data processing method based on underfitting and adaptive leakage compensation according to the present invention. Detailed Implementation

[0080] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0081] Existing seismic data denoising methods based on low-rank decomposition typically assume optimal parameters, such as subspace dimension and spectral shrinkage intensity, which can be estimated through local data features and separated from noise through fine-tuning. However, in real-world seismic data, the statistical characteristics of signal and noise exhibit significant spatial non-stationarity, and the optimal parameters vary considerably across different data blocks, making it difficult for these methods to achieve stable and consistent processing results globally. Current technologies generally consider signal leakage as an adverse consequence of inappropriate parameter selection and attempt to minimize leakage by optimizing parameters or strengthening constraints. However, this invention breaks through these limitations by treating underfitting as an active design mechanism. By controlling the distribution of signal energy between the signal subspace and the residual domain, a portion of the effective signal enters the residual in a controllable manner, thereby constructing a residual signal space with structural differences. Building upon this foundation, the present invention further identifies and recovers leaked signals in the residuals through a multi-domain consistency discrimination and selective reconstruction mechanism. This transforms the signal recovery problem, which originally relied on precise parameter selection, into a discrimination and recovery problem based on residual structural differences. This eliminates the need for precise estimation of the optimal parameters, fundamentally reducing the uncertainty of parameter selection and improving the stability and applicability of the method under complex non-stationary data conditions.

[0082] like Figure 6As shown, this invention is a seismic data processing method based on underfitting and adaptive leakage compensation. First, the original seismic data is segmented and frequency domain transformed. Then, an underfitting mechanism is introduced in the first-stage signal estimation. By limiting the signal subspace dimension and spectral attenuation intensity, some effective signal energy is transferred from the signal subspace to the residual domain in a controllable manner, thereby constructing a residual signal space with structural differences. Next, a correlation characterization model between the residual signal and the first-stage estimation result is established in the residual domain, and the leakage signal component in the residual is independently identified based on a multi-domain consistency discrimination criterion. Subsequently, selective reconstruction is performed only on the regions identified as having leakage signals to obtain leakage signal estimates. Finally, the leakage signal estimates are fused with the first-stage signal estimation results to obtain the final seismic signal output.

[0083] The underfitting driving mechanism and the selective reconstruction process work synergistically: the underfitting driving mechanism transforms the signal leakage that is difficult to avoid in traditional methods into a usable information carrier and concentrates it in the residual domain; the selective reconstruction uses this residual structure as a basis to identify and recover the leaked signal, thereby achieving decoupling between signal recovery and noise suppression.

[0084] Compared to existing methods, the core of this invention lies not in optimizing parameter selection strategies, but in reconstructing the solution to the signal recovery problem. Specifically, this invention constructs an underfit-driven information redistribution mechanism to transfer signal energy originally coupled with parameter selection errors to the residual space. Combined with structural discrimination and selective recovery processes, this transforms signal recovery from an optimization problem dependent on precise parameters into a discrimination and recovery problem based on residual structural differences. Therefore, stable signal recovery results can be obtained under uniform parameter conditions without optimizing parameters for different data blocks individually. This significantly reduces reliance on local data statistical characteristics and human experience, improving the applicability and scalability of the method in complex, non-stationary seismic data. By introducing a synergistic mechanism of underfit-driven and selective reconstruction, this invention achieves a shift from "parameter-driven processing" to "structure-driven processing," improving amplitude fidelity and processing stability while ensuring noise suppression, providing a new technical path for high-fidelity seismic data processing.

[0085] This invention relates to a seismic data processing method based on underfitting-driven and adaptive leakage compensation. Through the synergistic effect of the underfitting-driven mechanism and selective reconstruction, it transforms the signal recovery problem, which originally relied on precise parameter selection, into a recovery problem based on residual structure discrimination. This forms a parameter tolerance mechanism, making the processing results insensitive to parameter changes. Specifically, it includes the following steps:

[0086] S1. The original seismic data is divided into blocks and frequency domain transformation is performed. An underfitting driving mechanism is introduced to estimate the signal of the processed seismic data. By limiting the dimension of the signal subspace and the spectral attenuation intensity, some effective signal energy is transferred from the signal subspace to the residual domain in a controllable manner, thereby constructing a residual signal space with structural differences.

