CN114236610B - Iterative seismic data unmixing method and system based on depth convolution network prior - Google Patents
Iterative seismic data unmixing method and system based on depth convolution network prior Download PDFInfo
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Abstract
The invention discloses an iterative seismic data unmixing method and system based on depth convolution network prior, which reads aliasing acquisition seismic data and an aliasing operation operator; introducing an auxiliary variable by using an ADMM algorithm, processing input seismic data by using a RealSN-DnCNN network, optimally solving the auxiliary variable by using network output and gradient descent, and alternately updating a seismic data target signal by using network output and an auxiliary variable parameter; and repeating until the unmixing is completed. The method can fully utilize the public seismic data set as a training set to fully train the CNN, thereby greatly improving the generalization capability and the industrial practicability of the network; the trained CNN is used as a solver of an optimization subproblem in an ADMM iterative framework, and effective signals can be recovered from aliasing acquired seismic data with high fidelity.
Description
Technical Field
The invention belongs to the technical field of seismic exploration data processing, and particularly relates to an iterative seismic data unmixing method and system based on depth convolution network prior.
Background
Seismic aliasing acquisition is an efficient seismic acquisition technique. The traditional seismic data acquisition needs a long time to acquire subsequent migration and inversion data, and the cost is high. In order to improve the acquisition efficiency, the aliasing acquisition of the seismic data plays an important role in recent years, and the method can excite the seismic source for many times at different spatial positions within a short time, thereby fundamentally shortening the exploration time, reducing the economic cost and even improving the data quality. However, this acquisition also causes mutual interference between the effective seismic signals, which presents a great challenge to the post-conventional processing and imaging workflow. In order to make the aliasing acquisition technique practical, it is necessary to study the unmixing method.
In recent years, deep learning strategies have played an important role in geophysical seismic data processing. In 2014, zhang et al proposed a Kernel Regularization Least Square (KRLS) method for fault detection in seismic recording, and a significant result was obtained by constructing and optimizing a network using KRLS; in 2017, jia and Ma propose to use linear interpolation data and raw data as network input and output, respectively, and use Support Vector Regression (SVR) to obtain the relationship between input and output, achieving effective seismic interpolation. Data-driven methods based on deep learning techniques have also been introduced into the field of seismic data unmixing. In particular, in 2020, sun et al collected 2 million practical examples, training a Convolutional Neural Network (CNN) for seismic data separation; zu et al embed the network trained with the synthetic and actual datasets into an iterative framework to further improve the unmixing effect. Although the above unmixing methods show excellent performance, the effectiveness of these techniques relies on a priori assumptions about the useful signal and often cannot accommodate different seismic data with highly complex structures.
The prior art is as follows:
deep neural network based unmixing. The method constructs a deep neural network framework that is trained using aliased data as input and unaliased data as output. And applying the trained network to the aliasing seismic data, and iteratively realizing the unmixing of the seismic data.
The prior art has the following disadvantages:
1. the target mapping of the network learning is complex, and great cost is needed when the seismic data with a highly complex structure are processed;
2. depending on the choice of training data set and manual parameters, there are limitations in industrial applications.
Disclosure of Invention
The technical problem to be solved by the invention is to provide an iterative seismic data unmixing method and system based on depth convolution network prior aiming at the defects in the prior art, and train a CNN Gaussian denoiser by using a public seismic data set so as to avoid the defect of generalization capability and use the CNN Gaussian denoiser as a regular term substitute for the optimization problem. In addition, the invention provides a RealSN-DnCNN framework, so that the theoretical convergence of the whole algorithm is ensured.
The invention adopts the following technical scheme:
an iterative seismic data unmixing method based on deep convolutional network prior is characterized by comprising the steps of collecting data from a public seismic data set by using an aliasing collection mode to serve as a training set, conducting Gaussian denoising training on a convolutional neural network by using the training set to obtain a convolutional neural network Gaussian denoiser, then inserting the trained convolutional neural network Gaussian denoiser into an iterative updating frame of an ADMM method, introducing auxiliary variables, processing seismic data by using a RealSN-DnCNN network, optimally solving the auxiliary variables by selecting gradient descent to obtain optimal parameters, and alternately updating target signals of the seismic data by using RealSN-DnCNN network output and the optimal parameters of the auxiliary variables through the iterative updating frame; and realizing seismic data unmixing.
