A robust sparse method for suppressing abnormal noise of seismic data

Abstract

The application provides a robust sparse method for suppressing abnormal noise of seismic data, and belongs to the technical field of seismic exploration data processing. The two-dimensional seismic data is modeled as a combination of effective signals, random noise and abnormal noise, the abnormal noise is modeled as a Laplace scale mixed distribution, the EM algorithm is used to solve the model, the SPGL1 algorithm is used to obtain sparse representation in the discrete cosine transform domain, and the noise component is suppressed in the iteration updating process.

Description

Technical Field

[0001] This invention relates to the field of seismic exploration data processing technology, and in particular to a robust sparsity method for suppressing anomalous noise in seismic data. Background Technology

[0002] In digital signal transmission and reception, noise is a significant factor affecting performance that cannot be ignored. Noise is generally a random additive signal that, when superimposed on a digital signal, distorts the signal and thus has an impact. Noise suppression has always been a problem that various fields have been striving to solve.

[0003] In actual seismic exploration, the geological information received by detectors contains various disturbances. Based on the characteristics of seismic interference waves, they can be divided into two main categories: coherent noise (regular interference waves) and random noise (irregular interference waves). Generally, regular interference waves are called coherent noise, and irregular interference waves are called random noise. Due to the influence of complex geological conditions and equipment, the reflected signals received by the detectors during seismic data imaging contain a large amount of random noise, directly affecting the continuity of the seismic data's phase axis and increasing the difficulty of subsequent data analysis and processing. The suppression of random noise in seismic data has become a key preprocessing step in the industrial seismic data processing workflow.

[0004] Isolated noise, poorly coupled detectors, wind, rain, and other factors can all contribute to the non-Gaussian nature of random noise. Whether on land or at sea, seismic data often exhibits spatial anomalous noise. Anomalous noise is a type of random noise with high amplitude and non-Gaussian distribution characteristics, and its properties often affect the performance of noise suppression methods based on the Gaussian distribution assumption.

[0005] Currently, noise suppression typically employs the fx-domain median filtering method. This method selects the median filter operator length based on the amplitude variation of the seismic data, then obtains the relative variation of the seismic data based on the average amplitude of each trace, and performs median filtering on the seismic data based on the relative variation to achieve a balance between maintaining effective signal and suppressing noise.

[0006] The existing technology has at least the following shortcomings:

[0007] 1. The median filter operator length cannot be adaptively changed according to the noise characteristics, which will lead to damage to the effective signal and incomplete suppression of noise.

[0008] 2. Statistical earthquake data extraction can result in significant residual noise after noise suppression. Summary of the Invention

[0009] To address the problems existing in the prior art, this invention provides a robust sparsity method for suppressing anomalous noise in seismic data. The two-dimensional seismic data is modeled as a combination of effective signal, random noise, and anomalous noise, and the anomalous noise is modeled as a Laplace-scale mixed distribution. The expectation-maximization algorithm (EM algorithm) is used to solve the model, and the sparse representation in the discrete cosine transform domain is obtained using the L1 norm spectral projection gradient algorithm (SPGL1 algorithm). The noise component is suppressed during the iterative update process.

[0010] This invention provides a robust sparsity method for suppressing anomalous noise in seismic data, comprising the following steps:

[0011] Step 01: Read the original seismic data containing anomalous noise, and model the seismic signal as a linear combination of effective signal, random noise, and anomalous noise; anomalous noise is a noise signal whose amplitude exceeds a preset amplitude threshold.

[0012] Step 02: Use the SPGL1 method to obtain the sparse representation estimate of the effective signal in the seismic data. Based on the sparse representation estimate, the fixed sparse transform dictionary, and the original seismic data, obtain the mixed estimate of the effective signal and the anomalous noise.

[0013] Step 03: Update the location and magnitude of sampling points containing abnormal noise;

[0014] Step 04: Repeat steps 02-03 until the abnormal noise in the original seismic data is suppressed.

[0015] Preferably, in step 01, the two-dimensional seismic data A in the original seismic data is regarded as a linear mixture of three independent signal components: effective signal B, random noise n, and anomalous noise e, as specifically expressed by the following formula:

[0016] A = B + n + e;

[0017] In the formula,

[0018] B represents the valid signal in the original seismic data;

[0019] n represents random noise in the original seismic data;

[0020] e represents abnormal noise in the original seismic data, where the signal amplitude exceeds a preset amplitude threshold.

