Seismic signal denoising method based on Surelet transformation

Abstract

The invention discloses a seismic signal denoising method based on Surelet transformation, and aims to effectively suppress noise and reserve useful signal details. The method comprises the following steps: firstly, preprocessing input seismic data to remove irrelevant parts and standardize the irrelevant parts so as to enhance the stability of the data; and then, decomposing the signal into sub-band coefficients of multiple scales and directions by using curvelet transform, and introducing an SURE algorithm to automatically select an optimal threshold value so as to maximize a denoising effect. And then, carrying out soft threshold or hard threshold processing on each sub-band coefficient to suppress noise. In order to further improve the denoising effect, a fast non-local mean (FNLM) algorithm is adopted to reduce residual noise, and gradient information weighted smoothing is combined with a directional smoothing diffusion algorithm. And finally, reconstructing the de-noised seismic signal through inverse Surelet transformation. According to the method, the defects of a traditional denoising technology are effectively overcome, the wide application potential in earthquake monitoring and analysis is shown, and the signal definition and interpretation accuracy can be remarkably improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of signal processing, and particularly relates to a seismic signal denoising method based on the Surelet transform. Background Art

[0002] In the field of seismic exploration, the removal of signal noise is the key to obtaining accurate underground structure information. Since seismic signals are often interfered by various noises, how to effectively remove the noise while preserving the effective signals has become an important challenge in seismic signal processing. Traditional signal denoising methods, such as Fourier transform, Wavelet Transform, Curvelet Transform, etc., although they can suppress noise to a certain extent, they still face problems such as loss of signal details, insufficient noise suppression, and high computational complexity.

[0003] Specifically, for the traditional Curvelet transform method, it performs well in multi-scale and multi-direction, and can capture the detailed structure of the signal. However, in practical applications, it is still difficult to solve the noise interference in complex signals, especially prone to pseudo-Gibbs phenomenon under high-noise conditions. To improve these problems, a denoising method based on the SURE (Stein Unbiased Risk Estimate) algorithm has been proposed, which uses an adaptive threshold to better suppress noise. However, the existing SURE-based denoising methods still face problems such as large computational amount and low processing efficiency.

[0004] The present invention proposes a seismic signal denoising method based on the Surelet transform, which combines the Curvelet transform and the SURE (Stein's Unbiased Risk Estimate) algorithm, and introduces means such as fast non-local means (FNLM) denoising and directional smoothing diffusion to more precisely suppress noise while retaining the effective information of seismic signals. Compared with traditional denoising methods (such as wavelet threshold denoising, Fourier transform filtering, etc.), this method has more advantages in retaining the non-stationary characteristics and directional details of seismic signals. Summary of the Invention

[0005] In order to solve the technical problems existing in the background art, the purpose of the present invention is to provide a seismic signal denoising method based on the Surelet transform. By combining the Surelet transform and the SURE estimate, the limitations of the traditional SURE method are overcome, and the denoising efficiency is significantly improved. Especially when dealing with complex seismic data, it can adaptively select the optimal threshold and efficiently remove noise.

[0006] To solve the technical problems, the technical solution of the present invention is as follows:

[0007] A seismic signal denoising method based on the Surelet transform, the method comprising:

[0008] S1: Obtain the original seismic signal data, remove the irrelevant parts and standardize the signal to obtain the preprocessed seismic signal;

[0009] S2: Apply the Curvelet transform to the preprocessed seismic signal to decompose the signal into subband coefficients of multiple scales and directions, obtaining the Surelet transform coefficients of multiple scales and directions, representing different frequency and direction characteristics of the signal;

[0010] S3: Based on the Surelet transform coefficients obtained in step S2, use the SURE algorithm to calculate the estimated values of each subband coefficient, automatically select the optimal threshold to maximize the denoising effect, and obtain the optimized threshold;

[0011] S4: Based on the Surelet transform coefficients and the selected optimal threshold, apply soft thresholding or hard thresholding to each subband coefficient to suppress noise and retain the effective signal components, obtaining the denoised coefficients after thresholding;

