A Method and System for Seismic Data Unmixing Using Self-Supervised Bayesian Deep Learning Networks

Abstract

This invention discloses a method and system for unmixing seismic data using a self-supervised Bayesian deep learning network. Based on the Bayesian variational inference principle, and leveraging the inherent learning capability of deep network structures, a self-supervised Bayesian neural network is proposed. Using a simple decoder network with a random vector as input, Bayesian variational inference is employed, and the weights of each node in the network are assumed to follow an independent Gaussian distribution to increase uncertainty during training. This allows for fitting of aliased seismic data to learn the distribution of effective signals, ultimately achieving high-precision separation of aliased seismic data. This invention effectively solves the separation problem during aliased seismic data acquisition and can be trained using a stochastic gradient descent algorithm to achieve adaptive parameter adjustment and optimization, improving the effectiveness and robustness in unmixing seismic data with varying noise levels.

Description

Technical Field

[0001] This invention belongs to the field of signal processing technology, specifically relating to a method and system for unmixing seismic data using a self-supervised Bayesian deep learning network. Background Technology

[0002] Overlapping seismic data acquisition can excite more seismic sources within the same acquisition time, resulting in higher acquisition density and spatial sampling rate, and increasing the number of times the subsurface medium is covered, thus obtaining high-quality, comprehensive acquisition results. However, the overlapping signals from multiple seismic sources pose a significant challenge to the data processing and interpretation of conventional seismic data. To facilitate post-acquisition analysis, it is necessary to separate the signals excited by single seismic sources from the multi-source overlapping acquisition data.

[0003] Traditional physics-driven demixing methods include filtering-based and inversion-based methods. Filtering methods simply treat the separation problem as a noise attenuation problem, while inversion methods solve the separation problem of aliased data as a linear inverse problem, aiming to estimate the required unknown unaliased data. However, both methods often rely on manual parameter tuning, such as filter length and the threshold for sparsity-enhancing transformation. The quality of parameter selection often affects the effective signal separation results from seismic data.

[0004] In recent years, deep learning has been introduced into the field of seismic data unmixing. When dealing with large datasets or complex data features, complex classification or regression problems often pose significant challenges to traditional methods such as statistical learning, especially in high-dimensional data scenarios. As one of the most popular deep learning algorithms, neural networks can automatically learn the features and relationships hidden in large datasets, thereby matching seismic data in a non-linear manner. However, in supervised learning, the features of the training dataset have a significant impact on model performance, such as the number of training samples, the correlation between the dataset and the target data, and the feature diversity of the training samples. When the features of the training dataset deviate significantly from the target data, the generalization ability of strongly supervised learning is often poor. Furthermore, in non-iterative noise suppression processes, over-reliance on the local coherence of the data can lead to low signal-to-noise ratio results. Especially in fields such as seismic exploration, constructing large-scale, high-quality, relevant training datasets is often very expensive; therefore, it is necessary to develop deep learning methods to solve the seismic data unmixing problem, providing advanced performance without requiring additional training data.

[0005] Disadvantages of existing technology:

[0006] 1. In most current supervised learning, the features of the training dataset have a significant impact on model performance. When the features of the training dataset deviate significantly from those of the target data, the generalization ability of strongly supervised learning is often poor.

[0007] 2. In non-iterative noise suppression processes, over-reliance on the local coherence of data may result in low signal-to-noise ratios. Summary of the Invention

[0008] The technical problem to be solved by the present invention is to provide a method and system for unmixing seismic data using a self-supervised Bayesian deep learning network, which addresses the shortcomings of the prior art and solves the technical problem of the difficulty in constructing samples for supervised deep learning.

[0009] The present invention adopts the following technical solution:

[0010] A seismic data unmixing method using self-supervised Bayesian deep learning networks includes the following steps:

[0011] S1. A random time jitter strategy is used to construct the aliasing matrix Γ. The aliased seismic data b is obtained by multiplying it with the effective seismic data d to be separated in the common detection domain, and a random noise factor n is introduced.

[0012] S2. Based on the physical meaning of the aliasing matrix Γ, the process of solving for the effective seismic data d to be separated is regarded as solving an underdetermined inversion optimization problem.

[0013] S3. Based on step S2, adopt the classic statistical reasoning framework, provide prior information about parameter θ, assume that parameter θ has a prior probability distribution p(θ), and find the maximum likelihood estimate of the parameter to be solved;

[0014] S4. Based on step S3, the maximum a posteriori estimate is the maximum likelihood estimate after introducing the prior of θ, by introducing uncertainty into the network model parameters; assume that the network model parameters p(θ) follow a Gaussian distribution to maximize this uncertainty, and under the Gaussian distribution, the posterior distribution and conjugate prior distribution of the weight parameters follow a Gaussian distribution.

[0015] S5. Based on step S4, the proposed Bayesian network-based method learns the approximation of the minimum error estimate. Based on the Gaussian hypothesis, the L2 norm is selected to characterize the error between the effective seismic data d and the maximum a posteriori estimate u. The joint distribution q(θ|μ,σ) of the independent normal distribution is used to approximate p(θ|b).

[0016] S6. Based on variational inference, the joint distribution of q(θ|μ,σ) obtained in step S5 is used to approximate p(θ|b) in the minimum error estimate, and the network prediction output is minimized. The distance between the two parameters, which is estimated by minimum error, is used to train an unsupervised Bayesian neural network. The prior distribution P(θ) of the model parameters is assumed to have zero mean and a standard deviation of . The independent and identically distributed normal distribution approximates it;

[0017] S7. Based on the results obtained in step S6, perform unsupervised Bayesian neural network training. According to the generative model concept, input the aliasing matrix Γ and the aliased common detection point gather b, and use a randomly generated matrix vector to achieve an approximate estimation of the effective signal, obtaining the estimated distribution parameter μ. * and σ * Then, we obtain an approximate q(θ|μ) of the posterior probability distribution p(θ|b). * ,σ * Monte Carlo sampling is used to obtain an approximate estimate of the network; after obtaining the estimated distribution parameters, the mixed seismic gathers to be unmixed are used as the input of the network to obtain the unmixed seismic data.

[0018] Preferably, in step S1, with the detector fixed and without considering noise during the acquisition process, a random time jitter strategy is used to construct the aliasing matrix σ, and the aliased seismic data b is specifically:

[0019] b = Γd + n.

[0020] Preferably, in step S2, effective seismic data is introduced, with θ = {θ i} as weight parameters of the neural network Using a randomly generated vector ε0 as the input to the network, a neural network is used. The single-source excited earthquake data d are estimated using the input ε0.

[0021] Preferably, in step S3, the random noise is assumed to have a variance of . Given a Gaussian distribution of random noise, and assuming that the parameter θ has a prior probability distribution p(θ), the maximum a posteriori estimate expands to:

[0022]

[0023] in, To use neural networks The estimated value of d for single-source excited earthquake data is obtained by inputting ε0.

[0024] Preferably, in step S4, the analytical formula Japanese style The maximum a posteriori (MAP) estimate is the maximum likelihood estimate of the prior θ. A self-supervised learning method based on a Bayesian neural network framework is employed. In the Bayesian neural network, convolution is defined as a Bayesian convolutional layer, and the convolution kernel is treated as a random variable. Based on the prior distribution and observed data, the posterior distribution is solved using Bayesian inference, resulting in a probability distribution describing the uncertainty of the convolution result. The target data size is H×W×C, where H represents the number of rows or height of the data matrix, W represents the number of columns or width of the data matrix, and C represents the number of channels of the data matrix. For seismic data, C=1, and the input is (H / 3 2)×(W / 32)×128, the Bayesian neural network is a decoder containing 5 decoding blocks; the first 4 decoding blocks are connected sequentially to an upsampling layer with a scaling factor of 2 and two Bayesian convolutional layers, with LeakyReLU introduced between the convolutional layers to introduce non-linearity, and the two Bayesian convolutional layers each have 128 channels; the last decoding block contains an upsampling layer with a scaling factor of 2 and three Bayesian convolutional layers with output channels of 64, 32 and C respectively, with two LeakyReLU inserted between the Bayesian convolutional layers and a Sigmoid layer added at the end.

[0025] More preferably, when processing seismic data, the last Bayesian convolutional layer has 1 channel.

[0026] Preferably, in step S5, the effective seismic data d is:

[0027]

[0028] Where p(θ|b) is the posterior probability distribution function of θ.

[0029] Preferably, in step S6, in each iteration of training the unsupervised Bayesian neural network, the standard normal distribution is used. Randomly select samples from the network and then generate network weights θ. i for:

[0030] θ i =μ i +log(1+exp(ρ i ))·ε

[0031] Where, μ i ρ is the mean parameter of the Gaussian distribution. o Both ε and ε are randomly selected relevant parameters.

[0032] Preferably, in step S7, the approximate estimate d of the network is... * for:

[0033]

[0034] Where, {θ j} is based on the distribution q(θ|μ * ,σ * The instantiation of the random parameter θ variable of ) is described, where T is the number of instantiations. Secondly, embodiments of the present invention provide a seismic data unmixing system based on a self-supervised Bayesian deep learning network, comprising:

[0035] The matrix module uses a random time jitter strategy to construct the aliasing matrix Γ, which is multiplied with the effective seismic data d to be separated in the common detection domain to obtain the aliased seismic data b, and a random noise factor n is introduced.

