CN115936990A - Synchronous processing method and system for multi-scale super-resolution and denoising of seismic data - Google Patents

Synchronous processing method and system for multi-scale super-resolution and denoising of seismic data Download PDF

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CN115936990A
CN115936990A CN202211586531.4A CN202211586531A CN115936990A CN 115936990 A CN115936990 A CN 115936990A CN 202211586531 A CN202211586531 A CN 202211586531A CN 115936990 A CN115936990 A CN 115936990A
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CN115936990B (en
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吕文君
齐振宇
张文婷
康宇
赵云波
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University of Science and Technology of China USTC
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Abstract

The invention discloses a method and a system for synchronously processing multi-scale super-resolution and denoising of seismic data, wherein the method comprises the following steps: carrying out down-sampling on the high-resolution seismic image to obtain a low-resolution seismic image, and constructing a training sample set; initializing a seismic reconstruction network, wherein the seismic reconstruction network comprises an autoencoder sub-network, a super-resolution sub-network and a multi-scale reconstruction sub-network; learning the seismic reconstruction network by using a multi-scale deep supervised learning strategy; and inputting the new seismic image into the trained seismic enhancement network to obtain a de-noised high-resolution seismic image and complete the reconstruction of seismic data. The invention has the following beneficial effects: the high-frequency information of the seismic image can be reserved, random noise is suppressed, geological structure information is effectively highlighted, the visual effect is more consistent with a human eye system, and the efficiency and accuracy of subsequent seismic interpretation can be effectively improved.

Description

Multi-scale super-resolution and denoising synchronous processing method and system for seismic data
Technical Field
The invention relates to the technical field of new generation information, in particular to a seismic data multi-scale super-resolution and denoising synchronous processing method and system.
Background
In the field of reservoir exploration, the geometrical shapes of fault and fracture networks play an important role in reservoir formation and migration of oil and gas, so that the fault and fracture networks in seismic images are accurately identified, and the method has important significance in finding oil and gas reservoirs. The traditional seismic image fault identification is carried out in an artificial mode, and a fault line is drawn on a seismic profile map manually by experienced geologists according to local characteristics of faults and the combination of the geological structure and the characteristics of a whole exploration area, so that a complete fault plane is obtained finally. The disadvantages of this method are also evident: the efficiency is low, and the identification accuracy rate greatly depends on the experience and knowledge of geological experts.
In recent years, with the continuous development of artificial intelligence technology, seismic image interpretation technology based on deep learning is also emerging, and a great deal of research shows that a model constructed based on a deep learning method can achieve good performance in the problem of seismic fault identification, but the seismic interpretation model is generally limited by low resolution and strong noise data. Due to the limitation of seismic acquisition and processing, the problems of low resolution and noise damage of field seismic data often exist, which brings huge challenges to subsequent seismic interpretation, so that super-resolution reconstruction and denoising are performed on the seismic data, and geological information with rich details is very necessary and worthy to recover.
Disclosure of Invention
The invention provides a seismic data multi-scale super-resolution and denoising synchronous processing method which can at least solve one of the technical problems.
In order to realize the purpose, the invention adopts the following technical scheme:
a method for synchronously processing multi-scale super-resolution and denoising of seismic data comprises the following steps,
s1, performing down-sampling on a high-resolution seismic image to obtain a low-resolution seismic image, and constructing a training sample set;
s2, initializing a seismic reconstruction network, wherein the seismic reconstruction network comprises a self-encoder sub-network, a super-resolution sub-network and a multi-scale reconstruction sub-network;
s3, learning the seismic reconstruction network by using a multi-scale depth supervised learning strategy;
and S4, inputting the new seismic image into the trained seismic enhancement network to obtain a de-noised high-resolution seismic image and complete the reconstruction of seismic data.
In another aspect, the present invention also discloses a computer readable storage medium storing a computer program, which when executed by a processor causes the processor to perform the steps of the method as described above.