[0087] S11. Data segmentation and frequency conversion:

[0088] The original seismic data volume The data is divided into several spatiotemporal blocks using overlapping windows of the same size. The expression for this block is:

[0089] ;

[0090] In the formula, For window operators, t is the time coordinate and x is the spatial coordinate;

[0091] S12. Perform a Fast Fourier Transform (FFT) on each data block along the time direction to convert it into a frequency-spatial domain data slice, expressed as:

[0092] ;

[0093] In the formula, The frequency is used to decouple the time dimension into independently processable frequency components through this transformation.

[0094] S13. Signal estimation under underfitting drive is performed using the damped multichannel singular spectrum analysis method.

[0095] For each frequency slice obtained in step S12 Perform the following sub-steps:

[0096] Extract the spatial vector of the current data block ;

[0097] In the formula, The number of spatial channels within the current window. , Let be the complex amplitude of the i-th channel on the frequency slice.

[0098] S14. Select the embedding dimension L, where L takes the value of... Construct the Hankel matrix ;

[0099] Among them, the number of columns The matrix elements are arranged according to the following rules:

[0100] ;

[0101] In the formula, i is the row index. j is the column index ,Right now It has the following form:

[0102] .

[0103] S15. Perform singular value decomposition on the Hankel matrix as follows:

[0104] ;

[0105] In the formula, and Let be unitary matrices formed by the left and right singular vectors, respectively. It is a diagonal matrix of singular values, with the singular values ​​arranged in descending order. .

[0106] S16. Employ an underfitting-driven mechanism, setting the number of retained singular values ​​N to a relatively small value, typically 2-4; the damping power K to a relatively small value, typically 2-4; and defining a noise threshold. The first N singular values ​​are weighted using a damped spectrum shrinkage operator. The weighting formula is as follows:

[0107] ;

[0108] In the formula, These are the weighted singular values. This is a small regularization constant to prevent the denominator from being zero; its value is 10. -6 Magnitude.

[0109] The core design principle of this underfitting driving mechanism is that by artificially introducing conservative parameter constraints, the first stage prioritizes noise suppression stability, while allowing some effective signal energy to leak controllably into the residuals. This transforms the "error" in traditional methods into an information carrier that can be utilized later, laying the foundation for selective reconstruction in the second stage.

[0110] S17. Reconstruct the filtered Hankel matrix using the weighted singular values:

[0111] ;

[0112] In the formula, and These are the j-th left and right singular vectors, respectively.

[0113] S18. Recover the filtered spatial vector using inverse Hankel diagonal mean. Specifically: for The reconstructed spatial sequence is obtained by averaging the elements on all anti-diagonal lines.

[0114] S19. Repeat steps S13 to S18 for all frequency slices. After processing all frequency slices for each data block, transform the data back to the time domain using inverse fast Fourier transform (IFFT), and then stitch the data blocks together using the overlap-add method to obtain the damped MSSA estimation result. .

[0115] S2. The residual calculation and adaptive leakage compensation are performed by first identifying independently and then selectively reconstructing.

[0116] S21. Calculate the residual data volume:

[0117] ;

[0118] In the formula, The original earthquake data, This is the damped MSSA estimation result obtained in step 2. The residual contains random noise and the coherent signal energy from the first-stage leakage.

[0119] S22, transfer the residual data volume Compared with damped MSSA estimation results Divided into overlapping spatiotemporal windows The window size is consistent with the windowing parameters in step 1. In each window... Internally, perform the following two-step decoupling operation:

[0120] S23. Independent identification of leakage signals (pre-judgment);

[0121] A correlation characterization model is established between the residual signal and the estimation result. Multiple discrimination criteria, independent of subsequent reconstruction, are used to pre-judgment whether leakage signals exist within the window. Specifically, a combination of two or more of the following discrimination criteria is employed:

[0122] 1. Local correlation coefficient criterion: Calculate the residuals and Pearson correlation coefficient :

[0123] ;

[0124] when When the value is typically 0.3-0.5, a leakage signal is determined to exist within the window.

