A high-resolution radon domain multiple wave suppression method based on deep learning

Abstract

The application discloses a kind of high-resolution Radon domain multiple wave suppression methods based on deep learning, comprising the following steps: S1, data preprocessing: the seismic data collected is respectively subjected to conjugate Radon transformation and high-resolution Radon transformation;S2, sample and label data construction: make training dataset and test dataset;S3, data normalization or standardization: the training dataset and test dataset made are normalized or standardized processing;S4, model training: obtain nonlinear mapping relationship network model;S5, data prediction: output predicted high-resolution Radon domain data;S6, multiple wave suppression and primary wave extraction: obtain the primary wave data after suppressing multiple wave;S7, transfer learning strategy: adjust network parameters to adapt to different types of dataset.The application improves the calculation efficiency and multiple wave suppression effect, and helps to improve the quality and reliability of seismic exploration data.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of geological exploration, in particular to a high-resolution Radon domain multiple wave suppression method based on deep learning. BACKGROUND

[0002] Multiple wave suppression has been one of the key and difficult problems in seismic data processing, and the suppression precision directly affects the subsequent seismic imaging quality and seismic data interpretation. Existing multiple wave suppression methods are mainly divided into a filtering method based on signal theory and a prediction subtraction method based on wave equation theory. The filtering method uses the periodicity and separability of multiple waves for processing, and has high calculation efficiency, but has poor adaptability under complex geological conditions, which may cause damage to primary wave energy or incomplete multiple wave suppression. The prediction subtraction method based on wave equation can realize more accurate multiple wave suppression under different medium conditions and does not depend on prior information of underground medium, but has high calculation cost and is difficult to meet the demand of efficient processing.

[0003] The traditional Radon transform method uses the characteristic difference between multiple waves and primary waves in the Radon domain for multiple wave suppression, and is widely applied in actual production. However, the conventional Radon transform has the problems of low resolution and poor focusing effect, and it is difficult to realize high-precision wave field separation. The high-resolution Radon transform method developed subsequently improves the resolution of Radon domain data through iterative optimization, and the suppression effect of multiple waves is improved. However, since the method depends on matrix inversion operation, the calculation amount is large, the processing efficiency is low, and it is difficult to meet the rapid processing demand of large-scale seismic data. SUMMARY

[0004] The application provides a high-resolution Radon domain multiple wave suppression method based on deep learning, which constructs a nonlinear mapping relationship from low-resolution conjugate solution Radon domain data to high-resolution Radon domain data, uses a U-net network training model to replace the traditional matrix inversion iterative process, improves the calculation efficiency and reduces the calculation cost on the premise of ensuring the multiple wave suppression precision, and provides a more efficient and accurate method for seismic data processing.

[0005] A high-resolution Radon domain multiple wave suppression method based on deep learning comprises the following steps:

[0006] S1, data preprocessing: performing conjugate Radon transform and high-resolution Radon transform on the collected seismic data respectively to obtain low-resolution Radon domain data and high-resolution Radon domain data;

[0007] S2, sample and label data construction: based on low-resolution Radon domain data and high-resolution Radon domain data, sample and label data are constructed, and sample and label data are expanded through data augmentation to make training data set and test data set;

[0008] S3, data normalization or standardization: the prepared training data set and test data set are normalized or standardized;

[0009] S4, model training: the training data set is input into the U-net network for training to obtain a network model representing the nonlinear mapping relationship from low-resolution Radon domain data to high-resolution Radon domain data;

[0010] S5, data prediction: the test set data is input into the trained nonlinear mapping relationship network model, and the predicted high-resolution Radon domain data is output;

[0011] S6, multiple wave suppression and primary wave extraction: based on the predicted high-resolution Radon domain data, according to the characteristic difference between primary wave and multiple wave, the primary wave information is cut off and the multiple wave information is retained, the extracted multiple wave Radon domain data is subjected to Radon inverse transform, converted back to time domain, and the time domain multiple wave data is obtained, and the multiple wave data is subtracted from the acquired seismic data to obtain the primary wave data after suppressing multiple waves;

[0012] S7, transfer learning strategy: when the trained nonlinear mapping relationship network model is applied to the seismic data of a new area, the trained nonlinear mapping relationship network model is fine-tuned through the seismic data of the new area.

