Seismic denoising method based on MLReal transformation

Abstract

The invention provides an earthquake denoising method based on MLReal transformation. The earthquake denoising method based on the MLReal transformation comprises the following steps: step 1, selecting a target function; step 2, constructing a denoising neural network; 3, redefining training data; 4, redefining test data; and 5, inputting the redefined training data and test data into the neural network, and carrying out training loop iteration to obtain synthetic data with field data characteristics. According to the seismic denoising method based on MLReal transformation, important information of field seismic data is combined into a training process of synthetic data; and the successfully trained network is used for field seismic data denoising, so that the denoising effect is obviously improved.

Description

Technical Field

[0001] The invention relates to the technical field of oil and gas exploration seismic data processing, and in particular to a seismic denoising method based on MLReal transformation. Background Art

[0002] In the process of seismic data acquisition, various environmental factors and equipment interference will cause various noises in the collected seismic data, thus affecting the signal-to-noise ratio and resolution of the seismic profile, so it is very necessary to suppress the noise. With the continuous efforts of scholars from various countries, there have been great breakthroughs in the methods of seismic denoising, including fx deconvolution (Naghizadeh and Sacchi, 2012), Radon transform (Foster and Mosher, 1992; Hargreaves et al., 2001), curvelet transform (Cao et al., 2015), dictionary learning (Beckouche and Ma, 2014) and singular value decomposition (Sang Yu, 2014). These traditional methods have achieved certain results in dealing with noise, but when faced with very complex underground structures and complex collected seismic data, the processing results will be very unsatisfactory.

[0003] In recent years, with the vigorous development of deep learning theory and application, deep learning algorithms have been applied to various fields. In terms of seismic denoising, in 2018, Han Weixue achieved good results by constructing a CNN network and using it to remove random noise in seismic data; in 2019, Dong proposed an adaptive DnCNN based on high-order statistics to suppress low-frequency noise in the desert; in 2021, Fang Wenqian et al. proposed a dual residual network for random noise suppression of seismic signals to protect effective signals; in 2022, Mihai l-Antonio Chirtu divided seismic signals into two parts, noise and signal, in the time-frequency domain, and denoised them using the U-Net convolutional neural network structure, proving the feasibility of the method; in 2022, Zhang Hao proposed seismic denoising in the imaging domain based on conditional adversarial neural networks, which not only kept the image structure undistorted, but also suppressed various types of noise. With the continuous development of deep learning, it can be seen that there is great potential in seismic data denoising and it has become the mainstream in today's world.

[0004] However, the choice of training data during deep learning determines the performance of the neural network and its suitability for further datasets. In particular, in seismic applications, the choice is very important between manually labeling field seismic data or generating synthetic seismic data, both of which show serious limitations. The advantage of manually labeling field seismic data labels is that the data used to train the network may have the same characteristics as the future application network, but it is often limited by the performance of traditional methods for denoising, which cannot surpass the traditional methods required to generate labels; training with synthetic datasets overcomes this obstacle and allows completely noise-free labels to be generated for the training process. However, if the synthetic data is barely identical to the real dataset, it will affect the quality of the decisions made based on the data. Even if the synthetic data is really good, it is still a copy of the specific properties of the real dataset. The model looks for trends to copy, so some random behaviors may be ignored, which greatly affects the effect of denoising.

[0005] The challenge of training our neural network model on synthetic data is to generalize the trained model to real data, because the process requires careful identification of the training set and careful identification of the real noise and other variables contained between the synthetic data and the real data. In other words, synthetic data and real data are usually not from the same distribution, which is crucial to the success of training neural network models (Kouw, 2018). Therefore, many synthetically trained neural network models perform poorly on real data. On the other hand, the model provided by training on real data is usually as good as the accuracy of the labels determined by the artificial algorithm. Therefore, in this case, the data-driven nature of machine learning will be severely weakened (Zhou, 2017). Since synthetic data usually cannot capture the real situation of field data, our trained neural network (NN) in the inference stage performs poorly, which reduces the denoising effect. Therefore, how to inject as many field seismic data features as possible into synthetic data training, reduce the error between synthetic training data and real application data, and finally use it in seismic denoising tasks, is an urgent problem to be solved.