Specifically, the aliasing acquisition mode specifically includes:
the multiple seismic sources are sequentially fired with a given aliasing operator to alias all of the individual source data for reception by the same receiver array, with the aliasing acquiring the seismic data for a fixed receiver.
Further, the aliasing acquisition seismic data b is:
b＝Γd
wherein Γ is an aliasing operator constructed using different random time delay sequences, and d is a vector representation of a seismic data common-receiving point gather.
Specifically, the RealSN-DnCNN network is utilized to process seismic data, and the seismic data variable d is solved in a closed mode (k+1) The output data of the iterative update RealSN-DnCNN network is as follows:
d (k+1) ＝(Γ T Γ+ρI) -1 (Γ T b+ρ(x (k+1) +u (k) ))
wherein, gamma is an aliasing operator T For the transposition of aliasing operators, rho is a non-negative penalty coefficient, I is a unit matrix, b is aliasing acquired seismic data, and x (k+1) Auxiliary variable for the (k + 1) th update, u (k) Is the intermediate variable of the kth update.
Specifically, the step of alternately updating the seismic data target signal by using the network output and the auxiliary variable parameter specifically comprises the following steps:
aliasing the acquired seismic data b, aliasing operator Γ, and pseudo-unmixed seismic data d (0) ＝Γ T b, pre-training a RealSN-DnCNN prior model, total iteration number K and intermediate variable u (0) =0; updating the iteration number k for each iteration and calculating the auxiliary variable x (k+1) Seismic data variable d (k+1) And intermediate variable u (k+1) (ii) a Terminating when the iteration number K = K; outputting the unmixing result x (K) 。
Further, the pre-training of the RealSN-DnCNN network specifically comprises:
using an SEG public seismic data set as a sample of a training set, using clean data v to construct a training sample, and introducing additive white Gaussian noise with standard deviation of sigma; and taking the noisy seismic data y = v + n as RealSN-DnCN network input and the residual y-v as expected output, so that the RealSN-DnCNN network automatically searches for an inversion mapping operator theta between the noisy seismic data and the residual to obtain a noise component.
Further, an auxiliary variable x (k+1) Seismic data variable d (k+1) And an intermediate variable u (k+1) The calculation is as follows:
u (k+1) ＝u (k) +x (k+1) -d (k+1)
wherein x ≈ d is an auxiliary variable, u is an introduced intermediate variable, denoiser (g) is denoising network prior, lambda is nonnegative weight, and rho is nonnegative penalty coefficient.
Specifically, the RealSN-DnCNN network is of a 20-layer structure, the convolution layers of the RealSN-DnCNN network adopt 64 convolution kernels of which the sizes are 3 × 3, zero padding is used, residual mapping is learned by using the RealSN-DnCNN network, three additional single-sample convolution operations are introduced into each layer in each training step by the RealSN, and a loss function is optimized by using a random gradient descent method.
Further, the loss function loss is:
wherein the content of the first and second substances,
for residual mapping, <' >>
N pairs of training samples.
Another technical solution of the present invention is an iterative seismic data unmixing system based on a deep convolutional network prior, comprising:
the training module is used for constructing a training set by using the public seismic data set in an aliasing acquisition mode, and performing Gaussian denoising training on the convolutional neural network by using the training set to obtain a convolutional neural network Gaussian denoiser;
the demixing module is used for inserting the trained convolutional neural network Gaussian denoiser into an iterative updating frame of the ADMM method, introducing auxiliary variables, processing seismic data by using a RealSN-DnCNN network, optimally solving the auxiliary variables by selecting gradient descent to obtain optimal parameters, and alternately updating target signals of the seismic data by using the RealSN-DnCNN network output and the optimal parameters of the auxiliary variables through the iterative updating frame; and realizing seismic data unmixing.
