Random noise suppression method for Shearlet-TGV seismic data

Abstract

Addressing the advantages and disadvantages of Shearlet threshold shrinkage and TGV (Transient Transformer-TGV) seismic data, this invention proposes a Shearlet-TGV seismic data random noise suppression method. This invention uses the result of Shearlet threshold shrinkage as input to the TGV method, and then iteratively extracts effective signals from the TGV differential profile, superimposing them to obtain the optimal denoising result. The TGV method is used to suppress the boundary effects caused by Shearlet threshold shrinkage, while using the Shearlet threshold shrinkage result as input mitigates the "painting" effect of the TGV method. During the iteration process, the weight coefficients of the TGV regularization term are adaptively changed, continuously extracting effective information from the TGV differential profile, superimposing the effective signals, and thus estimating the optimal random noise removal result.

Description

Technical Field

[0001] This invention belongs to the field of earthquake data processing technology, and specifically relates to a method for suppressing random noise in earthquake data. Background Technology

[0002] Seismic data acquisition is typically subject to various noise interferences, such as those from the acquisition environment and the acquisition instruments. Seismic records contain a significant amount of random noise, which reduces the signal-to-noise ratio and identification accuracy, hindering subsequent data processing and final profile interpretation. Therefore, random noise suppression is one of the key steps in seismic data processing.

[0003] Sparse transform is one of the main methods for suppressing random noise. Based on the differences in the magnitude and distribution characteristics of the coefficients corresponding to the effective signal and random noise in the transform domain of seismic records, an appropriate threshold function and threshold calculation method are selected to separate the effective signal from the random noise, thereby achieving the purpose of removing random noise.

[0004] The Shearlet transform (Guo KH, Labate D. 2007. Optimally sparse multidimensional representation using shearlets. SIAM Journal on Mathematical Analysis, 39(1):298-318.) is a novel sparse transform method with multi-scale and multi-directional characteristics, which can effectively characterize the local features of signals. Compared with other multi-scale analysis methods, the Shearlet transform has a simpler mathematical structure, more delicate scale and direction representation, and uses fewer coefficients when approximating curves, making it suitable for processing seismic data containing texture, contour, and edge information. However, simple Shearlet threshold shrinkage can introduce boundary effects. This interference has a negative impact on the interpretation of seismic data in seismic data processing, and may introduce false horizons, affecting the final structural identification results.

[0005] The Total Variation (TV) method (Rudin L, Osher S, Fatemi E. 1992. Nonlinear total variation based noise removal minimization. Physica D, 60: 259-268.) can suppress random noise while preserving edge information, but it only considers the first derivative, which can easily cause the "oil-painting" effect. Bredies et al. (Bredies K, Kunisch K, Pock T. Total Generalized Variation. 2010. SIAM Journal on Imaging Sciences, 3(3): 492-526.) proposed the Generalized Total Variation (TGV) method, which fully considers the influence of higher-order derivatives. While balancing computational time and performance, it extends to the second derivative, which to some extent suppresses the "oil-painting" effect and improves the quality of the estimation results, but is sometimes not ideal. Summary of the Invention

[0006] Addressing the advantages and disadvantages of Shearlet threshold shrinkage and TGV (Transient Transformer-TGV) seismic data, this invention proposes a Shearlet-TGV seismic data random noise suppression method. This invention uses the result of Shearlet threshold shrinkage as input to the TGV method, and then iteratively extracts effective signals from the TGV differential profile, superimposing them to obtain the optimal denoising result. The TGV method is used to suppress the boundary effects caused by Shearlet threshold shrinkage, while simultaneously using the Shearlet threshold shrinkage result as input to mitigate the "painting" effect of the TGV method. During the iteration process, the weight coefficients of the TGV regularization term are adaptively changed, continuously extracting effective information from the TGV differential profile, superimposing the effective signals, and thus estimating the optimal random noise removal result.

[0007] The objective of this invention is achieved through the following technical solution:

[0008] A method for suppressing random noise in Shearlet-TGV seismic data includes the following steps:

[0009] Step 1: Read the 2D seismic data and perform Shearlet transformation on the 2D seismic data. The specific process is as follows:

[0010] s=S(u) (1)

[0011] In the formula, S represents the Shearlet forward transform, s represents the Shearlet coefficients, u represents the two-dimensional noisy seismic data, u = u0 + n, u0 represents the effective seismic signal, and n represents random noise;

[0012] Step 2: Perform threshold shrinkage and noise reduction on the Shearlet coefficients s. The specific process is as follows:

[0013] The hard thresholding function T retains large Shearlet coefficients and removes small Shearlet coefficients; the hard thresholding function T is defined as follows:

[0014]

