Seismic data denoising method based on improved anisotropic diffusion model

Abstract

The invention discloses a seismic data denoising method based on an improved anisotropic diffusion model. The method comprises the following steps: 1) obtaining original noise data to be denoised; 2) data preprocessing: performing Gaussian filtering processing on the original seismic data to obtain preprocessed seismic data; 3) constructing an improved anisotropic diffusion model; 4) setting an iteration error limit and parameters in the model; and 5) performing iterative calculation on the noise-containing data according to the improved anisotropic diffusion model to obtain an iterative result which is a seismic data denoising result. The seismic data denoising method is obtained by improving the anisotropic diffusion model, and the edge preserving and denoising effects of the seismic data are improved.

Description

Technical Field

[0001] The present invention relates to seismic data processing technology, and in particular to a seismic data denoising method based on an improved anisotropic diffusion model. Background Art

[0002] Anisotropic diffusion models have long been a focus of research in denoising. Noise attenuation methods based on diffusion equations are a digital image processing method and a research hotspot for image denoising. Compared to traditional linear filtering methods, diffusion filtering preserves image edge details during the denoising process and is widely used in image denoising research. The Weickert model is one of the most commonly used models. It incorporates structural analysis into diffusion filtering, where diffusion varies with direction, preserving the linear texture features of the image during denoising. This makes anisotropic diffusion filtering widely used in image processing.

[0003] In practical applications, the diffusion tensor is the core of the Weickert model. The method used to construct the diffusion tensor significantly influences the iterative results. Commonly used diffusion tensors include the coherence enhancement diffusion model and the edge enhancement model. The Weickert model diffuses in a single direction in smooth regions, inevitably leading to false edges and distortion during the denoising process. Summary of the Invention

[0004] The technical problem to be solved by the present invention is to provide a seismic data denoising method based on an improved anisotropic diffusion model in view of the defects in the prior art.

[0005] The technical solution adopted by the present invention to solve the technical problem is: a seismic data denoising method based on an improved anisotropic diffusion model, comprising the following steps:

[0006] 1) Obtain the original noise data to be denoised;

[0007] 2) Data preprocessing: Gaussian filtering is performed on the original seismic data to obtain preprocessed seismic data;

[0008] 3) Construct an improved anisotropic diffusion model;

[0009] Based on the anisotropic diffusion model, the second-order partial derivative is introduced, the coherence is used to distinguish the image features, the L2 norm is combined for iterative calculation, and the regularization term is added to the diffusion model to construct the edge preservation model;

[0010]

[0011] Where U0(x,y) is the original seismic data, (x,y) is the spatial coordinate, t represents the diffusion scale, div represents the divergence operator, ▽ represents the gradient operator, and D is the diffusion tensor that controls the diffusion; u1 represents the preprocessed seismic data, and u represents the denoised seismic data; γ is a coefficient parameter used to control the fidelity of the denoised u and the preprocessed u1;

[0012] 4) Setting the iterative error limits and parameters in the model;

[0013] 5) Perform iterative calculation on the noisy data according to the improved anisotropic diffusion model to obtain an iterative result, which is the denoising result of the seismic data.

[0014] According to the above scheme, the structure tensor used in constructing the improved anisotropic diffusion model in step 3) is:

[0015]

[0016] Among them, ε represents the stability coefficient, which ranges from 0 to 1; G represents the Gaussian kernel function, ρ and σ represent the standard deviation of the Gaussian kernel function, and * is the convolution symbol. is the gradient, is the transpose of the gradient;

[0017] The coherence is defined by the eigenvalues ​​of the structure tensor, which is formulated as:

[0018] Coh=(μ1-μ2) 2

[0019] Where μ1 and μ2 represent the two eigenvalues ​​of the structure tensor.

[0020] According to the above scheme, the diffusion tensor used in constructing the improved anisotropic diffusion model in step 3) is:

[0021]

[0022] Among them, v1 and v2 are the eigenvectors of the structure tensor, T represents the transpose operation, h is a constant, represents the modulus of the gradient, χ∈(0,1) is a positive constant close to zero, α∈(0,1), c is a constant, generally taken as 1, Coh represents coherence, τ1 and τ2 are both constants.

[0023] According to the above scheme, in step 5), when iteratively calculating the noisy data according to the improved anisotropic diffusion model, the directional gradient is calculated first, then the second-order partial derivative is calculated, then the coherence is calculated, and then the diffusion tensor is calculated. The above results are substituted into the following discrete iterative formula; the regularization term obtained by subtracting the previous iteration result from the preprocessed image is added to obtain the result of this iteration;

[0024] The discrete iteration formula is:

[0025]

[0026] According to the above scheme, in step 5), the number of iterations is replaced by the L2 norm, and in the iterative process, until |u t+1 -u t |<e, the iteration terminates, where e is the pre-set iteration error limit.

