CN111551988B - Seismic data anti-alias interpolation method combining deep learning and prediction filtering - Google Patents

Seismic data anti-alias interpolation method combining deep learning and prediction filtering Download PDF

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CN111551988B
CN111551988B CN202010325961.5A CN202010325961A CN111551988B CN 111551988 B CN111551988 B CN 111551988B CN 202010325961 A CN202010325961 A CN 202010325961A CN 111551988 B CN111551988 B CN 111551988B
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CN111551988A (en
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方文倩
付丽华
李宏伟
李志明
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China University of Geosciences
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    • G01V1/00—Seismology; Seismic or acoustic prospecting or detecting
    • G01V1/28—Processing seismic data, e.g. analysis, for interpretation, for correction
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    • G01V—GEOPHYSICS; GRAVITATIONAL MEASUREMENTS; DETECTING MASSES OR OBJECTS; TAGS
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Abstract

The invention provides a seismic data anti-alias interpolation method combining deep learning and prediction filtering, which comprises the following steps: constructing a training sample set and a test sample set according to the simulated seismic data; constructing a prediction error filter network, wherein the prediction error filter network comprises deep learning and prediction filtering, the deep learning utilizes training data to learn the mapping relation between missing seismic data and a non-stationary prediction filter, and the prediction filtering utilizes the non-stationary prediction filter obtained by learning to predict the missing seismic data; training the prediction error filter network by using a training sample set, and evaluating the performance of the prediction error filter network by using a test sample set; and performing anti-alias interpolation on the seismic data by using the trained prediction error filter network. The invention has the beneficial effects that: the advantages of deep learning and traditional filtering methods are integrated, and the method has higher calculation efficiency and less manual workload.

Description

Seismic data anti-alias interpolation method combining deep learning and prediction filtering
Technical Field
The invention relates to the technical field of seismic signal processing, in particular to a seismic data anti-alias interpolation method combining deep learning and prediction filtering.
Background
Physical or economic limitations often present the problem of missing seismic traces or excessively large spatial sampling intervals in the acquired seismic signals, which can affect subsequent offset imaging, inversion and interpretation. The seismic difference problem is divided into irregular missing interpolation and regular missing interpolation, wherein the regular missing interpolation performs data up-sampling, the method is an expensive alternative method for dense space sampling, and the frequency aliasing phenomenon caused by overlarge space sampling interval can be removed.
Predictive filtering is an important class of seismic data anti-alias interpolation methods, for example, f-x domain anti-alias interpolation methods treat seismic records as a superposition of linear event axes, a Prediction Error Filter (PEF) estimated from low frequency f can be used to interpolate data of high frequency 2f, and the method is later generalized to t-x domain, f-x-y domain, and the like. However, the method is based on the linear event assumption, and the seismic data event is mostly non-linear, so that the windowing technology is considered in practical application to ensure that the data in the analysis window is approximately linear. A non-stationary filter is another interpolation method for processing nonlinear in-phase axis data, and the non-stationary filter models the solution of the filter coefficients as an underdetermined problem, and usually requires introducing a regularization term to constrain the smooth change of the filter.
In recent years, machine learning and deep learning technologies provide a new idea for interpolation problems, the advantages of big data can be utilized to break through the limitation of prior hypothesis, characteristics are automatically mined from the data, and the manual workload is greatly reduced. For example, Support Vector Regression (SVR) is used to learn a continuous regression hyperplane from training data to represent the relationship between missing data and output complete data. Deep learning is a subclass of machine learning, a deep neural network can extract characteristics of a data higher layer in a nonlinear manner compared with SVR (singular value decomposition), the existing research comprises the steps of using a residual error network to interpolate regular missing data, generating antagonistic network pair post-stack gap missing data interpolation, interpolating random missing data by a U-net network and the like, different network structures are built by the methods, mapping from degraded data (missing or pre-interpolation) to complete data is learned from a large amount of training data, the trained network can be directly used for interpolation of similar data, but mapping with universality on different data is difficult to learn, and due to the inexplicability of the deep network, the interpolation principle of the methods is difficult to interpret, and the interpolation effect is difficult to predict.