[0021] Preferably, step 01 includes the following steps:

[0022] Step 010: Select the component distribution, composition parameters and iteration number of the Laplace scale mixture model according to the composition and complexity of the noise components in the seismic data, and process the random noise and anomalous noise in the noise components separately;

[0023] Step 011: Select a fixed sparse transform dictionary based on the degree of noise suppression of effective signals in the seismic data and the waveform characteristics of the effective signals;

[0024] Step 012: Model the anomalous noise as a Laplace-scale mixed distribution.

[0025] Preferably, the component distribution in the Laplace-scale mixed distribution is determined based on the complexity of the anomalous noise components.

[0026] Preferably, the anomalous noise e is modeled using a Laplace scale mixture model, and the number of iterations is determined based on the complexity of the anomalous noise e. The complexity is mainly determined by the acquired seismic data, specifically involving the degree to which the anomalous noise disrupts the effective signal and the magnitude of random noise; the greater the complexity, the greater the number of iterations.

[0027] Preferably, the sparse dictionary is fixed as a discrete cosine transform.

[0028] Preferably, the discrete cosine transform is as follows:

[0029]

[0030] in,

[0031] M is the number of time-domain sampling points;

[0032] N is the number of seismic data traces;

[0033] f(x,y) is a discrete cosine function;

[0034] F(u,v) is the function after the positive transform of the discrete cosine function;

[0035] u and v are coordinates in a two-dimensional uv coordinate system; u = 0, 1, 2, L, M-1, v = 0, 1, 2, L, N-1;

[0036] x and y are coordinates in a two-dimensional xy coordinate system, x = 0, 1, 2, L, M-1, y = 0, 1, 2, L, N-1;

[0037] α(u,v) is the magnitude of the discrete cosine function positive transform at coordinates (u,v), and we have:

[0038] α(u,v)=α(u)α(v)

[0039]

[0040]

[0041] The inverse discrete cosine transform is as follows:

[0042]

[0043] Preferably, the anomalous noise e is modeled as a Laplace-scale mixture model, specifically as follows:

[0044]

[0045] in,

[0046] i represents the i-th sampling point in each channel;

[0047] e i The value of the abnormal noise at the i-th sampling point;

[0048] μ i The parameters are those of a Laplace distribution with zero mean and a scale of 1.

[0049] k i The inverse scaling parameter of the Laplace distribution, which follows a gamma distribution with parameters α and β, is specifically determined by the following formula:

[0050]

[0051] in,

[0052] The α and β distributions are the shape and inverse scaling parameters of the gamma distribution;

[0053] P(k i ) represents k i The probability density distribution function;

[0054]

[0055] Preferably, based on the latent variable v introduced by the EM algorithm i The abnormal noise e is solved using the following formula:

[0056]

[0057] in,

[0058] P(k i |e i ) represents the conditional probability of the Laplace scale mixture model with respect to anomalous noise.

[0059] Preferably, the standard deviation of random noise σ n Solve using the following formula:

[0060]

[0061] Where N is the number of seismic data traces.

[0062] Preferably, steps 02-04 specifically involve iteratively solving for the three signal components of the two-dimensional seismic data A: the effective signal B, random noise n, and anomalous noise e, including the following steps:

[0063] Initialization: Initialize the inverse scaling parameter k of the Laplace distribution and its probability density function P(k) in the Laplace scale mixture model, the total number of iterations T, and the fixed sparse transform dictionary D of discrete cosines;

[0064] Iteration steps: Increment by 1 in each iteration t and update the calculation:

[0065]

[0066]

[0067]

[0068] in,

[0069] k is the inverse scaling parameter of the Laplace distribution, which is derived from the inverse scaling parameter k of the Laplace distribution at each sampling point of each seismic data trace. i constitute;

[0070] θ represents the sparse representation coefficients of the effective signal;

[0071] This is the estimate of the coefficients of the sparse representation of the effective signal in the t-th iteration;

[0072] This is the estimate of the anomalous noise in the t-th iteration;

[0073] Let be the standard deviation of the random noise estimated in the t-th iteration;

[0074] η is a balance parameter related to the sparsity of the sparsity coefficients;

[0075] Termination condition: when The iteration terminates when the value is less than the preset value, or when the number of iterations reaches t=T.

[0076] Output: Sparse representation coefficients of the effective signal And the effective signal B = Dθ.

[0077] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0078] (1) This invention models the anomalous noise components contained in two-dimensional seismic data using a Laplace scale mixed distribution, distinguishing them from random noise that follows the Gaussian assumption. It adaptively suppresses high-energy anomalous noise through iterative updates, achieving efficient suppression of anomalous noise while protecting the effective signal.