[0036] The solution module, based on the physical meaning of the aliasing matrix Γ obtained from the matrix module, treats the process of solving for the effective seismic data d to be separated as solving an underdetermined inversion optimization problem;

[0037] The estimation module, based on the solution module, adopts the classic statistical inference framework. By providing prior information about the parameter θ, and assuming that the parameter θ has a prior probability distribution p(θ), it finds the maximum likelihood estimate of the parameter to be solved.

[0038] The module is introduced based on the estimation module. The maximum a posteriori estimation is the maximum likelihood estimation after introducing the prior of θ. Uncertainty is introduced into the network model parameters. It is assumed that the network model parameters p(θ) follow a Gaussian distribution to maximize this uncertainty. Under the Gaussian distribution, the posterior distribution and conjugate prior distribution of the weight parameters also follow a Gaussian distribution.

[0039] The characterization module, based on the introduction module, uses a Bayesian network-based method to learn an approximation of the minimum error estimate. We assume that the L2 norm is used to characterize the error between the effective seismic data d and the maximum a posteriori estimate u, and the joint distribution q(θ|μ,σ) of the independent normal distribution is used to approximate p(θ|b).

[0040] The training module, based on variational inference, uses the joint distribution of q(θ|μ,σ) obtained from the characterization module to approximate p(θ|b) in the minimum error estimate, thereby minimizing the network's predicted output. The distance between the two parameters, which is estimated by minimum error, is used to train an unsupervised Bayesian neural network. The prior distribution p(θ) of the model parameters is assumed to have zero mean and a standard deviation of . The independent and identically distributed normal distribution approximates it;

[0041] The output module, based on the results obtained from the training module, performs unsupervised Bayesian neural network training. Following the generative model approach, it takes the aliasing matrix Γ and the aliased common detection point gather b as input, and uses a randomly generated matrix vector to approximate the effective signal, obtaining the estimated distribution parameters μ. * and σ * Then, we obtain an approximate q(θ|μ) of the posterior probability distribution p(θ|b). * ,σ* Monte Carlo sampling is used to obtain an approximate estimate of the network; after obtaining the estimated distribution parameters, the mixed seismic gathers to be unmixed are used as the input of the network to obtain the unmixed seismic data.

[0042] Compared with the prior art, the present invention has at least the following beneficial effects:

[0043] This invention presents a seismic data demixing method using a self-supervised Bayesian deep learning network. Based on a simple decoder, it effectively estimates and reconstructs seismic data. First, unlike discriminative models that establish a mapping between input and output by extracting features, this method, based on generative principles, estimates the distribution of training data to reconstruct the signal. Second, it introduces Bayesian convolution, transforming the traditional assumption that network weights follow a specific distribution into a learning process of distribution parameters. This introduced uncertainty helps correct prediction biases caused by the network architecture, achieving a higher level of signal prediction. Furthermore, this method requires no additional data, making it highly practical. Compared to strongly supervised learning, this method can adaptively approximate the estimation of unaliased effective seismic signals without relying on additional data. Unlike traditional convolutional neural networks, the Bayesian neural network constructs a self-supervised Bayesian neural network, learning the probability distribution of weights rather than a fixed, structured weight, thus reducing problems such as network overfitting.

[0044] Furthermore, the seismic data aliasing process generates incoherent wavefields. When the coherence between the effective signal and interference is weak, the effective signal in the aliased seismic data can be separated using demixing methods. The key to seismic data aliasing acquisition lies in designing an aliasing scheme that allows for the acquisition of as much information as possible within the same timeframe, while simultaneously enabling effective separation of the aliased signals through algorithms. Therefore, the design of incoherence characteristics should be considered in the design of seismic aliasing acquisition strategies. Introducing randomness into the source excitation sequence during the aliasing acquisition process can enhance the incoherence characteristics. This invention introduces random time jitter during source excitation, generating incoherent wavefields that retain complete temporal and spatial distances, which is crucial for the separation of effective signals from aliased seismic data.

[0045] Furthermore, based on the physical meaning of the aliasing matrix Γ, the process of solving d is regarded as solving an underdetermined inversion optimization problem; by introducing the definition of effective seismic data, θ={θ i} as weight parameters of the neural network Using a randomly generated vector ε0 as the network input, it is possible to use a neural network. The effective seismic data D is estimated using the input ε0.

[0046] Furthermore, by adopting the classic statistical inference framework, solving the objective function means finding the maximum likelihood estimate of the parameters to be solved. Considering that the network weight parameter θ has obvious redundancy, the maximum likelihood estimate is prone to overfitting. By providing prior information for the parameter θ, assuming that the parameter θ has a prior probability distribution p(θ), the maximum a posteriori can reduce the adverse effects of network parameter redundancy on the inverse problem solution objective.

[0047] Furthermore, maximum a posteriori (MAP) estimation is the maximum likelihood estimation after introducing a prior value of θ. To address the problem that MAP estimation is insufficient to effectively resolve the ambiguity of solutions generated in the null space, thus failing to yield a uniquely determined solution, a self-supervised learning method based on a Bayesian neural network framework is proposed, referencing the Dropout concept. This method reduces overfitting by introducing uncertainty into the network model parameters. It is assumed that the network model parameters p(θ) follow a Gaussian distribution to maximize this uncertainty. Furthermore, under the Gaussian distribution assumption, the posterior and conjugate prior distributions of the weight parameters also follow a Gaussian distribution. The set of multiple repeated implementations of the Bayesian model will provide more accurate prediction results than a single deterministic model. (Analysis follows...) Japanese style The maximum a posteriori (MAP) estimate is a maximum likelihood estimate that introduces a prior to θ. While an early stopping strategy can add an implicit prior to the MAP estimate, this strategy is not applicable when solving for non-invertible matrices Γ. In this case, the MAP estimate of the latter form is insufficient to effectively resolve the ambiguity of the solution generated in the null space, failing to yield a uniquely determined solution. Furthermore, the proposed Bayesian network-based method learns an approximation of the minimum error estimate, using the L2 norm based on the Gaussian hypothesis to characterize the error between the effective signal d and the MAP estimate u. Due to the large number of weights and various nonlinear structures in neural network structures, the posterior probability distribution function p(θ|b) of θ is often difficult to calculate. Therefore, the joint distribution q(θ|μ,σ) of independent normal distributions is used to approximate p(θ|b). From the perspective of Bayesian approximation, the proposed Bayesian network-based method learns an approximation of the minimum error estimate. Addressing the difficulties of maximum a posteriori and maximum likelihood estimation, this invention proposes a self-supervised learning method based on a Bayesian neural network (BNN) framework and applies it to the problem of seismic data unmixing. Traditional neural networks, based on maximum likelihood parameter estimation and gradient descent algorithms, assume that the weight parameters have a fixed value in each training iteration. When the network model is complex and the number of network parameters is large, overfitting is likely to occur under limited training datasets. When an early stopping strategy is introduced to avoid overfitting, convolutional neural networks can predict a deterministic structured result. Dropout, on the other hand, introduces uncertainty into the network training process, randomly discarding some model units to reduce overfitting. Introducing uncertainty is an effective approach to avoid overfitting. Similar to Dropout, introducing uncertainty into the network model parameters can also reduce overfitting. Specifically, the network weight parameters of a BNN are not deterministic but rather random variables following a certain probability distribution. The network does not update deterministic weights but rather the parameters of the probability distribution of these random weights. The motivation for addressing underdetermined inversion problems stems from the uncertainty of the network model (i.e., the uncertainty of the weights), which helps correct generation bias caused by the network architecture. A set of multiple repeated implementations of a Bayesian model can provide more accurate predictions than a single deterministic model. Assuming the network model parameters follow a Gaussian distribution maximizes this uncertainty, and under this Gaussian distribution assumption, the posterior and conjugate prior distributions of the weight parameters also follow Gaussian distributions, which is computationally efficient. Furthermore, based on variational inference, the joint distribution of q(θ|μ,σ) from step S5 is used to approximate p(θ|b) in the minimum error estimation, by minimizing the network's predicted output. Training an unsupervised Bayesian neural network by estimating the distance between the two with minimum error is equivalent to training the proposed network by minimizing the KL divergence between them. However, minimizing the KL divergence is difficult to obtain for an arbitrary distribution. To further simplify the problem, assume that the prior distribution p(θ) of the model parameters has zero mean and a standard deviation of . The independent and identically distributed normal distribution is used as an approximation; the joint distribution of q(θ|μ,σ) defined above is used to approximate p(θ|b) in the minimum error estimation, and the proposed network is trained by minimizing the KL divergence between the two; for an arbitrary distribution, minimizing the KL divergence is difficult to obtain, so the problem needs to be simplified. Furthermore, suppose the prior distribution p(θ) can be obtained from a distribution with zero mean and a standard deviation of σ. The independent and identically distributed normal distribution approximates the data well. For the data fidelity term in the expression, one instance of parameter θ is drawn from the distribution q(θ|μ,σ) each time to approximate the expectation at each iteration, thus improving computational efficiency. This can be seen as a variant of the stochastic gradient descent algorithm, while for each estimated standard deviation σ... i All of these must satisfy the non-negativity property. Assuming the variational posterior is a diagonal Gaussian distribution, we obtain a sample of network weights by sampling from a standard normal distribution and adjusting the mean and standard deviation. We then employ reparameterization techniques.

