CN111368680A - Wave atom transformation-based deep learning anti-aliasing seismic data regularization method - Google Patents

Abstract

The invention belongs to the technical field of geoscience, and particularly relates to a deep learning anti-aliasing seismic data regularization method based on wave-atom transformation, which comprises the following steps of 1, preparing a training data set; 2. preparing a wave atomic domain sample label; 3. network input and label setting; 4. setting a deep learning network model G structure; 5. setting a loss function; 6. training a network model; 7. and (5) carrying out regularized testing on the seismic data. According to the good distribution characteristics of the seismic data in the wave atomic domain, a space domain and wave atomic domain combined learning deep convolution neural network model is established, the seismic data are regularized by combining the characteristics of the space domain and the wave atomic domain, the training evaluation indexes of the model adopt space domain and wave atomic domain errors and f-k domain errors to jointly constrain regularization errors, network parameters are fed back and adjusted, and the accuracy and generalization capability of the seismic data regularization network model are improved.

Description

Wave atom transformation-based deep learning anti-aliasing seismic data regularization method

The technical field is as follows:

the invention belongs to the technical field of geoscience, and particularly relates to a deep learning anti-aliasing seismic data regularization method based on wave-atom transformation.

Background art:

at present, with the rapid development of big data and artificial intelligence, the problems of the traditional seismic data rule method are expected to be solved by using a new technology. The purpose of seismic exploration is to obtain accurate images of the subsurface formations, and ideally the sampling of the seismic wavefield should be regular and dense. If modern instrumentation is used to perform dense sampling in a specific time space, this is technically and computationally feasible, but since the cost of the field data acquisition process accounts for more than 80% of the overall seismic exploration cost, the seismic data are often sparsely sampled in the spatial direction due to economic considerations, which results in less data being acquired; in addition, due to the influence of surface obstacles and instrument hardware faults, bad acquisition channels can be caused; in addition, during marine seismic data acquisition, plume drift of the cable can also cause uneven sampling. These can be attributed to the problem of seismic data irregularities that can cause errors in subsequent processing and interpretation and even false results.

Seismic data regularization is one of the basic problems of seismic data processing, and expert and scholars at home and abroad begin to research the problem from the eighties of the last century and develop methods. These methods can be basically classified into the following six categories: the method comprises a regularization technology based on coherent dip interpolation, a regularization technology based on filtering, a regularization technology based on wave field continuation operators, a regularization technology based on a transform domain, a regularization technology based on compressed sensing and a regularization technology based on deep learning.

In the regularization method, the regularization technology based on compressed sensing and the regularization technology based on machine learning are not limited by geological prior information of the target block, and the regularization effect is only related to the characteristics of data, has high operation efficiency and is a hotspot of current research. The compression sensing-based regularization technology has the basic principle that irregular seismic data are regarded as a small number of signal projection values of complete seismic data, and accurate or approximate reconstruction of the data can be realized at a receiving end through a sparsity constraint regularization method, so that the bottleneck of the Nyquist sampling theorem is broken through. However, the method has the problems that in the process of solving the regularized ill-defined inverse problem, a sparse constraint optimization method is basically adopted, and the method is greatly influenced by data sparse prior, so that the result is unstable.

The basic principle of the regularization technology based on deep learning is that the distribution characteristics of seismic data of a target block are obtained through training of samples with large data volumes, and then the actual values of missing seismic channels at corresponding positions are predicted by utilizing the characteristics, so that the purpose of recovering the missing channels in irregular data is achieved. Chinese patent [ CN201910599289.6] adopts deep convolution to generate a confrontation network to train a training set, and adopts Wassertein distance as a training and judging index of a seismic data generation model; and reconstructing the seismic data by adopting a seismic data generation model, and optimizing the gradient of the objective function by adopting a back propagation algorithm and a standard gradient-based optimization algorithm so as to minimize the difference between the reconstructed data and the missing data. The existing mode solves the problem that the traditional seismic data reconstruction algorithm needs to meet the Nyquist sampling theorem limit; the problem that sparse bases of seismic data reconstructed by using a compressed sensing algorithm are difficult to select is solved, but the problem of insufficient spatial domain feature extraction is not solved.

In the current seismic data regularization method, the regularization technology based on deep learning is a hotspot which is widely concerned at present and can also obtain superior results compared with the traditional method, but the current scheme has the following problems: in the process of obtaining the sample characteristics, a spatial convolution mode is basically adopted to obtain spatial characteristic information, good characteristics of seismic data in certain transform domains are ignored, errors are calculated by mostly single distances in the aspect of training and judging index function definition, and the errors are not considered from the perspective of frequency spectrum, for example, chinese patent [ CN201910599289.6 ]. These defects may cause the reconstruction quality to fail to achieve the ideal effect in the complex terrain, and even cause the aliasing phenomenon, so that the regularization result is too smooth, and the imaging effect is not ideal.