[0013] Optionally, the data preprocessing in S1 comprises:

[0014] S11, construction of parabolic Radon transform: the forward transform and inverse transform of parabolic Radon transform are established in the time domain;

[0015] S12, discretization and frequency domain conversion: the Radon transform is discretized, and is converted to the frequency domain through Fourier transform;

[0016] S13, conjugate solution: low-resolution conjugate solution Radon domain data are calculated from the discretized and frequency domain converted seismic data;

[0017] S14, sparse constraint high-resolution Radon transform: a frequency domain sparse constraint algorithm is introduced, a variable weight matrix is added to the objective function, and the solution of the frequency domain parabolic Radon transform is obtained by minimizing the objective function, and the sparse constraint high-resolution Radon frequency domain solution is updated through iterative solution, and is represented as:

[0018] ;

[0019] wherein, represents high-resolution Radon domain data obtained by step-by-step iteration, and respectively represent a Radon transform operator and a conjugate operator thereof, is a weighting coefficient, represents a constraint matrix constructed using a previous result, , is a weighting matrix of a model space, and D represents original seismic data;

[0020] S15, introducing deep learning optimization calculation: adopting a deep learning method, a nonlinear mapping model from conjugate solution Radon domain data to high-resolution Radon domain data is constructed.

[0021] Optionally, the parabolic Radon transform is represented as:

[0022] ;

[0023] .

[0024] Optionally, the discretization and frequency domain conversion in S12 include:

[0025] S121, discretization: discretizing the Radon transform, represented as:

[0026] ;

[0027] ;

[0028] S122, frequency domain conversion: converting the Radon transform to the frequency domain through Fourier transform, represented as:

[0029] ;

[0030] ;

[0031] The conjugate approximate solution of the Radon transform is in the form of a matrix in the frequency domain, represented as:

[0032] ;

[0033] ;

[0034] ;

[0035] .

[0036] wherein, represents the conjugate solution Radon domain data.

[0037] Optionally, the nonlinear mapping model is represented as:

[0038] .

[0039] Optionally, 70% of the data amount in the augmented sample and label data is used as the training data set, and 30% of the data amount is used as the test data set.

[0040] Optionally, the model training in S5 includes:

[0041] S51, training data input: taking the training data set as the input of the U-net network, and learning the nonlinear mapping relationship between the low-resolution conjugate solution Radon domain data and the high-resolution Radon domain data by using the U-net network;

[0042] S52, network optimization and loss calculation: the mean square error loss function is used to measure the error between the predicted value and the true value;

[0043] S53, model updating: by continuously updating the network parameters, the nonlinear mapping relationship is optimized, and the nonlinear mapping relationship network model representing the mapping from the low-resolution conjugate solution Radon domain data to the high-resolution Radon domain data is obtained.

[0044] Optionally, the U-net network mapping relationship is represented as:

[0045] ;

[0046] wherein, represents the Radon domain data predicted by the network model, represents the conjugate solution Radon domain data, represents the selected network structure, i.e. the U-net network, represents the network parameters, i.e. the network weights obtained by training and bias .

[0047] Optionally, the mean square error loss function is represented as:

[0048] ;

[0049] wherein, represents the high-resolution Radon domain data, i.e. the true value.

[0050] Optionally, the transfer learning strategy in S7 includes:

[0051] S71, network pre-training: based on the seismic data of the new area, a training data set and a test data set of the new area are made, and a nonlinear mapping relationship network model is pre-trained, and the obtained pre-trained nonlinear mapping relationship network model will be used as the basis for transfer learning;

[0052] S72, network model trimming: the pre-trained nonlinear mapping relationship network model is imported, some parameters are locked and directly used, and the remaining parameters are trained again using the training data set of the new area, and the fine tuning of the parameters in the pre-trained nonlinear mapping relationship network model is completed.