[0125] 2. Energy Consistency Criterion: Calculate the ratio of residual energy to the energy of the first-stage result.

[0126] ;

[0127] like Within the preset range Internal (typical value) =0.05, If the ratio is 0.5 and remains stable relative to the neighborhood window, then a leakage signal is determined to exist.

[0128] 3. Phase Consistency Criterion: Calculate the phase difference between the residual and the result of the first stage:

[0129] ;

[0130] If the phase difference is concentrated near zero, the phase consistency index is: If so, it is determined that a leakage signal exists.

[0131] 4. Matched Filter Response Energy Criterion (Auxiliary Verification): By solving the non-stationary least squares matched filtering problem, the filter response energy criterion is obtained. Its objective function is:

[0132] ;

[0133] In the formula, This represents the convolution operation. For short convolutional filters, This is the Tikhonov regularization parameter, which takes the value of a positive real number (typically 0.01-0.1).

[0134] Calculate filter energy:

[0135] ;

[0136] when Greater than the preset threshold (For example, taking twice the average energy of the filter within the window) as an auxiliary criterion for judgment.

[0137] A comprehensive judgment rule is adopted: A combination of the above criteria is used for voting. When at least two criteria determine that a leakage signal exists, the presence of a leakage signal (identification mark) is confirmed for that window. =1); otherwise, it is determined as a no-leakage signal ( =0). This independent identification step ensures that subsequent reconstruction operations only target the window where leakage signals actually exist, avoiding false recovery noise introduced by blind filtering.

[0138] S3. Selective reconstruction of leakage signals, i.e., post-processing;

[0139] Only for identification marks The window with =1 performs a reconstruction operation: the matched filter... Acting on ,calculate The estimated leakage signal within this window is obtained. .

[0140] For identification marks A window with =0, let =0, no reconstruction operation is performed.

[0141] The estimation results of all windows are combined using an overlapping window stitching method to obtain a complete leakage signal estimate. .

[0142] S4. Signal Fusion: The estimated leakage signal is restored to the damped MSSA result to obtain the final high-fidelity random noise suppression result.

[0143] .

[0144] In this invention, there is a synergistic effect between the underfitting driving mechanism and selective reconstruction: the underfitting state actively introduced in the first stage allows signal leakage to be controllably concentrated in the residual, providing a clear processing target for the second stage; the second stage accurately identifies the leakage component through independent identification criteria and performs selective reconstruction based on the identification results, avoiding false recovery of random noise. The synergistic effect of these two mechanisms produces the novel technical characteristic of "parameter tolerance." Even if the first stage uses non-optimal parameters, the second stage can still achieve high-fidelity recovery through independent identification and selective reconstruction, significantly reducing the sensitivity to parameter selection. In this invention, the underfitting driving mechanism includes limiting the signal subspace dimension and spectral attenuation intensity. By artificially introducing conservative parameter constraints, part of the signal energy is retained in the residual domain, thereby achieving controllable transfer of signal energy.

[0145] In this invention, the correlation characterization model is constructed based on at least one of the following information: the local correlation coefficient between the residual and the first-stage result, the energy consistency index, and the frequency or phase consistency index; leakage signal identification employs a combination of the above criteria to ensure the reliability of the identification results; selective reconstruction is performed only on windows identified as having leakage signals, avoiding false recovery noise introduced by blind filtering. Selective reconstruction is achieved by solving a non-stationary filtering model with regularization constraints. The parameters of the filtering model are dynamically adjusted according to local data characteristics, including the filter length and the regularization coefficient.

[0146] This invention innovatively introduces an independent identification step, employing a decoupling mechanism of independent identification followed by selective reconstruction, explicitly decoupling identification and reconstruction into two independent steps. First, leakage components in the residual are pre-judged using multiple independent discrimination criteria (local correlation coefficient, energy consistency, phase consistency, etc.), and reconstruction is only performed on windows confirmed to contain leakage signals. This pre-judgment and post-processing approach ensures the reconstruction operation has a clear target orientation, avoiding the erroneous recovery noise problem that may result from blind filtering in existing matched filtering methods.