Disclosure of Invention
In view of the above, the invention provides a seismic data anti-aliasing interpolation method combining deep learning and predictive filtering, which considers a non-stationary Prediction Error Filter (PEF) in a t-x domain, designs a relationship between network learning degraded data and a Filter, inputs the relationship into missing data and outputs the relationship into a Filter coefficient, and then reconstructs a missing seismic trace by using the Filter.
The invention provides a seismic data anti-alias interpolation method combining deep learning and prediction filtering, which comprises the following steps of:
s1, carrying out spatial down-sampling of different scales on simulated seismic data to expand a sample set, randomly intercepting a plurality of data blocks with the size of M multiplied by N from the expanded sample set, then dividing the data blocks into a training sample set and a testing sample set, wherein M represents the row number of the data blocks, and N represents the column number of the data blocks;
s2, constructing a prediction error filter network, wherein the prediction error filter network comprises deep learning and prediction filtering, the deep learning is realized by a residual error network, and the residual error network learns the mapping relation between the missing seismic data and the non-stationary prediction filter by utilizing training data; the prediction filtering uses a non-stationary prediction filter obtained by learning to predict missing seismic data;
s3, training the prediction error filter network by using the training sample set obtained in the step S1, and evaluating the performance of the prediction error filter network by using the test sample set; and performing anti-alias interpolation on the seismic data by using the trained prediction error filter network.
Further, the spatial down-sampling of different scales in step S1 includes performing 2-fold down-sampling and 4-fold down-sampling on the simulated seismic data, and the training sample set and the test sample set are intercepted from different shot records of the simulated seismic data.
Further, in step S2, the input of the residual network is seismic data with missing rules
Figure GDA0002968322960000031
P (t, x) denotes integrity in the time-space domainT represents reflection time, x represents spatial data, Mask represents a masking operator for constructing the seismic data with rule missing,
Figure GDA0002968322960000034
representing a Hadamard product; the output of the residual error network is the coefficient A of the non-stationary prediction filter, the matrix size of the coefficient A is (2r +1) xMxN, and r represents the radius of the non-stationary prediction filter.
Further, in step S2, the residual network is formed by stacking 7 residual blocks, each of the residual blocks includes two convolutional layers, a convolutional kernel of the convolutional layers has a size of 5 × 5, the nonlinear activation function uses a Relu function, and a batch normalization layer is used to accelerate convergence; except the convolution layers of the first layer and the last layer, the number of input channels and output channels of the other convolution layers is 64; the residual error network is a coding and decoding structure of one-time down-sampling and one-time up-sampling, wherein the down-sampling is realized by a convolution layer with the step size of 2, and the up-sampling is realized by transposition convolution.
Further, in step S2, the specific process of predicting the missing seismic data by using the learned non-stationary prediction filter in the prediction filtering is as follows:
predicting the x +1 st seismic data by using the x seismic data:
Figure GDA0002968322960000032
wherein the content of the first and second substances,
Figure GDA0002968322960000033
represents the prediction result of the x +1 th trace of seismic data at time t, P (t + k, x) represents the x-th trace of seismic data at time t + k, a (k, t, x) represents the k-th coefficient of the non-stationary prediction filter at (t, x), k is-r, -r +1, …, r.
Further, in step S3, the specific process of training the prediction error filter network by using the training sample set obtained in step S1 is as follows:
using original and complete data blocks in a training sample set as label data Y, and constructing seismic data with rule missing by using Mask operator Mask
Figure GDA0002968322960000041
Wherein, X0Is a two-dimensional matrix of M × N, and then the seismic data X with the missing rule is processed0Normalized to [ -1,1 [ ]]Obtaining data X, thereby constructing a training sample pair (X, Y); the normalization mode is that X ═ X0/max(|xi,jI)), X represents normalized seismic data, X0Seismic data representing missing rules of input, xi,jRepresents X0In the elements in the ith row and the jth column, i is more than 0 and less than or equal to M, j is more than 0 and less than or equal to N, and i and j are positive integers.