[0012] S5: For the denoised coefficients after thresholding, use the non-local means FNLM algorithm to perform weighted averaging on non-local similarities, further remove the residual noise, and output the denoised signal coefficients;

[0013] S6: Based on the FNLM-denoised coefficients obtained in step S5, apply the directional smoothing diffusion algorithm to perform weighted smoothing based on the gradient direction of the signal, further suppress noise, enhance the details of the signal, output the smoothed denoised coefficients, and retain the directional characteristics and details of the signal;

[0014] S7: Perform the inverse Surelet transform on the smoothed denoised coefficients to reconstruct the time-domain signal, the finally denoised seismic signal, removing noise and retaining the details of the effective signal.

[0015] Further, in step S2, the calculation of the Curvelet transform and the Surelet transform coefficients includes:

[0016] S201: First, obtain the preprocessed seismic signal data to ensure that the signal has removed the irrelevant parts and is standardized;

[0017] S202: Apply the Curvelet Transform to the standardized seismic signal to decompose the signal into subband coefficients of multiple scales and directions. The purpose of the Curvelet transform is to capture different characteristics of the signal at multiple scales of frequency and direction. Specifically, the signal f(x) is represented by the Curvelet transform as:

[0018]

[0019] Among them, C s,ω is the curvelet coefficient at scale s and direction ω, and ψ s,ω (x) is the curvelet basis function corresponding to the scale and direction;

[0020] S203: The coefficients (C s,ω ) obtained at multiple scales and directions represent different frequency characteristics of the signal. Each coefficient contains the local frequency information of the signal and is ready to enter the next step of SURE threshold calculation.

[0021] Furthermore, in step S3, the SURE algorithm calculates the optimal threshold, including:

[0022] S301: According to the curvelet transform coefficient C s,ω obtained in step S2, the SURE algorithm is applied for denoising processing on each sub-band. The Stein Unbiased Risk Estimate algorithm automatically calculates the optimal threshold through the estimation of the coefficient, reducing noise while retaining the effective signal;

[0023] S302: The SURE algorithm determines the threshold λ s,ω by calculating the estimation error. The specific formula is as follows:

[0024]

[0025] Among them, is the signal estimate after threshold processing, and λ s,ω is the optimal threshold. Minimizing the SURE error can obtain the optimal denoising coefficient;

[0026] S303: By calculating the threshold of the minimum SURE estimate value, the optimal threshold λ s,ω at each scale and direction is obtained and applied to the subsequent threshold processing step.

[0027] Furthermore, in step S4, applying threshold processing includes:

[0028] S401: Using the optimal threshold λ s,ω obtained in step S3, threshold processing is performed on each sub-band coefficient. According to the selected threshold method, i.e., hard threshold or soft threshold, the coefficient is processed as follows:

[0029] Hard threshold processing: For each coefficient C s,ω the following formula is applied:

[0030]

[0031] Soft threshold processing: For each coefficient C s,ωApply the following formula:

[0032]

[0033] Furthermore, in step S5, non-local means FNLM denoising includes:

[0034] S501: Apply the non-local means FNLM algorithm to further denoise the coefficients processed by the threshold in step S4. The FNLM algorithm is based on the non-local similarity of the image or signal and reduces the residual noise by weighted averaging. The weighted average of each pixel or coefficient is determined by its similarity to the surrounding pixels or coefficients;

[0035] S502: Use the FNLM algorithm for each signal coefficient C s,ω Use the following weighted average formula:

[0036]

[0037] where ω i is the similarity weight between the signal coefficient C i and the current coefficient C s,ω

[0038] Furthermore, in step S6, directional smoothing diffusion includes:

[0039] S601: Based on the coefficients processed in step S5, apply the directional smoothing diffusion algorithm. This algorithm performs weighted smoothing according to the gradient information of the signal, enhances the details of the signal, and suppresses noise at the same time. The specific steps include calculating the gradient direction of the signal and performing weighted diffusion on the signal along the main direction;

[0040] S602: The diffusion process is carried out according to the following formula:

[0041]

[0042] where u is the coefficient of the signal, D is the diffusion coefficient, ▽u is the gradient of the signal, and the diffusion process controls the diffusion intensity through a regularization parameter to balance diffusion and signal protection;

[0043] S603: The smoothed coefficients are used to retain the directional characteristics and details of the signal, and further suppress noise at the same time.