Compared with the prior art, the invention has at least the following beneficial effects:
the invention discloses an iterative seismic data unmixing method based on deep convolutional network prior, which integrates a convolutional neural network Gaussian noise eliminator as the prior of seismic data unmixing, uses a public seismic data set as a training set to perform CNN Gaussian noise elimination training, then inserts the trained CNN Gaussian noise eliminator into an iterative update frame of an ADMM algorithm, and adaptively realizes seismic data unmixing. And (3) taking advantages of a model-based driving method and a data-based driving method, modeling the solution-mixing process into an inverse problem, and performing optimized iterative solution by using an ADMM algorithm.
Furthermore, the aliasing acquisition seismic data set used in the invention sequentially excites a plurality of seismic sources by reasonably designing the aliasing operation operator, so that all single seismic source data are aliased and then received by the same receiver array, and for a fixed receiver, the aliasing acquisition seismic data greatly saves the seismic data acquisition time.
Furthermore, noise influence is neglected, and incoherent components are introduced into aliasing data by the random time delay sequence, so that the aliasing acquisition data can be represented in a noise form in a specific transformation domain, and an objective function of the unmixing problem is simplified.
Furthermore, the network output and the auxiliary variable parameters are used for alternately updating the seismic data target signal, so that the efficiency of the algorithm is improved, and the reliability of the unmixing result is improved, specifically: aliasing acquisition seismic data b, aliasing operator Γ, and pseudo-unmixed seismic data d (0) ＝Γ T b, pre-training a RealSN-DnCNN prior model, total iteration number K and intermediate variable u (0) =0; updating the iteration number k for each iteration and calculating the auxiliary variable x (k+1) Seismic data variable d (k+1) And intermediate variable u (k+1) (ii) a Terminating when the iteration number K = K; outputting the unmixing result x (K) 。
Furthermore, the network output is used for selecting gradient descent to optimally solve the auxiliary variable, so that a large operation amount caused by inversion is avoided.
Further, pre-training the RealSN-DnCNN network in the iterative framework to obtain a prior gaussian noise remover, specifically: using an SEG public seismic data set as a sample of a training set, using clean data v to construct the training sample, and introducing additive white Gaussian noise with standard deviation sigma; and taking the noisy seismic data y = v + n as RealSN-DnCN network input and the residual y-v as expected output, so that the RealSN-DnCNN network automatically searches for an inversion mapping operator theta between the noisy seismic data and the residual to obtain a noise component.
Further, under the framework of ADMM algorithm, the unmixing problem can be converted into the auxiliary variable x (k+1) Seismic data variable d (k+1) And intermediate variable u (k+1) Is solved iteratively.
Furthermore, the RealSN-DnCNN network is of a 20-layer structure, the convolution layer of the RealSN-DnCNN network adopts 64 convolution kernels with the size of 3 x 3, zero padding is used, the RealSN-DnCNN network is used for learning residual mapping, three additional single-sample convolution operations are introduced into each layer in each training step by the RealSN, a random gradient descent method is used for optimizing a loss function, and overall network convergence is effectively guaranteed.
Further, the loss function loss with better effect is used for processing the non-Gaussian seismic data.