Further, the prediction error filter network is trained by using the constructed training sample pair (X, Y), and the specific process is as follows:
inputting data X into the residual error network, and performing primary prediction on the label data Y according to the non-stationary prediction filter coefficient A output by the residual error network to obtain the result Y of the 1 st prediction(1)：
Figure GDA0002968322960000042
Wherein i is more than 0 and less than or equal to M, j is more than 0 and less than or equal to N, i and j are positive integers, Y(1)Column 1 to N-1 data in (a) is a prediction of column 2 to N data in the tag data Y, a (k, i, j) represents the kth coefficient of the non-stationary prediction filter at (i, j), k ═ r, -r +1, …, r;
and performing multi-step prediction on the label data Y according to the coefficient A of the non-stationary prediction filter:
Figure GDA0002968322960000043
wherein, Y(l+1)Represents the prediction result of the (l +1) th step, Y(l)Representing the prediction result in the first step;
using L1Norm constraint prediction knotThe distance of the effect from the tag data Y, thus resulting in a loss function:
Figure GDA0002968322960000044
wherein S represents the number of tracks of the most predicted seismic traces; and optimizing a loss function by using an adam gradient descent method, and completing one round of training of the prediction error filter network. The batch size of the adam gradient descent method is 48, the initial learning rate is 0.001, and 15 training rounds are completed by multiplying the learning rate by 0.1 every 5 training rounds.
Further, in step S3, when the performance of the prediction error filter network is evaluated by using the test sample set, the evaluation indexes adopted are that the reconstructed signal-to-noise ratio is:
Figure GDA0002968322960000051
wherein the content of the first and second substances,
Figure GDA0002968322960000052
representing the result of seismic data interpolation of test samples of a test sample set using said prediction error filter network, YtRepresenting the label data in the test sample set,
Figure GDA0002968322960000053
representing the square of the F-norm.
The technical scheme provided by the invention has the beneficial effects that: the invention integrates the advantages of deep learning and prediction filtering methods, has better generalization and interpretability in the filtering reconstruction process compared with other deep learning methods, and has better adaptivity to different data; compared with the traditional prediction filtering method, the method can use GPU parallel computation, has higher computation efficiency, and does not need windowing strategy and manual parameter adjustment.
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FIG. 1 is four exemplary diagrams of a training sample set provided by an embodiment of the present invention;
FIG. 2 is a schematic diagram of a prediction error filter network according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of a residual error network provided in an embodiment of the present invention;
FIG. 4 is a schematic illustration of rule-missing seismic data provided by an embodiment of the present invention;
FIG. 5 is a graph comparing interpolation results of the PEFNet method and the ResNet, f-x, PWD methods provided by embodiments of the present invention;
fig. 6 is a schematic diagram of an interpolation result of the PEFNet method provided by the embodiment of the invention on real data.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, embodiments of the present invention will be further described with reference to the accompanying drawings.
The embodiment of the invention provides a seismic data anti-alias interpolation method combining deep learning and prediction filtering, which adopts two-dimensional simulation seismic data and comprises the following steps:
s1, constructing a training sample set and a testing sample set according to the simulated seismic data: the simulation seismic data are subjected to spatial downsampling of different scales to expand a sample set, a plurality of data blocks with the size of M multiplied by N are randomly intercepted from the simulation seismic data and are divided into a training sample set and a test sample set, M represents the row number of the data blocks, and N represents the column number of the data blocks.