[0006] In the Chinese patent application with application number: CN202210523847.2, a method for denoising seismic data based on convolutional neural networks is involved. First, an initial data set is constructed, and a cyclic generative adversarial convolutional neural network is constructed. The cyclic generative adversarial convolutional neural network uses the structure of a cyclic generative adversarial network as the main network. The structure of the cyclic generative adversarial network includes a generator and a discriminator. The non-local neural network is connected as a residual to the convolutional layers of the generator, and the PatchGAN output method is used in the discriminator instead of the original fully connected method. Then the ring-generated adversarial convolutional neural network is trained, and finally the noisy seismic data is denoised. Experiments have verified that the denoising effect of the invented method is good.

[0007] In the Chinese patent application with application number: CN202211250180.X, a seismic denoising method based on convolutional neural network and visual transformation neural network is involved, which relates to the field of information processing technology. The present invention collects noisy seismic data, performs denoising on the noisy seismic data, obtains multiple denoised seismic data blocks, constructs a seismic data set including a training set, a validation set and a test set, and constructs a seismic data denoising network based on convolutional neural network and visual transformation neural network. After the seismic data denoising network is trained with the training set, the denoising effect of the trained seismic data denoising network is debugged with the validation set, and after the seismic data denoising network with the best denoising effect is obtained, the trained seismic data denoising network is used to remove the noise of the noisy seismic data blocks in the test set to obtain the seismic data after the noise is removed. The invention effectively improves the denoising performance of seismic data, reduces the training cost, and is conducive to the rapid and accurate acquisition of underground medium structural information.

[0008] In the Chinese patent application with application number: CN202111337078.9, an unsupervised seismic data denoising method based on a deep tensor neural network is involved, which is applied to the field of seismic data processing and aims at the problem of poor denoising performance in the prior art. The present invention first uses SURE to replace the MSE cost function to convert data denoising into a corresponding unsupervised regression model. After that, a SURE-TCNN network framework is established, following the tNN framework and the transformation-based t-product, which is an extension of the t-product of the traditional tNN framework. Taking advantage of the advantages in the t-product, the tensor-based SURE-TCNN can be split into a separate matrix-based SURE-CNN for each front or time slice in the time-frequency domain, which is easy to solve and more attractive. Finally, synthetic and real data experiments show that the proposed method achieves superior performance compared with the SOTA denoising method.

[0009] In the Chinese patent application with application number: CN201710334723.9, a seismic wave denoising method based on the combination of adaptive filtering and wavelet transform is involved, which solves how to extract effective signals that are conducive to analysis and interpretation from mixed signals, suppress noise, that is, highlight effective signals, and try to remove interference signals to achieve the purpose of signal-noise separation. First, consider using the time delay estimation method to quickly find useful signals. At this time, the useful signal still contains noise in some frequency bands; then use the wavelet denoising method to realize the partial noise that overlaps with the useful signal spectrum, achieve the purpose of fine denoising, and finally obtain clean and effective seismic wave data, which can reflect the true situation of underground geological structure and make correct and reasonable detection of geological conditions.

[0010] The above existing technologies are all significantly different from the present invention and fail to solve the technical problem we want to solve. Therefore, we have invented a new seismic denoising method based on MLReal transformation. Summary of the invention

[0011] The purpose of the present invention is to provide a seismic denoising method based on MLReal transformation with significantly improved denoising effect.

[0012] The object of the present invention can be achieved by the following technical measures: a seismic denoising method based on MLReal transform, the seismic denoising method based on MLReal transform comprises:

[0013] Step 1, select the objective function;

[0014] Step 2: Build a denoising neural network;

[0015] Step 3, redefine the training data;

[0016] Step 4, redefine the test data;

[0017] Step 5: Input the redefined training data and test data into the neural network, perform training cycle iterations, and obtain synthetic data with the characteristics of field data.

[0018] The purpose of the present invention can also be achieved by the following technical measures:

[0019] The seismic denoising method based on MLReal transformation also includes, before step 1, in order to solve the difference between the distribution of the training data and the test data set, it is necessary to define an error limit to ensure the minimum value of the difference measure.

[0020] When defining the error limit, the formula used is:

[0021] ε t (NN)≤ε s (NN)+d(P s (x s ),P t (x t ))+λ

[0022] ε t (NN) represents the error bound during testing, ε s (NN) represents the error limit during training, P s (x s ) is the probability distribution of the training data, P t (x t) is the probability distribution of the test data, d(,) represents the distance between the marginal distribution of the test set and the training set, and λ represents the optimal joint error of the neural network model between the source data set and the target data set; therefore, the upper limit of the error of the test is ε t (NN) by ε s (NN), d(,) and λ are guided by these three parameters.