In conclusion, the unmixing process is regarded as an inversion problem, the ADMM algorithm is used for optimization, the trained RealSN-DnCNN network is used as a prior item, the aliasing seismic data are iteratively solved, the influence of manual parameter selection on the unmixing method is reduced, and the efficiency and the reliability of the unmixing algorithm are improved.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a RealSN-DnCNN network structure for use with the present invention;
FIG. 2 is a schematic diagram of a portion of the SEG public data set data employed in the present invention;
fig. 3 is a diagram of clean effective signals of a simulated seismic data set, where (a) is a clean effective signal of a 32 th common receiving point gather in the simulated seismic data set acquired by aliasing provided by the embodiment of the present invention, (b) is pseudo-unmixed data obtained by performing aliasing on the effective signal shown in fig. 3A, (c) is an effective signal of a common receiving point gather of the simulated seismic data acquired by aliasing processed by the method of the present invention, and (d) is a difference between fig. 3 (a) and fig. 3 (c);
FIG. 4 is a schematic diagram of an aliasing acquisition actual seismic dataset employed by the present invention;
fig. 5 is a clean effective signal of an actual seismic dataset, where (a) is a clean effective signal obtained by aliasing the 32 th common receiving point gather in the actual seismic dataset according to the embodiment of the present invention, (b) is pseudo-unmixed data obtained by performing aliasing on the effective signal shown in fig. 5 (a), (c) is an effective signal obtained by processing the aliasing acquisition actual seismic dataset common receiving point gather according to the method of the present invention, and (d) is a difference value between fig. 5 (a) and fig. 5 (c);
FIG. 6 is a block flow diagram of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, not all, embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In the description of the present invention, it should be understood that the terms "comprises" and/or "comprising" indicate the presence of the stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof.
It is also to be understood that the terminology used in the description of the invention herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the invention. As used in the specification of the present invention and the appended claims, the singular forms "a," "an," and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise.
It should be further understood that the term "and/or" as used in this specification and the appended claims refers to and includes any and all possible combinations of one or more of the associated listed items.
Various structural schematics according to the disclosed embodiments of the invention are shown in the drawings. The figures are not drawn to scale, wherein certain details are exaggerated and possibly omitted for clarity of presentation. The shapes of various regions, layers and their relative sizes and positional relationships shown in the drawings are merely exemplary, and deviations may occur in practice due to manufacturing tolerances or technical limitations, and a person skilled in the art may additionally design regions/layers having different shapes, sizes, relative positions, according to actual needs.
The invention provides an iterative seismic data unmixing method based on a deep convolution network prior, which trains a CNN network by using a public seismic data set, integrates the trained neural network Gaussian denoising prior into an ADMM algorithm, and realizes the aim of unmixing seismic data through iterative optimization.
Referring to fig. 6, the iterative seismic data unmixing method based on depth convolution network prior of the present invention includes the following steps:
s1, reading aliasing acquisition seismic data and an aliasing operation operator;
in seismic data aliasing acquisition, a plurality of seismic sources are excited in a certain sequence by using a given aliasing operator, so that all single seismic source data are aliased and then received by the same receiver array. Ignoring the noise effects, for a fixed receiver, the aliased acquisition seismic data b is modeled as:
b＝Γd
wherein Γ is an aliasing operator constructed using different random time delay sequences, and d is a vector representation of a seismic data common-receiving point gather.
S2, introducing auxiliary variables by using an ADMM algorithm, processing input seismic data by using a RealSN-DnCNN network, optimally solving the auxiliary variables by using network output and selection gradient reduction, and alternately updating seismic data target signals by using network output and auxiliary variable parameters;
the method for alternately updating the seismic data target signal by utilizing the network output and the auxiliary variable specifically comprises the following steps:
initialization: aliasing acquisition seismic data b, aliasing operator Γ, and pseudo-unmixed seismic data d (0) ＝Γ T b, pre-training a RealSN-DnCNN prior model, total iteration times K and an intermediate variable u (0) ＝0；
Iteration: updating the iteration number k for each iteration and calculating
u (k+1) ＝u (k) +x (k+1) -d (k+1)
Wherein x ≈ d is an auxiliary variable, u is an introduced intermediate variable, denoiser (g) is denoising network prior, lambda is nonnegative weight, and rho is nonnegative penalty coefficient;
and (4) termination conditions: when the iteration times K = K;
and (3) outputting: unmixing result x (K) 。
The steps of processing input seismic data by using the RealSN-DnCNN network are as follows:
constructing a RealSN-DnCNN network model, wherein the DnCNN network is a 20-layer structure, 64 convolution kernels with the size of 3 x 3 are adopted in each convolution layer, zero padding is used for keeping the size of input and output, and the network learns residual error mapping; the RealSN-DnCNN network is a result obtained by performing spectrum normalization improvement on the DnCNN network convolution layer so as to more accurately constrain the Lipschitz constant of the network; specifically, realSN introduces three additional single-sample convolution operations for each layer in each training step; during each forward pass of the neural network, the RealSN sequentially performs:
step1: performing a convolution operation using a linear convolution kernel;
step2: carrying out normalization processing on the linear convolution kernel by utilizing the estimated spectrum norm;
pre-training the RealSN-DnCNN network, using an SEG public seismic data set as a sample of a training set, using clean data v in the SEG public seismic data set to construct a training sample, and introducing additive white Gaussian noise with standard deviation of sigma; taking the noisy seismic data y = v + n as network input and the residual y-v as expected output, and enabling the network to automatically find an inversion mapping operator theta between the noisy seismic data and the residual so as to obtain a noise component and realize the aim of signal-noise separation;
the loss function was optimized using a random gradient descent method:
wherein the content of the first and second substances,
for residual mapping, <' > based on>
N pairs of training samples.