[0044] Furthermore, in step S7, inverse Surelet transform and signal reconstruction include:

[0045] S701: Perform an inverse Surelet transform on the smoothed coefficients in step S6 to reconstruct the time-domain signal and obtain the final denoised seismic signal;

[0046] ​S702: The result of the inverse transform is to remove noise and retain the details of the signal, and the finally output signal is used for subsequent analysis or processing.

[0047] Compared with the prior art, the advantages of the present invention are as follows:

[0048] Adaptive threshold selection: Through the SURE algorithm, the optimal threshold is automatically calculated, eliminating the limitations of manual threshold selection. It can be dynamically adjusted according to the noise level and signal distribution characteristics to ensure the optimal denoising effect.

[0049] Reduction of the pseudo-Gibbs phenomenon: The SURE algorithm can adaptively adjust the threshold, avoiding the common pseudo-Gibbs phenomenon in traditional curvelet transform methods and better retaining signal details.

[0050] Improvement of denoising efficiency: Combining the Surelet transform, integrating the multi-scale characteristics of the curvelet transform and the adaptive processing of the SURE algorithm, greatly improves the computational efficiency of the denoising process.

[0051] Efficient denoising: Compared with traditional denoising methods, the solution of the present invention can more effectively suppress noise, especially in a high-noise environment, and can better retain the effective information of seismic signals.

[0052] Enhancement of signal quality: The signal after denoising processing has a significant improvement in quality indicators such as signal-to-noise ratio (SNR) and peak signal-to-noise ratio (PSNR), ensuring the reliability of seismic data in subsequent analysis. Description of the Drawings

[0053] Figure 1 The main flowchart of a seismic signal denoising method based on the Surelet transform according to the present invention; Detailed Embodiment

[0054] The following describes the specific embodiments of the present invention in conjunction with embodiments:

[0055] It should be noted that the structures, ratios, sizes, etc. shown in this specification are only used to cooperate with the content disclosed in the specification for those skilled in this technology to understand and read, and are not used to limit the limiting conditions under which the present invention can be implemented. Any modification of the structure, change of the proportional relationship or adjustment of the size, without affecting the effects that the present invention can produce and the purposes that can be achieved, should still fall within the scope covered by the technical content disclosed in the present invention.

[0056] At the same time, the terms such as "upper", "lower", "left", "right", "middle" and "one" cited in this specification are only for the convenience of clear narration, and are not used to limit the scope under which the present invention can be implemented. The change or adjustment of their relative relationships, without substantial change in the technical content, should also be regarded as the scope within which the present invention can be implemented.

[0057] Example 1:

[0058] As Figure 1 shown, this example proposes a seismic signal denoising method based on the Surelet transform. By combining multiple techniques such as curvelet transform, SURE algorithm, non-local means denoising (FNLM), and directional smoothing diffusion, efficient noise suppression and signal detail preservation are achieved. Compared with traditional methods, this technology can better adapt to the complexity of seismic signals and has broad application prospects in seismic monitoring, source mechanism research, etc. The method specifically includes:

[0059] 1. Data preprocessing

[0060] Before performing the Surelet transform, the input seismic data is first standardized and irrelevant parts are removed, such as zero-value filling areas or instrument noise, to improve the stability of subsequent denoising steps.

[0061] 2. Surelet transform

[0062] The Surelet transform is an adaptive denoising method based on the wavelet domain. It uses adaptive threshold selection to enhance the signal processing effect. In this method, first, the seismic signal is decomposed into sub-band coefficients of multiple scales and directions through the curvelet transform to ensure fine analysis of the signal in different frequency ranges.

[0063] (1) Curvelet transform

[0064] The curvelet transform is more effective than the traditional wavelet transform in processing seismic signals because: the curvelet transform can better capture the directional characteristics of the signal (especially suitable for the wavefront propagation mode of seismic signals). It can extract local amplitude characteristics at multiple scales, which is beneficial for removing non-stationary noise.