[0048] Furthermore, unsupervised Bayesian neural network training is performed. Based on the generative model concept, for the unsupervised Bayesian neural network in this invention, only the aliasing matrix Γ and the aliased common detection point gather b need to be input. A randomly generated matrix vector can then be used to approximate the effective signal, yielding the estimated distribution parameter μ. * and σ * Then, we can obtain an approximate q(θ|μ) of the posterior probability distribution p(θ|b). * ,σ * ), then, the approximate estimate d of MMSE * The expression will also be characterized. However, since the integral term in the expression is still difficult to solve during the solution process, Monte Carlo sampling is often used in practice to obtain an approximate estimate of the network. After obtaining the estimated distribution parameters, the mixed seismic gathers to be unmixed are used as the input of the network to obtain the unmixed seismic data. For the Bayesian neural network of this invention, the training data and the test data are the same.

[0049] An approximate estimate of the effective signal is achieved using a randomly generated matrix vector, through the formula... After training, the estimated distribution parameters μ are obtained. * and σ * Then, we obtain an approximate q(θ|μ) of the posterior probability distribution p(θ|b). * ,σ *After the network training is completed, the aliased seismic gathers to be demixed are used as the network input to obtain the demixed seismic data. For the Bayesian neural network of this invention, the training data and the test data are the same. It is understood that the beneficial effects of the second aspect mentioned above can be found in the relevant descriptions in the first aspect above, and will not be repeated here.

[0050] In summary, this invention can effectively solve the separation problem when acquiring aliased seismic data, and can be trained using the stochastic gradient descent algorithm to achieve adaptive adjustment and optimization of parameters, thereby improving the effectiveness and robustness in unmixing seismic data with different noise levels.

[0051] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0052] Figure 1 This is a flowchart of the main process of the present invention;

[0053] Figure 2 This is a schematic diagram of the self-supervised Bayesian neural network structure of the present invention;

[0054] Figure 3 This is a schematic diagram of the earthquake data velocity model of the present invention, in which different colors represent different velocities and characterize different inter-layer impedance characteristics.

[0055] Figure 4 This is a schematic diagram of the simulated data aliasing co-detector point gather for training and testing the self-supervised Bayesian neural network of the present invention, wherein (a) is the first simulated data example with clean and unaliased data, and (b) is the 48th simulated data example with clean and unaliased data.

[0056] Figure 5 This is a schematic diagram of the real aliased co-detector point gathers of the self-supervised Bayesian neural network used for training and testing from the open-source dataset of this invention. (a) is the first clean and unaliased actual data example, and (b) is the 48th clean and unaliased actual data example.

[0057] Figure 6 In the absence of random noise, based on the self-supervised Bayesian neural network proposed in this invention, using MAE and MSE as loss functions respectively, and trained with simulated data aliasing common detector point gathers, the first simulated aliasing data demixing result is obtained, where (a) is the first data pseudo demixing (0.01dB), (b) is the first data pseudo demixing difference, (c) is the first data MAE result (36.55dB), (d) is the first data MAE result difference, (e) is the first data MSE result (36.94dB), and (f) is the first data MSE result difference;

[0058] Figure 7 In the absence of random noise, based on the self-supervised Bayesian neural network proposed in this invention, MAE and MSE are used as loss functions respectively. After training with the common detector gather of simulated data aliasing, the demixing result of the 48th simulated aliasing data is obtained. Among them, (a) is the pseudo demixing result of the 48th data (0.02dB), (b) is the pseudo demixing difference of the 48th data, (c) is the MAE result of the 48th data (35.87dB), (d) is the difference of the MAE result of the 48th data, (e) is the MSE result of the 48th data (33.07dB), and (f) is the difference of the MSE result of the 48th data.

[0059] Figure 8 The diagram shows the average amplitude spectrum of the unmixed results of the 1st and 48th simulated aliased data under the condition of no random noise. (a) is the average amplitude spectrum of the unmixed results of the 1st simulated data, and (b) is the average amplitude spectrum of the unmixed results of the 48th simulated data.

[0060] Figure 9 The comparison of the 16th channel of the demixing results of the 1st and 48th simulated aliased data in the time domain under the condition of no random noise is shown in (a) and (b).

[0061] Figure 10 In the case of random noise, based on the self-supervised Bayesian neural network proposed in this invention, with MAE and as loss functions, after training using the common detector gather of simulated data aliasing, the demixing results of the 1st and 48th simulated aliasing data are obtained, where (a) is the MAE result of the 1st data (40.02dB) and (b) is the MAE result of the 48th data (35.15dB);

[0062] Figure 11 In the case of random noise, based on the self-supervised Bayesian neural network proposed in this invention, with MAE as the loss function, after training using the common detector gather of simulated data aliasing, the difference between the demixing results of the 1st and 48th simulated aliasing data is obtained, where (a) is the difference of the MAE result of the 1st data and (b) is the difference of the MAE result of the 48th data.

[0063] Figure 12In the absence of random noise, based on the self-supervised Bayesian neural network proposed in this invention, MAE and MSE are used as loss functions respectively. After training with real aliased co-detector point gathers from open source datasets, the first simulated aliased data demixing result is obtained. Among them, (a) is the first data pseudo demixing (3.26dB), (b) is the first data pseudo demixing difference, (c) is the first data MAE result (23.77dB), (d) is the first data MAE result difference, (e) is the first data MSE result (22.13dB), and (f) is the first data MSE result difference.

[0064] Figure 13 In the absence of random noise, based on the self-supervised Bayesian neural network proposed in this invention, MAE and MSE are used as loss functions respectively. After training with real aliased co-detector point gathers from open source datasets, the demixing result of the 48th simulated aliased data is obtained. Among them, (a) is the pseudo demixing result of the 48th data (2.72dB), (b) is the pseudo demixing difference of the 48th data, (c) is the MAE result of the 48th data (17.94dB), (d) is the difference of the MAE result of the 48th data, (e) is the MSE result of the 48th data (13.31dB), and (f) is the difference of the MSE result of the 48th data.

[0065] Figure 14 The diagram shows the average amplitude spectrum of the unmixed results of the 1st and 48th real aliased data under the condition of no random noise. (a) is the average amplitude spectrum of the unmixed result of the 1st actual data, and (b) is the average amplitude spectrum of the unmixed result of the 48th actual data.

[0066] Figure 15 The comparison of the 16th channel of the demixing results of the 1st and 48th real aliased data in the time domain under the condition of no random noise is shown. (a) is the comparison of the 16th channel of the demixing result of the 1st actual data in the time domain, and (b) is the comparison of the 16th channel of the demixing result of the 48th actual data in the time domain.

[0067] Figure 16 In the case of random noise, based on the self-supervised Bayesian neural network proposed in this invention, MAE and MSE are used as loss functions respectively. After training with real aliased co-detector point gathers from open source datasets, the demixing results of the 1st and 48th real aliased data are obtained. Among them, (a) is the MAE result of the 1st data (24.70dB) and (b) is the MAE result of the 48th data (18.64dB).

[0068] Figure 17In the case of random noise, based on the self-supervised Bayesian neural network proposed in this invention, MAE and MSE are used as loss functions respectively. After training with real aliased co-detector point gathers from open source dataset, the difference of the demixing result of the 48th real aliased data is obtained. Among them, (a) is the difference of the MAE result of the 1st data and (b) is the difference of the MAE result of the 48th data.

[0069] Figure 18 A schematic diagram of a computer device provided in an embodiment of the present invention;

[0070] Figure 19 This is a block diagram of a chip provided according to an embodiment of the present invention. Detailed Implementation

[0071] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0072] In the description of this invention, it should be understood that the terms "comprising" and "including" indicate the presence of the described features, integrals, steps, operations, elements and / or components, but do not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or collections thereof.

[0073] It should also be understood that the terminology used in this specification is for the purpose of describing particular embodiments only and is not intended to limit the invention. As used in this specification and the appended claims, the singular forms “a,” “an,” and “the” are intended to include the plural forms unless the context clearly indicates otherwise.

[0074] It should also be further understood that the term "and / or" as used in this specification and the appended claims refers to any combination and all possible combinations of one or more of the associated listed items, and includes such combinations. For example, A and / or B can represent three cases: A alone, A and B simultaneously, and B alone. Additionally, the character " / " in this invention generally indicates that the preceding and following objects have an "or" relationship.

[0075] It should be understood that although terms such as first, second, third, etc., may be used in the embodiments of the present invention to describe the preset range, these preset ranges should not be limited to these terms. These terms are only used to distinguish the preset ranges from one another. For example, without departing from the scope of the embodiments of the present invention, the first preset range may also be referred to as the second preset range, and similarly, the second preset range may also be referred to as the first preset range.

[0076] Depending on the context, the word "if" as used here can be interpreted as "when," "when," "in response to determination," or "in response to detection." Similarly, depending on the context, the phrase "if determination" or "if detection (of the stated condition or event)" can be interpreted as "when determination," "in response to determination," "when detection (of the stated condition or event)," or "in response to detection (of the stated condition or event)."

[0077] The accompanying drawings illustrate various structural schematic diagrams according to embodiments disclosed in this invention. These drawings are not to scale, and some details have been enlarged for clarity, and some details may have been omitted. The shapes of the various regions and layers shown in the drawings, as well as their relative sizes and positional relationships, are merely exemplary and may deviate from reality due to manufacturing tolerances or technical limitations. Furthermore, those skilled in the art can design regions / layers with different shapes, sizes, and relative positions as needed.