[0079] (2) The present invention models two-dimensional seismic data as a superposition of effective signal components, random noise components and anomalous noise components. The anomalous noise and random noise components are modeled independently, which helps to separate the two different types of noise and greatly reduces the residual anomalous noise after separation.

[0080] (3) This invention selects the Laplace scale mixture model instead of the Gaussian scale mixture model as the prior information of the anomalous noise, and infers that the anomalous noise in the seismic data is a sparser distribution. Its advantage is that the iterative solution problem obtained by the Laplace scale mixture model using the EM algorithm is very similar to that of BPDN. It can utilize the efficient algorithm developed for BPDN to bring huge computational advantages that the Gaussian scale mixture model cannot provide. Attached Figure Description

[0081] Figure 1 A graph of clean, simulated seismic data containing only valid signals;

[0082] Figure 2 A composite data graph of the effective signal, Gaussian random noise, and high-energy anomalous noise;

[0083] Figure 3 Obtained as an embodiment of the present invention Figure 2 Schematic diagram of effective signal in the middle;

[0084] Figure 4 Obtained as an embodiment of the present invention Figure 2 Schematic diagram of noise components;

[0085] Figure 5 A schematic diagram of actual two-dimensional pre-stack seismic data containing high-energy surge anomaly noise;

[0086] Figure 6 for Figure 5 A schematic diagram of amplitude spectrum analysis of anomalous noise in channels 50-60;

[0087] Figure 7 Obtained as an embodiment of the present invention Figure 5 Schematic diagram of effective signal in the middle;

[0088] Figure 8 Obtained as an embodiment of the present invention Figure 5 Schematic diagram of noise components;

[0089] Figure 9 for Figure 5 The actual seismic data shown are consistent with Figure 7 A schematic diagram of the amplitude spectrum of the effective signal is shown.

[0090] Figure 10This is a flowchart of a robust sparsity method for suppressing seismic data anomaly noise according to an embodiment of the present invention. Detailed Implementation

[0091] The following is in conjunction with the appendix Figure 1-10 The specific embodiments of the present invention will be described in detail below.

[0092] This invention provides a robust sparsity method for suppressing anomalous noise in seismic data, comprising the following steps:

[0093] Step 01: Read the raw seismic data containing anomalous noise and model the seismic signal as a linear combination of effective signal, random noise, and anomalous noise;

[0094] Step 02: Use the SPGL1 method to obtain the sparse representation estimate of the effective signal in the seismic data. Based on the sparse representation estimate, the fixed sparse transform dictionary, and the original seismic data, obtain the mixed estimate of the effective signal and the anomalous noise.

[0095] Step 03: Update the location and magnitude of sampling points containing abnormal noise;

[0096] Step 04: Repeat steps 02-03 until the abnormal noise in the original seismic data is suppressed.

[0097] According to a specific embodiment of the present invention, in step 01, the two-dimensional seismic data A in the original seismic data is regarded as a linear mixture of three independent signal components: effective signal B, random noise n, and anomalous noise e, as specifically expressed by the following formula:

[0098] A = B + n + e;

[0099] In the formula,

[0100] B represents the valid signal in the original seismic data;

[0101] n represents random noise in the original seismic data;

[0102] e represents abnormal noise in the original seismic data, where the signal amplitude exceeds a preset amplitude threshold.

[0103] According to a specific embodiment of the present invention, step 01 includes the following steps:

[0104] Step 010: Select the component distribution, composition parameters and iteration number of the Laplace scale mixture model according to the composition and complexity of the noise components in the seismic data, and process the random noise and anomalous noise in the noise components separately;

[0105] Step 011: Select a fixed sparse transform dictionary based on the degree of noise suppression of effective signals in the seismic data and the waveform characteristics of the effective signals;

[0106] Step 012: Model the anomalous noise as a Laplace-scale mixed distribution.

[0107] According to one specific embodiment of the present invention, the component distribution in the Laplace-scale mixed distribution is determined based on the complexity of the anomalous noise components.

[0108] According to a specific embodiment of the present invention, the anomalous noise e is modeled using a Laplace scale mixture model, and the number of iterations is determined based on the complexity of the anomalous noise e. The complexity is mainly determined by the acquired seismic data, specifically involving the degree of damage the anomalous noise causes to the effective signal and the magnitude of random noise; the greater the complexity, the greater the number of iterations.

[0109] According to a specific embodiment of the present invention, the sparse dictionary is fixed as a discrete cosine transform.