[0065] (2) Adaptive threshold selection of the SURE algorithm

[0066] The SURE algorithm is an unbiased risk estimation method that can automatically determine the optimal denoising parameters without relying on the signal-to-noise ratio. By calculating the SURE estimate value of each sub-band coefficient, a soft threshold or a hard threshold is adaptively selected to maximize the signal denoising effect. This method is particularly effective in the case of low signal-to-noise ratio because it can avoid signal distortion caused by over-denoising.

[0067] 3. Threshold processing

[0068] After obtaining the Surelet transform coefficients, threshold processing is used to suppress noise:

[0069] Soft Thresholding: Applicable to stationary noise, reducing high-frequency noise interference.

[0070] Hard Thresholding: Applicable to non-stationary noise, effectively retaining the main components of the signal.

[0071] Adaptive threshold strategy: Different thresholds are used for coefficients at different scales and directions to improve the noise suppression ability.

[0072] 4. Denoising by Fast Non-Local Means (FNLM)

[0073] The FNLM (Fast Non-Local Means) algorithm is a denoising method based on non-local similarity. Its basic idea is:

[0074] Using the weighted average of similar local structure information in the signal to suppress noise while maximizing the retention of the texture details of the original signal.

[0075] This method is particularly applicable to the repetitive characteristics of similar waveforms in seismic signals (such as the waveform patterns of P-waves and S-waves), and can enhance the smoothness of the signal.

[0076] 5. Directional Smoothing Diffusion

[0077] Directional Smoothing Diffusion is a smoothing method based on the gradient direction, mainly used for:

[0078] Suppressing residual noise: There may still be high-frequency noise after FNLM denoising, and Directional Smoothing Diffusion can further smooth the noise.

[0079] Enhancing signal structure: Through the weighted smoothing strategy, this method makes the wavefront boundary of the seismic signal clearer.

[0080] 6. Inverse Surelet Transform

[0081] After the above denoising process, perform the inverse Surelet transform on all processed coefficients to reconstruct the denoised seismic signal.

[0082] It can be understood that the present invention inputs the original seismic signal, and successively passes through data preprocessing, Surelet transform, SURE algorithm, threshold processing, FNLM denoising, and Directional Smoothing Diffusion, and finally outputs: the denoised seismic signal, with noise suppressed and signal details retained.

[0083] It can be understood that compared with traditional methods (such as wavelet threshold denoising, empirical mode decomposition (EMD), etc.), the advantages of this method are mainly reflected in: Directional enhancement: Curvelet transform can better extract the direction information of seismic waves, making the signal features clearer. Strong adaptability: The SURE algorithm automatically selects the optimal threshold without manually adjusting the denoising parameters, and is applicable to different types of seismic data. Efficient non-local denoising: The FNLM algorithm utilizes the local similarity of the signal and can effectively remove noise without damaging the seismic waveform structure. Gradient-optimized smoothing: Directional smoothing diffusion further optimizes the denoised signal, making the wavefront structure of seismic waves smoother and more continuous.

[0084] Embodiment 2:

[0085] In an alternative technical solution: A common alternative technical solution is a denoising method based on wavelet transform. Wavelet transform has the advantage of multi-scale analysis and can effectively separate signals and noise. By performing threshold processing on the coefficients after wavelet transform, noise can be suppressed. Common methods include soft threshold and hard threshold processing. This method has a relatively low computational complexity, but the denoising effect is relatively poor in a high-noise environment, and it is difficult to avoid the pseudo-Gibbs phenomenon. Advantages and disadvantages of this alternative: Advantages: Simple and easy to implement, relatively high computational efficiency, applicable to the case of low noise. Disadvantages: In a high-noise condition, the denoising effect is not as good as curvelet transform, and it is difficult to handle boundary effects and pseudo-Gibbs phenomena in complex signals.