[0053] The beneficial effects of the present application: the present application constructs a nonlinear mapping relationship from low-resolution conjugate solution Radon domain data to high-resolution Radon domain data through a deep learning method, uses the trained network model to improve the resolution of the Radon domain data, uses a U-net network for model training, and through steps such as data augmentation, normalization processing, and loss optimization, the network can accurately learn the characteristics of the multiple waves and primary waves in the Radon domain, and replace the iterative optimization process in the traditional method which relies on matrix inversion, thereby improving the calculation efficiency and wave field separation accuracy.

[0054] The present application, by using deep learning to establish a mapping relationship, can directly convert data without iterative solution, greatly reducing the consumption of computing resources, in addition, by introducing the transfer learning technology, the training cost is reduced, and the generalization ability of the model is improved, making it suitable for different types of seismic data processing needs, which helps to improve the quality and reliability of the seismic exploration data. BRIEF DESCRIPTION OF DRAWINGS

[0055] In order to more clearly illustrate the technical solutions in the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description only illustrate the present application, and those skilled in the art can also obtain other drawings according to these drawings without creative labor.

[0056] Figure 1 The flowchart of the pressing method of the embodiment of the present application;

[0057] Figure 2 The schematic diagram of the U-net network structure of the embodiment of the present application;

[0058] Fig. 3 is a schematic diagram of the test results of the model seismic data used in the embodiment of the present application, wherein Figure 3a is the original data, Figure 3b is the low-resolution conjugate solution data, Figure 3c is the high-resolution Radon domain data,Figure 3d Radon domain data predicted by the network, Figure 3e primary wave data after suppressing multiples based on the deep learning method;

[0059] Figure 4 is the test result of the embodiment of the present application on actual seismic data, wherein Figure 4a original data, Figure 4b low-resolution conjugate data, Figure 4c high-resolution Radon domain data, Figure 4d Radon domain data predicted by the network, Figure 4e primary wave data after suppressing multiples based on the deep learning method. DETAILED DESCRIPTION

[0060] The present application will be described in detail below with reference to the accompanying drawings and specific embodiments. It should be noted here that in order to make the embodiments more detailed, the following embodiments are the best, preferred embodiments, and other alternative ways can also be implemented by those skilled in the art for some known technologies; and the drawings are only used to more specifically describe the embodiments, and are not intended to specifically limit the present application.

[0061] It should be noted that in the specification, "one embodiment", "embodiment", "exemplary embodiment", "some embodiments" and the like indicate that the described embodiments can include a specific feature, structure or property, but not necessarily every embodiment includes the specific feature, structure or property. In addition, when a specific feature, structure or property is described in combination with an embodiment, it should be within the knowledge of those skilled in the related art to implement such a feature, structure or property in combination with other embodiments (whether or not explicitly described).

[0062] Generally, the terms can be understood at least in part from the use in context. For example, depending at least in part on the context, the term "one or more" as used herein can be used to describe any feature, structure, or characteristic in the singular or can be used to describe combinations of features, structures, or characteristics that are combinable into one or more instances. In addition, the term "based on" can be understood as not necessarily intending to convey a set of exclusive factors, but can instead, depending at least in part on the context, allow for the existence of other factors not necessarily explicitly described.