[0110] According to a specific embodiment of the present invention, the discrete cosine transform is as follows:

[0111]

[0112] in,

[0113] M is the number of time-domain sampling points;

[0114] N is the number of seismic data traces;

[0115] f(x,y) is a discrete cosine function;

[0116] F(u,v) is the function after the positive transform of the discrete cosine function;

[0117] u and v are coordinates in a two-dimensional uv coordinate system; u = 0, 1, 2, L, M-1, v = 0, 1, 2, L, N-1;

[0118] x and y are coordinates in a two-dimensional xy coordinate system, x = 0, 1, 2, L, M-1, y = 0, 1, 2, L, N-1;

[0119] α(u,v) is the magnitude of the discrete cosine function positive transform at coordinates (u,v), and we have:

[0120] α(u,v)=α(u)α(v)

[0121]

[0122]

[0123] The inverse discrete cosine transform is as follows:

[0124]

[0125] According to a specific embodiment of the present invention, the anomalous noise e is modeled as a Laplace-scale mixture model as follows:

[0126]

[0127] in,

[0128] i represents the i-th sampling point in each channel;

[0129] e i The value of the abnormal noise at the i-th sampling point;

[0130] μ i The parameters are those of a Laplace distribution with zero mean and a scale of 1.

[0131] k i The inverse scaling parameter of the Laplace distribution, which follows a gamma distribution with parameters α and β, is specifically determined by the following formula:

[0132]

[0133] in,

[0134] The α and β distributions are the shape and inverse scaling parameters of the gamma distribution;

[0135] P(k i ) represents k i The probability density distribution function;

[0136]

[0137] According to a specific embodiment of the present invention, based on the latent variable v introduced by the EM algorithm i The abnormal noise e is solved using the following formula:

[0138]

[0139] in,

[0140] P(k i |e i ) represents the conditional probability of the Laplace scale mixture model with respect to anomalous noise.

[0141] According to a specific embodiment of the present invention, the standard deviation of random noise σ n Solve using the following formula:

[0142]

[0143] Where N is the number of seismic data traces.

[0144] According to a specific embodiment of the present invention, steps 02-04 specifically involve iteratively solving for the three signal components of the two-dimensional seismic data A: the effective signal B, random noise n, and anomalous noise e, including the following steps:

[0145] Initialization: Initialize the inverse scaling parameter k of the Laplace distribution and its probability density function P(k) in the Laplace scale mixture model, the total number of iterations T, and the fixed sparse transform dictionary D of discrete cosines;

[0146] Iteration steps: Increment by 1 in each iteration t and update the calculation:

[0147]

[0148]

[0149]

[0150] in,

[0151] k is the inverse scaling parameter of the Laplace distribution, which is derived from the inverse scaling parameter k of the Laplace distribution at each sampling point of each seismic data trace. i constitute;

[0152] θ represents the sparse representation coefficients of the effective signal;

[0153] This is the estimate of the coefficients of the sparse representation of the effective signal in the t-th iteration;

[0154] This is the estimate of the anomalous noise in the t-th iteration;

[0155] Let be the standard deviation of the random noise estimated in the t-th iteration;

[0156] η is a balance parameter related to the sparsity of the sparsity coefficients;

[0157] Termination condition: when The iteration terminates when the value is less than the preset value, or when the number of iterations reaches t=T.

[0158] Output: Sparse representation coefficients of the effective signal And the effective signal B = Dθ.

[0159] Example 1

[0160] According to a specific embodiment of the present invention, the robust sparsity method for suppressing seismic data anomaly noise of the present invention will be described in detail below.

[0161] This invention provides a robust sparsity method for suppressing anomalous noise in seismic data, comprising the following steps:

[0162] Step 01: Read the raw seismic data containing anomalous noise and model the seismic signal as a linear combination of effective signal, random noise, and anomalous noise;

[0163] Step 02: Use the SPGL1 method to obtain the sparse representation estimate of the effective signal in the seismic data. Based on the sparse representation estimate, the fixed sparse transform dictionary, and the original seismic data, obtain the mixed estimate of the effective signal and the anomalous noise.

[0164] Step 03: Update the location and magnitude of sampling points containing abnormal noise;

[0165] Step 04: Repeat steps 02-03 until the abnormal noise in the original seismic data is suppressed.

[0166] Example 2

[0167] According to a specific embodiment of the present invention, the robust sparsity method for suppressing seismic data anomaly noise of the present invention will be described in detail below.