According to the technical scheme, the seismic data multi-scale super-resolution and denoising synchronous processing method has the following beneficial effects:
in the sampling stage on the network, a multi-scale reconstruction sub-network is introduced, a multi-scale depth supervision learning strategy is adopted, the characteristics of the seismic image in different scales are fully learned, and the characteristics under different receptive fields and granularities are integrated, so that the characteristic diagram generated by the decoder can contain richer semantic information, has more texture information and can describe a finer geological structure. The invention can retain the high-frequency information of the seismic image, inhibit random noise, effectively highlight the geological structure information, has a visual effect more in line with a human eye system, and can effectively improve the efficiency and accuracy of subsequent seismic interpretation.
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FIG. 1 is a schematic diagram of the method of the present invention.
Detailed Description
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.
As shown in fig. 1, the method for synchronously processing multi-scale super-resolution and denoising of seismic data in this embodiment includes the following steps,
s1, performing down-sampling on a high-resolution seismic image to obtain a low-resolution seismic image, and constructing a training sample set;
s2, initializing an earthquake reconstruction network, wherein the earthquake reconstruction network comprises a self-encoder sub-network, a super-resolution sub-network and a multi-scale reconstruction sub-network;
s3, learning the seismic reconstruction network by using a multi-scale depth supervised learning strategy;
and S4, inputting the new seismic image into the trained seismic enhancement network to obtain a de-noised high-resolution seismic image and complete the reconstruction of seismic data.
The following is a detailed description:
as shown in fig. 1, the present invention is described by taking the maximum down-sampling order K =4 as an example. The embodiment discloses a method and a system for synchronously processing multi-scale super-resolution and denoising of seismic data, which comprises the following steps S1 to S4:
s1, downsampling the high-resolution seismic image to obtain a low-resolution seismic image, and constructing a training sample set, wherein the method specifically comprises the following steps:
s11, for seismic image
Figure BDA0003986629550000031
m and n are the length and height of the seismic image, and subscripts hr, sr and lr represent high resolution, super resolution and low resolution; high resolution seismic image I hr Downsampling to obtain a low-resolution seismic image I lr =Down(I hr Θ), down represents a downsampling function, based on the downsampling function>
Figure BDA0003986629550000032
For the downsampling parameters, K =0,1,2,3, \ 8230, where K denotes the downsampling order, and/or>
Figure BDA0003986629550000033
Represents->
Figure BDA0003986629550000034
K =0 means no downsampling, i.e. downsampling
Figure BDA0003986629550000035
S12, a sheet I hr A corresponding group
Figure BDA0003986629550000036
Forming a training sample pair with independent identically distributed noise>
Figure BDA0003986629550000037
As an input to the network>
Figure BDA0003986629550000038
Supervised learning labels as a network at K =0,1,2,3, \ 8230;, K multi-scale output;
s2, initializing an earthquake reconstruction network, wherein the earthquake reconstruction network comprises a self-encoder sub-network, a super-resolution sub-network and a multi-scale reconstruction sub-network, and the earthquake reconstruction network specifically comprises the following parts:
s21, defining a seismic reconstruction network, specifically as follows:
the connection relationships of the three sub-networks are as follows:
the self-encoder sub-network is one of artificial neural networks, an encoder extracts features, a decoder reconstructs data, and a self-encoder is a U-shaped encoder-decoder network and comprises K downsampling blocks and corresponding K upsampling blocks; k downsample blocks of
Figure BDA0003986629550000039
Comprises the following components:
Figure BDA00039866295500000310
