Weak Signal Extraction Method Based on Coherent Weighting Coefficient

Abstract

The present invention provides a weak signal extraction method based on a coherent weighting coefficient. The weak signal extraction method based on the coherent weighting coefficient includes: Step 1, input seismic data d; Step 2, perform conventional denoising processing on the seismic data; Step 3, define an operator for the coherent part between the effective signal data and the removed noise data in the form of a ω threshold; Step 4, obtain the coherence coefficient ω, and calculate the signal s<subgt;final< / subgt> and the noise n<subgt;final< / subgt> after denoising and extraction; Step 5, introduce orthogonality similarity for quality monitoring. The weak signal extraction method based on the coherent weighting coefficient can extract effective signals from the noise residual data, providing higher-quality data for subsequent seismic data processing work. Compared with traditional methods, it has greater technical advantages.

Description

Technical Field

[0001] The present invention relates to the technical field of oilfield development, and particularly to a method for extracting weak signals based on coherent weighting coefficients. Background Art

[0002] Since the emergence of seismic exploration technology, noise has been a key factor affecting seismic data processing and interpretation. Noise affects the signal-to-noise ratio and resolution of seismic data from acquisition to processing and then to interpretation. The importance of noise removal for the entire seismic data processing is self-evident. With the development of exploration technology, various noise removal methods have emerged in an endless stream. However, for current conventional noise removal methods, generally, some effective signals will remain in the noise profile, and this phenomenon is called energy leakage. Sometimes, this leaked energy cannot be ignored, and in some cases, this phenomenon will seriously reduce the signal-to-noise ratio and resolution of the data. Especially for the original acquisition data with single-point high density, the signal-to-noise ratio is relatively low, and the difference between noise and weak effective signals in the sparse domain is not significant. Therefore, there may still be effective signals in the residual data (removed noise) of the conventional method.

[0003] In conventional processing methods, due to unreasonable parameter selection or unreasonable noise removal assumptions, effective signals are usually damaged when removing noise, that is, the removed noise profile contains components of effective signals. For single-point high-density acquisition, the signal-to-noise ratio of the original acquisition data is relatively low. Through sparse constraint denoising reconstruction, noise can be effectively removed. However, the difference between some noise and weak effective signals in the sparse domain is not significant. Therefore, there may still be effective signals in the poor denoising profile.

[0004] In the Chinese patent application with the application number: CN201410116291.0, it relates to a method for extracting weak signals of microseismic adaptive independent component analysis, including the following steps: preprocessing each microseismic record, and then performing eigenvalue analysis to determine the number of independent components; using the ICA algorithm based on kurtosis to separate the observed signals to obtain the initial estimated value of the source signal; filtering the estimated value of each independent component using an improved adaptive prediction method to obtain the adaptive prediction filtering result of each independent component; during the calculation process, for a cyclic iteration error and weight coefficient, using the method of curve fitting for fitting, and then substituting the fitting result into the original formula for the next cycle of calculation; finally, performing weighted fusion on the adaptive prediction filtering results of each independent component to obtain the best prediction result. This invention can not only reduce the violent oscillation of the error but also make the algorithm result move towards the stable expected direction, and can effectively extract weak signals in microseismic records and improve their signal-to-noise ratio.

[0005] In the Chinese patent application with the application number CN201710596213.9, a reservoir prediction method for reflection coefficient inversion based on a weighted superposition noise suppression strategy is involved, including six main steps: ① Through noise perturbation analysis, determine the noise sources affecting the inversion effect and classify them into seismic noise and inversion noise; ② Conduct seismic noise suppression preprocessing on seismic data through post-stack wavelet frequency division method; ③ For the denoised seismic data, construct the key parameters for reflection coefficient inversion (inverse wavelet transform factor F, inversion dominant frequency band Q, inversion initial model S(n)); ④ Suppress the inversion noise through weighted superposition of inversion results with multiple regularization parameters to obtain the reflection coefficient inversion result; ⑤ Conduct quality control (QC) on the inversion result through spectral analysis and calibrated acoustic wave curves to obtain the final result data; Based on the reflection coefficient result data, conduct fine interpretation of sand bodies and predict the spatial distribution characteristics of sand bodies. Compared with other thin reservoir prediction methods, this method has strong inversion anti-noise performance, can eliminate thin layer interference in the original seismic data, greatly improve the prediction accuracy of thin layers, and reduce the oil and gas exploration risk.