[0023] In step 1, the network model is optimized using the test error bound as the objective function.

[0024] In step 1, the objective function is:

[0025] ε t (NN)≤ε s (NN)+d(P s (x s ),P t (x t ))+λ

[0026] Where ε t (NN) represents the error bound during testing, ε s (NN) represents the error limit during training, P s (x s ) is the probability distribution of the training data, P t (x t ) is the probability distribution of the test data, d(,) represents the distance between the marginal distribution of the test set and the training set, and λ represents the optimal joint error of the neural network model between the source data set and the target data set; therefore, the upper limit of the error of the test is ε t (NN) by ε s (NN), d(,) and λ are guided by these three parameters.

[0027] In step 2, a 4-layer residual U-Net neural network was constructed. The network used 32 filters as the initial filters, which doubled in each layer, resulting in 106M trainable parameters. The network was trained using 8092 training samples and 1024 validation samples. The number of epochs was 150 and the size of the image block was 64×64.

[0028] In step 3, during the training phase, the training data is T s Transformation allows the features of field data to be injected into synthetic data.

[0029] In step 3, T s Transformation

[0030]

[0031] Where k is the reference trace index from the synthetic input data, which is fixed for both synthetic and real data, and j is the index of the part from the real data, whether it comes from the shot point set or the seismic image. The operator represents cross-correlation, and the operator * represents convolution; in this equation, the synthetic profile of the input Cross-correlate with a reference trace from the profile and then with the reference trace and d from the real data ij The (j) randomly selected autocorrelated parts of the data are convolved; that is, before being input into the NN, each synthetic data block is cross-correlated with a single reference trace extracted from the data block; during training iterations, for each iteration, a random field data block is selected, autocorrelated on a trace-by-trace basis, and convolved with each cross-correlated synthetic data block, which becomes the input of the network.

[0032] In step 3, the randomly chosen j index for the autocorrelated real data is varied in each training iteration to allow for proper representation of the real data features on the training set.

[0033] Step 4, in the inference phase, by performing T t Transformation allows the features of the synthetic data to be injected into the target data.

[0034] In step 4, T t The transformation is:

[0035]

[0036] Where k is the reference track index from the synthetic input data, which is fixed for both synthetic and real data, j is the partial index from the real data, and the operator represents cross-correlation, operator * represents convolution, d ij is the real data, N s is the number of synthetic parts in the training set; i.e., for the inference phase, the real data undergoes a similar preprocessing process as the synthetic data in the training phase; however, in this phase, once the field data patches are cross-correlated with their reference traces, these patches are convolved with the block of the autocorrelation average of all synthetic training data patches.

[0037] In step 4, the randomly chosen j index for the autocorrelated real data is varied in each training iteration to allow for proper representation of the real data features on the training set.

[0038] In step 5, the redefined training data and test data are input into the neural network and the training cycle is iterated so that the test error objective function reaches the minimum value, that is, synthetic data with the characteristics of field data is obtained, which is finally used as the input of the network and finally used for denoising.

[0039] The seismic denoising method based on MLReal transformation in the present invention reduces the error between synthetic training data and real application data by using MLReal transformation, injects as many field seismic data features as possible into synthetic data training, and finally uses it in the seismic denoising task. Specifically, the present invention proposes an optimization algorithm based on seismic denoising. In order to maintain the characteristics of the original wave field, the synthetic data is trained with a neural network, and the training data and the real data are subjected to MLReal transformation, so that the important information of the field seismic data is combined into the training process of the synthetic data; finally, the successfully trained network is used for field seismic data denoising, so that the denoising effect is significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 It is a flowchart of a specific embodiment of the seismic denoising method based on MLReal transformation of the present invention;

[0041] Figure 2 It is a schematic diagram of an application example of seismic denoising of synthetic seismic data in a specific embodiment of the present invention;

[0042] Figure 3 It is a schematic diagram of an application example of denoising of vibroseis field seismic data in the desert area of ​​western China in a specific embodiment of the present invention;

[0043] Figure 4 It is a schematic diagram of an application example of denoising of field seismic data of explosive sources in eastern China in a specific embodiment of the present invention. DETAILED DESCRIPTION

[0044] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0045] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprising" and / or "including" are used in this specification, it indicates the presence of features, steps, operations and / or combinations thereof.