wherein
Figure BDA00039866295500000311
Is->
Figure BDA00039866295500000312
Characteristic map of the output, based on the comparison of the characteristic map and the reference value>
Figure BDA00039866295500000313
Is->
Figure BDA00039866295500000314
Is greater than or equal to>
Figure BDA00039866295500000315
K upsampling modules are
Figure BDA00039866295500000316
Comprising:
Figure BDA00039866295500000317
wherein, the first and the second end of the pipe are connected with each other,
Figure BDA00039866295500000318
is->
Figure BDA00039866295500000319
Characteristic map of the output, based on the comparison of the characteristic map and the reference value>
Figure BDA00039866295500000320
Is the combination of the encoder and decoder outputs on the k-order scale; conc is an abbreviation for Concatenate, indicating incorporation; for the case of K = K, ->
Figure BDA00039866295500000321
Figure BDA0003986629550000041
Is->
Figure BDA0003986629550000042
The parameters of (1);
super-resolution subnetwork
Figure BDA0003986629550000043
Obtaining a 0-order super-resolution seismic image->
Figure BDA0003986629550000044
Wherein theta is s Is a super-resolution subnetwork parameter;
k multi-scale reconstruction sub-networks
Figure BDA0003986629550000045
Comprising:
Figure BDA0003986629550000046
wherein the content of the first and second substances,
Figure BDA0003986629550000047
is->
Figure BDA0003986629550000048
The parameters of (1);
the three sub-networks are embodied as follows:
the coding part of the self-coder sub-network consists of 4 down-sampling modules, and the shallow to deep forms are respectively as follows:
Conv(1,64,3)+BN+ReLU+Conv(64,64,3)+BN+ReLU+Max
Conv(64,128,3)+BN+ReLU+Conv(128,128,3)+BN+ReLU+Max
Conv(128,256,3)+BN+ReLU+Conv(256,256,3)+BN+ReLU+Max
Conv(256,512,3)+BN+ReLU+Conv(512,512,3)+BN+ReLU+Max
conv () represents convolution operation, wherein 3 parameters in Conv are the number of input channels, the number of output channels and the side length of a square convolution kernel respectively, the convolution step length of Conv is 1, the filling is 1 so as to ensure that the size of a feature graph after convolution is unchanged, BN represents batch normalization, reLU is an activation function, max represents maximum pooling, and the kernel size is 2 multiplied by 2 and the step length is 2;
the decoding part of the self-encoder subnetwork consists of 1 feature mapping layer and 4 up-sampling modules, and the shallow-to-deep forms are respectively as follows:
Conv(512,1024,3)+BN+ReLU+Conv(1024,1024,3)+BN+ReLU+SubPix
Conv(512,1024,3)+BN+ReLU+Conv(1024,512,3)+BN+ReLU+SubPix
Conv(256,512,3)+BN+ReLU+Conv(512,256,3)+BN+ReLU+SubPixConv(128,256,3)+BN+ReLU+Conv(256,256,3)+BN+ReLU+SubPix
the convolution step length of the 4 up-sampling module output channels is respectively 256, 128, 64 and 64, conv is 1, the sub-pixel convolution layer is filled with 1, subPix, the up-sampling is completed by utilizing a channel recombination mode, and if the multiple of the up-sampling is 2, the number of the channels is reduced by 4 times after passing through the SubPix;
the form of the super-resolution subnetwork is specifically as follows:
Conv(64,128,9)+ReLU+SubPix+Conv(32,16,1)+ReLU+Conv(16,1,5)
wherein the step length of the three convolution layers is 1, and the filling values are 4, 0 and 2 respectively so as to ensure that the size of the characteristic diagram is unchanged;
the multi-scale reconstruction sub-network consists of 4 convolutional layers, and the form is as follows for the 1 st to 4 th scales respectively:
Conv(128,32,9)+ReLU+Conv(32,16,1)+ReLU+Conv(16,1,5)
Conv(128,64,9)+ReLU+Conv(64,16,1)+ReLU+Conv(16,1,5)
Conv(256,64,9)+ReLU+Conv(64,16,1)+ReLU+Conv(16,1,5)
Conv(512,64,9)+ReLU+Conv(64,16,1)+ReLU+Conv(16,1,5)
wherein, the filling values of the three convolution layers are respectively 4, 0 and 2;
s22, defining a loss function of the 0 th order scale, which is specifically as follows:
defining the high resolution reconstruction loss, and specifically for a single image, the following steps are carried out:
Figure BDA0003986629550000051
wherein | 1 Is a norm of 1, and N is the total number of pixel points of the seismic image;
Figure BDA0003986629550000052