The output of the RealSN-DnCNN network adopts gradient descent to optimally solve the auxiliary variables as follows:
and iteratively updating the RealSN-DnCNN network output data by solving the following formula through optimization:
solving by a closed form to obtain:
d (k+1) ＝(Γ T Γ+ρI) -1 (Γ T b+ρ(x (k+1) +u (k) ))
since the aliasing operator has a large rank, the inversion of the corresponding matrix consumes a large amount of resources, and therefore the optimization problem is solved by using a gradient descent method.
And S3, repeating the step S2 until the unmixing is finished.
In another embodiment of the present invention, an iterative seismic data unmixing system based on a depth convolution network prior is provided, where the system can be used to implement the iterative seismic data unmixing method based on a depth convolution network prior, and specifically, the iterative seismic data unmixing system based on a depth convolution network prior includes a training module and a unmixing module.
The training module constructs a training set by using an aliasing acquisition mode and utilizing a public seismic data set, and performs Gaussian denoising training on the convolutional neural network by using the training set to obtain a convolutional neural network Gaussian denoiser;
the demixing module is used for inserting the trained convolutional neural network Gaussian denoiser into an iterative updating frame of the ADMM method, introducing auxiliary variables, processing seismic data by using a RealSN-DnCNN network, optimally solving the auxiliary variables by selecting gradient descent to obtain optimal parameters, and alternately updating target signals of the seismic data by using the RealSN-DnCNN network output and the optimal parameters of the auxiliary variables through the iterative updating frame; and realizing seismic data unmixing.
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are some, but not all, embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The iterative seismic data unmixing method based on the depth convolution network prior is applied to the aliasing acquisition seismic data; the extensive experimental results on the synthetic data and the field data show that the method can realize the unmixing target of aliasing acquisition of the seismic data with higher effective signal fidelity.
Please refer to fig. 1, which is a RealSN-DnCNN network structure used in the present invention, the RealSN-DnCNN network has 20 layers, the convolution layer adopts 64 convolution kernels of 3 × 3 size, and zero padding is used to keep the input and output size, the network learns the residual mapping; the convolutional layer is modified for spectral normalization to more accurately constrain the Lipschitz constants of the network.
Please refer to fig. 2, which is a schematic diagram of a part of data of an SEG public data set used in the present invention, and the data set is used to pre-train a deep convolutional network.
Referring to fig. 3, a clean effective signal of the 32 th common receive point gather in the simulated seismic data set for aliasing acquisition according to the embodiment of the invention is shown in fig. 3 (a), and it can be seen that fig. 3 (a) has similar features to fig. 2. Fig. 3 (b) shows pseudo-downmix data obtained by aliasing the effective signal shown in fig. 3 (a), which contains a large amount of noise components. FIG. 3 (C) is a graph of the effective signal of the common receiving point gather of the aliased acquisition simulated seismic data processed by the method of the invention, and FIG. 3 (d) is the difference between FIG. 3 (a) and FIG. 3C. Comparing fig. 3 (a) with fig. 3 (c), it can be seen that the present invention can effectively achieve high-precision unmixing of aliased acquisition simulated seismic data; as can be seen from fig. 3 (d), the present invention effectively protects the effective signal while achieving the object of unmixing.