[0046] The seismic denoising method based on the MLReal algorithm reduces the error between synthetic training data and real application data by using MLReal transformation. In order to maintain the characteristics of the original wave field, the synthetic data is trained with a neural network and transformed with MLReal at the same time, so that the important information of the field seismic data is combined with the training process of the synthetic data, thereby achieving a good denoising effect.

[0047] like Figure 1 As shown, Figure 1 FIG. 1 is a flow chart of the seismic denoising method based on MLReal transformation of the present invention. Figure 1 In the process, before training the model, in order to solve the difference between the distribution of training data and test data set, it is necessary to define the error limit to ensure the minimum value of the difference metric:

[0048] ε t (NN)≤ε s (NN)+d(P s (x s ),P t (x t ))+λ

[0049] ε t (NN) represents the error bound during testing, ε s (NN) represents the error limit during training, P s (x s ) is the probability distribution of the training data, P t (x t ) is the probability distribution of the test data, d(,) represents the distance between the marginal distribution of the test set and the training set, and λ represents the optimal joint error of the neural network model between the source data set and the target data set. Therefore, the upper limit of the error of the test is ε t (NN) by ε s (NN), d(,) and λ are guided by these three parameters.

[0050] For most artificial intelligence and machine learning projects, it is essential to have a large and processed data set, but obtaining this data is usually a huge challenge. Not only must data be collected from the real world, but it must also be manually cleaned and labeled. Synthetic data is much easier than collecting and labeling real data, but synthetic data lacks the behavior and characteristics of real data. By performing MLReal transformation on training data and real data, important information from field seismic data can be incorporated into the training process of synthetic data; finally, the successfully trained network is used for field seismic data denoising, which significantly improves the denoising effect.

[0051] The implementation process of reducing the difference in probability distribution between training data and test data obtained by MLReal transformation in both the neural network training stage and the inference stage is as follows:

[0052] 1) Select the objective function: Use the test error limit as the objective function to optimize the network model. The objective function is:

[0053] ε t (NN)≤ε s (NN)+d(P s (x s ),P t (x t ))+λ

[0054] Where ε t (NN) represents the error bound during testing, ε s (NN) represents the error limit during training, P s (x s ) is the probability distribution of the training data, P t (x t ) is the probability distribution of the test data, d(,) represents the distance between the marginal distribution of the test set and the training set, and λ represents the optimal joint error of the neural network model between the source data set and the target data set. Therefore, the upper limit of the error of the test is ε t (NN) by ε s (NN), d(,) and λ are guided by these three parameters.

[0055] 2) Building a denoising neural network: We built a 4-layer residual U-Net neural network, which used 32 filters as the initial filters. The number of filters doubled with each layer, resulting in approximately 106M trainable parameters. The network was trained using 8092 training samples and 1024 validation samples. The number of epochs was 150 and the image block size was 64×64.

[0056] 3) Redefine the test data: During the training phase, the training data is T s Transformation allows the features of field data to be injected into synthetic data. s Transformation

[0057]

[0058] Where k is the reference trace index from the synthetic input data (fixed for both synthetic and real data), j is the index of the part from the real data, whether it comes from the shot point set or the seismic image, and the operator represents cross-correlation and operator * represents convolution. In this equation, we have the synthetic profile at the input Cross-correlate with a reference trace from the profile and then with the reference trace and d from the real data ij The (j) randomly selected autocorrelated parts of the data are convolved. That is, before being input to the NN, each synthetic data block is cross-correlated with a single reference trace extracted from the data block. During the training iterations, for each iteration, a random field data block is selected, autocorrelated on a trace-by-trace basis, and convolved with each cross-correlated synthetic data block, which becomes the input to the network.

[0059] The randomly chosen j index for the autocorrelation real data is varied in each training iteration to allow for proper representation of the real data features on the training set.