[0147] Example 1

[0148] Synthetic data random noise suppression

[0149] This embodiment uses synthetic seismic data to verify the effectiveness of the method of the present invention. Figure 1 (a) is a noise-free real signal containing a linear in-phase axis; Figure 1 (b) is the added random noise; Figure 1 (c) represents noisy data (signal and noise superimposed), with a signal-to-noise ratio of approximately 5 dB. The method of this invention is used to... Figure 1 The data shown in (c) is processed using the following specific steps:

[0150] 1. The original seismic data is segmented and frequency domain transformed, and an underfitting driving mechanism is introduced to estimate the signal of the processed seismic data.

[0151] 11. Data partitioning and frequency conversion:

[0152] The noisy data was divided into overlapping spatiotemporal windows. The window size was chosen to be 40×40 (40 sampling points in the temporal direction and 40 channels in the spatial direction), with a window overlap rate of 50%. This window size... Figure 5 The results show that the model has a typical effective range, which can balance local stationarity and computational efficiency.

[0153] 12. Perform a Fast Fourier Transform (FFT) on each window along the time direction to obtain frequency-spatial domain data slices.

[0154] 13. Signal estimation under underfitting is achieved using damped multichannel singular spectrum analysis. For each frequency slice... Extract the spatial vector of the current window. , Let be the complex amplitude of the i-th channel on the frequency slice.

[0155] 14. Select the embedding dimension Construct the Hankel matrix Its elements are: .

[0156] 15. To Perform singular value decomposition: To obtain singular values .

[0157] 16. Employ an underfitting-driven mechanism: Set the number of singular values ​​to retain. Damping power Define noise threshold The first three singular values ​​are weighted using a damped spectrum shrinkage operator:

[0158] ;

[0159] Wherein, regularization constant =10 -6 This parameter combination actively introduces an underfitting state, sacrificing some signal energy to ensure that noise and artifacts are completely suppressed.

[0160] 17. Reconstruct the filtered Hankel matrix:

[0161] ;

[0162] 18. Perform inverse Hankel diagonal averaging to recover the filtered space vector. .

[0163] 19. Repeat steps 13-18 for all frequency slices. After processing all frequencies in the window, transform the data back to the time domain using inverse fast Fourier transform (IFFT), and then stitch all windows together using the overlap-add method to obtain the first-stage damped MSSA estimation result. .

[0164] Residual calculation and adaptive leakage compensation: independent identification followed by selective reconstruction.

[0165] 2. In the residual signal space, establish a correlation characterization model between the residual and the first-stage signal estimation results, and independently identify the leakage signal components in the residual based on the multi-domain consistency discrimination mechanism.

[0166] 21. Calculate the residuals:

[0167] ;

[0168] 22. The residual Compared with the results of the first phase Divide into overlapping spatiotemporal windows of the same size as in step 1 (40×40, overlapping). ).

[0169] In each window Internally, perform the following two-step decoupling operation:

[0170] 23. Independent identification of leakage signals (preliminary judgment)

[0171] Preliminary judgment is performed using a combination of discrimination criteria:

[0172] Local correlation coefficient: Calculation Set threshold =0.35.

[0173] Energy consistency: calculation Set the range =0.05, =0.5.

[0174] Phase consistency: Calculate the phase consistency index Set the threshold to 0.7.

[0175] Matched Filter Auxiliary Verification: Solving the Non-Stationary Least Squares Matched Filter The objective function is:

[0176] ;

[0177] The convolution filter length is 7, and the regularization parameter is... =0.05. Calculate the filter energy. Set threshold =0.1.

[0178] Comprehensive Judgment: When at least two criteria (excluding auxiliary verification) meet the threshold condition, the window is determined to have a leakage signal, and an identification flag is set. =1; otherwise =0.