[0168] This invention provides a robust sparsity method for suppressing anomalous noise in seismic data, comprising the following steps:

[0169] Step 01: Read the raw seismic data containing anomalous noise, and model the seismic signal as a linear combination of effective signal, random noise, and anomalous noise; specifically, as shown in the following formula:

[0170] A = B + n + e;

[0171] In the formula,

[0172] B represents the valid signal in the original seismic data;

[0173] n represents random noise in the original seismic data;

[0174] e represents abnormal noise in the original seismic data, where the signal amplitude exceeds a preset amplitude threshold.

[0175] Step 01 includes the following steps:

[0176] Step 010: Select the component distribution, composition parameters and iteration number of the Laplace scale mixture model according to the composition and complexity of the noise components in the seismic data, and process the random noise and anomalous noise in the noise components separately;

[0177] Step 011: Select a fixed sparse transform dictionary based on the degree of noise suppression of effective signals in the seismic data and the waveform characteristics of the effective signals;

[0178] Step 012: Model the anomalous noise as a Laplace-scale mixed distribution.

[0179] Step 02: Use the SPGL1 method to obtain the sparse representation estimate of the effective signal in the seismic data. Based on the sparse representation estimate, the fixed sparse transform dictionary, and the original seismic data, obtain the mixed estimate of the effective signal and the anomalous noise.

[0180] Step 03: Update the location and magnitude of sampling points containing abnormal noise;

[0181] Step 04: Repeat steps 02-03 until the abnormal noise in the original seismic data is suppressed.

[0182] Example 3

[0183] According to a specific embodiment of the present invention, the robust sparsity method for suppressing seismic data anomaly noise of the present invention will be described in detail below.

[0184] This invention provides a robust sparsity method for suppressing anomalous noise in seismic data, comprising the following steps:

[0185] Step 01: Read the raw seismic data containing anomalous noise, and model the seismic signal as a linear combination of effective signal, random noise, and anomalous noise; specifically, as shown in the following formula:

[0186] A = B + n + e;

[0187] In the formula,

[0188] B represents the valid signal in the original seismic data;

[0189] n represents random noise in the original seismic data;

[0190] e represents abnormal noise in the original seismic data, where the signal amplitude exceeds a preset amplitude threshold.

[0191] Step 01 includes the following steps:

[0192] Step 010: Select the component distribution, composition parameters and iteration number of the Laplace scale mixture model according to the composition and complexity of the noise components in the seismic data, and process the random noise and anomalous noise in the noise components separately;

[0193] Step 011: Select a fixed sparse transform dictionary based on the degree of noise suppression of effective signals in the seismic data and the waveform characteristics of the effective signals;

[0194] Step 012: Model the anomalous noise as a Laplace-scale mixture distribution; determine the component distribution in the Laplace-scale mixture distribution based on the complexity of the anomalous noise components. Model the anomalous noise e using the Laplace-scale mixture model, and then determine the number of iterations based on the complexity of the anomalous noise e. The complexity is mainly determined by the acquired seismic data, specifically involving the degree of damage the anomalous noise causes to the effective signal and the magnitude of random noise; the greater the complexity, the greater the number of iterations.

[0195] The anomalous noise e is modeled as a Laplace-scale mixture model, specifically as follows:

[0196]

[0197] in,

[0198] i represents the i-th sampling point in each channel;

[0199] e i The value of the abnormal noise at the i-th sampling point;

[0200] μ i The parameters are those of a Laplace distribution with zero mean and a scale of 1.

[0201] k i The inverse scaling parameter of the Laplace distribution, which follows a gamma distribution with parameters α and β, is specifically determined by the following formula:

[0202]

[0203] in,

[0204] The α and β distributions are the shape and inverse scaling parameters of the gamma distribution;

[0205] P(k i ) represents k i The probability density distribution function;

[0206]

[0207] The fixed sparse dictionary is represented by the discrete cosine transform, and the positive discrete cosine transform is as follows:

[0208]

[0209] in,

[0210] M is the number of time-domain sampling points;

[0211] N is the number of seismic data traces;

[0212] f(x,y) is a discrete cosine function;

[0213] F(u,v) is the function after the positive transform of the discrete cosine function;

[0214] u and v are coordinates in a two-dimensional uv coordinate system; u = 0, 1, 2, L, M-1, v = 0, 1, 2, L, N-1;

[0215] x and y are coordinates in a two-dimensional xy coordinate system, x = 0, 1, 2, L, M-1, y = 0, 1, 2, L, N-1;

[0216] α(u,v) is the magnitude of the discrete cosine function positive transform at coordinates (u,v), and we have:

[0217] α(u,v)=α(u)α(v)

[0218]

[0219]

[0220] The inverse discrete cosine transform is as follows:

[0221]

[0222] Step 02: Use the SPGL1 method to obtain the sparse representation estimate of the effective signal in the seismic data. Based on the sparse representation estimate, the fixed sparse transform dictionary, and the original seismic data, obtain the mixed estimate of the effective signal and the anomalous noise.