[0063] A high-resolution Radon domain multiple suppression method based on deep learning, comprising the following steps:

[0064] S1, the collected seismic data is respectively subjected to conjugate Radon transformation and high-resolution Radon transformation to obtain low-resolution Radon domain data and high-resolution Radon domain data. First, the forward and inverse transformations of parabolic Radon transformation are represented as:

[0065] (1a)

[0066] (1b)

[0067] The corresponding discrete transform is expressed as:

[0068] (2a)

[0069] (2b)

[0070] After Fourier transform and conversion to the frequency domain, we get:

[0071] (3a)

[0072] (3b)

[0073] Each frequency component can be represented in the following matrix form:

[0074] (4a)

[0075] (4b)

[0076] in and It can be represented as:

[0077] (5a)

[0078] (5b)

[0079] Written in matrix component form:

[0080] (6a)

[0081] (6b)

[0082] This transformation is applied to the acquired seismic data to calculate low-resolution conjugate solution Radon domain data. Observing the above formula, it can be found that the matrix... and It's not an orthogonal matrix, so it can't be used directly. express The inverse, using conjugate solutions The directly obtained Radon domain data is not the true Radon parameter, resulting in poor focusing and low resolution. Therefore, a least squares algorithm is used to solve the problem. First, the objective function is constructed:

[0083] (7)

[0084] Mode denotes the norm, denotes the regularization term, which is mainly used to constrain the smoothness of the solution to ensure the stability of the solution. The partial derivative is obtained by taking the partial derivative of both sides of the equation:

[0085] (8)

[0086] Thus, the solution of the Radon transform is obtained, which is the conventional least squares solution:

[0087] (9)

[0088] where I is the identity matrix, denotes the conjugate solution Radon domain data, and the operator is expressed as:

[0089] (10)

[0090] In the least squares solution, the regularization term selected is a fixed value, which can improve the stability of the solution but also reduces the resolution of the Radon domain data to some extent, increasing the difficulty of separating the primary wave and the multiple wave in the Radon domain. From a mathematical point of view, the regularization term is added (damping factor) to improve the stability of the solution during the solution process, but no constraint conditions are added to the regularization term, which makes the solution obtained by this method not unique, not meeting the uniqueness of the solution. Therefore, the frequency domain space sparse constraint algorithm is introduced, which uses the model-related information to constrain the regularization term and improves the resolution of the Radon domain data through continuous iteration and update.

[0091] The objective function constructed by this algorithm is:

[0092] (11)

[0093] The solution of the frequency domain parabolic Radon transform is obtained by minimizing the objective function:

[0094] (12)

[0095] where , is the weighted matrix of the model space, which is a diagonal matrix.

[0096] Unlike the least squares Radon transform, the constraint term here is no longer a fixed factor but is related to the value of , which can change with the change of value. When the energy diverges, the corresponding constraint value increases, thereby achieving the effect of converging energy and improving focusing. At this time, the expression of the frequency domain solution becomes:

[0097] (13)

[0098] wherein, represents the constraint matrix constructed by the previous result, and the high-resolution data with better focusing effect in the Radon domain is finally obtained through step-by-step iteration. Since the focusing effect of the conjugate solution Radon domain data is poor, it can be found through equation (13) that there is a certain nonlinear mapping relationship between the conjugate solution Radon domain data and the high-resolution Radon domain data:

[0099] (14)

[0100] wherein, represents the high-resolution Radon domain data obtained through step-by-step iteration, and the relationship between the two is constructed through the matrix The inverse calculation of the matrix is large in amount and needs to be updated iteratively to improve the resolution of the Radon domain data, which is high in cost. Therefore, the deep learning method is introduced into the Radon transform multiple wave suppression, the mapping relationship from the conjugate solution Radon domain data to the high-resolution Radon domain data is constructed, the process of iteratively solving the matrix is effectively avoided, and the calculation cost is reduced.

[0101] S2, the conjugate solution Radon domain data and the high-resolution Radon domain data are taken as the sample and the label data, respectively. The conjugate solution Radon domain data has poor focusing effect, and direct cutting and separation can easily damage the effective information. The multiple wave and the primary wave in the high-resolution Radon transform domain have obvious differences in characteristics and good aggregation, and it is easy to realize the separation of the multiple wave and the protection of the primary wave information. In the network training of the deep learning method, the number and quality of the training data directly affect the accuracy of the network model construction and determine whether the nonlinear mapping relationship from the input to the target output can be well constructed. Especially in the multiple wave suppression, since the multiple wave and the primary wave have similar forms and both have periodicity and continuity, the difference between the data characteristics is very small, which requires that the network itself has the ability of feature extraction while meeting the requirements of the training data in quality and quantity. The final effect in the deep learning is largely determined by the selected label data, and the high-resolution Radon domain result can separate the primary wave and the multiple wave with high precision, which is very suitable as the label data set.