[0179] 3. Selective reconstruction of leakage signals (post-processing)

[0180] Only for Calculate the reconstruction for a window with a value of 1: The estimated leakage signal within this window is obtained. .for A window with =0, let =0.

[0181] The estimation results of all windows are stitched together in an overlapping manner to obtain a complete leakage signal estimate. .

[0182] 4. Signal fusion:

[0183] The final output is a high-fidelity random noise suppression result:

[0184] .

[0185] The processing result is as follows Figure 2 As shown. Figure 2 (c) is the signal estimated by the method of the present invention. Figure 2 (d) Noise removed. Comparison with standard MSSA results. Figure 2 (a) Figure 2 (b) In contrast, the noise removed by standard MSSA exhibits significant coherent signal leakage, see Figure 2 (b) shows the energy parallel to the linear in-phase axis, while the noise removed by the method of this invention is shown in [reference]. Figure 2 (d) It exhibits statistical randomness, with no coherent structural residue and no obvious leakage. This indicates that the independent identification step of the present invention successfully distinguishes the leakage signal from random noise, and selective reconstruction avoids erroneous recovery of noise, achieving high-fidelity recovery.

[0186] Example 2

[0187] Random noise suppression of field data

[0188] This embodiment uses actual field seismic data containing random noise to verify the applicability of the method of the present invention, such as... Figure 3 As shown, this data is a pre-stack gather from a certain work area. It has a low signal-to-noise ratio, poor continuity of reflection phase axes, and requires high amplitude fidelity for subsequent AVO analysis.

[0189] The processing parameters remained consistent with Example 1, and the independent identification criteria used the same combined thresholds as in Example 1. The field data was processed using the exact same steps as in Example 1. The processing results are as follows: Figure 4 As shown, Figure 4 (c) is the signal estimated by the method of the present invention. Figure 4 (d) Noise removed. Compared with standard MSSA results, Figure 4 (a) Figure 4 (b) In contrast, the noise removed by standard MSSA, Figure 4 (b) The presence of a clear reflective in-phase axis structure indicates that the method, while suppressing noise, damages the effective signal, resulting in signal leakage; whereas the noise removed by the method of this invention, Figure 4 (d) The statistical randomness, clean random noise, and absence of geological structural residue indicate that the effective signal is completely preserved in the output profile. Field data verified the reliability and amplitude fidelity of the method of this invention in complex real-world data.

[0190] The synergistic effect was used to verify the parameter tolerance: To verify the synergistic effect of underfitting-driven and selective reconstruction in the method of this invention, the same synthesized data was processed using standard MSSA, damped MSSA, and the complete method of this invention, with the window size gradually increasing from 20×20 to 80×80. The output signal-to-noise ratio (SNR) was calculated, and the results are as follows. Figure 5 As shown, the signal-to-noise ratio (SNR) of standard MSSA decreased significantly from 9.4 dB to 6.9 dB; the SNR of traditional damped MSSA (first stage only) decreased from 8.5 dB to 5.8 dB, and amplitude deviation was observed; the SNR of the method of this invention remained higher than the former two (7.7-10.6 dB) across all window sizes, and the decrease was more gradual. This comparison demonstrates that this invention is not a simple combination of damped MSSA and matched filtering, but rather achieves a novel parameter tolerance characteristic through the synergistic effect of underfitting-driven and selective reconstruction. Even with significant changes in window size, this invention can maintain a high SNR recovery effect, while traditional methods suffer a sharp performance decline due to parameter sensitivity. In particular, the independent identification stage of this invention avoids the noise that may be introduced by the blind recovery of traditional matched filtering, resulting in cleaner residuals and a higher SNR. This invention achieves decoupling of noise suppression and signal fidelity, significantly reducing the method's sensitivity to parameter selection and resolving the long-standing contradiction between stability and fidelity in seismic data processing.