[0223] Based on the latent variable v introduced by the EM algorithm i The abnormal noise e is solved using the following formula:

[0224]

[0225] in,

[0226] P(k i |e i ) represents the conditional probability of the Laplace scale mixture model with respect to anomalous noise.

[0227] random noise standard deviation σ n Solve using the following formula:

[0228]

[0229] Where N is the number of seismic data traces.

[0230] Step 03: Update the location and magnitude of sampling points containing abnormal noise;

[0231] Step 04: Repeat steps 02-03 until the abnormal noise in the original seismic data is suppressed.

[0232] Example 4

[0233] According to a specific embodiment of the present invention, the robust sparsity method for suppressing seismic data anomaly noise of the present invention will be described in detail below.

[0234] This invention provides a robust sparsity method for suppressing anomalous noise in seismic data, comprising the following steps:

[0235] Step 01: Read the raw seismic data containing anomalous noise, and model the seismic signal as a linear combination of effective signal, random noise, and anomalous noise; specifically, as shown in the following formula:

[0236] A = B + n + e;

[0237] In the formula,

[0238] B represents the valid signal in the original seismic data;

[0239] n represents random noise in the original seismic data;

[0240] e represents abnormal noise in the original seismic data, where the signal amplitude exceeds a preset amplitude threshold.

[0241] Step 01 includes the following steps:

[0242] Step 010: Select the component distribution, composition parameters and iteration number of the Laplace scale mixture model according to the composition and complexity of the noise components in the seismic data, and process the random noise and anomalous noise in the noise components separately;

[0243] Step 011: Select a fixed sparse transform dictionary based on the degree of noise suppression of effective signals in the seismic data and the waveform characteristics of the effective signals;

[0244] Step 012: Model the anomalous noise as a Laplace-scale mixture distribution; determine the component distribution in the Laplace-scale mixture distribution based on the complexity of the anomalous noise components. Model the anomalous noise e using the Laplace-scale mixture model, and then determine the number of iterations based on the complexity of the anomalous noise e. The complexity is mainly determined by the acquired seismic data, specifically involving the degree of damage the anomalous noise causes to the effective signal and the magnitude of random noise; the greater the complexity, the greater the number of iterations.

[0245] The anomalous noise e is modeled as a Laplace-scale mixture model, specifically as follows:

[0246]

[0247] in,

[0248] i represents the i-th sampling point in each channel;

[0249] e iThe value of the abnormal noise at the i-th sampling point;

[0250] μ i The parameters are those of a Laplace distribution with zero mean and a scale of 1.

[0251] k i The inverse scaling parameter of the Laplace distribution, which follows a gamma distribution with parameters α and β, is specifically determined by the following formula:

[0252]

[0253] in,

[0254] The α and β distributions are the shape and inverse scaling parameters of the gamma distribution;

[0255] P(k i ) represents k i The probability density distribution function;

[0256]

[0257] The fixed sparse dictionary is represented by the discrete cosine transform, and the positive discrete cosine transform is as follows:

[0258]

[0259] in,

[0260] M is the number of time-domain sampling points;

[0261] N is the number of seismic data traces;

[0262] f(x,y) is a discrete cosine function;

[0263] F(u,v) is the function after the positive transform of the discrete cosine function;

[0264] u and v are coordinates in a two-dimensional uv coordinate system; u = 0, 1, 2, L, M-1, v = 0, 1, 2, L, N-1;

[0265] x and y are coordinates in a two-dimensional xy coordinate system, x = 0, 1, 2, L, M-1, y = 0, 1, 2, L, N-1;

[0266] α(u,v) is the magnitude of the discrete cosine function positive transform at coordinates (u,v), and we have:

[0267] α(u,v)=α(u)α(v)

[0268]

[0269]

[0270] The inverse discrete cosine transform is as follows:

[0271]

[0272] Step 02: Use the SPGL1 method to obtain the sparse representation estimate of the effective signal in the seismic data. Based on the sparse representation estimate, the fixed sparse transform dictionary, and the original seismic data, obtain the mixed estimate of the effective signal and the anomalous noise.

[0273] Based on the latent variable v introduced by the EM algorithm i The abnormal noise e is solved using the following formula:

[0274]

[0275] in,

[0276] P(k i |e i ) represents the conditional probability of the Laplace scale mixture model with respect to anomalous noise.