[0015] In the formula, C is the constant transformation, λ is the root mean square of the Shearlet coefficient at a certain scale angle, which varies with scale and angle, and σ is the noise standard deviation;

[0016] Step 3: Perform an inverse Shearlet transform on the retained Shearlet coefficients to obtain the Shearlet threshold shrinkage and denoising result u. S The specific process is as follows:

[0017] u S =S -1 (T(s)) (3)

[0018] In the formula, S -1 Represents the Shearlet inverse transform, u S This represents the result of Shearlet threshold shrinkage denoising;

[0019] Step 4, put u S The result of Shearlet-TGV joint denoising is obtained by processing the input of TGV. ST The specific process is as follows:

[0020] u ST =TGV(u S (4)

[0021] In the formula, u ST This represents the result of Shearlet-TGV joint denoising. TGV can be expressed as a combination of the first-order difference p and its derivative ζ(p), defined as follows:

[0022]

[0023] In the formula, α0 and α1 are weighting coefficients;

[0024] Step 5: Due to the damage to the effective signal caused by the TGV denoising method, its difference profile u R =uS -u ST In the process, the remaining effective signal will be obtained; through iterative analysis of the Shearlet-TGV joint denoising results, the TGV difference profile u of each iteration will be continuously improved. R The remaining valid information is extracted, superimposed, and then the denoising result is obtained; the specific process is as follows:

[0025]

[0026] In the formula, k represents the number of iterations, u k R-ST u represents the effective signal extracted from the k-th TGV difference profile. D This indicates the final denoising result;

[0027] Since the noise content varies after each Shearlet thresholding process, the weight coefficients α0 and α1 in TGV need to be updated. Given initial values, the weight coefficients are defined as follows:

[0028]

[0029] The denoising result u is given by iterative calculation until the stopping criterion is met or the maximum number of iterations is reached. D .

[0030] Compared with the prior art, the advantages of the present invention are as follows:

[0031] 1. First, perform Shearlet domain threshold shrinkage, then perform TGV. Shearlet transformation can effectively partition seismic data, giving it the best sparse representation in the Shearlet domain. Threshold shrinkage can effectively remove random noise. Using the result of Shearlet domain threshold shrinkage as input to the TGV method can reduce the "painting" effect of TGV.

[0032] 2. TGV has the ability to remove random noise and can effectively protect the boundaries of seismic signals. It can effectively suppress the boundary effects caused by the Shearlet shrinkage threshold.

[0033] 3. In the outer iterative loop of the method proposed in this paper, an adaptive weight coefficient is used to cope with the changes in TGV input, thereby ensuring that the best TGV estimation result can be obtained in each iteration. Attached Figure Description

[0034] Figure 1 This is a single-shot record diagram of theoretical seismic data;

[0035] (a) Theoretical data; (b) Noisy theoretical data;

[0036] Figure 2 The results and partial views show the random noise suppression effect;

[0037] (a) TGV; (b) Shearlet threshold shrinkage; (c) The method of the present invention;

[0038] Figure 3 This is the difference profile between the noisy data and the denoised results;

[0039] (a) TGV; (b) Shearlet threshold shrinkage; (c) The method of the present invention. Detailed Implementation

[0040] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0041] Example

[0042] A method for suppressing random noise in Shearlet-TGV seismic data includes the following steps:

[0043] Step 1: Using a computer, read the two-dimensional noisy seismic data and perform a Shearlet forward transform on it. The specific sub-steps are as follows:

[0044] like Figure 1 As shown in (a), this is a simulated single-shot record of two-dimensional seismic data. To test the random noise suppression method, random noise was added to the theoretical data. The signal-to-noise ratio of the noisy seismic data was 6 dB. Figure 1 As shown in (b). Shearlet transform is performed on the noisy two-dimensional seismic data:

[0045] s=S(u) (1)

[0046] In the formula, S represents the Shearlet forward transform, s represents the Shearlet coefficients, u represents the two-dimensional noisy seismic data, u = u0 + n, u0 represents the effective seismic signal, and n represents random noise.

[0047] Step 2: Perform threshold shrinkage and noise reduction on the Shearlet coefficients s. The specific calculation process is as follows:

[0048] The hard thresholding function T retains larger Shearlet coefficients and removes smaller Shearlet coefficients. The hard thresholding function T is defined as follows:

[0049]

[0050] In the formula, C is the constant transformation, λ is the root mean square of the Shearlet coefficient at a certain scale angle, which varies with scale and angle, and σ is the noise standard deviation.