[0078] This invention provides a seismic data unmixing method using a self-supervised Bayesian deep learning network. Based on the Bayesian variational inference principle, it constructs a self-supervised Bayesian neural network by utilizing the inherent learning capability of the deep network structure. This network learns not deterministic parameters, but rather the distribution of those parameters. Before unmixing, the seismic data is preprocessed, and then unmixed using Bayesian inference, resulting in more reliable and accurate unmixing results. The method can be trained using stochastic gradient descent to achieve adaptive parameter adjustment and optimization.

[0079] Please see Figure 1 This invention discloses a method for unmixing seismic data using a self-supervised Bayesian deep learning network, comprising the following steps:

[0080] S1. With the detector fixed and no noise during the acquisition process, a random time jitter strategy is used to construct the aliasing matrix Γ. The aliased seismic data b is obtained by multiplying it with the effective seismic data d to be separated in the common detection domain. A random noise factor n is introduced to take into account the influence of random noise.

[0081] The random time jitter strategy is as follows:

[0082] Seismic data aliasing is a process that generates incoherent wavefields. When the coherence between the effective signal and interference is weak, the effective signal in the aliased seismic data can be separated using demixing methods. The key to successful seismic data aliasing acquisition lies in designing an aliasing scheme that allows for the acquisition of as much information as possible within the same timeframe, while simultaneously enabling effective separation of the aliased signals through algorithms. Therefore, the design of seismic aliasing acquisition strategies should incorporate consideration of incoherence characteristics. Introducing randomness into the source excitation sequence during aliasing acquisition can enhance incoherence. This invention introduces random time jitter during source excitation, generating incoherent wavefields that retain complete temporal and spatial distances, which is crucial for separating the effective signal from the aliased seismic data.

[0083] Furthermore, after adopting the random time jitter strategy, the aliased seismic data b is specifically as follows:

[0084] In multi-source acquisition, if d represents the seismic data acquired by a single source, and b(t,r) represents the signal recorded by the r-th detector at time t during multi-source acquisition, the acquired seismic data can be represented as:

[0085]

[0086] Where t∈{1,...,N-1}Δt represents different sampling times, Δt is the sampling time interval (Δt is not fixed but random), and N is the total number of sampling points recorded by the detector. s Let d(t+τ) be the total number of seismic sources that the r-th detector can effectively record. i ,s i r) represents the earthquake originating from the i-th single source s i Random time delay or jitter τ i The signal at time t is excited and acquired by the r-th detector.

[0087] Furthermore, the aliasing matrix Γ is constructed to represent the aliased seismic data b as follows:

[0088] The aliasing matrix Γ = [H1,…,H n ], where H i H represents the set partitioned by columns in the aliasing matrix. i Represented as:

[0089]

[0090] in, For a size of N s ×N s unit array, 0 i1 For a size of N0×N sA zero matrix of size 0 i2 For a size of (NN) s -N0)×N s The zero matrix. N0 is the source excitation delay, which varies with the excitation sequence of sources at different locations and known random time jitter.

[0091] The common receiving domain is selected as the effective domain for primarily separating effective signals. In the common receiving domain, a random time-dithered aliasing acquisition technique is employed with a fixed detector. Rewritten as:

[0092] b=Γd

[0093] Where b represents the aliased seismic data; Γ is the aliasing matrix including time jitter; and d is the effective seismic data to be separated. Based on the physical meaning of the aliasing matrix, the solution to the above equation is underdetermined. However, since actual seismic data acquisition systems are often affected by random noise, considering the influence of noise, this invention re-describes b = Γd to obtain:

[0094] b=Γd+n

[0095] Where n represents the noise component introduced when the observation system acquires seismic data.

[0096] It is worth noting that the noise referred to in this invention is the noise introduced during system observation.

[0097] Taking seismic exploration systems as an example, traditional seismic exploration involves various types of noise, such as surge noise and random noise. Since super-Gaussian distributed noise, such as surge noise, still presents challenges in suppressing noise in seismic data, this invention does not consider the introduction of anomalous noise in aliased acquisitions, but only considers random noise components.

[0098] S2. Based on the physical meaning of the aliasing matrix Γ, the process of solving d is regarded as solving an underdetermined inversion optimization problem.

[0099] Introducing the definition of effective seismic data as θ={θ i} as weight parameters of the neural network Using a randomly generated vector ε0 as the input to the network, a neural network is used. The effective seismic data d is estimated using the input ε0;

[0100] The d-estimation of single-source triggered earthquake data is as follows:

[0101]

[0102] Combining the expression b = Γd + n in step S1 with the above formula, we have:

[0103]

[0104] S3. Based on step S2, assume that the random noise follows a variance of . Using a Gaussian distribution and a classic statistical inference framework, solving the objective function means finding the maximum likelihood estimate of the parameters to be solved. Considering that the network weight parameters θ have obvious redundancy, the maximum likelihood estimate is prone to overfitting. By providing prior information about the parameters θ, assuming that the parameters θ have a prior probability distribution p(θ), the maximum a posteriori can reduce the adverse effects of network parameter redundancy on the inverse problem solution objective.

[0105] Solving the objective function means finding the maximum likelihood estimate of the parameters to be solved, specifically:

[0106] In the classic statistical inference framework, solving the objective function means finding the maximum likelihood estimate of the parameters to be solved. The maximum likelihood estimate of d can be solved by the following formula:

[0107]

[0108] Here, dist(,) represents the distance between data points, determined by the characteristics of the data. The network weight parameters θ exhibit significant redundancy, which can lead to overfitting in maximum likelihood estimation. By providing prior information about the parameters θ, maximum a posteriori (MAP) can mitigate the adverse effects of network parameter redundancy on the inverse problem's solution objective.

[0109] In this invention, we first assume that the random noise follows a variance of . Gaussian distribution:

[0110]

[0111] Given a Gaussian distribution of random noise, and assuming that the parameter θ has a prior probability distribution p(θ), then the maximum a posteriori estimate can be expanded as follows:

[0112]

[0113] In the above equation, the L2 norm is used to represent the distance dist(,), but when the random noise does not follow a Gaussian distribution, the solution to the above equation is often not optimal. In seismic data processing, using the L1 norm to suppress random noise is a commonly used method.

[0114] S4. Based on step S3, the maximum a posteriori (MAP) estimate is the maximum likelihood estimate after introducing the prior of θ. To address the problem that MAP is insufficient to effectively resolve the ambiguity of solutions generated in the null space and cannot yield a unique solution, a self-supervised learning method based on a Bayesian neural network framework is proposed, referencing the Dropout concept. This method reduces overfitting by introducing uncertainty into the network model parameters. It is assumed that the network model parameters p(θ) follow a Gaussian distribution to maximize this uncertainty. Furthermore, under the Gaussian distribution assumption, the posterior and conjugate prior distributions of the weight parameters also follow a Gaussian distribution. The set of multiple repeated implementations of the Bayesian model will provide more accurate prediction results than a single deterministic model.

[0115] Inspired by the Dropout concept, this paper proposes a self-supervised learning method based on a Bayesian neural network framework. This method reduces overfitting by introducing uncertainty into the network model parameters. Specifically:

[0116] Through analysis Japanese style It can be seen that the maximum a posteriori (MAP) estimate is a maximum likelihood estimate that introduces a prior to θ. While the early stopping strategy can add an implicit prior to the MAP estimate, this strategy is not applicable when solving for non-invertible matrices Γ. In this case, the MAP estimate of the latter form is insufficient to effectively resolve the ambiguity of the solution generated in the null space, and a uniquely determined solution cannot be obtained.

[0117] To address the challenges of maximum a posteriori (MAP) and maximum likelihood (MLR) estimation, this invention proposes a self-supervised learning method based on a Bayesian neural network (BNN) framework and applies it to the seismic data unmixing problem. Traditional neural networks, based on maximum likelihood parameter estimation and gradient descent algorithms, assume the weights have fixed values ​​during each training iteration. When the network model is complex and has a large number of parameters, overfitting is likely to occur, especially with limited training datasets. While early stopping strategies can prevent overfitting, convolutional neural networks can predict a deterministic, structured result. Dropout, on the other hand, introduces uncertainty into the network training process, randomly discarding certain model units to reduce overfitting. Introducing uncertainty is an effective approach to avoid overfitting. Similar to Dropout, introducing uncertainty into the network model parameters can also reduce overfitting.

[0118] Specifically, the network weights of a BNN are not deterministic but rather random variables following a certain probability distribution. The network does not update deterministic weights, but rather the parameters of the probability distribution of these random weights. The motivation for handling underdetermined inversion problems stems from the uncertainty of the network model (i.e., the uncertainty of the weights), which helps correct generation biases caused by the network architecture. A set of multiple repeated implementations of a Bayesian model can provide more accurate predictions than a single deterministic model. Assuming that the network model parameters follow a Gaussian distribution maximizes this uncertainty, and under this Gaussian distribution assumption, both the posterior and conjugate prior distributions of the weight parameters follow a Gaussian distribution, which is computationally advantageous.