[0277] random noise standard deviation σ n Solve using the following formula:

[0278]

[0279] Where N is the number of seismic data traces.

[0280] Step 03: Update the location and magnitude of sampling points containing abnormal noise;

[0281] Step 04: Repeat steps 02-03 until the abnormal noise in the original seismic data is suppressed.

[0282] Steps 02-04 specifically involve iteratively solving for the three signal components of the two-dimensional seismic data A: the effective signal B, random noise n, and anomalous noise e. This includes the following steps:

[0283] Initialization: Initialize the inverse scaling parameter k of the Laplace distribution and its probability density function P(k) in the Laplace scale mixture model, the total number of iterations T, and the fixed sparse transform dictionary D of discrete cosines;

[0284] Iteration steps: Increment by 1 in each iteration t and update the calculation:

[0285]

[0286]

[0287]

[0288] in,

[0289] k is the inverse scaling parameter of the Laplace distribution, which is derived from the inverse scaling parameter k of the Laplace distribution at each sampling point of each seismic data trace. i constitute;

[0290] θ represents the sparse representation coefficients of the effective signal;

[0291] This is the estimate of the coefficients of the sparse representation of the effective signal in the t-th iteration;

[0292] This is the estimate of the anomalous noise in the t-th iteration;

[0293] Let be the standard deviation of the random noise estimated in the t-th iteration;

[0294] η is a balance parameter related to the sparsity of the sparsity coefficients;

[0295] Termination condition: when The iteration terminates when the value is less than the preset value, or when the number of iterations reaches t=T.

[0296] Output: Sparse representation coefficients of the effective signal And the effective signal B = Dθ.

[0297] like Figure 1 and Figure 2 The image shows simulated seismic data containing three phase axes, totaling 64 channels, with 512 sampling points and a sampling interval of 2 ms. As can be seen, Figure 2 The presence of Gaussian random noise and high-energy anomaly noise significantly reduces the signal-to-noise ratio of the seismic data, disrupts the phase axis of the effective signal, and affects the usability of the seismic data in subsequent processing.

[0298] Processing with a Laplace-scale hybrid robust sparse representation method to suppress seismic data anomaly noise Figure 2 The effective signal and noise component results obtained from the seismic data are shown below. Figure 3 and Figure 4 As shown. Figure 3 As shown, the obtained effective signal contains almost no residual abnormal noise; Figure 4 As shown, almost no effective signal is visible in the obtained noise components. Furthermore, through comparison... Figure 1 Real and valid signals and Figure 3 It can be seen that the present invention can effectively suppress abnormal noise while protecting the valid signal.

[0299] like Figure 5The image shows actual two-dimensional pre-stack seismic data containing high-energy surge noise. It can be seen that this actual data is severely affected by surge noise. Surge noise has high-energy non-Gaussian characteristics, which largely obscures the in-phase axes of the effective signals in the seismic data, significantly increasing the difficulty of subsequent processing.

[0300] Furthermore, such as Figure 6 The image shows the pair. Figure 5 Normalized amplitude spectrum analysis was performed on the anomalous noise portion of channels 50-60. It can be seen that the energy of the surge noise in the amplitude spectrum is mainly concentrated in the low-frequency part. The Laplace-scale hybrid robust sparse representation method for suppressing anomalous noise in seismic data was used for processing. Figure 5 The effective signal and noise component results obtained from the actual seismic data are shown below. Figure 7 and Figure 8 As shown. From Figure 7 It can be observed that abnormal noise in the effective signal is well suppressed; from Figure 8 It can be observed that the suppressed noise components contain almost no effective signal. Based on the above analysis, this demonstrates that the method proposed in this invention can effectively suppress high-energy non-Gaussian surge noise in actual seismic data.

[0301] Furthermore, Figure 9 As shown Figure 5 The actual seismic data shown are consistent with Figure 7 The amplitude spectrum of the effective signal is shown. From Figure 9 As can be seen, the effective signal amplitude spectrum is strongly suppressed in the low-frequency part compared with the amplitude spectrum of the original noisy actual seismic data, indicating that the method of the present invention has a strong suppression effect on surge noise and does not lose the effective signal frequency components, indicating that the method can better protect the effective signal.

[0302] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention are included within the scope of protection of the present invention.