[0060] 4) Redefine test data: In the inference phase, by T t Transformation, so that the characteristics of the synthetic data are injected into the target data. t The transformation is:

[0061]

[0062] Where k is the reference track index from the synthetic input data (fixed for both synthetic and real data), j is the partial index from the real data, and the operator represents cross-correlation, operator * represents convolution, d ij is the real data, N s is the number of synthetic parts in the training set. That is, for the inference phase, the real data undergoes a similar preprocessing process as the synthetic data in the training phase. However, in this phase, once the wild data patches are cross-correlated with their reference traces, these patches are convolved with the block of the autocorrelation average of all synthetic training data patches.

[0063] The randomly chosen j index for the autocorrelation real data is varied in each training iteration to allow for proper representation of the real data features on the training set.

[0064] 5) Input the redefined training data and test data into the neural network and perform training cycle iterations so that the test error objective function reaches the minimum value, that is, synthetic data with the characteristics of field data is obtained, which is finally used as the input of the network and finally used for denoising.

[0065] The following are several specific embodiments of the present invention.

[0066] Embodiment 1:

[0067] like Figure 2 As shown in the figure, the seismic denoising method based on MLReal transform is used to denoise the synthetic seismic data simulated in the laboratory. On the basis of the simulated noise-free seismic data, strong noise with a signal-to-noise ratio of 1:1 is added, as shown in Figure 2 As shown in a. It can be seen that the phase axis of the shallow layer can still be distinguished, but the reflection signal of the medium and deep layers cannot be distinguished. After seismic denoising based on MLReal transformation, as shown in Figure 2 As shown in Figure b, the reflection events of the entire layer, especially the middle and deep layers, are well restored, and the hyperbolic shape is clearly visible. At the same time, the signal of the middle and shallow layers is also improved to a certain extent.

[0068] Embodiment 2:

[0069] like Figure 3 As shown in the figure, the seismic denoising method based on MLReal transform is used to denoise the vibroseis field seismic data in the desert area of ​​western China. After cross-correlation processing of the vibroseis data, the noisy data is obtained, as shown in Figure 3 As shown in a. The signal-to-noise ratio of this data is low, and the deep reflections are submerged in the noise and are difficult to identify. Figure 3 b is the denoised data. It can be seen that the seismic denoising method based on MLReal transform has done a good job in removing noise from shallow, medium and deep layers. In the denoising process, the effective signal is not damaged. The overall signal-to-noise ratio and the continuity of the reflection phase axis are significantly improved.

[0070] Embodiment 3:

[0071] like Figure 4 As shown in the figure, the seismic denoising method based on MLReal transform is used to denoise the field seismic data of explosive sources in eastern China. By performing MLReal transform on the training data and test data, the important information of the field seismic data is combined with the training process of the actual data, and finally the trained network is used for denoising the field seismic data. Figure 4 a is the noisy data, Figure 4 b is the denoised data. Although the signal-to-noise ratio of this data is relatively high, the noise in the medium and short offset range is still very strong. After the application of seismic denoising based on MLReal transform, the strong noise is significantly removed, and the reflection phase axis that was originally submerged in the noise is clearly visible. It can be seen that the quality of the single-shot gather before and after denoising is significantly improved.

[0072] The seismic denoising method based on the MLReal algorithm described in the present invention first uses T s Transform the training data; secondly, in order to make the distribution of the training set and the test set similar after the change, in the inference stage, similar T t Transformation converts the actual data, T s Transformation and T tThe transformations are collectively called MLReal transformations, which allow important information from field seismic data to be incorporated into the training process of synthetic data. Finally, the successfully trained network is used for denoising field seismic data, which significantly improves the denoising effect.

[0073] Finally, it should be noted that the above is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art can still modify the technical solutions recorded in the aforementioned embodiments or replace some of the technical features therein with equivalents. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

[0074] Except for the technical features described in the specification, all other technical features are known technologies to those skilled in the art.

Claims

1. A seismic denoising method based on MLReal transform, characterized in that: The seismic denoising method based on MLReal transformation includes: Step 1, select the objective function; Step 2: Build a denoising neural network; Step 3, redefine the training data; Step 4, redefine the test data; Step 5: Input the redefined training data and test data into the neural network, perform training cycle iterations, and obtain synthetic data with the characteristics of field data.

2. The seismic denoising method based on MLReal transform according to claim 1, characterized in that: The seismic denoising method based on MLReal transformation also includes, before step 1, in order to solve the difference between the distribution of the training data and the test data set, it is necessary to define an error limit to ensure the minimum value of the difference measure.