Because seismic exploration is expensive, a large amount of open actual data is lacked, and the actual data is often lacked, a training set is constructed by using simulation data, the prediction error filter network constructed in the step S2 in this embodiment can be directly used for reconstruction of actual seismic data after training on the simulation data is completed, and the prediction error filter network can be further fine-tuned by using the actual seismic data under the condition of actual complete seismic data. In the embodiment, a training sample set and a test sample set are constructed by using 500-cannon simulated seismic data, in order to increase the diversity of local slopes of the data, firstly, the data are expanded by using spatial down-sampling modes with different scales, specifically, 2-time down-sampling and 4-time down-sampling are respectively carried out on the seismic data in space, and the obtained slopes are respectively 2 times and 4 times of the original seismic data; for each sampling mode, 8000M multiplied by N data blocks are randomly intercepted from the downsampling result of 1-400 cannon seismic data to form a training sample set, 2000M multiplied by N data blocks are randomly intercepted from the downsampling result of 401-500 cannon seismic data to form a test sample set, M represents the row number of the data blocks (namely the time of the seismic data), and N represents the column number of the data blocks (namely the number of seismic traces). Preferably, M-N-128. It should be noted that, in this embodiment, the left and right directions of the data blocks in the sample set are also reversed with a probability of 50%, so as to satisfy the diversity of the training data. Referring to fig. 1, which is four examples of training sample sets, the abscissa (Trace number) represents the number of seismic traces and the ordinate (Time sample number) represents the sampling Time point.
S2, constructing a prediction error filter network (PEFNet): the PEFNet includes a deep learning portion and a prediction filtering portion, referring to fig. 2, the deep learning is implemented by a residual network f that learns the mapping relationship between missing seismic data and non-stationary prediction filters from a large amount of training data.
Specifically, the input to the residual network f is regularly missing seismic data
Figure GDA0002968322960000071
P (t, x) represents the complete seismic data in the time-space (t-x) domain, t represents reflection time, x represents spatial data, and Mask represents a Mask operator for constructing the seismic data with regular deletion, in the embodiment, the seismic data is constructed by adopting even trace deletion, so that the elements of odd columns in the Mask are 1, the elements of even columns in the Mask are 0,
Figure GDA0002968322960000074
representing the hadamard product. The output of the residual network f is the coefficient a of the t-x domain non-stationary prediction filter, whose size is (2r +1) × M × N, where r denotes the radius of the non-stationary prediction filter, and in this embodiment, r is 3.
Referring to fig. 3, the residual network f is formed by stacking 7 residual blocks Block1, Block2, … … and Block7, the input of the residual Block1 is the input of the residual network f, the output of each residual Block is then used as the input of the next residual Block, and the output of the residual Block7 is the output of the residual network f; each residual block comprises two convolution layers, the size of a convolution kernel is 5 multiplied by 5, a Relu function is used as a nonlinear activation function, and a batch normalization layer (BN) is used for accelerating convergence; except the first layer and the last layer of convolution layer, the number of input channels and output channels of the other convolution layers is 64; the residual network f is a coding and decoding structure of one-time downsampling and one-time upsampling, wherein downsampling coding is carried out after a residual Block Block1, downsampling is realized by a convolutional layer with the step size of 2, upsampling decoding is carried out after a residual Block Block4, and upsampling is realized by transposition convolution.
The prediction filtering uses a non-stationary prediction filter obtained by residual error network f learning, and the x +1 st seismic data is predicted by the x seismic data:
Figure GDA0002968322960000072
wherein the content of the first and second substances,
Figure GDA0002968322960000073
represents the x +1 th trace seismic data prediction at time t, P (t + k, x) represents the x th trace seismic data at time t + k, a (k, t, x) represents the k-th coefficient of the filter at (t, x), k-r, -r +1, …, r.
S3, training the PEFNet by using the training sample set obtained in the step S1, and evaluating the network performance by using the test sample set; and performing anti-alias interpolation on the seismic data by using the PEFNet after the training is finished.
Specifically, an original complete data block in a training sample set is used as label data Y, and an even channel of seismic data is artificially set to be 0 to obtain seismic data X with a rule missing0Wherein X is0Is a two-dimensional matrix of M × N, and then the seismic data X with the missing rule is processed0Normalized to [ -1,1 [ ]]Get data X in between, thus constructing a training sample pair (X, Y). Normalized by X ═ X0/max(|xi,jI)), X represents normalized seismic data, X0Seismic data representing missing rules of input, xi,jRepresents X0In the elements in the ith row and the jth column, i is more than 0 and less than or equal to M, j is more than 0 and less than or equal to N, and i and j are positive integers.