Claims

1. A robust sparsity method for suppressing anomalous noise in seismic data, characterized in that, Includes the following steps: Step 01: Read the raw seismic data containing anomalous noise and model the seismic signal as a linear combination of effective signal, random noise, and anomalous noise; In step 01, the two-dimensional seismic data A in the original seismic data is regarded as a linear mixture of three independent signal components: effective signal B, random noise n, and anomaly noise e, as shown in the following formula: A = B + n + e; In the formula, B represents the valid signal in the original seismic data; n represents random noise in the original seismic data; e represents abnormal noise in the original seismic data, where the signal amplitude exceeds a preset amplitude threshold. Step 01 includes the following steps: Step 010: Select the component distribution, composition parameters and iteration number of the Laplace scale mixture model according to the composition and complexity of the noise components in the seismic data, and process the random noise and anomalous noise in the noise components separately; Step 011: Select a fixed sparse transform dictionary based on the degree of noise suppression of effective signals in the seismic data and the waveform characteristics of the effective signals; Step 012: Model the anomalous noise as a Laplace-scale mixed distribution; Step 02: Use the SPGL1 method to obtain the sparse representation estimate of the effective signal in the seismic data. Based on the sparse representation estimate, the fixed sparse transform dictionary, and the original seismic data, obtain the mixed estimate of the effective signal and the anomalous noise. Step 03: Update the location and magnitude of sampling points containing abnormal noise; Step 04: Repeat steps 02-03 until the abnormal noise in the original seismic data is suppressed.

2. The robust sparsity method for suppressing seismic data anomaly noise according to claim 1, characterized in that, The component distribution in the Laplace-scale mixture distribution is determined based on the complexity of the anomalous noise components.

3. The robust sparsity method for suppressing seismic data anomaly noise according to claim 2, characterized in that, Using the Laplace scale mixture model to analyze anomalous noise Modeling is performed, and then based on abnormal noise The complexity determines the number of iterations.

4. The robust sparsity method for suppressing seismic data anomaly noise according to claim 1, characterized in that, The fixed sparse dictionary is the discrete cosine transform.

5. The robust sparsity method for suppressing seismic data anomaly noise according to claim 4, characterized in that, The discrete cosine transform is as follows: in, M is the number of time-domain sampling points; N is the number of seismic data traces; f ( x,y () is the discrete cosine function; F ( u,v () is the function after the positive transform of the discrete cosine function; , These are coordinates in a two-dimensional UV coordinate system. , ; and The coordinates are in a two-dimensional xy coordinate system. , ; For the positive transform of the discrete cosine function in coordinate system The amplitude at that point, and we have: The inverse discrete cosine transform is as follows: 。 6. The robust sparsity method for suppressing seismic data anomaly noise according to claim 5, characterized in that, The anomalous noise e is modeled as a Laplace-scale mixture model, specifically as follows: ； in, i For each of the first i One sampling point; e i The abnormal noise is located at the th i The value of each sampling point; The parameters are those of a Laplace distribution with zero mean and a scale of 1. To obey parameters and The inverse scaling parameter of the Laplace distribution of the gamma distribution is determined by the following formula: ； in, and The distribution exhibits a gamma distribution shape and inverse scaling parameters; P ( k i )express k i The probability density distribution function; 。 7. The robust sparsity method for suppressing seismic data anomaly noise according to claim 6, characterized in that, Latent variables introduced by the EM algorithm The abnormal noise e is solved using the following formula: ； in, Let be the conditional probability of the Laplace-scale mixture model with respect to anomalous noise.

8. The robust sparsity method for suppressing seismic data anomaly noise according to claim 7, characterized in that, random noise standard deviation Solve using the following formula: in, This refers to the number of channels in the earthquake data.

9. The robust sparsity method for suppressing seismic data anomaly noise according to claim 8, characterized in that, Steps 02-04 specifically involve iteratively solving for the three signal components of the two-dimensional seismic data A: the effective signal B, random noise n, and anomalous noise e. This includes the following steps: Initialization: Initialize the inverse scaling parameter k of the Laplace distribution and its probability density function in the Laplace-scaled mixture model. P ( k Total number of iterations T Discrete Cosine Fixed Sparse Transform Dictionary D ; Iteration steps: Each iteration Increase by 1 and update the calculation: ； ； ； in, k is the inverse scaling parameter of the Laplace distribution, which is derived from the inverse scaling parameter of the Laplace distribution at each sampling point of each seismic data trace. constitute; For the sparse representation coefficients of the effective signal; For the effective signal sparse representation coefficients, the first The estimation of the next iteration; For abnormal noise The estimation of the next iteration; For random noise The standard deviation of the estimate in the next iteration; It is a balance parameter related to the sparsity of the sparsity coefficient; Termination condition: when Less than the preset value, or the number of iterations reaches When the iteration terminates; Output: Sparse representation coefficients of the effective signal and valid signals .

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