[0027] The beneficial effects produced by the present invention are:

[0028] This paper develops a seismic data denoising method by improving the anisotropic diffusion model. Second-order partial derivatives and coherence are added to the anisotropic diffusion model, and a regularization term is incorporated into the diffusion model to enhance edge preservation and denoising of seismic data. The present invention modifies the diffusion tensor of the denoising algorithm model, resulting in better denoising and edge preservation, enhancing the visual quality of the image. The L2 norm is used to control the number of iterations, making the model more generalizable. The addition of the regularization term improves seismic data fidelity, resulting in superior performance compared to traditional methods in processing seismic data. BRIEF DESCRIPTION OF THE DRAWINGS

[0029] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following is a brief introduction to the drawings required for use in the embodiments. It should be understood that the following drawings only show certain embodiments of the present application and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without creative work.

[0030] Figure 1 is a schematic diagram of a method flow in an embodiment of the present invention;

[0031] Figure 2 is the original image before denoising according to an embodiment of the present invention;

[0032] Figure 3 This is a diagram of the Weickert1 denoising result according to an embodiment of the present invention;

[0033] Figure 4 This is a diagram of the Weickert2 denoising result of an embodiment of the present invention;

[0034] Figure 5 This is a result diagram after the proposed denoising according to an embodiment of the present invention. DETAILED DESCRIPTION

[0035] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0036] like Figure 1 As shown, a seismic data denoising method based on an improved anisotropic diffusion model includes the following steps:

[0037] 1) First read the original seismic data to be denoised, then perform Gaussian filtering on the noisy data to obtain preprocessed data;

[0038] 2) Based on the anisotropic diffusion model, second-order partial derivatives are introduced to construct a structure tensor. Coherence is used to distinguish image features and construct a diffusion tensor. A regularization term is added to the diffusion model, and iterative calculations are performed in combination with the L2 norm to construct an edge-preserving model.

[0039]

[0040] The diffusion tensor is:

[0041]

[0042] Where v1 and v2 are the eigenvectors of the structure tensor, T represents the transpose operation, and h is a constant. represents the modulus of the gradient, χ∈(0,1) is a positive constant close to zero, α∈(0,1), c is generally taken as 1, Coh represents coherence, τ1 and τ2 are both constants.

[0043] 3) Setting the iterative error limit and the parameters in the model;

[0044] 4) The noisy seismic data are iteratively calculated based on the improved anisotropic diffusion model to obtain the iterative results. The result of each iteration is the denoising result. The signal-to-noise ratio, structural similarity, and root mean square error of the denoised seismic data are calculated and compared to demonstrate the denoising effect. In each iteration, the directional gradient and second-order partial derivatives are calculated first, then the structural tensor is calculated, and then the diffusion tensor is calculated. The above calculation results are substituted into the discrete iterative formula, which is:

[0045]

[0046] Add the regularization term obtained by subtracting the result of the previous iteration from the preprocessed data to obtain the result of this iteration.

[0047] Calculate the L2 norm to minimize the objective function and determine whether to terminate the iteration.

[0048] Example 1

[0049] Example 1 is a denoising experiment on seismic data. In the experiment, the method of the present invention is compared with several other methods. Weickert1 shows that the diffusion tensor is constructed by using the selective coherence enhancement diffusion model. The denoising results are shown in FIG. Figure 3 , Weickert2 indicates that the edge-enhanced diffusion model is selected to construct the diffusion tensor, and the denoising results are shown in Figure 4 , Proposed represents a seismic data denoising method based on anisotropic diffusion model improved by L2 norm, and its denoising results are shown in Figure 5 . Figure 2 The original seismic data used in the denoising experiment of this invention is 1151×1273. The denoising performance of the model is verified using the signal-to-noise ratio (SNR), structural similarity (SSIM), and root mean square error (RMSE). The results are shown in Table 1. The parameters are set as follows: Δt = 0.1, γ = 0.01, α = 0.0001, and χ = 0.0000001.

[0050] Table 1 Evaluation of denoising results of Example 1

[0051] method SNR SSIM RMSE Weickert1 8.8714 0.9408 0.0760 Weickert2 7.7653 0.9003 0.9857 Method of the present invention 12.1987 0.9704 0.5917

[0052] The parameters involved in the denoising experiment are all fixed values.

[0053] Comparing Weickert1, Weickert2, and the method of the present invention, Weickert1 and Weickert2 introduce second-order partial derivative information. Weickert1 selects a coherent enhancement diffusion model to construct the diffusion tensor, while Weickert2 selects an edge enhancement diffusion model to construct the diffusion tensor. As can be seen from the results in Table 1, when the parameters remain consistent, the denoising capabilities of Weickert1h and Weickert2 are not much different, and the differences in the signal-to-noise ratio, structural similarity, and root mean square error after denoising are relatively small. However, the proposed method of the present invention improves the denoising capability and has higher fidelity and structural similarity.