The current regularization method for deep learning all singly utilizes the information of a space domain or a transform domain, combines the space domain and a wave atomic domain on the basis of deep learning, establishes a deep convolution neural network model for combined learning according to the property that the wave atomic domain has good texture surface feature depiction, enhances the robustness of the network model, improves the accurate reconstruction of seismic data, and highlights the texture detail feature of the seismic data

The invention content is as follows:

the invention aims to provide an anti-aliasing seismic data regularization method and a flow for time-space domain and wave atomic domain joint deep learning.

The technical scheme adopted by the invention is as follows: the seismic data regularization method comprises the following steps:

step one, training data set preparation:

performing spatial transformation processing on samples of seismic data in a training set, wherein the method comprises rotating angle and mirror image turning, increasing sample data of a data set, and cutting the sample data into slice data x with the size of 256 × 256, wherein the slice data x is used as the minimum unit of a training sample;

irregular seismic data are simulated by taking seismic channels with the extraction proportion r from complete seismic data as empty channels, the extraction method is to respectively simulate 3 irregular situations by utilizing complete random extraction, partial random extraction and uniform extraction methods, the irregular situations of the bad channels are simulated and collected by random extraction, the irregular situations of simulated uneven sampling are randomly extracted in partial areas, and the irregular situations of sparse sampling are simulated by the uniform extraction method;

copying 15 parts of each seismic data slice, dividing the 15 parts of seismic data slices into 3 groups, and respectively simulating samples of the 3 kinds of irregular data, wherein 5 parts of each group are respectively extracted under 5 different proportions r by adopting a corresponding extraction method, namely r is respectively 10%, 20%, 30%, 40% and 50%, generating blank seismic channels, and obtaining a plurality of irregular seismic data slice samples y with corresponding labels of x;

step two: wave atomic domain sample label preparation:

the wave atom transformation is completed by adopting a tool box (http:// www.waveatom.org /) code, the parameters of the transformation are (p ═ direct ', pat ═ p'), each slice data x generates 2 wave atom domain slice coefficients of 256 × 256, and the slice coefficients are respectively set as c₁And c₂；

Step three: network input and tag setting:

taking the irregular seismic data slice data y obtained in the step one as input, and taking the original seismic slice data x obtained in the step one and the slice coefficient c obtained in the step two₁And c₂Respectively serving as labels, and training a joint learning network model G;

step four: and (3) setting the structure of the deep learning network model G:

the deep learning network model G is divided into 2 sub-networks which are respectively a feature extraction network and a wave source sub-system number prediction network, irregular data is input as the input of the feature extraction network, and the input is subjected to a series of operations such as convolution, normalization, activation and the like; then, estimating corresponding wave atomic coefficients in a wave atomic coefficient prediction network, and generating pre-measured rule data by utilizing inverse transformation of a wave atomic coefficient matrix;

the network model is set as:

(1) feature extraction subnetwork

The sub-network is used for taking irregular seismic data as input of the network and extracting a feature map of the data, wherein the size of each layer of convolution kernels of the convolution network is 3 × 3, the step length is 1, the input data and the output data of each layer are the same, the calculation complexity is reduced, the feature map after convolution is subjected to normalization and activation functions, and then the next layer of convolution operation is carried out, 3 operations of the convolution layer, the normalization layer and the activation functions are defined into one group, each two groups are used as a residual block and total 5 residual blocks, the number of the convolution kernels in each residual block is 32, 64, 64, 128 and 256 in sequence, and the jump connection is arranged between every two residual blocks by utilizing the characteristic of residual learning;