[0006] In the Chinese patent application with the application number CN201610859232.1, a method for extracting seismic weighted average instantaneous frequency based on synchrosqueezing transform is involved. Based on the three-parameter wavelet transform, this invention obtains a more accurate and sparse time-frequency representation by estimating the rearrangement criterion (instantaneous frequency) and then performing energy rearrangement to more accurately determine the effective signal energy distribution space; On this basis, threshold denoising is introduced to perform noise suppression; Finally, an estimation method for the weighted instantaneous frequency of the noisy signal is given. By calculating the instantaneous frequencies of noise-free and noisy synthetic seismic records and comparing the anti-noise performance of different methods, the calculation results of this method have good anti-noise performance and accuracy. Applying this method to actual data can more clearly depict the characteristics of the reservoir.

[0007] The above prior arts are all quite different from the present invention and fail to solve the technical problems we want to solve. Therefore, we have invented a new method for extracting weak signals based on coherent weighting coefficients. Summary of the Invention

[0008] The purpose of the present invention is to provide a method for extracting weak signals based on coherent weighting coefficients that can avoid the loss of effective signals during the seismic data denoising process, ensure the amplitude preservation and fidelity of the denoising process, and provide high-quality data for subsequent data processing work.

[0009] The purpose of the present invention can be achieved by the following technical measures: A method for extracting weak signals based on coherent weighting coefficients, which includes:

[0010] Step 1, input seismic data d;

[0011] Step 2: Perform conventional denoising on the seismic data;

[0012] Step 3: Define the operator for the coherent part between the effective signal data and the removed noise data in the form of an ω threshold;

[0013] Step 4: Calculate the coherence coefficient ω, and calculate the signal s final and the noise n final ;

[0014] Step 5: Introduce orthogonality similarity for quality monitoring.

[0015] The object of the present invention can also be achieved by the following technical measures:

[0016] In Step 1, it is assumed that the seismic data collected in the field consists of two parts, s and n, representing the pure signal and the pure noise respectively. That is, the observed seismic data d is recorded as:

[0017] d = s + n (3-1).

[0018] Based on the conventional denoising method, perform conventional denoising on the seismic data to obtain the denoised signal s1 and the removed noise n1 obtained from the conventional denoising process, as shown in Equation (3-2)

[0019] d = s1 + n1 (3-2).

[0020] In Step 3, there is coherence between the remaining effective signal in the noise profile and the denoised effective data. To extract the remaining effective signal from the noise profile, define the operator for the coherent part between the effective signal data and the removed noise data in the form of an ω threshold.

[0021] In Step 3, the defined ω threshold form is:

[0022]

[0023] Define the recovered signal part as follows:

[0024] s restore = ω1·n1 (3-4)

[0025] And, the final signal s final and the final noise n final are:

[0026] s final = s1 + s restore (3-5)

[0027] n final = n1 - s restore (3-6)

[0028] where v1 and v2 are the upper and lower threshold limits, and v n,s (t, x) represents the coherence between the effective signal profile and the noise profile; v1 and v2 are determined according to the proportion of signal and noise at each point; the greater the upper threshold limit v2, the higher the credibility of the operator for extracting the effective signal. For some uncertain signal points, v1 allows a smooth change in weight; the reliable signal points in the noise profile should have a small but measurable coherence similarity.

[0029] In step 3, at each moment t, the coherence coefficient v n,s (t, x) with a window length of m can be expressed as:

[0030]

[0031] where s0(i) and n0(i) respectively represent the effective signal data after conventional denoising and the removed noise data; for simplicity, v n,s,m (t, x) is represented by ω1.