[0102] Subsequently, the data augmentation is performed by means of turning over, multi-angle rotation, adding different degrees of noise and mutual combination, 70% of the data amount is randomly selected as a training data set, and the remaining is as a test data set. In order to guarantee the requirement of network training to the data amount, improve the training effect and generalization ability of the network, the data set is expanded through the data enhancement. The commonly used data enhancement methods in the present stage of deep learning mainly include cutting, turning over, scaling, different angle rotation, translation transformation and adding various noises. In order to increase the data amount while guaranteeing the authenticity of the seismic data, the data augmentation is mainly performed by means of turning over, multi-angle rotation, adding different degrees of noise and mutual combination, so as to improve the learning ability and generalization ability of the network model and improve the noise immunity.

[0103] S3, normalizing or standardizing the prepared data set. Before the neural network training, the data set is usually normalized or standardized, because in the training process, the gradient descent in the back propagation is utilized to continuously iteratively optimize the corresponding weight and bias to finally obtain the expected nonlinear mapping relationship, but if the input data size difference is large, the extracted feature attribute dimension will be different, so that it is difficult to seek the optimal solution and slow down the convergence speed. The present application adopts the method of directly dividing the data absolute value maximum to normalize the data, so that the data is located in the interval [-1, 1].

[0104] S4, the training data set is input into the U-net network for training, and a network model capable of representing the nonlinear mapping relationship from the low-resolution conjugate solution Radon domain data to the high-resolution Radon domain data is obtained. At this time, the network learning basic principle is expressed by formula as follows:

[0105] (15)

[0106] In the formula, represents the Radon domain data predicted by the network model, represents the conjugate solution Radon domain data. represents the selected network structure, and the U-net network is adopted in the present application. represents the network weight and bias to be obtained through training. Similarly, the mean square error loss function is utilized to measure the error between the predicted value and the true value:

[0107] (16)

[0108] In the formula, The high-resolution Radon domain data is represented as a real value, and the training process of the network is a process of minimizing the error, and through a large amount of data participating in training, the network parameters are iteratively updated, and finally the training is completed to obtain a nonlinear mapping relationship network model capable of representing the low-resolution conjugate solution Radon domain data to the high-resolution Radon domain data.

[0109] S5, inputting the test set data into the network model obtained after training, outputting the predicted high-resolution Radon domain data.

[0110] S6, according to the characteristic difference between the primary wave and the multiple wave, cutting the primary wave information and retaining the multiple wave information, and performing Radon inverse transformation back to the time domain, subtracting the multiple wave data in the above step from the original data to obtain the primary wave data after suppressing the multiple wave.

[0111] S7, for the application of the network model to the seismic data in a new area, firstly, the pre-trained network model is imported and part of the parameters in the network model is locked, then the remaining parameters are further trained based on the pre-trained network model to adjust the parameters of the original network model, instead of retraining a new network, which can effectively accelerate the convergence speed and reduce the training cost. Finally, the adjusted network model can be applied to the Radon domain low-resolution conjugate approximate solution generated by the new data.

[0112] The above-mentioned high-resolution Radon domain multiple wave suppression method based on deep learning of the application utilizes the deep learning tool to establish the nonlinear mapping relationship between the low-resolution conjugate approximate solution Radon domain data and the high-resolution Radon domain data, and further provides an efficient Radon domain inversion and multiple wave suppression method, improves the calculation speed and the accuracy of multiple wave separation, and can better adapt to different types of seismic data in different work areas.