3. The seismic denoising method based on MLReal transform according to claim 2, characterized in that: When defining the error limit, the formula used is: ε t (N N) ≤ ε s (NN)+d(P s (x s ),P t (x t ))+λ ε t (NN) represents the error bound during testing, ε s (NN) represents the error limit during training, P s (x s ) is the probability distribution of the training data, P t (x t ) is the probability distribution of the test data, d(,) represents the distance between the marginal distribution of the test set and the training set, and λ represents the optimal joint error of the neural network model between the source data set and the target data set; therefore, the upper limit of the error of the test is ε t (NN) by ε s (NN), d(,) and λ are guided by these three parameters.

4. The seismic denoising method based on MLReal transformation according to claim 1, characterized in that: In step 1, the network model is optimized using the test error bound as the objective function.

5. The seismic denoising method based on MLReal transformation according to claim 4, characterized in that: In step 1, the objective function is: ε t (N N) ≤ ε s (NN)+d(P s (x s ),P t (x t ))+λ Where ε t (NN) represents the error bound during testing, ε s (NN) represents the error limit during training, P s (x s ) is the probability distribution of the training data, P t (x t ) is the probability distribution of the test data, d(,) represents the distance between the marginal distribution of the test set and the training set, and λ represents the optimal joint error of the neural network model between the source data set and the target data set; therefore, the upper limit of the error of the test is ε t (NN) by ε s (NN), d(,) and λ are guided by these three parameters.

6. The seismic denoising method based on MLReal transformation according to claim 1, characterized in that: In step 2, a 4-layer residual U-Net neural network was constructed. The network used 32 filters as the initial filters, which doubled in each layer, resulting in 106M trainable parameters. The network was trained using 8092 training samples and 1024 validation samples. The number of epochs was 150 and the size of the image block was 64×64.

7. The seismic denoising method based on MLReal transform according to claim 1, characterized in that: In step 3, during the training phase, the training data is T s Transformation allows the features of field data to be injected into synthetic data.

8. The seismic denoising method based on MLReal transformation according to claim 7, characterized in that: In step 3, T s Transformation Where k is the reference trace index from the synthetic input data, which is fixed for both synthetic and real data, and j is the index of the part from the real data, whether it comes from the shot point set or the seismic image. The operator represents cross-correlation, and the operator * represents convolution; in this equation, the synthetic profile of the input Cross-correlate with a reference trace from the profile and then with the reference trace and d from the real data ij The (j) randomly selected autocorrelated parts of the data are convolved; that is, before being input into the NN, each synthetic data block is cross-correlated with a single reference trace extracted from the data block; during training iterations, for each iteration, a random field data block is selected, autocorrelated on a trace-by-trace basis, and convolved with each cross-correlated synthetic data block, which becomes the input of the network.

9. The seismic denoising method based on MLReal transformation according to claim 8, characterized in that: In step 3, the randomly chosen j index for the autocorrelated real data is varied in each training iteration to allow for proper representation of the real data features on the training set.

10. The seismic denoising method based on MLReal transformation according to claim 1, characterized in that: Step 4, in the inference phase, by performing T t Transformation allows the features of the synthetic data to be injected into the target data.

11. The seismic denoising method based on MLReal transformation according to claim 10, characterized in that: In step 4, T t The transformation is: Where k is the reference track index from the synthetic input data, which is fixed for both synthetic and real data, j is the partial index from the real data, and the operator represents cross-correlation, operator * represents convolution, d ij is the real data, N s is the number of synthetic parts in the training set; i.e., for the inference phase, the real data undergoes a similar preprocessing process as the synthetic data in the training phase; however, in this phase, once the field data patches are cross-correlated with their reference traces, these patches are convolved with the block of the autocorrelation average of all synthetic training data patches.

12. The seismic denoising method based on MLReal transformation according to claim 11, characterized in that: In step 4, the randomly chosen j index for the autocorrelated real data is varied in each training iteration to allow for proper representation of the real data features on the training set.

13. The seismic denoising method based on MLReal transformation according to claim 1, characterized in that: In step 5, the redefined training data and test data are input into the neural network and the training cycle is iterated so that the test error objective function reaches the minimum value, that is, synthetic data with the characteristics of field data is obtained, which is finally used as the input of the network and finally used for denoising.

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