[0191] In this invention, the underfitting driving mechanism includes limiting the signal subspace dimension and spectral attenuation intensity. By introducing conservative parameter constraints, the signal energy is partially retained in the residual domain, thereby achieving controllable transfer of signal energy. The first-stage signal estimation is achieved through multichannel singular spectrum analysis, including constructing a Hankel matrix and performing singular value decomposition, and reconstructing the signal after weighted processing of the singular values. The residual is obtained from the difference between the original seismic data and the first-stage signal estimation result, and the residual simultaneously contains random noise and leakage signal components introduced by the underfitting mechanism. The multi-domain consistency discrimination mechanism is based on at least two of the following discrimination criteria: local correlation, energy consistency, phase consistency, or matched filter response characteristics. The multi-domain consistency discrimination adopts a combined judgment method; when at least two discrimination criteria meet preset conditions, a leakage signal is determined to exist. Leakage signal identification and selective reconstruction are decoupled operations; the identification process is executed independently of the reconstruction process. Selective reconstruction is achieved through a non-stationary filtering model with regularization constraints, and the model parameters are adaptively adjusted according to local data characteristics. The seismic data is divided into multiple data blocks through overlapping windows, and the complete data is restored through weighted stitching. The underfitting-driven mechanism and selective reconstruction work synergistically, making the signal leakage generated in the first stage the recovery target in the second stage, thus achieving fault tolerance for parameter selection errors. This method transforms the signal recovery problem, which originally depended on optimal parameter selection, into a discrimination and recovery problem based on residual structural differences through the underfitting-driven mechanism and residual structuring. This changes the signal recovery process from a parameter optimization problem to a structural discrimination problem, thereby reducing dependence on local data statistical properties and improving the stability of the method under non-stationary data conditions.

[0192] It will be understood by those skilled in the art that the present invention is not limited to the specific embodiments described herein, and that various obvious changes, readjustments, and substitutions can be made by those skilled in the art without departing from the scope of protection of the present invention. Therefore, although the present invention has been described in detail through the above embodiments, the present invention is not limited to the above embodiments, and may include more other equivalent embodiments without departing from the concept of the present invention, and the scope of the present invention is determined by the scope of the appended claims.

Claims

1. A seismic data processing method based on underfitting-driven and adaptive leakage compensation, characterized in that, Includes the following steps: S1. The original seismic data is divided into blocks and frequency domain transformation is performed. An underfitting driving mechanism is introduced to estimate the signal of the processed seismic data. By limiting the dimension of the signal subspace and the spectral attenuation intensity, some effective signal energy is transferred from the signal subspace to the residual domain in a controllable manner, thereby constructing a residual signal space with structural differences. S2. In the residual signal space, establish a correlation characterization model between the residual and the signal estimation results, and independently identify the leakage signal components in the residual based on the multi-domain consistency discrimination mechanism. S3. Based on the identification results of step S2, reconstruction is performed only on the windows where leakage signals exist to obtain the estimated leakage signals within the windows. The estimation results of all windows are combined to obtain the complete leakage signal estimate. S4. The leakage signal estimate obtained in step S3 is fused with the signal estimate result in step S1 to obtain the final seismic signal output.

2. The seismic data processing method based on underfitting and adaptive leakage compensation according to claim 1, characterized in that, In step S1, the original seismic data is divided into blocks and subjected to frequency domain transformation, specifically including the following steps: S11, Transfer the original seismic data volume The data is divided into several spatiotemporal blocks using overlapping windows, and its expression is as follows: ； In the formula, For window operators, t is the time coordinate and x is the spatial coordinate; S12. Perform a Fast Fourier Transform on each data block along the time direction to convert it into a frequency-spatial domain data slice, expressed as: ； In the formula, The frequency is used to decouple the time dimension into independently processable frequency components through this transformation.