the convergence of training can be accelerated, but the texture details of the generated super-resolution image are too smooth, so that structural similarity SSIM is introduced, an SSIM function is based on the assumption that structural information is extracted when human eyes watch the image, a model is more sensitive to the local structural change of the image, high-frequency information such as the edge and the details of the image is reserved, and the reconstructed super-resolution image is more suitable for a human visual system;
defining a high-resolution structural similarity loss, specifically for a single image as follows:
SSIM(x,y)=[l(x,y) α ·[c(x,y) β ·[s(x,y) γ
where x, y are the two images to be evaluated, α, β, γ are the corresponding weights, and 0.15, 0.29, 0.31, l (x, y), c (x, y), s (x, y) can be taken to represent three measurements between x and y, i.e., the brightness or amplitude, contrast, and texture in the seismic image
Figure BDA0003986629550000053
Figure BDA0003986629550000054
Figure BDA0003986629550000055
Wherein, mu xy Representing the mean, σ, of the images x, y xy Representing the standard deviation, σ, of the images x, y xy Is the covariance between the images x and y, c 1 ,c 2 ,c 3 Is three constants, can be set as c 1 =10 -4
Figure BDA0003986629550000056
Finally, a loss function of 0 th order scale is obtained, and for a single image, the loss function is:
Figure BDA0003986629550000057
where a is the weight coefficient of the loss function, which can be generally set to 0.6;
s23, defining a loss function of the kth scale, wherein k is greater than 0, and the method specifically comprises the following steps:
for the
Figure BDA0003986629550000061
Reconstructed image with resolution +>
Figure BDA0003986629550000062
Focusing on whether the reconstructed image looks more like an original seismic image or not rather than focusing on the matching degree of the pixel points;
defining a k-order perceptual loss, for a single image, namely:
Figure BDA0003986629550000063
where φ represents a certain layer of output of the pre-trained VGG network, N φ Representing the total number of pixel points of the output image of the layer;
define the k-order lattice loss, for a single image, i.e.:
Figure BDA0003986629550000064
wherein N is g Representing the total number of elements of a Gram matrix, namely a Gram matrix;
defining a k-order smoothing loss, for a single image, namely:
Figure BDA0003986629550000065
wherein (, j) represents the location of a pixel point in the image; the addition of the smoothing loss term can enable the edge of the generated seismic image to be clearer, further eliminate noise in the seismic image and improve the performance of subsequent seismic interpretation;
finally, a loss function of the kth order scale is obtained, k >0, and for a single image, namely:
Figure BDA0003986629550000066
wherein, γ 1 And gamma 2 Contributions for balancing the three loss terms, which may be set to 5 and 0.4;
s24, initializing the seismic reconstruction network, wherein random initialization can be adopted;
s3, learning the seismic reconstruction network by using a multi-scale depth supervised learning strategy, which specifically comprises the following steps:
pre-training the whole network to wait
Figure BDA0003986629550000067
After stabilization, add->
Figure BDA0003986629550000068
To the k-th>Training the 0-order scale network until the model converges; the model is optimized during training using an Adam optimizer, where the first order moment estimate is set to an exponential decay rate of 0.9, the second order moment estimate is set to an exponential decay rate of 0.99, the epsilon parameter is used to prevent division by zero during implementation and is therefore set to a very small number, e.g., 10 -8 (ii) a The learning rate is initialized to 10 -4 When the loss tends to be smooth, the learning rate is reduced to 10 -5
And S4, inputting the new seismic image into the trained seismic enhancement network to obtain a de-noised high-resolution seismic image and complete the reconstruction of seismic data.
The embodiment of the invention can keep the high-frequency information of the seismic image, inhibit random noise, effectively highlight the geological structure information, have visual effect more in line with a human eye system, and effectively improve the efficiency and accuracy of subsequent seismic interpretation.