(2) wave source sub-coefficient prediction sub-network

Setting the sizes of all convolution kernels to be 3 × 3, setting the step length to be 1 and filling the step length to be 1, respectively predicting coefficient matrixes corresponding to two wave atom sub-bands by the two parallel sub-networks, and finally performing inverse transformation on the predicted wave atom coefficients to generate time-space domain regular data;

step five: setting a loss function:

joint error function of joint spatial, wave atomic and fourier domain loss errors:

loss_total＝μloss_waveatom+νloss_space+ηloss_f-k

loss_spaceis defined as:

x is real seismic data, and x' is prediction regularization data;

it is difficult to capture the frequency texture details of seismic data due to the mean square error constraint of the spatial domain in order to improve the maximumFinally, the data detail texture quality is regulated, and wave atom loss is introduced to help the recovery and reconstruction of the data texture; let C ═ C₁,c₂) And

respectively representing real and predicted wave atomic coefficients, proposing the loss based on a wave atomic domain as a wave atomic domain mean square error, and capturing the detail information of a wave source sub-domain; is defined as:

in order to prevent the aliasing phenomenon from occurring in the regularization result, original rule data X and rule data X ' generated by prediction are subjected to Fourier transform to obtain X and X ', and loss error loss of the original rule data X and the rule data X ' is calculated_f-kIs defined as:

joint error function: loss_total＝μloss_waveatom+νloss_space+ηloss_f-kWherein loss_waveatomThe mean square error of the wave atomic domain prediction coefficient and the actual coefficient is used for improving the recovery of texture details; loss_spacePredicting the mean square error of the data and the actual data for the traditional spatial domain, and using the mean square error to constrain the error of the seismic data of the spatial domain; loss_f-kIs f-k domain error and is used for eliminating aliasing, mu, v and η are balance factors;

step six: training a network model:

inputting the irregular samples obtained in the first step to the fifth step into y, the original data label x and the wave atom decomposition coefficient c thereof₁And c₂The network outputs the corresponding wave atom prediction coefficient

And

and itGenerating spatial prediction data X' after inverse transformation, and obtaining the wave atomic domain error loss through Fourier transformation of the original rule data and the prediction data by X and X_waveatomError in spatial domain_spaceFourier domain error loss_f-kFinally, the joint error loss is obtained_totalAdjusting network parameters through forward transmission and backward feedback of the deep convolutional neural network, and storing the adjusted network parameters;

step seven: and (3) seismic data regularization testing:

organizing irregular seismic data in the test set into a slice seismic y, inputting the slice seismic y into a convolutional neural network model G with trained and adjusted parameters, and generating wave atomic domain coefficients

And

will be provided with

And

and performing wave-atom inverse transformation to obtain wave-atom domain predicted seismic data x', namely the regularized seismic data generated after restoration.

The invention has the beneficial effects that: the method comprises the steps of establishing a space domain and wave atomic domain combined learning deep convolution neural network model according to good distribution characteristics of seismic data in a wave atomic domain, regularizing the seismic data by combining the characteristics of the space domain and the wave atomic domain, and feeding back and adjusting network parameters by using space domain, wave atomic domain errors and f-k domain error combined constraint regularization errors as training and judging indexes of the model, so that the accuracy and the generalization capability of the seismic data regularization network model are improved. Compared with the prior art, the wave atomic domain deep learning convolution joint network structure is established in the technical scheme, the characteristics of seismic data in a space domain and a wave atomic domain are fully combined, the deep convolution network is trained, the generalization capability and the convergence capability of the network are improved, and the problem that the regularized data is partially fuzzy due to the fact that the prior art learns the characteristics caused by network parameters only through spatial domain characteristics or the combination of traditional transform domain characteristics such as wavelets and the like is solved. Compared with the prior art of the same type, the method has the good regularization effect of keeping the texture information of the seismic data and resisting the false frequency.

Description of the drawings:

FIG. 1 is a flow chart of a first embodiment;

FIG. 2 is a diagram of a joint learning network model according to the first embodiment;

FIG. 3 is a diagram of an optional original regular seismic data slice sample 1 according to the second embodiment;

FIG. 4 is a sample 2 diagram of an optional original regular seismic data slice according to the second embodiment;

FIG. 5 is a f-k domain spectrogram of seismic data slice sample 1 of example two;

FIG. 6 is a f-k domain spectrogram of seismic data slice sample 2 of example two;

FIG. 7 is a graph of irregular seismic data including 50% random missing traces according to example two;

FIG. 8 is a graph of sparsely sampled irregular seismic data including 50% uniformly missing traces according to example two;

FIG. 9 is a graph showing the result of the regularization process of the present method in the second embodiment 1;

FIG. 10 is a graph of the result of the regularization process of the present method in accordance with the second embodiment;

FIG. 11 is a graph of the f-k domain spectrum of the regularization processing result 1 of the method according to the second embodiment;

fig. 12 is a f-k domain spectrum diagram of the regularization processing result 2 of the method in the second embodiment.