[0051] Step 3: Perform an inverse Shearlet transform on the retained Shearlet coefficients to obtain the Shearlet threshold shrinkage and denoising result. The specific process is as follows:

[0052] u S =S -1 (T(s)) (3)

[0053] In the formula, S -1 Represents the Shearlet inverse transform, u S This represents the result of Shearlet threshold shrinking and denoising. For example... Figure 2 As shown in (b) Figure 2 (b) shows the Shearlet threshold shrinkage denoising results, which indicate a good overall effect and sufficient suppression of random noise. Figure 3 (b) shows the corresponding differential profile, where almost no effective signal is observed, but due to the influence of the Shearlet shrinkage threshold... Figure 2 (b) The edges of the in-phase axes produce a more obvious “boundary effect”.

[0054] Step 4, put u S It is processed as input to the TGV. The specific process is as follows:

[0055] u ST =TGV(u S (4)

[0056] In the formula, u ST This represents the result of Shearlet-TGV joint denoising. TGV can be expressed as a combination of the first-order difference p and its derivative ζ(p), defined as follows:

[0057]

[0058] In the formula, α0 and α1 are weighting coefficients.

[0059] Step 5: Due to the damage to the effective signal caused by the TGV denoising method, its difference profile u R =u S -u ST In the process, the remaining valid signal will be obtained. Through iterative processing of the Shearlet-TGV joint denoising, the TGV difference profile u is continuously improved from each iteration. R The remaining valid information is extracted and superimposed to obtain a satisfactory denoising result. The specific process is as follows:

[0060]

[0061] In the formula, k represents the number of iterations. u represents the effective signal extracted from the k-th TGV difference profile. D This represents the final denoising result.

[0062] Since the noise content varies after each Shearlet thresholding process, the weight coefficients α0 and α1 in TGV need to be updated. Given initial values, the adaptive weights are defined as follows:

[0063]

[0064] The denoising result u is given by iterative calculation until the stopping criterion is met or the maximum number of iterations is reached. D .like Figure 2 As shown in (c) Figure 2 (c) is the result obtained by the method of the present invention, compared with TGV ( Figure 2 (a) shows the denoising results of the TGV method. Compared with the Shearlet threshold shrinkage denoising method, it achieves the best random noise suppression effect, while generating minimal human influence and effectively protecting the boundary of the reflection phase axis.

Claims

1. A Shearlet-TGV seismic data random noise suppression method, characterized in that, It comprises the following steps: Step 1, reading two-dimensional seismic data, and performing Shearlet transform on the two-dimensional seismic data; Step 2, performing threshold shrinkage denoising on the Shearlet coefficient s; Step 3, inverse Shearlet transform is performed on the reserved Shearlet coefficients to obtain the result of Shearlet threshold shrinkage denoising ; Step 4, the result of Shearlet threshold shrinkage denoising As the input of TGV, the result of Shearlet-TGV joint denoising is obtained ; Step 5, by iterating the Shearlet-TGV joint denoising results, constantly extracting the remaining effective information from the TGV difference profile of each iteration superposition, and then obtaining the denoising result; The specific processing process is as follows: (6) In the formula, k represents the number of iterations, represents the effective signal extracted from the TGV difference profile of the kth time, represents the final denoising result; Since the results after each time of Shearlet threshold denoising contain different noise, the weight coefficient in TGV needs to be updated and ; The final denoising result is given by iterative calculation until the stop criterion is satisfied or the maximum iteration number is reached .

2. The Shearlet-TGV seismic data random noise suppression method of claim 1, wherein, In step 1, the specific process of the two-dimensional seismic data Shearlet transform is as follows: (1) In the formula, S represents a Shearlet forward transform, s represents a Shearlet coefficient, u represents two-dimensional seismic data containing noise, u0 represents an effective seismic signal, and n represents random noise.

3. The Shearlet-TGV seismic data random noise suppression method of claim 2, wherein, In step 2, the specific calculation process of the threshold shrinkage denoising on the Shearlet coefficient s is as follows: The large Shearlet coefficients are retained by a hard threshold function T, and the small Shearlet coefficients are removed; the hard threshold function T used is defined as (2) where C is a constant transform, is the root mean square of the Shearlet coefficients at a certain scale and angle, which varies with scale and angle, is the standard deviation of the noise.

4. The Shearlet-TGV seismic data random noise suppression method of claim 3, wherein, In step 3, the specific processing process of the Shearlet inverse transform on the retained Shearlet coefficients to obtain the Shearlet threshold shrinkage denoising result is as follows: (3) wherein denotes the Shearlet inverse transform, denotes the result of the Shearlet thresholding denoising.

5. The Shearlet-TGV seismic data random noise suppression method of claim 1, wherein, In step 4, the result of the Shearlet threshold shrinkage denoising is obtained As the input of TGV, the result of Shearlet-TGV joint denoising is obtained The specific processing process is as follows: (4) wherein denotes the result of the joint Shearlet-TGV denoising, TGV can be represented as a combination of the first order difference and its derivative defined as follows (5) In the formula, and are weight coefficients.

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