In yet another aspect, the present invention also discloses a computer readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of any of the methods described above.
In yet another aspect, the present invention also discloses a computer device comprising a memory and a processor, the memory storing a computer program, the computer program, when executed by the processor, causing the processor to perform the steps of any of the methods as described above.
In a further embodiment provided by the present application, there is also provided a computer program product comprising instructions which, when run on a computer, cause the computer to perform the steps of any of the methods of the above embodiments.
It is understood that the system provided by the embodiment of the present invention corresponds to the method provided by the embodiment of the present invention, and the explanation, the example and the beneficial effects of the related contents can refer to the corresponding parts in the method.
It will be understood by those skilled in the art that all or part of the processes of the methods of the embodiments described above can be implemented by a computer program, which can be stored in a non-volatile computer-readable storage medium, and can include the processes of the embodiments of the methods described above when the program is executed. Any reference to memory, storage, database or other medium used in the embodiments provided herein can include non-volatile and/or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically Programmable ROM (EPROM), electrically Erasable Programmable ROM (EEPROM), or flash memory. Volatile memory can include Random Access Memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in a variety of forms such as Static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), double Data Rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous Link DRAM (SLDRAM), rambus (Rambus) direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM).
All possible combinations of the technical features in the above embodiments may not be described for the sake of brevity, but should be considered as being within the scope of the present disclosure as long as there is no contradiction between the combinations of the technical features.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (6)

1. A synchronous processing method of multi-scale super-resolution and denoising of seismic data is characterized by comprising the following steps,
s1, performing down-sampling on a high-resolution seismic image to obtain a low-resolution seismic image, and constructing a training sample set;
s2, initializing an earthquake reconstruction network, wherein the earthquake reconstruction network comprises a self-encoder sub-network, a super-resolution sub-network and a multi-scale reconstruction sub-network;
s3, learning the seismic reconstruction network by using a multi-scale depth supervised learning strategy;
and S4, inputting the new seismic image into the trained seismic enhancement network to obtain a de-noised high-resolution seismic image and complete the reconstruction of seismic data.
2. The seismic data multi-scale super-resolution and denoising synchronous processing method according to claim 1, wherein: s1, down-sampling the high-resolution seismic image to obtain a low-resolution seismic image, and constructing a training sample set, wherein the method specifically comprises the following steps:
s11, for seismic image
Figure FDA0003986629540000011
m and n are the length and height of the seismic image, and subscripts hr, sr and lr represent high resolution, super resolution and low resolution; high resolution seismic image I hr Downsampling to obtain a low-resolution seismic image I lr =Down(I hr Θ), down represents a downsampling function, based on the downsampling function>
Figure FDA0003986629540000012
For the down-sampling parameters, K =0,1,2,3, \ 8230, K denotes the down-sampling order,
Figure FDA0003986629540000013
represents->
Figure FDA0003986629540000014
K =0 means no downsampling, i.e. downsampling
Figure FDA0003986629540000015
S12, a sheet I hr A corresponding group
Figure FDA0003986629540000016
Forming a training sample pair with independent identically distributed noise>
Figure FDA0003986629540000017
As an input to the network>
Figure FDA0003986629540000018
The supervised learning label is output in K =0,1,2,3, \ 8230;, K multi-scale as a network.