[0032] In step 4, in order to better control the coherence coefficient, the smooth regularization and triangular smoothing algorithms of Fomel and Claerbout are introduced to solve the coherence coefficient.

[0033] In step 4, after adding the local smooth constraint, the solution of the coherence coefficient is transformed into the following problem:

[0034]

[0035] where S1 = diag(s1), and for simplicity, ω1 is used to represent v n,s,m (t, x); R represents the smooth regularization operator, n1 is the removed noise, and s1 is the signal after denoising;

[0036] By using the shaping regularization method to add the smooth constraint, the above equation becomes:

[0037] ω1 = [λ 2 I + T(S1 T S1 - λ 2 I)] -1 T(S1 T n1) (3 - 9)

[0038] where T represents the triangular smoothing operator, λ is the scale parameter, λ = S1 T S1, and I is the identity matrix.

[0039] In step 4, using the coherence coefficient calculated above and substituting it into equations (3 - 5) and (3 - 6), the final signal s final after denoising extraction and the final noise n final can be obtained:

[0040] s final =s1+ω1·n1=(I+diag[ω1])n1 (3-10)

[0041] n final =n1-ω1·n1=d-s1-ω1n1=d-(I+diag[ω1])n1 (3-11).

[0042] In step 5, Fomel defines the orthogonal similarity between two vectors a and b:

[0043]

[0044] c1 and c2 are obtained by solving the two least squares problems in equation (3-13):

[0045]

[0046]

[0047] Where A = diag(a), B = diag(b);

[0048] Combined with the smooth constraint shaping regularization, the above formula can be written as:

[0049]

[0050]

[0051] Where λ1=||B T B||2λ2=||A T A||2.

[0052] The coherence-weighted weak signal extraction method of this invention extracts the effective signal energy from the removed noise profile using a weighting factor. The extracted effective signal is then added to the original denoised profile to produce the final denoised profile. This ensures fidelity and amplitude preservation throughout the pre-stack denoising process, maximizing the separation of effective signals from surface rolls.

[0053] Compared with the existing weak signal extraction technology, the present invention is a supplement and improvement to the conventional denoising method. The present invention has the following advantages:

[0054] It is possible to extract some effective signals from the residual profile after conventional denoising, preventing the loss of effective signals. Although the extracted effective signals are weak, they are indispensable in actual data processing. Especially for single-point high-density data, the loss of weak effective signals will reduce the signal-to-noise ratio and resolution of the data. The present invention provides a method for extracting weak effective signals based on the coherence coefficient, which can extract effective signals from noise residual data, providing higher-quality data for subsequent seismic data processing, and having greater technical advantages compared with traditional methods. BRIEF DESCRIPTION OF THE DRAWINGS

[0055] Figure 1 It is a flowchart of a specific embodiment of the weak signal extraction method based on the coherence weighting coefficient of the present invention;

[0056] Figure 2 It is a schematic diagram of single-point high-density original single-shot data in Embodiment 1 of the present invention;

[0057] Figure 3 In Embodiment 1 of the present invention, for Figure 2 it is a schematic diagram of the effective signals obtained after conventional denoising of the original data therein;

[0058] Figure 4 In Embodiment 1 of the present invention, for Figure 2 it is a schematic diagram of the residual data obtained after conventional denoising of the original data therein;

[0059] Figure 5 In Embodiment 1 of the present invention, for Figure 4 it is a schematic diagram of some effective signals obtained after coherent weighting extraction of the residual data therein;

[0060] Figure 6 In Embodiment 1 of the present invention, adding the Figure 5 effective signals extracted therein back to the Figure 3 effective signals therein to obtain a schematic diagram of the finally noise-suppressed effective signals;

[0061] Figure 7 In Embodiment 1 of the present invention, subtracting the Figure 4 effective signals in Figure 5 from the residual data in

[0062] Figure 8 it is a schematic diagram of the finally denoised residual data;