Referring to fig. 4, a schematic diagram of an actual seismic data set acquired by aliasing according to the present invention is shown, where the spatial sampling interval of each sample of the data set is 12.5 meters, and the time sampling interval is 2 milliseconds; the number of sampling points per trace of the simulated seismic data set is 512.
Referring to fig. 5, fig. 5 (a) shows a clean effective signal of the 32 th common receiving point gather in the actual seismic data set acquired by aliasing according to the embodiment of the present invention, and it can be seen that fig. 5 (a) has similar features to fig. 2. Fig. 5 (b) shows pseudo-downmix data obtained by performing aliasing on the effective signal shown in fig. 5 (a), which contains a large amount of noise components. FIG. 5 (c) is the effective signal of the common receiving point gather of the aliasing acquisition actual seismic data obtained by the processing of the method of the invention, and FIG. 5 (d) is the difference between FIG. 5 (a) and FIG. 5 (c). Comparing fig. 5 (a) with fig. 5 (c), it can be seen that the present invention can effectively achieve unmixing of aliasing acquired actual seismic data; as can be seen from fig. 5 (d), the present invention achieves the object of unmixing without significantly impairing the effective signal.
The model and actual data calculation example shows that the iterative seismic data unmixing method based on the depth convolution network prior improves the depth network and can realize seismic data high-quality unmixing in the iterative updating process of the ADMM algorithm.
In summary, the iterative seismic data unmixing method and system based on the depth convolution network prior of the invention have the following advantages:
1) The method uses the CNN network as the prior of the solution mixing optimization subproblem, and can learn the mapping function in a self-adaptive manner;
2) The trained CNN is used in the ADMM algorithm framework, so that the operation cost is greatly reduced, and the algorithm can be converged more quickly.
As will be appreciated by one skilled in the art, embodiments of the present application may be provided as a method, system, or computer program product. Accordingly, the present application may take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Furthermore, the present application may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, and the like) having computer-usable program code embodied therein.
The present application is described with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the application. It will be understood that each flow and/or block of the flowchart illustrations and/or block diagrams, and combinations of flows and/or blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer program instructions. These computer program instructions may 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, create means for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be stored in a computer-readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer-readable memory produce an article of manufacture including instruction means which implement the function specified in the flowchart flow or flows and/or block diagram block or blocks.
These computer program instructions may also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart flow or flows and/or block diagram block or blocks.
The above-mentioned contents are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modification made on the basis of the technical idea of the present invention falls within the protection scope of the claims of the present invention.
Claims (10)
1. An iterative seismic data unmixing method based on depth convolution network prior is characterized in that a training set is constructed by using a public seismic data set in an aliasing acquisition mode, and the training set is used for carrying out Gaussian denoising training on a convolution neural network to obtain a convolution neural network Gaussian denoiser; inserting the trained convolutional neural network Gaussian noise eliminator into an iterative update frame of an ADMM method, introducing an auxiliary variable, processing seismic data by using a RealSN-DnCNN network, optimally solving the auxiliary variable by selecting gradient descent to obtain an optimal parameter, and alternately updating a target signal of the seismic data by using the RealSN-DnCNN network output and the optimal parameter of the auxiliary variable through the iterative update frame to realize seismic data unmixing.
2. The iterative seismic data unmixing method based on the deep convolutional network prior as claimed in claim 1, wherein the aliasing acquisition mode specifically is:
the multiple seismic sources are sequentially fired with a given aliasing operator to alias all of the individual source data for reception by the same receiver array, with the aliasing acquiring the seismic data for a fixed receiver.
3. The iterative seismic data unmixing method based on the deep convolutional network prior of claim 2, wherein the aliasing acquisition seismic data b is:
b＝Γd
wherein, Γ is an aliasing operator, and d is a vector representation of the seismic data common receiving point gather.