[0086] In an alternative technical solution: An alternative is a denoising method based on Non-Local Means (NLM). The NLM method performs weighted averaging by calculating the similarity between image patches to suppress noise. By globally modeling the similarity of the image, it can effectively remove noise while retaining image details. Advantages and disadvantages of this alternative: Advantages: Applicable to non-local similarity in images / signals, can better remove noise, especially has a good effect on signals with rich details. Disadvantages: Relatively high computational complexity, low efficiency when processing large-scale data.

[0087] In an alternative technical solution: A denoising method based on deep learning. In recent years, deep learning methods have been widely applied to the field of signal denoising. By training a convolutional neural network (CNN) or other deep neural networks based on a large amount of noisy training data, the network can automatically learn the features of noise suppression and achieve denoising through an end-to-end learning process. Advantages and disadvantages of this alternative: Advantages: Can adapt to various different types of noise, automatically extract features, wide range of applications. Disadvantages: Requires a large amount of training data and computing resources, and for small sample data or cases with relatively complex noise types, it may require a long training time.

[0088] Those skilled in the art should understand that the embodiments of the present invention can be provided as a method, a system, or a computer program product. Therefore, the present invention can take the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware aspects. Moreover, the present invention can take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) that contain computer-usable program code.

[0089] The present invention is described with reference to the flowcharts and / or block diagrams of methods, apparatuses (systems), and computer program products according to embodiments of the present invention. It should be understood that each flow and / or block in the flowchart and / or block diagram, as well as the combination of flows and / or blocks in the flowchart and / or block diagram, can be realized by computer program instructions. These computer program instructions can be provided to the processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing devices to generate a machine, such that the instructions executed by the processor of the computer or other programmable data processing devices generate means for realizing the functions specified in one Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0090] These computer program instructions can also be stored in a computer-readable memory that can direct a computer or other programmable data processing device to work in a specific manner, such that the instructions stored in the computer-readable memory generate a manufactured article including instruction means that realize the functions specified in one Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0091] These computer program instructions can also be loaded onto a computer or other programmable data processing device, such that a series of operation steps are executed on the computer or other programmable device to generate a computer-implemented process, and thus the instructions executed on the computer or other programmable device provide steps for realizing the functions specified in one Figure 1 one flow or multiple flows and / or blocks Figure 1 one block or multiple blocks.

[0092] The preferred embodiments of the present invention have been described in detail above, but the present invention is not limited to the above embodiments. Within the knowledge scope of those of ordinary skill in the art, various changes can be made without departing from the purpose of the present invention.

[0093] Many other changes and modifications can be made without departing from the concept and scope of the present invention. It should be understood that the present invention is not limited to specific embodiments, and the scope of the present invention is defined by the appended claims.

Claims

1. A seismic signal denoising method based on Surelet transform, characterized in that: The method comprises: S1: Obtain the original seismic signal data, remove irrelevant parts and standardize the signal to obtain the preprocessed seismic signal; S2: Apply the curvelet transform to the preprocessed seismic signal to decompose the signal into sub-band coefficients of multiple scales and directions, and obtain Surelet transform coefficients of multiple scales and directions to represent the different frequency and direction characteristics of the signal; S3: Based on the coefficients after Surelet transformation obtained in step S2, the estimated value of each subband coefficient is calculated using the SURE algorithm, and the optimal threshold is automatically selected to maximize the denoising effect, thereby obtaining the optimized threshold; S4: Based on the Surelet transform coefficient and the selected optimal threshold, soft threshold or hard threshold processing is applied to each subband coefficient to suppress noise and retain the effective signal component to obtain the denoising coefficient after threshold processing; S5: For the denoising coefficients processed by the threshold, a non-local mean FNLM algorithm is used to perform weighted averaging on non-local similarity to further remove residual noise, and output the denoised signal coefficients; S6: Based on the FNLM denoising coefficients obtained in step S5, a directional smoothing diffusion algorithm is applied to perform weighted smoothing based on the gradient direction of the signal to further suppress noise, enhance signal details, and output smoothed denoising coefficients to retain the directional characteristics and details of the signal; S7: Perform inverse Surelet transform on the smoothed denoising coefficients to reconstruct the time domain signal, and finally obtain the denoised seismic signal, removing noise and retaining the details of the effective signal.