[0063] Figure 9 In Embodiment 2 of the present invention, for Figure 8 it is a schematic diagram of the effective signals obtained after conventional denoising of the original data therein;

[0064] Figure 10 Schematic diagram of the residual data obtained after performing conventional denoising processing on the Figure 8 original data in Embodiment 2 of the present invention;

[0065] Figure 11 Schematic diagram of a partial effective signal obtained after performing coherent weighted extraction on the Figure 10 residual data in Embodiment 2 of the present invention;

[0066] Figure 12 Schematic diagram of the final effective signal after noise suppression obtained by adding the effective signal extracted in Figure 11 to the effective signal in Figure 9 in Embodiment 2 of the present invention;

[0067] Figure 13 Schematic diagram of the final denoised residual data obtained by subtracting the effective signal in Figure 10 from the residual data in Figure 11 in Embodiment 2 of the present invention. Detailed implementation manners

[0068] It should be noted that the following detailed description is exemplary and is intended to provide further illustration of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those of ordinary skill in the technical field to which the present invention belongs.

[0069] It should be noted that the terms used herein are only for describing specific implementation manners and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they specify the presence of features, steps, operations, and / or combinations thereof.

[0070] The following are several specific embodiments of applying the present invention.

[0071] Embodiment 1

[0072] In Specific Embodiment 1 of applying the present invention, as Figure 1 shown, Figure 1 is a flowchart of the weak signal extraction method based on coherent weighting coefficient of the present invention. The weak signal extraction method based on coherent weighting coefficient includes the following steps:

[0073] (1) First, assume that the seismic raw data collected in the field as Figure 2 shown is composed of two parts, s and n, representing the pure signal and pure noise respectively, that is, the observed seismic data d is denoted as

[0074] d = s + n (3-1)

[0075] (2) Then, based on the conventional denoising method, perform conventional denoising processing on the seismic data, and the denoised signal s1 obtained from the conventional denoising process can be obtained (as shown in Figure 3 ), and the removed noise n1 (as shown in Figure 4 ), as shown in Eqs. (2-2) and (2-3).

[0076] d = s1 + n1 (3-2)

[0077] In the case of ideal denoising, the signal s ≈ s1 and n ≈ n1 after denoising processing. However, this ideal situation does not exist in actual processing. The main reasons are twofold: unreasonable parameter selection and insufficient denoising assumptions. For the conventional denoising method, there must be some effective signals remaining in the noise profile, and sometimes these remaining effective signals cannot be ignored. Especially for single-point high-density data, this phenomenon will seriously reduce the signal-to-noise ratio and resolution of the data.

[0078] (3) There is coherence between the effective signals remaining in the noise profile and the effective data after denoising. To extract the remaining effective signals from the noise profile, define the operator of the coherent part between the effective signal data and the removed noise data as the ω threshold form:

[0079]

[0080] Define the recovered signal part (as shown in Figure 5 ) as follows:

[0081] s restore = ω1·n1 (3-4)

[0082] Moreover, the final signal s final and the final noise n final are:

[0083] s final = s1 + s restore (3-5)

[0084] n final = n1 - s restore (3-6)

[0085] where v1 and v2 are the upper and lower limits of the threshold, and v n,s(t, x) represents the coherence between the effective signal profile and the noise profile. v1 and v2 are determined according to the proportion of signal and noise at each point. When the upper threshold v2 is larger, the credibility of the operator for extracting the effective signal is higher. For some uncertain signal points, v1 allows a smooth change in weight. Of course, the reliable signal points in the noise profile should have a small but measurable coherent similarity. v1 generally takes values between 0.1 and 0.2, and v2 generally takes values between 0.2 and 0.3.

[0086] At each time t, the coherence coefficient v with a window length of m n,s (t, x) can be expressed as:

[0087]

[0088] where s0(i) and n0(i) represent the effective signal data and the removed noise data after conventional denoising respectively. For simplicity, v n,s,m (t, x) is denoted by ω1.