4. The iterative seismic data unmixing method based on deep convolutional network prior of claim 1, wherein the seismic data are processed by using a RealSN-DnCNN network, and a seismic data variable d is solved in a closed form (k+1) The output data of the iterative update RealSN-DnCNN network is as follows:
d (k+1) ＝(Γ T Γ+ρI) -1 (Γ T b+ρ(x (k+1) +u (k) ))
wherein, gamma is an aliasing operator T For the transposition of aliasing operators, rho is a non-negative penalty coefficient, I is a unit matrix, b is aliasing acquired seismic data, and x (k+1) Auxiliary variable, u, updated for the (k + 1) th iteration (k) Intermediate variables updated for the kth iteration.
5. The iterative seismic data unmixing method based on the deep convolutional network prior as claimed in claim 1, wherein the alternately updating seismic data target signals by using the network output and the auxiliary variable parameters specifically comprises:
aliased acquisition seismic data bOperator of aliasing operation gamma, pseudo-unmixed seismic data d (0) ＝Γ T b, pre-training a RealSN-DnCNN prior model, total iteration times K and an intermediate variable u (0) =0; the iteration number k of each iteration update is calculated, and an auxiliary variable x is calculated (k+1) Seismic data variable d (k+1) And intermediate variable u (k+1) (ii) a Terminating when the iterative updating times K = K; outputting the unmixing result x (K) 。
6. The iterative seismic data unmixing method based on deep convolutional network prior of claim 5, wherein the pre-training of the RealSN-DnCNN network specifically comprises:
using an SEG public seismic data set as a sample of a training set, using clean data v to construct the training sample, and introducing additive white Gaussian noise with standard deviation sigma; and taking the noise-containing seismic data y = v + n as the input of the RealSN-DnCNN network, and taking the residual error y-v as the expected output, so that the RealSN-DnCNN network automatically searches for an inversion mapping operator theta between the noise-containing seismic data and the residual error to obtain a noise component.
7. The method of claim 5, wherein the auxiliary variable x is an integer multiple of the prior of the deep convolutional network (k+1) Seismic data variable d (k+1) And intermediate variable u (k+1) The calculation is as follows:
u (k+1) ＝u (k) +x (k+1) -d (k+1)
wherein x ≈ d is an auxiliary variable, u is an introduced intermediate variable, denoiser (·) is a denoising network prior, λ is nonnegative weight, ρ is a nonnegative penalty coefficient, and d is (k) Updating result for k iteration of seismic data variable number u (k) And d is the vector representation of the seismic data common receiving point gather, and b is aliasing acquired seismic data.
8. The iterative seismic data unmixing method based on the deep convolutional network prior of claim 1, wherein the RealSN-DnCNN network has a 20-layer structure, the convolutional layers of the RealSN-DnCNN network adopt 64 convolutional kernels of 3 × 3 size, zero padding is used, residual mapping is learned by using the RealSN-DnCNN network, three additional single-sample convolution operations are introduced into each layer in each training step by the RealSN, and a loss function is optimized by using a random gradient descent method.
9. The method of iterative seismic data unmixing based on deep convolutional network priors of claim 8, wherein the loss function loss is:
wherein the content of the first and second substances,
for residual mapping, <' > based on>
For N pairs of training samples, y i Input sample data for the ith network, v i And the ith label data corresponding to the network input is used, theta is a network weight parameter, and y is noisy seismic data.
10. An iterative seismic data unmixing system based on a deep convolutional network prior, comprising:
the training module is used for constructing a training set by using the public seismic data set in an aliasing acquisition mode, and performing Gaussian denoising training on the convolutional neural network by using the training set to obtain a convolutional neural network Gaussian denoiser;
the demixing module is used for inserting the trained convolutional neural network Gaussian denoiser into an iterative updating frame of the ADMM method, introducing auxiliary variables, processing seismic data by using a RealSN-DnCNN network, optimally solving the auxiliary variables by selecting gradient descent to obtain optimal parameters, and alternately updating target signals of the seismic data by using the RealSN-DnCNN network output and the optimal parameters of the auxiliary variables through the iterative updating frame; and realizing seismic data unmixing.
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