[0119] In Bayesian Neural Networks (BNNs), a convolution layer based on the Bayesian neural network concept is defined as a Bayesian convolutional layer. Bayesian convolution is a Bayesian-based convolution method applicable to image processing, signal processing, and other fields. Compared to traditional convolution methods, Bayesian convolution not only utilizes prior knowledge to estimate the convolution kernel but also provides a probability distribution to describe the uncertainty of the convolution result. Specifically, traditional convolution methods are trained with deterministic weights, resulting in a deterministic network weight set. Bayesian convolution, however, treats the convolution kernel as a random variable and uses Bayesian inference to solve for the posterior distribution based on the prior distribution and observed data, thus obtaining a probability distribution describing the uncertainty of the convolution result.

[0120] Furthermore, for the target data, its size is defined as H×W×C, where H represents the number of rows or height of the data matrix, W represents the number of columns or width of the data matrix, and C represents the number of channels of the data matrix. In RGB images, C=3, while for seismic data, C=1. To reconstruct an H×W two-dimensional seismic data matrix, the network's input is (H / 32)×(W / 32)×128, where 128 is the number of channels in the intermediate network layers. This network is a decoder containing five decoding blocks. The first four decoding blocks each sequentially connect an upsampling layer with a scaling factor of 2 and two Bayesian convolutional layers, with LeakyReLU introduced between the convolutional layers to introduce non-linearity. Both Bayesian convolutional layers have 128 channels. The last decoding block contains an upsampling layer with a scaling factor of 2 and three Bayesian convolutional layers with output channels of 64, 32, and C respectively. Similarly, two LeakyReLU layers are inserted between the Bayesian convolutional layers, and a Sigmoid layer is added at the end. When processing seismic data, the last Bayesian convolutional layer has 1 channel.

[0121] S5. Based on step S4, the proposed Bayesian network-based method learns an approximation of the minimum error estimate. The L2 norm is selected based on the Gaussian hypothesis to characterize the error between the effective signal d and the maximum a posteriori estimate u. Since the neural network structure has a large number of weights and various nonlinear structures, the a posteriori probability distribution function p(θ|b) of θ is often difficult to calculate. Therefore, the joint distribution q(θ|μ,σ) of independent normal distributions is used to approximate p(θ|b).

[0122] Based on the Gaussian model, the L2 norm is used to characterize the error between the effective seismic data d and the maximum a posteriori estimate u. Specifically:

[0123] From the perspective of Bayesian approximation, the proposed Bayesian network-based method learns an approximation of the minimum error estimate:

[0124]

[0125] Where p(θ|b) is the posterior probability distribution function of θ, and the L2 norm is selected based on the Gaussian hypothesis to characterize the error between the two. Due to the large number of weights and various nonlinear structures in neural network structures, p(θ|b) is often difficult to calculate. This invention uses the joint distribution q(θ|μ,σ) of independent normal distributions to approximate p(θ|b):

[0126]

[0127] Where, μ={μ i} represents the mean parameter of a Gaussian distribution, σ = {σ i} represents the standard deviation parameter of the Gaussian distribution.

[0128] Combined Japanese style get:

[0129]

[0130] S6. Based on steps S2 and S5, and using variational inference, the joint distribution of q(θ|μ,σ) from step S5 is used to approximate p(θ|b) in the minimum error estimation, thereby minimizing the network prediction output. Training an unsupervised Bayesian neural network by estimating the distance between the two with minimum error is equivalent to training the proposed network by minimizing the KL divergence between them. However, minimizing the KL divergence is difficult to obtain for an arbitrary distribution. To further simplify the problem, assume that the prior distribution p(θ) of the model parameters has zero mean and a standard deviation of . The independent and identically distributed normal distribution approximates it;

[0131] Based on variational inference, the proposed network is trained by minimizing the KL divergence between the two, specifically as follows:

[0132] Training the network involves minimizing the network's predicted output in the above equation. This is achieved by considering the distance between the minimum error estimate and the minimum error estimate. Based on variational inference, the joint distribution of q(θ|μ,σ) defined above is used to approximate p(θ|b) in the minimum error estimate, and the proposed network is trained by minimizing the KL divergence between them.

[0133]

[0134] Minimizing the KL divergence for an arbitrary distribution is difficult, therefore a simplification of the problem is necessary. Further, suppose the prior distribution p(θ) can be derived from a distribution with zero mean and a standard deviation of... The independent and identically distributed normal distribution is a good approximation of this. It can be expressed as:

[0135]

[0136] Combined Mode Japanese style Transform into:

[0137]

[0138] Among them are:

[0139]

[0140] For the data fidelity term in the expression, one instance of parameter θ is drawn from the distribution q(θ|μ,σ) each time to approximate the expectation at each iteration, thereby improving computational efficiency. This can be seen as a variant of the stochastic gradient descent algorithm, while for each estimated standard deviation σ... i All of these must satisfy the non-negativity property. Assuming the variational posterior is a diagonal Gaussian distribution, we obtain a sample of network weights by sampling from a standard normal distribution and adjusting the mean and standard deviation. Using the reparameterization technique, we adjust the standard deviation σ... i Represented as:

[0141] σ i =log(1+exp(ρ) i ))

[0142] In each iteration of BNN training, the standard normal distribution is used. Randomly select samples from the network and then generate network weights:

[0143] θ i =μ i +log(1+exp(ρi ))·ε

[0144] S7. Based on step S6, unsupervised Bayesian neural network training is performed. According to the generative model concept, for the unsupervised Bayesian neural network in this invention, only the aliasing matrix Γ and the aliased common detection point gather b need to be input. An approximate estimation of the effective signal can be achieved using a randomly generated matrix vector, yielding the estimated distribution parameter μ. * and σ * Then, we can obtain an approximate q(θ|μ) of the posterior probability distribution p(θ|b). * ,σ * ), then, the approximate estimate d of MMSE * The expression will also be characterized. However, since the integral term in the expression is still difficult to solve during the solution process, Monte Carlo sampling is often used in practice to obtain an approximate estimate of the network. After obtaining the estimated distribution parameters, the mixed seismic gathers to be unmixed are used as the input of the network to obtain the unmixed seismic data. For the Bayesian neural network of this invention, the training data and the test data are the same.

[0145] The BNN is trained to obtain the estimated distribution parameters μ. * and σ * Specifically:

[0146] When training an unsupervised Bayesian neural network, based on the generative model concept, the unsupervised Bayesian neural network in this invention only requires inputting the aliasing matrix Γ and the aliased common detection point gather b. An approximate estimate of the effective signal is achieved using a randomly generated matrix vector, and the formula is used... After training, the estimated distribution parameters μ are obtained. * and σ * This yields an approximate q(θ|μ) of the posterior probability distribution p(θ|b). * , σ * Therefore, the approximate estimate of MMSE is:

[0147]

[0148] although and q(θ|μ * ,σ * While all of these have explicit forms, the integrals described above remain difficult to solve. Instead, in practice, Monte Carlo sampling is used to obtain an approximate estimate of the network:

[0149]

[0150] Where, {θ j} is based on the distribution q(θ|μ * ,σ * The instantiation of the random parameter θ variable of ), where T is the number of instantiations.

[0151] After the network training is completed, the mixed seismic gathers to be demixed are used as the input of the network to obtain the demixed seismic data. For the Bayesian neural network of this invention, the training data and the test data are the same.

[0152] In another embodiment of the present invention, a seismic data unmixing system based on a self-supervised Bayesian deep learning network is provided. This system can be used to implement the above-mentioned seismic data unmixing method based on a self-supervised Bayesian deep learning network. Specifically, the seismic data unmixing system based on a self-supervised Bayesian deep learning network includes a matrix module, a solution module, an estimation module, an input module, a characterization module, a training module, and an output module.

[0153] Among them, the matrix module uses a random time jitter strategy to construct the aliasing matrix Γ, which is multiplied with the effective seismic data d to be separated in the common detection domain to obtain the aliased seismic data b, and introduces a random noise factor n;

[0154] The solution module, based on the physical meaning of the aliasing matrix Γ obtained from the matrix module, treats the process of solving for the effective seismic data d to be separated as solving an underdetermined inversion optimization problem;

[0155] The estimation module, based on the solution module, adopts the classic statistical inference framework. By providing prior information about the parameter θ, and assuming that the parameter θ has a prior probability distribution p(θ), it finds the maximum likelihood estimate of the parameter to be solved.

[0156] The module is introduced based on the estimation module. The maximum a posteriori estimation is the maximum likelihood estimation after introducing the prior of θ. Uncertainty is introduced into the network model parameters. It is assumed that the network model parameters p(θ) follow a Gaussian distribution to maximize this uncertainty. Under the Gaussian distribution, the posterior distribution and conjugate prior distribution of the weight parameters also follow a Gaussian distribution.

[0157] The characterization module, based on the introduction module, uses a Bayesian network-based method to learn an approximation of the minimum error estimate. We assume that the L2 norm is used to characterize the error between the effective seismic data d and the maximum a posteriori estimate u, and the joint distribution q(θ|μ,σ) of the independent normal distribution is used to approximate p(θ|b).