The specific implementation mode is as follows:

example one

Referring to fig. 1 and 2, a deep learning anti-aliasing seismic data regularization method based on wave atom transformation is characterized in that: the seismic data regularization method comprises the following steps:

step one, training data set preparation:

performing spatial transformation processing on samples of seismic data in a training set, wherein the method comprises rotating angle and mirror image turning, increasing sample data of a data set, and cutting the sample data into slice data x with the size of 256 × 256, wherein the slice data x is used as the minimum unit of a training sample;

irregular seismic data are simulated by taking seismic channels with the extraction proportion r from complete seismic data as empty channels, the extraction method is to respectively simulate 3 irregular situations by utilizing complete random extraction, partial random extraction and uniform extraction methods, the irregular situations of the bad channels are simulated and collected by random extraction, the irregular situations of simulated uneven sampling are randomly extracted in partial areas, and the irregular situations of sparse sampling are simulated by the uniform extraction method;

copying 15 parts of each seismic data slice, dividing the 15 parts of seismic data slices into 3 groups, and respectively simulating samples of the 3 kinds of irregular data, wherein 5 parts of each group are respectively extracted under 5 different proportions r by adopting a corresponding extraction method, namely r is respectively 10%, 20%, 30%, 40% and 50%, generating blank seismic channels, and obtaining a plurality of irregular seismic data slice samples y with corresponding labels of x;

step two: wave atomic domain sample label preparation:

the wave atom transformation is completed by adopting a tool box (http:// www.waveatom.org /) code, the parameters of the transformation are (p ═ direct ', pat ═ p'), each slice data x generates 2 wave atom domain slice coefficients of 256 × 256, and the slice coefficients are respectively set as c₁And c₂；

Step three: network input and tag setting:

taking the irregular seismic data slice data y obtained in the step one as input, and taking the original seismic slice data x obtained in the step one and the slice coefficient c obtained in the step two₁And c₂Respectively serving as labels, and training a joint learning network model G;

step four: and (3) setting the structure of the deep learning network model G:

the deep learning network model G is divided into 2 sub-networks which are respectively a feature extraction network and a wave source sub-system number prediction network, irregular data is input as the input of the feature extraction network, and the input is subjected to a series of operations such as convolution, normalization, activation and the like; then, estimating corresponding wave atomic coefficients in a wave atomic coefficient prediction network, and generating pre-measured rule data by utilizing inverse transformation of a wave atomic coefficient matrix;

the network model is set as:

(1) feature extraction subnetwork

The sub-network is used for taking irregular seismic data as input of the network and extracting a feature map of the data, wherein the size of each layer of convolution kernels of the convolution network is 3 × 3, the step length is 1, the input data and the output data of each layer are the same, the calculation complexity is reduced, the feature map after convolution is subjected to normalization and activation functions, and then the next layer of convolution operation is carried out, 3 operations of the convolution layer, the normalization layer and the activation functions are defined into one group, each two groups are used as a residual block and total 5 residual blocks, the number of the convolution kernels in each residual block is 32, 64, 64, 128 and 256 in sequence, and the jump connection is arranged between every two residual blocks by utilizing the characteristic of residual learning;

(2) wave source sub-coefficient prediction sub-network

Setting the sizes of all convolution kernels to be 3 × 3, setting the step length to be 1 and filling the step length to be 1, respectively predicting coefficient matrixes corresponding to two wave atom sub-bands by the two parallel sub-networks, and finally performing inverse transformation on the predicted wave atom coefficients to generate time-space domain regular data;

step five: setting a loss function:

joint error function of joint spatial, wave atomic and fourier domain loss errors:

loss_total＝μloss_waveatom+νloss_space+ηloss_f-k

loss_spaceis defined as:

x is real seismic data, and x' is prediction regularization data;

because the mean square error constraint of a space domain is difficult to capture the frequency texture details of the seismic data, in order to improve the texture quality of the final regularized data details, wave atom loss is introduced to help the recovery and reconstruction of the data texture; let C ═ C₁,c₂) And

respectively representing real and predicted wave atomic coefficients, proposing the loss based on a wave atomic domain as a wave atomic domain mean square error, and capturing the detail information of a wave source sub-domain; is defined as:

in order to prevent the aliasing phenomenon from occurring in the regularization result, original rule data X and rule data X ' generated by prediction are subjected to Fourier transform to obtain X and X ', and loss error loss of the original rule data X and the rule data X ' is calculated_f-kIs defined as:

joint error function: loss_total＝μloss_waveatom+νloss_space+ηloss_f-kWherein loss_waveatomThe mean square error of the wave atomic domain prediction coefficient and the actual coefficient is used for improving the recovery of texture details; loss_spacePredicting the mean square error of the data and the actual data for the traditional spatial domain, and using the mean square error to constrain the error of the seismic data of the spatial domain; loss_f-kIs f-k domain error and is used for eliminating aliasing, mu, v and η are balance factors;

step six: training a network model:

inputting the irregular samples obtained in the first step to the fifth step into y, the original data label x and the wave atom decomposition coefficient c thereof₁And c₂The network outputs the corresponding wave atom prediction coefficient