[0054] Example 2

[0055] During the denoising process, as the number of iterations increases, the diffusion tensor's effectiveness in removing high-frequency noise increases accordingly, affecting the noise suppression effect. To highlight the advantages of the present invention, in Example 3, the present invention does not use the L2 norm to achieve optimal denoising. Instead, a fixed number of iterations is used to control denoising, with all other parameters remaining the same. When the number of iterations is 50, the numerical analysis comparison of the signal-to-noise ratio and structural similarity is shown in Table 2.

[0056] Table 2 Evaluation of denoising results of Example 2

[0057] method SNR SSIM RMSE Weickert1 14.6381 0.9844 0.0391 Weickert2 13.3826 0.9750 0.5163 The present invention 18.1377 0.9924 0.2986

[0058] It is not difficult to find from Table 2 that in Example 3, even if the L2 norm is not used as the objective function, when other parameters are controlled to be consistent, the improved diffusion tensor construction algorithm proposed in the present invention has great advantages in denoising, and the signal-to-noise ratio and similarity are also improved.

[0059] It should be understood that those skilled in the art can make improvements or changes based on the above description, and all such improvements and changes should fall within the scope of protection of the appended claims of the present invention.

Claims

1. A seismic data denoising method based on an improved anisotropic diffusion model, characterized in that: The following steps are involved: 1) Obtain the original noise data to be denoised; 2) Data preprocessing: Gaussian filtering is performed on the original seismic data to obtain preprocessed seismic data; 3) Construct an improved anisotropic diffusion model; Based on the anisotropic diffusion model, the second-order partial derivative is introduced, the coherence is used to distinguish the image features, the L2 norm is combined for iterative calculation, and the regularization term is added to the diffusion model to construct the edge preservation model; Where U0(x,y) is the original seismic data, (x,y) is the spatial coordinate, t represents the diffusion scale, div represents the divergence operator, ▽ represents the gradient operator, and D is the diffusion tensor that controls the diffusion; u1 represents the preprocessed seismic data, and u represents the denoised seismic data; γ is a coefficient parameter used to control the fidelity of the denoised u and the preprocessed u1; 4) Setting the iterative error limits and parameters in the model; 5) Perform iterative calculation on the noisy data according to the improved anisotropic diffusion model to obtain an iterative result, which is the denoising result of the seismic data.

2. The seismic data denoising method based on the improved anisotropic diffusion model according to claim 1, characterized in that: The structural tensor used in constructing the improved anisotropic diffusion model in step 3) is: Among them, ε represents the stability coefficient, which ranges from 0 to 1; G represents the Gaussian kernel function, ρ and σ represent the standard deviation of the Gaussian kernel function, * is the convolution symbol, ▽u σ is the gradient, is the transpose of the gradient; The coherence is defined by the eigenvalues ​​of the structure tensor, which is formulated as: Coh=(μ1-μ2) 2 Where μ1 and μ2 represent the two eigenvalues ​​of the structure tensor.

3. The seismic data denoising method based on the improved anisotropic diffusion model according to claim 1, characterized in that: The diffusion tensor used in constructing the improved anisotropic diffusion model in step 3) is: Among them, v1 and v2 are the eigenvectors of the structure tensor, T represents the transpose operation, h is a constant, |▽u| represents the modulus of the gradient, χ∈(0,1) is a positive constant close to zero, α∈(0,1), c is a constant, Coh represents coherence, and τ1 and τ2 are both constants.

4. The seismic data denoising method based on the improved anisotropic diffusion model according to claim 1, characterized in that: In step 5), when performing iterative calculations on noisy data according to the improved anisotropic diffusion model, first calculate the directional gradient, then calculate the second-order partial derivative, then calculate the coherence, and then calculate the diffusion tensor. Substitute the above results into the following discrete iterative formula; add the regularization term obtained by subtracting the previous iteration result from the preprocessed image to obtain the result of this iteration: The discrete iteration formula is: u t+1 (x,y)=u t (x,y)+Δt(div(D * ▽u t (x,y)))+λ[u1(x,y)-u t (x,y)]。 5. The seismic data denoising method based on the improved anisotropic diffusion model according to claim 1 is characterized in that In step 5), the number of iterations is replaced by the L2 norm. During the iteration process, until |u t+1 -u t |<e, the iteration terminates, where e is the pre-set iteration error limit.

6. A server comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the method according to any one of claims 1 to 5 is implemented.

7. A computer-readable storage medium, characterized in that The computer-readable storage medium stores computer instructions, and the computer instructions are used to enable a processor to implement the method according to any one of claims 1 to 5 when executed.

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