[0158] The training module, based on variational inference, uses the joint distribution of q(θ|μ,σ) obtained from the characterization module to approximate p(θ|b) in the minimum error estimate, thereby minimizing the network's predicted output. The distance between the two parameters, which is estimated by minimum error, is used to train an unsupervised Bayesian neural network. The prior distribution p(θ) of the model parameters is assumed to have zero mean and a standard deviation of . The independent and identically distributed normal distribution approximates it;

[0159] The output module, based on the results obtained from the training module, performs unsupervised Bayesian neural network training. Following the generative model approach, it takes the aliasing matrix Γ and the aliased common detection point gather b as input, and uses a randomly generated matrix vector to approximate the effective signal, obtaining the estimated distribution parameters μ. * and σ * Then, we obtain an approximate q(θ|μ) of the posterior probability distribution p(θ|b). * ,σ * Monte Carlo sampling is used to obtain an approximate estimate of the network; after obtaining the estimated distribution parameters, the mixed seismic gathers to be unmixed are used as the input of the network to obtain the unmixed seismic data.

[0160] In another embodiment of the present invention, a terminal device is provided, comprising a processor and a memory. The memory stores a computer program, which includes program instructions. The processor executes the program instructions stored in the computer storage medium. The processor may be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. It is the computing and control core of the terminal, suitable for implementing one or more instructions, specifically suitable for loading and executing one or more instructions to achieve a corresponding method flow or corresponding function. The processor described in this embodiment can be used for the operation of a seismic data unmixing method using a self-supervised Bayesian deep learning network, including:

[0161] A random time jitter strategy is used to construct an aliasing matrix Γ. This matrix is ​​multiplied by the seismic data to be separated, d, in the common detection domain to obtain aliased seismic data b, with a random noise factor n introduced. Based on the physical meaning of the aliasing matrix Γ, the process of solving for the seismic data to be separated, d, is considered as solving an underdetermined inversion optimization problem. A classical statistical inference framework is adopted, providing prior information about the parameter θ. Assuming that the parameter θ has a prior probability distribution p(θ), the maximum likelihood estimate of the parameter to be solved is found. The maximum a posteriori estimate is the maximum likelihood estimate after introducing the prior information about θ, by introducing uncertainty into the network model parameters. The network model parameters p(θ) follow a Gaussian distribution to maximize this uncertainty. Furthermore, under a Gaussian distribution, the posterior and conjugate prior distributions of the weight parameters also follow a Gaussian distribution. The Bayesian network-based method learns an approximation of the minimum error estimate. Based on the Gaussian assumption, the L2 norm is used to characterize the error between the effective seismic data d and the maximum a posteriori estimate u. The joint distribution q(θ|μ,σ) of the independent normal distributions is used to approximate p(θ|b). Based on variational inference, the joint distribution of q(θ|μ,σ) is used to approximate p(θ|b) in the minimum error estimate, by minimizing the network prediction output. The distance between the two parameters, which is estimated by minimum error, is used to train an unsupervised Bayesian neural network. The prior distribution p(θ) of the model parameters is assumed to have zero mean and a standard deviation of . The independent and identically distributed normal distribution is approximated; an unsupervised Bayesian neural network is trained, and based on the generative model idea, the aliasing matrix Γ and the aliased common detection point gather b are input. A randomly generated matrix vector is used to achieve an approximate estimate of the effective signal, and the estimated distribution parameter μ is obtained. * and σ * Then, we obtain an approximate q(θ|μ) of the posterior probability distribution p(θ|b). * ,σ * Monte Carlo sampling is used to obtain an approximate estimate of the network; after obtaining the estimated distribution parameters, the mixed seismic gathers to be unmixed are used as the input of the network to obtain the unmixed seismic data.

[0162] Please see Figure 18 The terminal device is a computer device. In this embodiment, the computer device 60 includes a processor 61, a memory 62, and a computer program 63 stored in the memory 62 and executable on the processor 61. When executed by the processor 61, the computer program 63 implements the fluid composition calculation method in the reservoir stimulation wellbore of this embodiment. To avoid repetition, details are omitted here. Alternatively, when executed by the processor 61, the computer program 63 implements the functions of each model / unit in the seismic data unmixing system of the self-supervised Bayesian deep learning network of this embodiment. To avoid repetition, details are omitted here.

[0163] Computer device 60 can be a desktop computer, laptop, handheld computer, cloud server, or other computing device. Computer device 60 may include, but is not limited to, a processor 61 and a memory 62. Those skilled in the art will understand that... Figure 18 This is merely an example of computer device 60 and does not constitute a limitation on computer device 60. It may include more or fewer components than shown, or combine certain components, or different components. For example, computer device may also include input / output devices, network access devices, buses, etc.

[0164] The processor 61 may be a central processing unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor may be a microprocessor or any conventional processor.

[0165] The memory 62 can be an internal storage unit of the computer device 60, such as a hard disk or RAM of the computer device 60. The memory 62 can also be an external storage device of the computer device 60, such as a plug-in hard disk, Smart Media Card (SMC), Secure Digital (SD) card, Flash Card, etc., equipped on the computer device 60.

[0166] Furthermore, the memory 62 may include both internal storage units of the computer device 60 and external storage devices. The memory 62 is used to store computer programs and other programs and data required by the computer device. The memory 62 can also be used to temporarily store data that has been output or will be output.

[0167] Please see Figure 19 The terminal device is a chip. In this embodiment, the chip 600 includes a processor 622, which may be one or more, and a memory 632 for storing computer programs executable by the processor 622. The computer program stored in the memory 632 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processor 622 may be configured to execute the computer program to perform the aforementioned seismic data unmixing method using a self-supervised Bayesian deep learning network.

[0168] Additionally, chip 600 may also include a power supply component 626 and a communication component 650. The power supply component 626 can be configured to perform power management of chip 600, and the communication component 650 can be configured to enable communication of chip 600, such as wired or wireless communication. Furthermore, chip 600 may also include an input / output (I / O) interface 658. Chip 600 can operate on an operating system stored in memory 632.

[0169] In another embodiment of the present invention, a storage medium is provided, specifically a computer-readable storage medium (Memory). This computer-readable storage medium is a memory device in a terminal device used to store programs and data. It is understood that the computer-readable storage medium here can include both the built-in storage medium in the terminal device and extended storage media supported by the terminal device. The computer-readable storage medium provides storage space that stores the terminal's operating system. Furthermore, this storage space also stores one or more instructions suitable for loading and execution by a processor. These instructions can be one or more computer programs (including program code). It should be noted that the computer-readable storage medium here can be high-speed RAM or non-volatile memory, such as at least one disk storage device.

[0170] One or more instructions stored in a computer-readable storage medium can be loaded and executed by a processor to implement the corresponding steps of the seismic data unmixing method related to the self-supervised Bayesian deep learning network in the above embodiments; one or more instructions in the computer-readable storage medium are loaded and executed by the processor in the following steps:

[0171] A random time jitter strategy is used to construct an aliasing matrix Γ. This matrix is ​​multiplied by the seismic data to be separated, d, in the common detection domain to obtain aliased seismic data b, with a random noise factor n introduced. Based on the physical meaning of the aliasing matrix p, the process of solving for the seismic data to be separated, d, is considered as solving an underdetermined inversion optimization problem. A classical statistical inference framework is adopted, providing prior information about the parameter θ. Assuming that parameter θ has a prior probability distribution p(θ), the maximum likelihood estimate of the parameter to be solved is found. The maximum a posteriori estimate is the maximum likelihood estimate after introducing the prior information about θ, by introducing uncertainty into the network model parameters. The network model parameters p(θ) follow a Gaussian distribution to maximize this uncertainty. Furthermore, under a Gaussian distribution, the posterior and conjugate prior distributions of the weight parameters also follow a Gaussian distribution. The Bayesian network-based method learns an approximation of the minimum error estimate. Based on the Gaussian assumption, the L2 norm is used to characterize the error between the effective seismic data d and the maximum a posteriori estimate u. The joint distribution q(θ|μ,σ) of the independent normal distributions is used to approximate p(θ|b). Based on variational inference, the joint distribution of q(θ|μ,σ) is used to approximate p(θ|b) in the minimum error estimate, by minimizing the network prediction output. The distance between the two parameters, which is estimated by minimum error, is used to train an unsupervised Bayesian neural network. The prior distribution p(θ) of the model parameters is assumed to have zero mean and a standard deviation of . The independent and identically distributed normal distribution is approximated; an unsupervised Bayesian neural network is trained, and based on the generative model idea, the aliasing matrix Γ and the aliased common detection point gather b are input. A randomly generated matrix vector is used to achieve an approximate estimate of the effective signal, and the estimated distribution parameter μ is obtained. * and σ * Then, we obtain an approximate q(θ|μ) of the posterior probability distribution p(θ|b). * ,σ * Monte Carlo sampling is used to obtain an approximate estimate of the network; after obtaining the estimated distribution parameters, the mixed seismic gathers to be unmixed are used as the input of the network to obtain the unmixed seismic data.

[0172] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0173] This invention aims to verify the actual unmixing performance of self-supervised Bayesian deep learning networks, as detailed below:

[0174] First, according to Figure 2 The cascaded deep neural network framework shown constructs the dataset. In this example, a layered model is used for aliasing acquisition of numerical simulation data to synthesize the simulated data. Figure 3 The velocity model used in the simulation is shown, with a vertical depth of 2000 meters. To make the simulation data more consistent with actual geological conditions, the first 1524 meters of the model containing velocity anomalies were specifically selected for simulation. A total of 128 geophones and 128 seismic sources were horizontally positioned during the simulation. The spacing between seismic sources was 12 meters, and the spacing between geophones was also chosen to be equal at 12-meter intervals. All geophones and seismic sources were located on the Earth's surface. Figure 4 Showing based on Figure 2 The aliased co-detector gather was obtained by simulating the velocity model constructed in the middle. The sampling time interval of this data is 0.002 seconds, the number of sampling points is 750, the single source excitation data is 128 channels, and the inter-channel interval is 12 meters.