And

generating spatial prediction data X' after inverse transformation, and obtaining the wave atomic domain error loss through Fourier transformation of the original rule data and the prediction data by X and X_waveatomError in spatial domain_spaceFourier domain error loss_f-kFinally, the joint error loss is obtained_totalAdjusting network parameters through forward transmission and backward feedback of the deep convolutional neural network, and storing the adjusted network parameters;

step seven: and (3) seismic data regularization testing:

organizing irregular seismic data in the test set into a slice seismic y, inputting the slice seismic y into a convolutional neural network model G with trained and adjusted parameters, and generating wave atomic domain coefficients

And

will be provided with

And

and performing wave-atom inverse transformation to obtain wave-atom domain predicted seismic data x', namely the regularized seismic data generated after restoration.

Firstly, expressing the texture characteristics of seismic data through a wave atomic domain; taking the processed irregular acoustic seismic data as the input of a convolutional neural network, taking the characteristics of wave atomic domain data and actual irregular data as labels, and constructing a spatial domain and wave atomic domain combined deep learning network structure; the error function uses a joint error function combining the wave atomic domain, the spatial domain and the f-k domain.

Example two

Referring to fig. 3-12, the training of the convolutional network model in the present method mainly comprises two parts, forward propagation of data and backward propagation of errors. Firstly, setting parameters of model training, and initializing the weight W and the bias b of each layer of the network; and then, carrying out a forward propagation process of model training, and inputting the irregular data y as the characteristics of the network model. And after the output of the model is obtained, performing back propagation operation, comparing the output of the model with the label to obtain the error of the output of the model and the label, adjusting the weight and the bias of the model by an Adam optimization algorithm until the convergence condition is met, and finishing the training of the network model to obtain the trained network model.

The experimental platform configuration of this example: the computer operating system is Ubutu18.04, the GPU is NVIDA GTX-2080, the deep learning network model is built by using a pytorech 0.4 and python2.7, and the operating environment of the wave source sub-transformation toolbox adopts Matlab2017 b. The specific process is implemented as follows:

1 seismic data training set preprocessing

1.1 reading sgy files

Reading a seismic data sgy format file through a segyio.open function of a toolkit segyio, wherein the definition of the function is as follows: open (file, mode ═ r "), where file is the path of the file to be opened and mode is the file access mode. The calling mode of the invention is as follows: open (file "r") as segyfile, reads the sgy file and names segyfile.

1.2 sample clipping of seismic data

Firstly, loading seismic data into a memory by using a segyfile. Next, a three-dimensional matrix is defined to store sample slice data, the size of the three-dimensional matrix is (5000,256,256), and a two-dimensional window with the size of 256 × 256 is slid in the seismic original gather data through cyclic traversal, each time the two-dimensional window is slid, one sample is added to x, and the total number of samples is 5000.

1.3 irregular seismic data simulation

Extracting a certain proportion of channels R from the complete seismic data sample as blank channels through a numpy scientific calculation toolkit to simulate irregular data, wherein R is the ratio of effective seismic channels (non-extracted seismic channels) to the total number of channels, and three irregular data conditions are simulated according to different distribution of the blank channels:

(1) the method is characterized in that the condition of collecting bad channels is simulated by using seismic channels which are completely randomly extracted as blank channels, and the implementation mode is as follows:

obtaining the total number n of extracted blank channels by sampling rate R, wherein n is round (256 is (1-R))

y＝x

b＝list(range(0,256))

random.shuffle(b)

c＝b[0:n]

for i in range(256):

if i in c:

y[:,:,i]＝0

Irregular data y is obtained.

(2) The method is characterized in that partial randomly-extracted seismic channels are used as blank channels to simulate the condition of uneven sampling, and the implementation mode is as follows:

the range phi for extracting the blank channels is set firstly, then the blank channels with the total number of n are extracted in the designated area phi by a method similar to the implementation (1), and the areas outside the phi are not extracted.