3. The seismic data multi-scale super-resolution and denoising synchronous processing method according to claim 2, wherein: s2, initializing a seismic reconstruction network, wherein the seismic reconstruction network comprises an autoencoder sub-network, a super-resolution sub-network and a multi-scale reconstruction sub-network, and the specific steps are as follows:
s21, defining a seismic reconstruction network, specifically as follows:
the connection relationships of the three sub-networks are as follows:
the self-encoder sub-network is one of artificial neural networks, an encoder extracts features, a decoder reconstructs data, and a self-encoder is a U-shaped encoder-decoder network and comprises K downsampling blocks and corresponding K upsampling blocks; k downsampling blocks of
Figure FDA0003986629540000019
Comprising:
Figure FDA00039866295400000110
wherein
Figure FDA00039866295400000111
Is->
Figure FDA00039866295400000112
Output characteristic map>
Figure FDA00039866295400000113
Is->
Figure FDA00039866295400000114
Is greater than or equal to>
Figure FDA00039866295400000115
K upsampling modules are->
Figure FDA00039866295400000116
Comprises the following components:
Figure FDA00039866295400000117
wherein the content of the first and second substances,
Figure FDA00039866295400000118
is->
Figure FDA00039866295400000119
Characteristic map of the output, based on the comparison of the characteristic map and the reference value>
Figure FDA00039866295400000120
Is the combination of the encoder and decoder outputs on the k-order scale; conc is an abbreviation for Concatenate, indicating incorporation; for the case of K = K, ->
Figure FDA00039866295400000121
Figure FDA00039866295400000122
Is->
Figure FDA00039866295400000123
The parameters of (a);
super-resolution subnetwork
Figure FDA0003986629540000021
Obtaining a 0-order super-resolution seismic image->
Figure FDA0003986629540000022
Wherein theta is s Is a super-resolution subnetwork parameter; />
K multi-scale reconstruction sub-networks
Figure FDA0003986629540000023
Comprises the following components:
Figure FDA0003986629540000024
wherein, the first and the second end of the pipe are connected with each other,
Figure FDA0003986629540000025
is->
Figure FDA0003986629540000026
The parameters of (1);
the three sub-networks are embodied as follows:
the coding part of the self-coder subnetwork consists of 4 down-sampling modules, and the shallow to deep forms are respectively as follows:
Conv(1,64,3)+BN+ReLU+Conv(64,64,3)+BN+ReLU+Max
Conv(64,128,3)+BN+ReLU+Conv(128,128,3)+BN+ReLU+Max
Conv(128,256,3)+BN+ReLU+Conv(256,256,3)+BN+ReLU+Max
Conv(256,512,3)+BN+ReLU+Conv(512,512,3)+BN+ReLU+Max
wherein Conv () represents convolution operation, wherein 3 parameters in Conv are the number of input channels, the number of output channels and the side length of a square convolution kernel respectively, the convolution step size of Conv is 1, the filling is 1 to ensure that the size of a feature graph after convolution is unchanged, BN represents batch normalization, reLU is an activation function, max represents maximum pooling, and the kernel size is 2 multiplied by 2 and the step size is 2;
the decoding part of the self-encoder subnetwork consists of 1 feature mapping layer and 4 up-sampling modules, and the shallow-to-deep forms are respectively as follows:
Conv(512,1024,3)+BN+ReLU+Conv(1024,1024,3)+BN+ReLU+SubPix
Conv(512,1024,3)+BN+ReLU+Conv(1024,512,3)+BN+ReLU+SubPix
Conv(256,512,3)+BN+ReLU+Conv(512,256,3)+BN+ReLU+SubPix
Conv(128,256,3)+BN+ReLU+Conv(256,256,3)+BN+ReLU+SubPix
the convolution step length of the 4 up-sampling module output channels is respectively 256, 128, 64 and 64, conv is 1, the filling is 1, subPix represents a sub-pixel convolution layer, the up-sampling is completed by utilizing a channel recombination mode, and if the multiple of the up-sampling is 2, the number of the channels is reduced by 4 times after passing through the SubPix;
the form of the super-resolution subnetwork is specifically as follows:
Conv(64,128,9)+ReLU+SubPix+Conv(32,16,1)+ReLU+Conv(16,1,5)
wherein the step length of the three convolution layers is 1, and the filling values are 4, 0 and 2 respectively so as to ensure that the size of the characteristic diagram is unchanged;
the multi-scale reconstruction sub-network consists of 4 convolutional layers, and the form is as follows for the 1 st to 4 th scales respectively:
Conv(128,32,9)+ReLU+Conv(32,16,1)+ReLU+Conv(16,1,5)
Conv(128,64,9)+ReLU+Conv(64,16,1)+ReLU+Conv(16,1,5)
Conv(256,64,9)+ReLU+Conv(64,16,1)+ReLU+Conv(16,1,5)
Conv(512,64,9)+ReLU+Conv(64,16,1)+ReLU+Conv(16,1,5)
wherein, the filling values of the three convolution layers are respectively 4, 0 and 2;
s22, defining a loss function of 0 th order scale, specifically as follows:
defining the high resolution reconstruction loss, and specifically for a single image, the following steps are carried out:
Figure FDA0003986629540000031
wherein | 1 Is a norm of 1, and N is the total number of pixel points of the seismic image;
Figure FDA0003986629540000032
the convergence of training can be accelerated, but the texture details of the generated super-resolution image are too smooth, so that structural similarity SSIM is introduced;
defining a high-resolution structural similarity loss, specifically for a single image as follows:
SSIM(x,y)=[l(x,y)] α ·[c(x,y)] β ·[s(x,y)] γ
where x, y are the two images to be evaluated, and α, β, γ are the corresponding weights, it is possible to take 0.15, 0.29, 0.31, l (x, y), c (x, y), s (x, y) to represent the three measurements between x and y, i.e. the brightness or amplitude, contrast and structure in the seismic image
Figure FDA0003986629540000033
Figure FDA0003986629540000034
Figure FDA0003986629540000035
Wherein, mu xy Representing the mean, σ, of the images x, y xy Representing the standard deviation, σ, of the images x, y xy Is the covariance between the images x and y, c 1 ,c 2 ,c 3 Is three constants set as c 1 =10 -4
Figure FDA0003986629540000036
Finally, a loss function of 0 th order scale is obtained, and for a single image, namely:
Figure FDA0003986629540000037
wherein a is a weight coefficient of the loss function;
s23, defining a loss function of the kth scale, wherein k is greater than 0, and the method comprises the following specific steps:
for the
Figure FDA0003986629540000038
Reconstructed image with resolution +>
Figure FDA0003986629540000039
Not focusing on the matching degree of the pixel points, but focusing on the reconstructed image from the visual point of viewWhether to resemble more of the original seismic image;
defining a k-order perceptual loss, for a single image, namely:
Figure FDA00039866295400000310
where φ represents a certain layer of output of the pre-trained VGG network, N φ Representing the total number of pixel points of the layer of output image;
define the k-order lattice loss, for a single image, i.e.:
Figure FDA00039866295400000311
wherein N is g Represents the total number of elements of the Gram matrix, gram being Gram;
defining a k-order smoothing loss, for a single image, namely:
Figure FDA0003986629540000041
wherein (, j) represents the location of a pixel point in the image;
finally, a loss function of the kth order scale is obtained, k is greater than 0, and for a single image, namely:
Figure FDA0003986629540000042
wherein, gamma is 1 And gamma 2 Contributions for balancing the three loss terms, set to 5 and 0.4;
and S24, initializing the seismic reconstruction network, and adopting random initialization.
4. The seismic data multi-scale super-resolution and denoising synchronous processing method according to claim 3, wherein: s3, learning the seismic reconstruction network by using a multi-scale deep supervised learning strategy, which specifically comprises the following steps:
pre-training the whole network to wait
Figure FDA0003986629540000043
After stabilization, add->
Figure FDA0003986629540000044
To the k-th>Training the 0-order scale network until the model converges; the model was optimized during training using an Adam optimizer, where the first order moment estimate was set to an exponential decay rate of 0.9, the second order moment estimate was set to an exponential decay rate of 0.99, the epsilon parameter was used to prevent division by zero in the implementation; the learning rate is initialized to 10 -4 When the loss tends to be smooth, the learning rate is reduced to 10 -5
5. The seismic data multi-scale super-resolution and denoising synchronous processing method according to claim 4, wherein: epsilon parameter set to 10 -8
6. A computer-readable system, in which a computer program is stored which, when being executed by a processor, causes the processor to carry out the steps of the method according to any one of claims 1 to 5.
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