[0175] Please see Figure 2 The network model consists of five decoding blocks. The first four blocks each contain an upsampling layer with a scaling factor of 2 and two Bayesian convolutional layers, with LeakyReLU interleaved between the convolutional layers to introduce non-linearity. Each Bayesian convolutional layer has 128 channels. The last decoding block contains an upsampling layer with a scaling factor of 2 and three Bayesian convolutional layers with 64, 32, and 1 output channels respectively. Again, two LeakyReLU interleaved between the Bayesian convolutional layers, and a Sigmoid layer is added at the end.

[0176] Considering both the efficiency of aliasing acquisition and the difficulty of dealiasing, after designing and testing experiments, parameters were selected to construct the aliasing matrix Γ, with an aliasing degree of 1 and a random time jitter range within 200 time sampling points (which can be considered as [0, 0.4] s in simulated data and [0, 0.8] s in actual data). Furthermore, the Bayesian neural network selected in this example approximates the unaliased effective seismic signal by inputting a random data vector, achieving the goal of dealiasing in a self-supervised manner. Based on the generative model concept, for the network, only the aliasing matrix Γ and the aliased seismic data b need to be input to achieve an approximate estimation of the effective signal using a randomly generated matrix vector, thus realizing the training of the self-supervised Bayesian neural network. Using a model based on... Figure 2 The aliased common detector gathers obtained by the velocity model simulation constructed in the middle (e.g. Figure 4 ) and real co-detection point data from open-source datasets (such as Figure 5 The obtained mixed co-detector point gathers were used for network training. The simulated co-detector point data had a sampling time interval of 0.002 seconds, with 750 sample points extracted. The single-source excitation data consisted of 128 channels with a channel spacing of 12 meters. The real co-detector point data had 512 sample points per channel per data slice, each containing 128 channels, with a channel spacing of 12.5 meters and a sampling time interval of 0.004 seconds per channel. This example network was trained for 300,000 epochs.

[0177] Furthermore, for the Bayesian neural network in this example, each data point serves as both training and testing data. To demonstrate the effectiveness of the method, we again utilize data based on... Figure 2 The aliased common detector gathers obtained by the velocity model simulation constructed in the middle (e.g. Figure 9 ) and real aliased co-detector point gathers from open-source datasets (such as Figure 10 To verify the effectiveness of the network, given that the effective signals used to construct the dataset are known, the signal-to-noise ratio (SNR) is introduced to objectively evaluate the demixing results. The result obtained from unmixing is d, where d is the true value.

[0178] The signal-to-noise ratio expression is:

[0179]

[0180] This example discusses the impact of the presence or absence of random noise and different loss functions on the unmixing accuracy of the proposed method. In the absence of random noise, MAE and MSE are used as loss functions, respectively. The time-domain plot of the unmixing result obtained from the first simulation data using a self-supervised Bayesian neural network is shown below. Figure 6 As shown. Figure 6 (a) is the result obtained by using pseudo-demixing on the first data point. Figure 6 (c) shows the MAE result for the first data point. Figure 6 (e) shows the MSE result for the first data point. The signal-to-noise ratios (SNRs) for the three data points are 0.01 dB, 36.55 dB, and 36.94 dB, respectively. (Comparison) Figure 6 (a) False unmixing results Figure 6 (c) MAE results and Figure 6 (e) The MSE results show that the proposed demixing method based on Bayesian neural networks can effectively recover effective signals by utilizing uncertain weights. Whether based on MAE loss or MSE loss, it can solve high-level demixing tasks. Figure 7 The results of the 48th data point obtained using the Bayesian neural network-based demixing method proposed in this invention are presented. Figure 7(b) shows the difference in the pseudo-demixing noise in the MAE results. Figure 7 (d) and the difference between MSE results Figure 7 In (f), the signal is almost completely suppressed, and there is almost no effective signal in the result difference plot. The signal-to-noise ratio (SNR) of the pseudo-unmixed data is 0.02 dB. The MAE method can achieve a high-quality result with an SNR of 35.87 dB, while MSE can achieve a recovery of 33.07 dB SNR. In the first data set, the SNR difference between MAE and MSE results is very small. However, in the 48th data set, which has more complex data characteristics, MAE shows a more beneficial characteristic in seismic data processing compared to MSE. This may be due to the wide range of effective signal energy in seismic data, where MSE focuses too much on high-amplitude signals, thus limiting its performance. This paper also plots the mean amplitude spectra of the first and 48th data sets and the time-domain comparison of the 16th trace data, such as... Figure 8 and Figure 9 As shown in the figure, a comparison clearly shows that in both the first and 48th data points, the MAE and MSE results almost completely overlap with the original clean, unaliased effective signal in the time-frequency domain, demonstrating a high degree of approximation of the effective signal in the recovery.

[0181] Furthermore, based on the expression n = Γd + n, this example introduces random noise following a Gaussian distribution to explore the network's robustness and effectiveness in the face of noise introduction. Noise is introduced into the aliased data, and the MAE method is used to extract and recover the effective signal. For example... Figure 10 The demixing results introduce random noise into the simulated data. The first data result achieves a demixing effect of 39.07 dB, while the 48th data result achieves 34.36 dB. The difference profile between the two datasets is shown below. Figure 11 The near absence of signal demonstrates the unique advantage of the proposed method in noise immunity. Notably, compared to the noiseless scenario, the network prediction results after introducing Gaussian random noise achieve a higher signal-to-noise ratio. This can be attributed to the fact that the Bayesian neural network's learning of the weight parameter distribution effectively suppresses Gaussian noise.

[0182] Furthermore, the effectiveness of the method is verified using real-world data. The real-world data consists of the 1st, 16th, 32nd, and 48th common receiver gathers from the dataset, which are aliased, similar to the simulated data. This example will first discuss the network performance under noise-free conditions and then use real-world data for verification and testing. The results obtained using the MAE and MSE methods for the first dataset are shown below. Figure 12 As shown, pseudo-demixing with a signal-to-noise ratio of 3.26 dB introduces a stripe interference component. Results obtained using MAE and MSE methods are as follows... Figure 12 (c) and Figure 12 As shown in (e), demixing results with signal-to-noise ratios of 23.77 dB and 22.13 dB are achieved, respectively. This is compared to the MAE difference. Figure 12 (d) shows a result with almost no effective signal, and the MSE difference is... Figure 12 (f) contains some point-like components, meaning that some interference remains unsuppressed after unmixing. For example... Figure 13 As shown, the proposed method can also achieve unmixing even with complex data features. The pseudo-unmixing of the 48th data point is 2.72 dB, while the MSE result achieves an improvement of 13.31 dB. In comparison, MAE achieves even better unmixing quality, reaching 17.94 dB. A comparison of the MAE and MSE results in the first data point shows that MAE is more suitable for data with large amplitude differences, such as seismic signals. The comparison of the average amplitude spectrum and time-domain waveforms also demonstrate the superiority of MAE over MSE in handling seismic unmixing problems. Figure 14 To plot the amplitude comparison, in Figure 14 (b) The amplitude comparison of the 48th data point shows that, compared with the MSE result, the MAE can more effectively approximate the effective signal, especially in the low and high frequency ranges. Figure 15 The 16th time-domain comparison plot is drawn. Figure 15 (b) The 48th data result shows that, compared with the MAE result, the MSE result has a large noise component around the 2.3 second mark, which needs further noise suppression.

[0183] Furthermore, having achieved excellent results with noisy simulated data, this example also incorporates the noisy condition into the solution of the unmixing problem for actual seismic data. Gaussian white noise is introduced as random noise and added to the aliased seismic data to form the primary acquisition signal of the detector. Figure 4-13 (a) and Figure 4-13 (b) shows the demixing results for the first and 48th data points, obtained using MAE as the loss function. The first data point achieves a signal-to-noise ratio (SNR) of 23.63 dB, while the 48th data point achieves 18.50 dB. Similar to the conclusion that introducing noise into simulated data can improve network performance, the Gaussian random noise introduced into the actual data in this example also improves the accuracy of the network in estimating the data, resulting in a higher SNR compared to the noise-free case.

[0184] The above simulation and actual seismic data unmixing examples illustrate that the seismic data unmixing method based on a self-supervised Bayesian deep learning network proposed in this invention can overcome the difficulties of supervised deep learning sample construction and improve the effectiveness and robustness of unmixing seismic data with different noise levels.

[0185] In summary, this invention presents a self-supervised Bayesian deep learning network-based seismic data unmixing method and system. It implements a self-supervised deep learning unmixing method, which differs from discriminative models that establish a mapping between input and output by extracting features. Based on generative thinking, this invention can estimate the distribution of training data to achieve signal reconstruction. It can unmix seismic data without relying on data other than the training samples, demonstrating high practicality. Furthermore, by introducing Bayesian neural network concepts, the traditional method of assuming network weights follow a certain distribution is transformed into learning the distribution parameters. This introduced uncertainty can correct prediction biases caused by the network architecture, achieving a higher level of signal prediction.

[0186] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0187] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0188] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this invention can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementations should not be considered beyond the scope of this invention.