(3) The method is characterized in that seismic channels extracted at uniform intervals are used as blank channels to simulate the sparse sampling condition, and the implementation mode is as follows:

the sampled empty tracks are first sampled at a sampling rate R with a uniform spacing step n, n equal to round (1/(1-R)), and then are sampled within the entire gather by a method similar to that of (1).

2 sample label preparation:

the deep learning network model designed by the invention needs to process data of a space domain and a wave atom domain, so labels need to be respectively arranged in the space domain and the wave atom domain.

2.1 spatial domain labels: the original seismic slice data sample x obtained in process 1 was implemented.

2.2 wave atomic domain label wave source sub-transformation is realized by calling a tool box function through a Matlab API in python, firstly, a data wave source sub-transformation function fwa sym is written in the Matlab, the function is defined as fwa2sym (s, pat, tp), wherein tp is 'directional', pat is 'p', and s is original seismic slice data.

3, designing a network structure of the joint learning model G: the network model of the invention can be divided into two parts, namely a feature extraction network and a wave atomic coefficient prediction network.

3.1 feature extraction network design

The sub-network mainly comprises convolution, batch normalization and activation function operations, and the relevant standard functions related to the Pythrch are described as follows:

the convolutional layer was constructed using the standard function defined in the pytorech: conv2d (in _ channels, out _ channels, kernel _ size, stride, padding), where in _ channels represents the number of input channels, out _ channels represents the number of output channels, stride specifies the step size of the convolution kernel sliding, and padding is the size of the edge padding.

The batch normalization function BatchNorm2d (num _ features) can not only increase the convergence speed of the model, but also prevent the data from causing unstable network performance due to overlarge data before ReLU is carried out, and the parameter num _ features is the quantity of features in the parameter num _ features

The ReLU layer function defines: ReLU (), the output result of the previous convolutional layer is input to the ReLU activation function, and the function is called to perform nonlinear mapping.

In order to simplify the implementation process, firstly, 3 operations of convolution, batch normalization and activation functions are defined as one group, each two groups are used as one residual block, the feature extraction network is composed of 5 residual blocks, and the key code defined by the residual block function is as follows:

the key code of the residual block forward transfer forward function is as follows:

output＝self.relu1(self.bn1(self.conv1(x)))

output＝self.conv2(output)

output＝self.relu2(self.bn2(torch.add(output,identity_data)))

return output

and then extracting each residual block in the sub-network by utilizing the nn. sequential connection characteristics to form a network.

3.2 wave atomic coefficient prediction network design

In the characteristic extraction network processing process, after input data pass through 5 residual blocks, output characteristics are respectively input into two parallel wave atom coefficient prediction subnets, and the extracted characteristics are used for respectively predicting 2 coefficient matrixes of wave atoms. Next, convolution, batch normalization and activation operations are set on two parallel subnets, and here, similar implementation 3.1 first defines the residual block function of the wave atomic coefficient prediction subnetwork for feature extraction of the prediction layer, and then connects these residual learning blocks to form two parallel wave atomic coefficient prediction subnets.

3.3 defining the whole network structure, connecting the characteristic extraction sub-network with the wave atomic coefficient prediction sub-network in the whole network structure, and setting the output of the first wave atomic coefficient sub-band prediction sub-network as out _0 and the output of the second wave atomic coefficient sub-band prediction sub-network as out _ 1. Splicing the two predicted wave atomic coefficient matrixes into out, outputting the result through a network, and using the following codes:

out＝torch.cat((out_0,out_1),1)

4 design loss function:

after the network architecture of the network model is determined, a common loss function loss _ MSE (x, y) function is defined firstly and used for calculating the mean square error between x and y, and the loss function in the invention is based on the function.

4.1 wave atomic domain loss function

And dividing the tensor matrix obtained by the network output defined in the last step into two wave atomic domain prediction coefficients waveatom _ prediction [: 0: 1: ], waveatom _ prediction [: 1: ].

And (3) decomposing the wave atom of the regular data into target _ waveatom, wherein the decomposed wave original domain coefficient sub-band slice labels are respectively as follows:

waveatom_c1＝target_waveatom[:,0:1,:,:]

waveatom_c2＝target_waveatom[:,1:,:,:]

the loss function of the wave atomic coefficients is here calculated as:

loss_c1＝lossMSE(waveatom_predict[:,0:1,:,:],waveatom_c1)，

loss_c2＝lossMSE(waveatom_predict[:,1:,:],waveatom_c2)

4.2 loss function of time-domain data

And (3) loss _ img is loss _ MSE (img _ prediction, x), wherein img _ prediction is prediction rule data obtained by inverse transformation of the wave atom prediction coefficient, and x is initial rule data of a label.