3. The seismic data processing method based on underfitting and adaptive leakage compensation according to claim 2, characterized in that, In step S1, an underfitting driving mechanism is introduced to estimate the signal of the processed seismic data, specifically including the following steps: S13. For each frequency slice obtained in step S12 Extract the spatial vector of the current data block. ; In the formula, The number of spatial channels within the current window. , Let be the complex amplitude of the i-th channel on the frequency slice; S14. Select the embedding dimension L, where L takes the value of... Construct the Hankel matrix ; Among them, the number of columns The matrix elements are arranged according to the following rules: ； In the formula, i is the row index. j is the column index ,Right now It has the following form: ； S15. Perform singular value decomposition on the Hankel matrix: ； In the formula, and Let be unitary matrices formed by the left and right singular vectors, respectively. It is a diagonal matrix of singular values, with the singular values ​​arranged in descending order. ; S16. Employ an underfitting driving mechanism, setting the number of singular values ​​N to be retained; the damping power K; and defining the noise threshold. The first N singular values ​​are weighted using a damped spectrum shrinkage operator. The weighting formula is as follows: ； In the formula, These are the weighted singular values. It is the small regularization constant; S17. Reconstruct the filtered Hankel matrix using the weighted singular values: ； In the formula, and These are the j-th left and right singular vectors, respectively; S18. Recover the filtered spatial vector using inverse Hankel diagonal mean. ; S19. Repeat steps S13 to S18 for all frequency slices. After processing all frequency slices for each data block, transform the data back to the time domain using an inverse fast Fourier transform. Then, stitch the data blocks together using an overlapping and adding method to obtain the damped MSSA estimation result for the first stage. .

4. The seismic data processing method based on underfitting and adaptive leakage compensation according to claim 3, characterized in that, Step S16: Set the number of singular values ​​N to be retained to 2-4; set the damping power K to 2-4. The value is 10 -6 Magnitude.

5. The seismic data processing method based on underfitting and adaptive leakage compensation according to claim 4, characterized in that, Step S18: Recover the filtered spatial vector using inverse Hankel diagonal averaging. Specifically: for The reconstructed spatial sequence is obtained by averaging the elements on all anti-diagonal lines.

6. The seismic data processing method based on underfitting and adaptive leakage compensation according to claim 5, characterized in that, Step S2 specifically includes the following steps: S21. Calculate the residual data volume : ； In the formula, The original earthquake data, The damping MSSA estimation result obtained in step S19; S22, transfer the residual data volume Compared with damped MSSA estimation results Divided into overlapping spatiotemporal windows The window size is consistent with the windowing parameters in step S11; S23. Establish a correlation characterization model between the residual signal and the estimation result, and use at least two discrimination criteria to pre-judge whether there is a leakage signal within the window.

7. The seismic data processing method based on underfitting and adaptive leakage compensation according to claim 6, characterized in that: Step S23: The discrimination criteria include at least two of the following: local correlation coefficient criterion, energy consistency criterion, phase consistency criterion, and matched filter response energy criterion. When at least two criteria determine that a leakage signal exists, it is confirmed that a leakage signal exists in the window; otherwise, it is determined that there is no leakage signal. Among them, the local correlation coefficient criterion is used to calculate the residual. and Pearson correlation coefficient : ； when When this happens, it is determined that a leak signal exists within the window; The energy consistency criterion is the ratio of the calculated residual energy to the energy of the first-stage result: ； like Within the preset range If the ratio is stable relative to the neighborhood window, then a leakage signal is determined to exist. The phase consistency criterion is the phase difference between the calculated residual and the result of the first stage: ； If the phase difference is concentrated near zero, the phase consistency index is: If so, it is determined that a leakage signal exists; The matched filter response energy criterion is obtained by solving the non-stationary least squares matched filter problem. Its objective function is: ； In the formula, This represents the convolution operation. For short convolutional filters, This is the Tikhonov regularization parameter, which takes the value of a positive real number; Calculate filter energy: ； when Greater than the preset threshold When, it serves as an auxiliary basis for judgment.

8. The seismic data processing method based on underfitting and adaptive leakage compensation according to claim 7, characterized in that: Step S3 specifically involves: only identifying the marker. Reconstruction is performed in the window with a value of 1, and the matched filter is applied. Acting on ,calculate The estimated leakage signal within this window is obtained. ; Set the window identified as having no leakage signal to zero directly.

9. A seismic data processing method based on underfitting and adaptive leakage compensation according to claim 6, characterized in that: In step S11, the data blocks are divided using overlapping windows with the same window size. In steps S19 and S24, the data blocks are spliced ​​using overlapping addition or weighted splicing.

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