[0089] (4) To better control the coherence coefficient, the smooth regularization and triangular smoothing algorithms of Fomel and Claerbout are introduced to solve the coherence coefficient. After adding the local smooth constraint, the solution of the coherence coefficient is transformed into the following problem:

[0090]

[0091] where S1 = diag(s1), and for simplicity, v n,s,m (t, x) is denoted by ω1. R represents the smooth regularization operator. By using the shaping regularization method to add the smooth constraint, the above formula becomes:

[0092] ω1 = [λ 2 I + T(S1 T S1 - λ 2 I)] -1 T(S1 T n1) (3 - 9)

[0093] where T represents the triangular smoothing operator, λ is the scale parameter, λ = S1 T S1, and I is the identity matrix.

[0094] Using the coherence coefficient calculated above and substituting it into equations (3 - 5) and (3 - 6), the final signal s final (as Figure 6 shown) and the final noise n final (as Figure 7 shown) can be obtained:

[0095] s final= s1 + ω1·n1 = (I + diag[ω1])n1 (3 - 10)

[0096] n final = n1 - ω1·n1 = d - s1 - ω1n1 = d - (I + diag[ω1])n1 (3 - 11)

[0097] (5) The noise and signal obtained from the above processing should not be similar, that is, the two are orthogonal. To facilitate the inspection of the effectiveness of signal extraction, orthogonal similarity is introduced for quality monitoring.

[0098] Fomel defined the orthogonal similarity between two vectors a and b:

[0099]

[0100] c1 and c2 are obtained by solving two least - squares problems in Equation (3 - 13):

[0101]

[0102]

[0103] Among them, A = diag(a), B = diag(b). The above solution is similar, combined with the shaping regularization of smooth constraints, and the above formula can be written as:

[0104]

[0105]

[0106] Among them, λ1 = ||B T B||2 λ2 = ||A T A||2.

[0107] Example 2:

[0108] In the specific Example 2 of applying the present invention, as Figure 1 shown, Figure 1 is the flowchart of the weak signal extraction method based on the coherent weighting coefficient of the present invention. The weak signal extraction method based on the coherent weighting coefficient includes the following steps:

[0109] (1) First, assume that the seismic raw data collected in the field as Figure 8 shown is composed of two parts, s and n, representing the pure signal and pure noise respectively. That is, the observed seismic data d is denoted as

[0110] d = s + n (3 - 1)

[0111] (2) Then, based on the conventional denoising method, the seismic data is subjected to conventional denoising processing, and the denoised signal s1 obtained from the conventional denoising process can be obtained (as shown in Figure 9 ), and the removed noise n1 (as shown in Figure 10 ), as shown in Equations (2-2) and (2-3)

[0112] d = s1 + n1 (3-2)

[0113] In the case of ideal denoising, the denoised signal s ≈ s1 and n ≈ n1. However, this ideal situation does not exist in actual processing. There are two main reasons: unreasonable parameter selection and insufficient denoising assumptions. For the conventional denoising method, there must be some effective signals remaining in the noise profile, and sometimes these remaining effective signals cannot be ignored. Especially for single-point high-density data, this phenomenon will seriously reduce the signal-to-noise ratio and resolution of the data.

[0114] (3) There is coherence between the effective signals remaining in the noise profile and the effective data after denoising. To extract the remaining effective signals from the noise profile, an operator for the coherent part between the effective signal data and the removed noise data is defined in the form of a ω threshold:

[0115]

[0116] Define the recovered signal part (as shown in Figure 11 ) as follows:

[0117] s restore = ω1 · n1 (3-4)

[0118] And, the final signal s final and the final noise n final are:

[0119] s final = s1 + s restore (3-5)

[0120] n final = n1 - s restore (3-6)

[0121] where v1 and v2 are the upper and lower limits of the threshold, and v n,s (t,x) represents the coherence between the effective signal profile and the noise profile. v1 and v2 are determined according to the ratio of the signal to the noise at each point. When the upper threshold v2 is larger, the credibility of the operator for extracting the effective signal is higher. For some uncertain signal points, v1 allows a smooth change in weight. Of course, the reliable signal points in the noise profile should have a small but measurable coherent similarity. v1 generally takes values between 0.1 and 0.2, and v2 generally takes values between 0.2 and 0.3.