4.3 loss function in Fourier domain

loss _ fk is loss _ MSE (img _ predict _ fk, target _ fk), img _ predict _ fk is the prediction rule data img _ predict that is fourier transformed, target _ fk is the initial rule data x that is fourier transformed,

the joint loss function at this time is:

loss_total＝loss_c1+loss_c2+μ*loss_img+v*loss_fk

loss _ c1 and loss _ c2 are wave atomic coefficient errors, which are used for improving the recovery of texture details; loss _ img is the error between the traditional spatial domain prediction data and the actual data and is used for restricting the spatial domain seismic data error; the purpose of loss _ fk is to eliminate aliasing. μ and v are weights.

5 training and saving the network model:

inputting a random irregular slice data sample set y by using a joint learning model G established in the implementation process 3, transmitting the random irregular slice data sample set through a network model in a forward direction, and outputting a predicted wave atom coefficient waveatom _ predict, calling a tool box function by a Matlab API (application programming interface) to realize wave atom inverse transformation in the process, firstly writing a data wave source sub-inverse transformation function iwa2sym in Matlab, wherein the function is defined as iwa2sym (w, pat, tp), wherein tp is 'direct', and pat is 'p'; w is the superposition of the 2 wave atomic domain slice coefficient matrices. The method called by the invention comprises the following steps: iwa2sym (wavelet _ prediction, pat, tp), and data img _ prediction is obtained by inverse transformation of the matrix wavelet _ prediction.

The optimization function adopted by the implementation is an Adam function, the function calling statement is an optimizer _ wave ═ optim.adam (model.parameters (), lr ═ opt.lr, beta ═ opt.momentum,0.999, weight _ decay ═ 0.0005), lr sets the learning rate to 0.0002, stands are used for first-order moment and second-order moment estimation adjustment, weight _ decay sets the weight decay, and reduces the problem of model overfitting, the implementation is set to 0.0005, the implementation sets the number of training iterations to 100, and epon is set to 100.

6, testing the performance of the network model:

load function is called to obtain the network model stored in the implementation process 5, the function is defined as weights (load), the test set of irregular seismic data is input into the network model G to obtain a predicted wave atomic coefficient waveatom _ predict, and the waveatom _ predict is subjected to wave atomic inverse transformation to obtain final predicted regularized seismic data.

The implementation effect is as follows:

the 2 original seismic data slices in the test sample are given as fig. 3, fig. 4 and their respective corresponding f-k domain spectra as fig. 5, fig. 6.

Two irregular situations of missing trace sampling and sparse sampling with a sampling rate of 50% (50% of seismic traces are blank traces) are respectively given, as shown in fig. 7 and fig. 8, and peak signal-to-noise ratios (PSNR) are respectively as follows: 21.10dB, 18.59 dB. PSNR is defined as:

where x is the original complete seismic data and MSE is the mean square error between the two.

Fig. 9 and fig. 10 show the data obtained by this regularization, and PSNR are: 35.82dB, 38.06 dB. The result is seen to have a higher visual effect, and the PSNR is respectively improved by about 14dB and 19 dB. Fig. 11 and 12 show the frequency spectrums corresponding to the regularized data, and it can be seen that the regularized data of the method is closer to the original frequency spectrum at f-k, and has a higher anti-aliasing effect.

Claims (1)

1. A deep learning anti-aliasing seismic data regularization method based on wave atom transformation is characterized by comprising the following steps: the seismic data regularization method comprises the following steps:

step one, training data set preparation:

performing spatial transformation processing on samples of seismic data in a training set, wherein the method comprises rotating angle and mirror image turning, increasing sample data of a data set, and cutting the sample data into slice data x with the size of 256 × 256, wherein the slice data x is used as the minimum unit of a training sample;

irregular seismic data are simulated by taking seismic channels with the extraction proportion r from complete seismic data as empty channels, the extraction method is to respectively simulate 3 irregular situations by utilizing complete random extraction, partial random extraction and uniform extraction methods, the irregular situations of the bad channels are simulated and collected by random extraction, the irregular situations of simulated uneven sampling are randomly extracted in partial areas, and the irregular situations of sparse sampling are simulated by the uniform extraction method;

copying 15 parts of each seismic data slice, dividing the 15 parts of seismic data slices into 3 groups, and respectively simulating samples of the 3 kinds of irregular data, wherein 5 parts of each group are respectively extracted under 5 different proportions r by adopting a corresponding extraction method, namely r is respectively 10%, 20%, 30%, 40% and 50%, generating blank seismic channels, and obtaining a plurality of irregular seismic data slice samples y with corresponding labels of x;

step two: wave atomic domain sample label preparation:

the wave atom transformation is completed by adopting a tool box code, 2 wave atom domain slicing coefficients of 256 × 256 are generated for each slice data x, and the slicing coefficients are respectively set as c₁And c₂；