Training the PEFNet by using the constructed training sample pair (X, Y), specifically, inputting data X into a residual error network f, and predicting the label data Y for one time according to a non-stationary prediction filter coefficient A output by the residual error network f to obtain a result Y of the prediction in the step 1(1)：
Figure GDA0002968322960000081
Wherein, Y(1)Column 1 to N-1 data in (a) is a prediction of column 2 to N data in the tag data Y, a (k, i, j) represents the kth coefficient of the filter at (i, j), k ═ r, -r +1, …, r; the result Y of the 1 st prediction is again used by the filter coefficient A(1)Predicting to obtain the result Y of the 2 nd prediction(2)：
Figure GDA0002968322960000082
By means of L1The norm constrains the distance between the prediction result and the label data, thereby obtaining a loss function of the residual error network f:
Figure GDA0002968322960000083
finally, the loss function is optimized by using the adam gradient descent method, so that the PEFNet is trained by using a training sample set, wherein the batch size of the adam gradient descent method in the embodiment is 48, the initial learning rate is 0.001, and each 5 rounds of learning rates are multiplied by 0.1 for 15 rounds of training.
Evaluating the performance of the PEFNet by using a test sample set, wherein the evaluation indexes adopt a reconstruction signal-to-noise ratio:
Figure GDA0002968322960000091
wherein the content of the first and second substances,
Figure GDA0002968322960000092
representing the result of interpolation of seismic data using the PENset for the test samples in the test sample set, YtRepresenting the label data in the test sample set,
Figure GDA0002968322960000093
representing the square of the F-norm.
It should be noted that, when performing anti-alias interpolation on seismic data by using the PEFNet after training, firstly, the seismic data is constructed into a data block of M × N size, and is input as input data into the PEFNet after training, then a residual error network f in the PEFNet is used to obtain a coefficient of a non-stationary prediction filter, and finally, an interpolation result is obtained by using the coefficient of the non-stationary prediction filter through prediction filtering, specifically, the seismic data missing from even tracks in this embodiment is subjected to interpolation reconstruction:
Figure GDA0002968322960000094
wherein, n is more than 0 and less than 2 and less than or equal to 128, and n is a positive integer.
Referring to fig. 4, part (b) of fig. 4 is complete seismic data, the time and space sampling intervals of the complete seismic data are 2ms and 12.5m, respectively, and 121 seismic traces are provided, each seismic trace contains 450 time sampling points; part (a) of fig. 4 is regularly sampled data at an interval of 25m, and a more significant aliasing phenomenon can be observed where the slope is larger.
Referring to fig. 5, in this embodiment, comparing ResNet, f-x, PWD and the interpolation result of the PEFNet method proposed by the present invention to the simulated seismic data in fig. 4, the snr is 17.34dB, 15.94dB, 19.38dB, and 19.50dB, parts (a), (b), and (c) in fig. 5 are the reconstruction result, residual, and filter impulse response of the PEFNet method, parts (d) and (g) in fig. 5 are the reconstruction result and residual of the ResNet method, parts (e) and (h) in fig. 5 are the reconstruction result and residual of the f-x method, and parts (f) and (i) in fig. 5 are the reconstruction result and residual of the PWD method, respectively. As can be seen from fig. 5, compared with the other three methods, the PEFNet method can achieve better interpolation result and the overall signal-to-noise ratio is the highest; as can be seen from the interpolation result and the residual image, the f-x method has larger reconstruction error on the data of the bending in-phase axis and has a small amount of artifacts; the overall error of the ResNet method is greater than PEFNet, and as can be seen at the arrow in part (g) of fig. 5, the error of the ResNet method for the in-phase axis with a larger slope is significantly increased; as can be seen at the arrow in part (i) of fig. 5, the PWD method has a significant error at the intersection of the two in-phase axes since it can only estimate one local dip. As can be seen from the residual map shown in part (b) of fig. 5, the PEFNet method and the PWD method also have reduced performance at the intersection of the in-phase axes due to the use of filters of similar formats, but have smaller errors than the PWD method due to the filter of the PEFNet method having certain adaptivity. In addition, because the interpolation reconstruction of the PEFNet method is realized by prediction filtering, which can be explained to a certain extent, part (c) in fig. 5 is the impulse response of the filter output by the PEFNet method at four different positions, i.e. the continuous 15-channel prediction results of the filter on the impulse signal, and it can be seen that the filter output by the PEFNet is similar to a phase delay operator when the data conforms to a local plane wave model; under the condition that the two local plane waves are superposed, the PEFNet can be extracted to two different local inclination angle characteristics in a self-adaptive manner to a certain extent at the intersection point, and the fact that the trained PEFNet has certain popularization is shown.