[0113] In order to more clearly illustrate the above-mentioned method of the application, the following will illustrate the method with a specific embodiment.

[0114] Embodiment 1:

[0115] As shown in FIG. 3, the application is applied to the multi-layer medium model data, as shown in FIG. 3. Firstly, for the original data, the low-resolution conjugate solution Radon domain data is obtained by Radon transformation and using the conjugate approximation method, and the high-resolution Radon domain data is obtained by using the high-resolution Radon transformation. Figure 3a

[0116] The above-mentioned method of the application firstly obtains the low-resolution conjugate solution Radon domain data by Radon transformation and using the conjugate approximation method for the original data, as shown in FIG. 3. Figure 3b ​The high-resolution Radon domain data is obtained by using high-resolution Radon transform, as shown in the figure. Figure 3c As shown in the figure, the Radon domain data obtained by the conjugate solution has poor focusing effect and low resolution, the high-resolution Radon domain data has good energy focusing effect, the first-order wave and the multiple wave are obviously partitioned, and the resolution is high. However, the matrix inversion in the high-resolution Radon transform has large calculation amount, and the resolution of the Radon domain data needs to be updated iteratively, so that the calculation cost is high.

[0117] In order to solve the above problems, the deep learning method is introduced into the Radon transform multiple wave suppression, the mapping relationship from the conjugate solution Radon domain data to the high-resolution Radon domain data is constructed, the iterative solution of the matrix is effectively avoided, and the calculation cost is reduced. First, the network training data set is made, the conjugate solution data and the high-resolution Radon domain data shown in the figure are used as the training input and the label data respectively, and 100 groups of training data pairs are constructed. Figure 3b 、 3c In order to solve the above problems, the deep learning method is introduced into the Radon transform multiple wave suppression, the mapping relationship from the conjugate solution Radon domain data to the high-resolution Radon domain data is constructed, the iterative solution of the matrix is effectively avoided, and the calculation cost is reduced. First, the network training data set is made, the conjugate solution data and the high-resolution Radon domain data shown in the figure are used as the training input and the label data respectively, and 100 groups of training data pairs are constructed. Figure 2 In order to solve the above problems, the deep learning method is introduced into the Radon transform multiple wave suppression, the mapping relationship from the conjugate solution Radon domain data to the high-resolution Radon domain data is constructed, the iterative solution of the matrix is effectively avoided, and the calculation cost is reduced. First, the network training data set is made, the conjugate solution data and the high-resolution Radon domain data shown in the figure are used as the training input and the label data respectively, and 100 groups of training data pairs are constructed. Figure 3d As shown in the figure, the high-resolution Radon domain data predicted based on the deep learning is basically consistent with the high-resolution data calculated by the traditional method, and the noise in the original data is suppressed to a certain extent, the focusing effect is good and the resolution is high. The predicted high-resolution Radon domain data is cut according to the characteristic difference between the first-order wave and the multiple wave, the first-order wave information is reserved and the multiple wave information is reserved, and the Radon inverse transform is performed back to the time domain, the multiple wave data in the original data is subtracted, and the first-order wave data after suppressing the multiple wave is obtained, as shown in the figure. Figure 3eThe pre-training of the network is completed through model testing.

[0118] Embodiment 2

[0119] The part of the weight inside the network model pre-trained in the application is fixed, and then further training is carried out on the basis of relatively less new data to adjust the network model parameters, complete the migration training of the network, and improve the generalization ability and adaptability of the network to complex data.

[0120] For a set of actual seismic data as shown in Figure 4a , first, the low-resolution conjugate solution Radon domain data is obtained through Radon transform using conjugate approximation, and the high-resolution Radon domain data is obtained using high-resolution Radon transform, as shown in Figure 4b and 4c . As can be seen from the figures, there is serious tailing in the conjugate solution data, and the focusing effect is poor, which is not conducive to the separation of multiple waves, while the energy focusing effect in the high-resolution Radon domain data is obviously improved.