[0122] At each moment \(t\), the coherence coefficient \(v\) with a window length of \(m\) n,s (\(t,x\)) can be expressed as:

[0123]

[0124] where \(s_0(i)\) and \(n_0(i)\) represent the effective signal data after conventional denoising and the removed noise data respectively. For simplicity, \(v\) n,s,m (\(t,x\)) is denoted by \(\omega_1\).

[0125] (4) To better control the coherence coefficient, the smooth regularization and triangular smoothing algorithms of Fomel and Claerbout are introduced to solve the coherence coefficient. After adding the local smooth constraint, the solution of the coherence coefficient is transformed into the following problem:

[0126]

[0127] where \(S_1 = diag(s_1)\), and for simplicity, \(v\) n,s,m (\(t,x\)) is denoted by \(\omega_1\). \(R\) represents the smooth regularization operator. Using the shaping regularization method to add the smooth constraint, the above equation becomes:

[0128] \(\omega_1=[\lambda\) 2 \(I + T(S_1\) T \(S_1-\lambda\) 2 \(I)] -1 \(T(S_1\) T \(n_1)\ (3 - 9)

[0129] where \(T\) represents the triangular smoothing operator, \(\lambda\) is the scale parameter, \(\lambda = S_1\) T \(S_1\), and \(I\) is the identity matrix.

[0130] Substituting the coherence coefficient calculated above into equations (3 - 5) and (3 - 6), the final signal \(s\) final (as Figure 12 shown) and the final noise \(n\) final (as Figure 13 shown) can be obtained:

[0131] \(s\) final \(=s_1+\omega_1\cdot n_1=(I + diag[\omega_1])n_1\ (3 - 10)

[0132] \(n\) final \(=n_1-\omega_1\cdot n_1=d - s_1-\omega_1n_1=d-(I + diag[\omega_1])n_1\ (3 - 11)

[0133] (5) The noise and signal obtained from the above processing should not be similar, that is, they are orthogonal. To facilitate the inspection of the effectiveness of signal extraction, orthogonal similarity is introduced for quality monitoring.

[0134] Fomel defined the orthogonal similarity between two vectors a and b:

[0135]

[0136] c1 and c2 are obtained by solving two least-squares problems in Equation (3-13):

[0137]

[0138]

[0139] where A = diag(a) and B = diag(b). The above solution is similar. Combining the shaping regularization with smooth constraints, the above equation can be written as:

[0140]

[0141]

[0142] where λ1 = ||B T B||2 λ2 = ||A T A||2.

[0143] The present invention can extract effective information from the residual data (removed noise) by calculating the coherent similarity between the results of conventional denoising and the difference results in the process of seismic data processing, thereby ensuring the fidelity and amplitude preservation of the entire pre-stack denoising process and maximizing the separation of effective signals and noise. The present invention is not only applicable to single-point high-density data but also suitable for all seismic data that requires denoising processing. For the difference data after denoising, different weighting scales are set according to the fidelity of each signal point, thereby constructing a weighting operator to measure the effective signal component of that point. There is similarity between the common signal parts of the data after denoising and the removed noise data, and this similarity is relatively small. The common similar parts are extracted and added back to the data after denoising, and finally the data after denoising is obtained, maximizing the fidelity and amplitude preservation of the denoising process, and having wide applicability and popularization and application value.

[0144] Finally, it should be noted that the above are only preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or perform equivalent replacements for some of the technical features. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

[0145] Except for the technical features described in the specification, the rest are known technologies to those skilled in the art.