Step three: network input and tag setting:

taking irregular seismic data slice data y obtained in the step one as input, and taking original seismic slice data x obtained in the step one and slices obtained in the step twoCoefficient c₁And c₂Respectively serving as labels, and training a joint learning network model G;

step four: and (3) setting the structure of the deep learning network model G:

the deep learning network model G is divided into 2 sub-networks which are respectively a feature extraction network and a wave source sub-system number prediction network, irregular data is input as the input of the feature extraction network, and the input is subjected to a series of operations such as convolution, normalization, activation and the like; then, estimating corresponding wave atomic coefficients in a wave atomic coefficient prediction network, and generating pre-measured rule data by utilizing inverse transformation of a wave atomic coefficient matrix;

the network model is set as:

(1) feature extraction subnetwork

The sub-network is used for taking irregular seismic data as input of the network and extracting a feature map of the data, wherein the size of each layer of convolution kernels of the convolution network is 3 × 3, the step length is 1, the input data and the output data of each layer are the same, the calculation complexity is reduced, the feature map after convolution is subjected to normalization and activation functions, and then the next layer of convolution operation is carried out, 3 operations of the convolution layer, the normalization layer and the activation functions are defined into one group, each two groups are used as a residual block and total 5 residual blocks, the number of the convolution kernels in each residual block is 32, 64, 64, 128 and 256 in sequence, and the jump connection is arranged between every two residual blocks by utilizing the characteristic of residual learning;

(2) wave source sub-coefficient prediction sub-network

Setting the sizes of all convolution kernels to be 3 × 3, setting the step length to be 1 and filling the step length to be 1, respectively predicting coefficient matrixes corresponding to two wave atom sub-bands by the two parallel sub-networks, and finally performing inverse transformation on the predicted wave atom coefficients to generate time-space domain regular data;

step five: setting a loss function:

joint error function of joint spatial, wave atomic and fourier domain loss errors:

loss_total＝μloss_waveatom+νloss_space+ηloss_f-k

loss_spaceis defined as:

x is real seismic data, and x' is prediction regularization data;

because the mean square error constraint of a space domain is difficult to capture the frequency texture details of the seismic data, in order to improve the texture quality of the final regularized data details, wave atom loss is introduced to help the recovery and reconstruction of the data texture; let C ═ C₁,c₂) And

respectively representing real and predicted wave atomic coefficients, proposing the loss based on a wave atomic domain as a wave atomic domain mean square error, and capturing the detail information of a wave source sub-domain; is defined as:

in order to prevent the aliasing phenomenon from occurring in the regularization result, original rule data X and rule data X ' generated by prediction are subjected to Fourier transform to obtain X and X ', and loss error loss of the original rule data X and the rule data X ' is calculated_f-kIs defined as:

joint error function: loss_total＝μloss_waveatom+νloss_space+ηloss_f-kWherein loss_waveatomThe mean square error of the wave atomic domain prediction coefficient and the actual coefficient is used for improving the recovery of texture details; loss_spacePredicting the mean square error of the data and the actual data for the traditional spatial domain, and using the mean square error to constrain the error of the seismic data of the spatial domain; loss_f-kIs f-k domain error and is used for eliminating aliasing, mu, v and η are balance factors;

step six: training a network model:

inputting the irregular samples obtained in the first step to the fifth step into y, the original data label x and the wave atom decomposition coefficient c thereof₁And c₂The network outputs the corresponding wave atom prediction coefficient

And

generating spatial prediction data X' after inverse transformation, and obtaining the wave atomic domain error loss through Fourier transformation of the original rule data and the prediction data by X and X_waveatomError in spatial domain_spaceFourier domain error loss_f-kFinally, the joint error loss is obtained_totalAdjusting network parameters through forward transmission and backward feedback of the deep convolutional neural network, and storing the adjusted network parameters;

step seven: and (3) seismic data regularization testing:

organizing irregular seismic data in the test set into a slice seismic y, inputting the slice seismic y into a convolutional neural network model G with trained and adjusted parameters, and generating wave atomic domain coefficients

And

will be provided with

And

and performing wave-atom inverse transformation to obtain wave-atom domain predicted seismic data x', namely the regularized seismic data generated after restoration.

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