[0121] In order to solve the problem of low computational efficiency of the traditional high-resolution Radon transform method, the deep learning method is introduced to replace the process of Radon domain inversion. Although the high-resolution data can be quickly predicted through the neural network, the previous network model is based on the model and is trained, and the effect on complex seismic data may not be ideal. If the network is retrained, the training of the network will consume a lot of time, and considering the complexity of the actual seismic data, the requirement for the amount and scale of the training data is also higher, and the training cost will be further increased. In order to reduce the time consumption of training and improve the generalization ability of the network model, the transfer learning strategy is adopted in the application, part of the network model parameters trained in embodiment 1 is imported and fixed, and the remaining part normally participates in the training process. From Figure 4b and 4c , a set of training data pairs are constructed from the conjugate solution data and the high-resolution Radon domain data, and the sample is further expanded by means of shearing, flipping, scaling, different angle rotation, translation transformation and adding various noises, etc. 70% of the data amount is randomly selected as the training data set, and the remaining is as the test data set. The characteristic of transfer learning is that the training process is equivalent to adjusting the weight inside the original network, rather than training a new network from scratch, this training strategy can reduce the demand for data set, and the network training can quickly reach convergence, the training cost is significantly reduced, and the adaptability of the model to other types of data is improved. The high-resolution Radon domain data predicted by the network is shown in Figure 4d , and compared with Figure 4cAs a result, the network predicted data realizes ideal Radon domain energy focusing while suppressing background noise, and using the data can effectively realize multiple wave suppression, as shown in Figure 4e

[0122] The present application encompasses any substitutions, modifications, equivalent methods and schemes made to the essence and scope of the present application. In order to make the public have a thorough understanding of the present application, specific details are described in the following preferred embodiments of the present application, and the present application can also be fully understood without the description of these details to those skilled in the art. In addition, in order to avoid unnecessary confusion to the essence of the present application, well-known methods, processes, procedures, elements and circuits, etc. are not described in detail.

[0123] The above is only the preferred embodiment of the present application, and it should be pointed out that for ordinary skilled in the art, without departing from the principles of the present application, a number of improvements and refinements can also be made, which should be considered as the protection scope of the present application.​

Claims

1. A high-resolution Radon domain multiple suppression method based on deep learning, characterized in that, Includes the following steps: S1, Data preprocessing: Perform conjugate Radon transform and high-resolution Radon transform on the acquired seismic data to obtain low-resolution Radon domain data and high-resolution Radon domain data respectively. S2, Sample and Label Data Construction: Sample and label data are constructed based on low-resolution Radon domain data and high-resolution Radon domain data, and the sample and label data are expanded by data augmentation to create training and test datasets; S3, Data Normalization or Standardization: Normalize or standardize the prepared training and test datasets; S4, Model Training: Input the training dataset into the U-net network for training to obtain a network model representing the nonlinear mapping relationship from low-resolution Radon domain data to high-resolution Radon domain data. S5, Data Prediction: Input the test set data into the trained nonlinear mapping network model, and output the predicted high-resolution Radon domain data. S6, Multiple suppression and primary extraction: Based on the predicted high-resolution Radon domain data, primary wave information is removed and multiple wave information is retained according to the characteristic differences between primary and multiple waves. The extracted multiple wave Radon domain data is subjected to inverse Radon transform and converted back to the time domain to obtain time domain multiple wave data. The multiple wave data is then subtracted from the acquired seismic data to obtain primary wave data after multiple suppression. S7, Transfer learning strategy: When applying the trained nonlinear mapping network model to seismic data in a new region, the trained nonlinear mapping network model is fine-tuned using the seismic data in the new region. The data preprocessing in S1 includes: S11, Construction of the parabolic Radon transform: The forward and inverse parabolic Radon transforms are constructed in the time domain; S12, Discretization and Frequency Domain Transformation: The Radon transform is discretized and then transformed into the frequency domain using the Fourier transform; S13, Conjugate Solution: Low-resolution conjugate solution Radon domain data is obtained by calculating the discretized and frequency-domain transformed seismic data; S14, Sparse-Constrained High-Resolution Radon Transform: A frequency-domain sparse-constraint algorithm is introduced, incorporating a variable weight matrix into the objective function. The solution for the frequency-domain parabolic Radon transform is obtained by minimizing the objective function. After iterative solving, the frequency-domain solution of the sparse-constrained high-resolution Radon transform is updated, denoted as... ； in, This represents high-resolution Radon domain data obtained through iterative steps. and Let them represent the Radon transform operator and its conjugate operator, respectively. These are weighting coefficients. This represents the constraint matrix constructed using the previous result. , Let D be the weighting matrix in the model space, and let D represent the original seismic data. S15, Introducing Deep Learning to Optimize Computation: Using deep learning methods, a nonlinear mapping model is constructed from low-resolution Radon domain data to high-resolution Radon domain data.