Please refer to fig. 6, which shows the result of processing the real data obtained from the PEFNet method, wherein the data is the two-dimensional ocean shot points obtained from the survey of the deep water in the gulf of mexico, and the two-dimensional ocean shot points contain complex diffraction events caused by salt bodies. In fig. 6, (a) is data with twice sampling interval, (b) is original complete data, (c) and (d) are interpolation result and residual of PEFNet, respectively, the signal-to-noise ratio is 17.02dB, and the residual graph shown in (d) shows that the invention has good adaptability to real data with crossed in-phase axes.
In this document, the terms front, back, upper and lower are used to define the components in the drawings and the positions of the components relative to each other, and are used for clarity and convenience of the technical solution. It is to be understood that the use of the directional terms should not be taken to limit the scope of the claims.
The features of the embodiments and embodiments described herein above may be combined with each other without conflict.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents, improvements and the like that fall within the spirit and principle of the present invention are intended to be included therein.

Claims (7)

1. A seismic data anti-aliasing interpolation method combining deep learning and prediction filtering is characterized by comprising the following steps:
s1, carrying out spatial down-sampling of different scales on simulated seismic data to expand a sample set, randomly intercepting a plurality of data blocks with the size of M multiplied by N from the expanded sample set, then dividing the data blocks into a training sample set and a testing sample set, wherein M represents the row number of the data blocks, and N represents the column number of the data blocks;
s2, constructing a prediction error filter network, wherein the prediction error filter network comprises deep learning and prediction filtering, the deep learning is realized by a residual error network, and the residual error network learns the mapping relation between the missing seismic data and the non-stationary prediction filter by utilizing training data; the prediction filtering uses a non-stationary prediction filter obtained by learning to predict missing seismic data;
s3, training the prediction error filter network by using the training sample set obtained in the step S1, and evaluating the performance of the prediction error filter network by using the test sample set; performing anti-alias interpolation on the seismic data by using the trained prediction error filter network;
in step S2, the input of the residual error network is seismic data with missing rules
Figure FDA0002968322950000011
P (t, x) represents the complete seismic data in the time-space domain, t represents reflection time, x represents spatial data, Mask represents the masking operator used to construct the seismic data for rule-missing,
Figure FDA0002968322950000013
representing a Hadamard product; the output of the residual error network is a coefficient A of the non-stationary prediction filter, the matrix size of the coefficient A is (2r +1) xMxN, and r represents the radius of the non-stationary prediction filter;
in step S3, the specific process of training the prediction error filter network by using the training sample set obtained in step S1 is as follows:
using original and complete data blocks in a training sample set as label data Y, and constructing seismic data with rule missing by using Mask operator Mask
Figure FDA0002968322950000012
Wherein, X0Is a two-dimensional matrix of M × N, and then the seismic data X with the missing rule is processed0Normalized to [ -1,1 [ ]]Obtaining data X, thereby constructing a training sample pair (X, Y), and training the prediction error filter network by using the constructed training sample pair (X, Y);
the specific process of training the prediction error filter network by using the constructed training sample pair (X, Y) is as follows:
inputting data X into the residual error network, and performing primary prediction on the label data Y according to the non-stationary prediction filter coefficient A output by the residual error network to obtain the result Y of the 1 st prediction(1)：
Figure FDA0002968322950000021
Wherein i is more than 0 and less than or equal to M, j is more than 0 and less than or equal to N, i and j are positive integers, Y(1)Column 1 to N-1 of (1) are for column 2 to column 2 of tag data YN columns of data are predicted, a (k, i, j) represents the kth coefficient of the non-stationary prediction filter at (i, j), k ═ r, -r +1, …, r;
and performing multi-step prediction on the label data Y according to the coefficient A of the non-stationary prediction filter:
Figure FDA0002968322950000022
wherein, Y(l+1)Represents the prediction result of the (l +1) th step, Y(l)Representing the prediction result in the first step;
using L1The norm constrains the distance of the prediction result and the label data Y, thereby yielding a loss function:
Figure FDA0002968322950000023
wherein S represents the number of tracks of the most predicted seismic traces; and optimizing a loss function by using an adam gradient descent method, and completing one round of training of the prediction error filter network.