Claims

1. A method for extracting weak signals based on coherent weighting coefficients, characterized in that The weak signal extraction method based on the coherent weighting coefficient includes: Step 1: Input seismic data d; Step 2: Conduct conventional denoising processing on the seismic data; Step 3: Define the operator of the coherent part between the effective signal data and the removed noise data in the form of ω threshold; Step 4, obtain the coherence coefficient ω and calculate the signal s final after denoising and extraction, and the noise n final ; Step 5: Introduce orthogonal similarity for quality monitoring; In Step 3, there is coherence between the residual effective signal in the noise profile and the effective data after denoising. To extract the residual effective signal from the noise profile, the operator of the coherent part between the effective signal data and the removed noise data is defined in the form of ω threshold; In Step 3, the defined form of ω threshold is: Define the recovered signal part as follows: s restore = ω1·n1 (3-4) and the final signal s final and the final noise n final are as follows: s fina l = s1 + s restore (3 - 5) n fina l = n1 - s restore (3 - 6) where v1 and v2 are the upper and lower limits of the threshold, and v n,s (t,x) represents the coherence between the effective signal profile and the noise profile; v1 and v2 are determined according to the proportion of signal and noise at each point; the higher the upper threshold v2, the higher the credibility of the operator for extracting the effective signal. For some uncertain signal points, v1 allows a smooth change in weight; the reliable signal points in the noise profile should have a small but measurable coherent similarity.

2. The weak signal extraction method based on the coherent weighting coefficient according to claim 1, characterized in that In Step 1, assume that the seismic data collected in the field consists of two parts, s and n, representing the pure signal and pure noise respectively. That is, the observed seismic data d is denoted as: d = s + n (3-1).

3. The weak signal extraction method based on the coherent weighting coefficient according to claim 1, characterized in that In Step 2, based on the conventional denoising method, conduct conventional denoising processing on the seismic data to obtain the denoised signal s1 and the removed noise n1 obtained by the conventional denoising process, as shown in Equation (3-2): d = s1 + n1 (3-2).

4. The weak signal extraction method based on the coherent weighting coefficient according to claim 1, characterized in that In step 3, at each moment t, the coherence coefficient v n,s (t, x) with a window length of m can be expressed as: Among them, s0(i) and n0(i) respectively represent the effective signal data after conventional denoising and the removed noise data; for simplicity, v n,s,m (t, x) is denoted by ω1.

5. The weak signal extraction method based on the coherent weighting coefficient according to claim 4, wherein In Step 4, to better control the coherence coefficient, introduce the smooth regularization and triangular smoothing algorithms of Fomel and Claerbout to solve the coherence coefficient.

6. The weak signal extraction method based on the coherent weighting coefficient according to claim 5, wherein, In Step 4, after adding the local smooth constraint, the solution of the coherence coefficient is transformed into the following problem: where S1 = diag(s1), and for simplicity, ω1 is used to represent v n,s,m (t, x); R represents a smooth regularization operator, n1 is the removed noise, and s1 is the denoised signal; Using the shaping regularization method to add the smooth constraint, the above equation becomes: where T represents the triangular smoothing operator, λ is the scale parameter, and I is the identity matrix.

7. The weak signal extraction method based on the coherent weighting coefficient according to claim 6, characterized in that In step 4, by substituting the coherence coefficient calculated above into equations (3-5) and (3-6), the final signal s after denoising and extraction can be obtained final and the final noise n final : s final = s1 + ω1·n1 = (I + diag[ω1])n1(3-10) n final = n1 - ω1·n1 = d - s1 - ω1n1 = d - (I + diag[ω1])n1 (3-11).

8. The weak signal extraction method based on the coherent weighting coefficient according to claim 7, characterized in that In Step 5, Fomel defines the orthogonal similarity between two vectors a and b: c1 and c2 are obtained by solving two least squares problems in Equation (3-13): where A = diag(a), B = diag(b); Combined with the shaping regularization with smooth constraint, the above equation can be written as: where λ1 = ||B T B||2, λ2 = ||A T A||2.

Images