[0189] In the embodiments provided by this invention, it should be understood that the disclosed devices / terminals and methods can be implemented in other ways. For example, the device / terminal embodiments described above are merely illustrative. For instance, the division of modules or units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0190] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0191] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0192] If the integrated module / unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, all or part of the processes in the methods of the above embodiments can also be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include: any entity or device capable of carrying the computer program code, recording media, USB flash drives, portable hard drives, magnetic disks, optical disks, computer memory, read-only memory (ROM), random-access memory (RAM), electrical carrier signals, telecommunication signals, and software distribution media, etc. It should be noted that the content included in the computer-readable medium can be appropriately added or removed according to the requirements of legislation and patent practice in the jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer-readable media do not include electrical carrier signals and telecommunication signals.

[0193] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0194] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0195] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0196] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A seismic data unmixing method using a self-supervised Bayesian deep learning network, characterized in that, Includes the following steps: S1. Constructing the aliasing matrix using a random time jitter strategy. Through the effective seismic data to be separated Multiplying in the common detection domain yields aliased seismic data. And introduce random noise factor ; S2, based on the aliasing matrix The physical meaning of this will be used to solve the problem of separating effective seismic data. The process can be viewed as solving an underdetermined inversion optimization problem; S3. Based on step S2, adopt a statistical inference framework and analyze the parameters. Provide prior information and set parameters There is a prior probability distribution Find the maximum likelihood estimate of the parameter to be solved; S4. Based on step S3, the maximum a posteriori estimate is... The introduction of prior and post-probability maximum likelihood estimation introduces uncertainty into the network model parameters; let the network model parameters be... Following a Gaussian distribution maximizes this uncertainty, and under a Gaussian distribution, the posterior and conjugate prior distributions of the weight parameters also follow a Gaussian distribution. (Analysis formula...) Japanese style The maximum a posteriori estimate is The introduction of prior maximum likelihood estimation To achieve this, a self-supervised learning method based on a Bayesian neural network framework is adopted. In the Bayesian neural network, convolution is defined as a Bayesian convolutional layer, and the convolution kernel is treated as a random variable. Based on the prior distribution and observed data, the posterior distribution is solved using Bayesian inference to obtain a probability distribution describing the uncertainty of the convolution result. The size of the target data is... H × W × C , H Indicates the number of rows or height of the data matrix. W Indicates the number of columns or width of the data matrix. C This indicates the number of channels in the data matrix; seismic data. C =1, input is ( H / 32)×( W The (32)×128 Bayesian neural network is a decoder containing five decoding blocks. The first four blocks sequentially connect an upsampling layer with a scaling factor of 2 and two Bayesian convolutional layers, with Leaky ReLU introduced between the convolutional layers to provide non-linearity. Each of the two Bayesian convolutional layers has 128 channels. The last decoding block contains an upsampling layer with a scaling factor of 2 and three output channels of 64, 32, and... C The Bayesian convolutional layers are also modified by inserting two LeakyReLU layers between them and adding a Sigmoid layer at the end. S5. The Bayesian network-based method learns an approximation of the minimum error estimate, based on the Gaussian model. L 2-norm for effective seismic data and maximum a posteriori estimation The interval error is characterized using the joint distribution of independent normal distributions. approximate ; S6. Based on variational inference, use the results obtained in step S5. The joint distribution is estimated to have approximately the minimum error in the mean. By minimizing the network's predicted output The distance between the two parameters is estimated using the minimum error estimation method, and an unsupervised Bayesian neural network is trained. The prior distribution of the model parameters is assumed to be... With zero mean and standard deviation The independent and identically distributed normal distribution approximates it; S7. Based on the results obtained in step S6, perform unsupervised Bayesian neural network training. Following the generative model concept, input the aliasing matrix. and the already aliased common detection point gather An approximate estimate of the effective signal is achieved using a randomly generated matrix vector, yielding the estimated distribution parameters. and Then, the posterior probability distribution is obtained. approximation Monte Carlo sampling is used to obtain an approximate estimate of the network; after obtaining the estimated distribution parameters, the mixed seismic gathers to be unmixed are used as the input of the network to obtain the unmixed seismic data.

2. The seismic data unmixing method using a self-supervised Bayesian deep learning network according to claim 1, characterized in that, In step S1, with the detector fixed and noise during the acquisition process ignored, a random time jitter strategy is used to construct the aliasing matrix. aliased seismic data Specifically: 。 3. The seismic data unmixing method using a self-supervised Bayesian deep learning network according to claim 1, characterized in that, In step S2, effective seismic data is introduced to... Neural network as weight parameters Using randomly generated vectors As input to the network, using a neural network and input Single-source triggered earthquake data Make an estimate.

4. The seismic data unmixing method using a self-supervised Bayesian deep learning network according to claim 1, characterized in that, In step S3, assume that the random noise follows a variance of . Given a Gaussian distribution of random noise, let the parameters be... There is a prior probability distribution The maximum a posteriori estimate expands to: in, To use neural networks and input Single-source triggered earthquake data The estimated value used for estimation.

5. The seismic data unmixing method using a self-supervised Bayesian deep learning network according to claim 1, characterized in that, When processing seismic data, the last Bayesian convolutional layer has 1 channel.

6. The seismic data unmixing method using a self-supervised Bayesian deep learning network according to claim 1, characterized in that, In step S5, effective seismic data for: in, for The posterior probability distribution function.

7. The seismic data unmixing method using a self-supervised Bayesian deep learning network according to claim 1, characterized in that, In step S6, in each iteration of training the unsupervised Bayesian neural network, the standard normal distribution is used. Randomly sample from (0,1) and then generate network weights. for: in, The mean parameter of the Gaussian distribution. and All parameters were randomly selected.

8. The seismic data unmixing method using a self-supervised Bayesian deep learning network according to claim 1, characterized in that, In step S7, the approximate estimation of the network... for: in, For distribution-based random parameters Instantiation of variables, T This represents the number of times the instance is instantiated.

9. A seismic data unmixing system using a self-supervised Bayesian deep learning network, characterized in that, include: The matrix module employs a random time jitter strategy to construct the aliasing matrix. Through the effective seismic data to be separated Multiplying in the common detection domain yields aliased seismic data. And introduce random noise factor ; The solver module, based on the aliasing matrix obtained from the matrix module... The physical meaning of this will be used to solve the problem of separating effective seismic data. The process can be viewed as solving an underdetermined inversion optimization problem; The estimation module, based on the solution module, adopts a statistical inference framework by analyzing the parameters. Provide prior information and set parameters There is a prior probability distribution Find the maximum likelihood estimate of the parameter to be solved; Introducing the module, based on the estimation module, the maximum a posteriori estimate is... The introduction of prior and post-probability maximum likelihood estimation introduces uncertainty into the network model parameters; let the network model parameters be... Following a Gaussian distribution maximizes this uncertainty, and under a Gaussian distribution, the posterior and conjugate prior distributions of the weight parameters also follow a Gaussian distribution. (Analysis formula...) Japanese style The maximum a posteriori estimate is The introduction of prior maximum likelihood estimation To achieve this, a self-supervised learning method based on a Bayesian neural network framework is adopted. In the Bayesian neural network, convolution is defined as a Bayesian convolutional layer, and the convolution kernel is treated as a random variable. Based on the prior distribution and observed data, the posterior distribution is solved using Bayesian inference to obtain a probability distribution describing the uncertainty of the convolution result. The size of the target data is... H × W × C , H Indicates the number of rows or height of the data matrix. W Indicates the number of columns or width of the data matrix. C This indicates the number of channels in the data matrix; seismic data. C =1, input is ( H / 32)×( W The (32)×128 Bayesian neural network is a decoder containing five decoding blocks. The first four blocks sequentially connect an upsampling layer with a scaling factor of 2 and two Bayesian convolutional layers, with Leaky ReLU introduced between the convolutional layers to provide non-linearity. Each of the two Bayesian convolutional layers has 128 channels. The last decoding block contains an upsampling layer with a scaling factor of 2 and three output channels of 64, 32, and... C The Bayesian convolutional layers are also modified by inserting two LeakyReLU layers between them and adding a Sigmoid layer at the end. The characterization module, based on the introduction module, uses a Bayesian network-based method to learn an approximation of the minimum error estimate. Let's assume we choose... L 2-norm for effective seismic data and maximum a posteriori estimation The interval error is characterized using the joint distribution of independent normal distributions. approximate ; The training module, based on variational inference, is obtained using the characterization module. The joint distribution is estimated to have approximately the minimum error in the mean. By minimizing the network's predicted output The distance between the two parameters is estimated using the minimum error estimation method, and an unsupervised Bayesian neural network is trained. The prior distribution of the model parameters is assumed to be... With zero mean and standard deviation The independent and identically distributed normal distribution approximates it; The output module, based on the results obtained from the training module, performs unsupervised Bayesian neural network training. Following the generative model concept, it inputs an aliasing matrix. and the already aliased common detection point gather An approximate estimate of the effective signal is achieved using a randomly generated matrix vector, yielding the estimated distribution parameters. and Then, the posterior probability distribution is obtained. approximation Monte Carlo sampling is used to obtain an approximate estimate of the network; after obtaining the estimated distribution parameters, the mixed seismic gathers to be unmixed are used as the input of the network to obtain the unmixed seismic data.

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