2. The seismic data anti-aliasing interpolation method combining deep learning and prediction filtering according to claim 1, wherein in step S2, the residual network is formed by stacking 7 residual blocks, each residual block comprises two convolutional layers, the convolutional layers have convolutional kernel sizes of 5 × 5, the nonlinear activation function adopts a Relu function, and convergence is accelerated by using a batch normalization layer; except the convolution layers of the first layer and the last layer, the number of input channels and output channels of the other convolution layers is 64; the residual error network is a coding and decoding structure of one-time down-sampling and one-time up-sampling, wherein the down-sampling is realized by a convolution layer with the step size of 2, and the up-sampling is realized by transposition convolution.
3. The seismic data anti-aliasing interpolation method combining deep learning and prediction filtering as claimed in claim 1, wherein in step S2, the specific process of predicting missing seismic data by using the non-stationary prediction filter obtained by learning in the prediction filtering is as follows:
predicting the x +1 st seismic data by using the x seismic data:
Figure FDA0002968322950000031
wherein the content of the first and second substances,
Figure FDA0002968322950000032
represents the prediction result of the x +1 th trace of seismic data at time t, P (t + k, x) represents the x-th trace of seismic data at time t + k, a (k, t, x) represents the k-th coefficient of the non-stationary prediction filter at (t, x), k is-r, -r +1, …, r.
4. The seismic data anti-aliasing interpolation method combining deep learning and prediction filtering of claim 1, wherein the batch size of the adam gradient descent method is 48, the initial learning rate is 0.001, and 15 training rounds are performed after every 5 rounds of learning rates are multiplied by 0.1, so that the training of the prediction error filter network is completed.
5. The seismic data anti-aliasing interpolation method combining deep learning and prediction filtering according to claim 1, wherein in step S3, when the performance of the prediction error filter network is evaluated by using the test sample set, the evaluation indexes adopted are the reconstructed signal-to-noise ratio:
Figure FDA0002968322950000033
wherein the content of the first and second substances,
Figure FDA0002968322950000034
representing the result of seismic data interpolation of test samples of a test sample set using said prediction error filter network, YtRepresenting a set of test samplesThe data of the tag is transmitted to the mobile terminal,
Figure FDA0002968322950000035
representing the square of the F-norm.
6. The method of claim 1, wherein the normalization is performed in a manner such that X ═ X0/max(|xi,jI)), X represents normalized seismic data, X0Seismic data representing missing rules of input, xi,jRepresents X0In the elements in the ith row and the jth column, i is more than 0 and less than or equal to M, j is more than 0 and less than or equal to N, and i and j are positive integers.
7. The seismic data anti-aliasing interpolation method of claim 1, wherein the spatial downsampling at different scales in step S1 comprises performing 2-fold downsampling and 4-fold downsampling on the simulated seismic data, and the training sample set and the testing sample set are intercepted from different shot records of the simulated seismic data.
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