2. The high-resolution Radon domain multiple suppression method based on deep learning according to claim 1, characterized in that, The parabolic Radon transform is expressed as: ； in, Represents earthquake data. Represents Radon field data, The time intercept of the parabola on the same phase axis. For curvature, For the two-way travel time of seismic waves.

3. The high-resolution Radon domain multiple suppression method based on deep learning according to claim 2, characterized in that, The discretization and frequency domain transformation in S12 include: S121, Discretization: Discretize the Radon transform as follows: ； ；[1] S122, Frequency Domain Transformation: The Radon transform is converted to the frequency domain using the Fourier transform, expressed as: ； ； The conjugate approximation solution of the Radon transform is in matrix form in the frequency domain, expressed as: ； ； ； in, This represents the Radon domain data of the conjugate solution.

4. The high-resolution Radon domain multiple suppression method based on deep learning according to claim 3, characterized in that, The nonlinear mapping model is expressed as follows: 。 5. The high-resolution Radon domain multiple suppression method based on deep learning according to claim 4, characterized in that, 70% of the augmented sample and label data is used as the training dataset, and 30% is used as the test dataset.

6. The high-resolution Radon domain multiple suppression method based on deep learning according to claim 5, characterized in that, The model training in S5 includes: S51, Training Data Input: The training dataset is used as the input to the U-net network to learn the nonlinear mapping relationship between low-resolution conjugate solution Radon domain data and high-resolution Radon domain data. S52, Network Optimization and Loss Calculation: Using the mean squared error loss function to measure the error between the predicted value and the true value; S53, Model Update: By iteratively updating the network parameters, the nonlinear mapping relationship is optimized to obtain a network model representing the nonlinear mapping relationship from low-resolution conjugate solution Radon domain data to high-resolution Radon domain data.

7. The high-resolution Radon domain multiple suppression method based on deep learning according to claim 6, characterized in that, The U-net network mapping relationship is represented as follows: ； in, This represents Radon domain data predicted using a network model. Represents Radon domain data for conjugate solutions. This indicates the selected network structure, namely the U-net network. This refers to the network parameters, i.e., the network weights that need to be obtained through training. and bias .

8. The high-resolution Radon domain multiple suppression method based on deep learning according to claim 7, characterized in that, The mean squared error loss function is expressed as follows: ； in, This represents high-resolution Radon domain data.

9. A high-resolution Radon domain multiple suppression method based on deep learning according to claim 8, characterized in that, The transfer learning strategies in S7 include: S71, Network Pre-training: Based on the seismic data of the new region, a training dataset and a test dataset for the new region are created, and the nonlinear mapping relationship network model is pre-trained. The resulting pre-trained nonlinear mapping relationship network model will serve as the basis for transfer learning. S72, Network Model Tuning: Import the pre-trained nonlinear mapping network model, lock and directly use some of its parameters, and retrain the remaining parameters using the training dataset of the new region to complete the fine-tuning of the parameters in the pre-trained nonlinear mapping network model.

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