2. A seismic signal denoising method based on Surelet transform according to claim 1, characterized in that: In step S2, the calculation of the curvelet transform and Surelet transform coefficients includes: S201: First, obtain pre-processed seismic signal data to ensure that irrelevant parts of the signal have been removed and the signal has been standardized; S202: Applying Curvelet Transform to the standardized seismic signal decomposes the signal into sub-band coefficients of multiple scales and directions. The purpose of Curvelet Transform is to capture different characteristics of the signal at multiple scales of frequency and direction. Specifically, the signal f(x) is expressed as: Among them, C s,ω is the curvelet coefficient at scale s and direction ω, ψ s,ω (x) is the curvelet basis function corresponding to scale and direction; S203: The coefficients of multiple scales and directions (C s,ω ) represents the different frequency characteristics of the signal. Each coefficient contains the local frequency information of the signal, ready for the next step of SURE threshold calculation.

3. A seismic signal denoising method based on Surelet transform according to claim 1, characterized in that: In step S3, the SURE algorithm calculates the optimal threshold, including: S301: Curvelet transform coefficients C obtained in step S2 s,ω , the SURE algorithm is applied to each subband for denoising. The Stein Unbiased Risk Estimate algorithm automatically calculates the optimal threshold by estimating the coefficients, reducing noise while retaining valid signals; S302: The SURE algorithm determines the threshold λ by calculating the estimation error s,ω , the specific formula is as follows: in, is the signal estimate after threshold processing, λ s,ω is the optimal threshold. Minimizing the SURE error can obtain the optimal denoising coefficient; S303: By calculating the threshold of the minimum SURE estimate, the optimal threshold λ in each scale and direction is obtained. s,ω , and apply it to the subsequent thresholding step.

4. A method for denoising seismic signals based on Surelet transform according to claim 1, characterized in that: In step S4, threshold processing is applied, including: S401: Use the optimal threshold λ obtained in step S3 s,ω , threshold processing is performed on each subband coefficient. Depending on the selected threshold method, that is, hard threshold or soft threshold, the coefficient is processed as follows: Hard threshold processing: For each coefficient C s,ω Apply the following formula: Soft threshold processing: For each coefficient C s,ω Apply the following formula:

5. A seismic signal denoising method based on Surelet transform according to claim 1, characterized in that: In step S5, the non-local mean FNLM denoising includes: S501: applying the non-local mean FNLM algorithm to further denoise the coefficients after threshold processing in step S4. The FNLM algorithm is based on the non-local similarity of the image or signal and reduces the residual noise by weighted average. The weighted average of each pixel or coefficient is determined by its similarity with surrounding pixels or coefficients. S502: Using the FNLM algorithm for each signal coefficient C s,ω Use the following weighted average formula: Among them, ω i is the signal coefficient C i With the current coefficient C s,ω The similarity weight between them.

6. A method for denoising seismic signals based on Surelet transform according to claim 1, characterized in that: In step S6, directional smooth diffusion includes: S601: Based on the coefficients processed in step S5, a directional smoothing diffusion algorithm is applied. The algorithm performs weighted smoothing according to the gradient information of the signal, enhances the details of the signal, and suppresses noise. The specific steps include calculating the gradient direction of the signal and performing weighted diffusion on the signal along the main direction; S602: The diffusion process is performed according to the following formula: Among them, u is the coefficient of the signal, D is the diffusion coefficient, ▽u is the gradient of the signal, and the diffusion process controls the diffusion intensity through the regularization parameter to balance diffusion and signal protection; S603: The smoothed coefficients are used to retain the directional characteristics and details of the signal while further suppressing noise.

7. A method for denoising seismic signals based on Surelet transform according to claim 1, characterized in that: In step S7, the inverse Surelet transform and signal reconstruction include: S701: performing inverse Surelet transform on the smoothing coefficient in step S6, reconstructing the time domain signal, and obtaining the final denoised seismic signal; S702: The result of the inverse transformation is to remove noise and retain signal details, and the final output signal is used for subsequent analysis or processing.

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