A three-dimensional seismic data interpolation method based on cross-dimension migration

Abstract

The application belongs to the technical field of seismic exploration and artificial intelligence, and particularly relates to a three-dimensional seismic data interpolation method based on cross-dimension migration, which comprises the following steps: constructing a two-dimensional seismic data interpolation method training, verification and testing data set, constructing a two-dimensional seismic data interpolation network, constructing a two-dimensional loss function, two-dimensional network model pre-training and verification, network parameter extraction, constructing a three-dimensional seismic data interpolation method training, verification and testing data set, constructing a three-dimensional seismic data interpolation network based on cross-dimension migration, constructing a three-dimensional loss function, three-dimensional network parameter loading and freezing, three-dimensional network model fine-tuning, three-dimensional network model verification and network model application. The application learns the spatial correlation information of three-dimensional data through multiple SDA, can assist the Transformer to capture the spatial correlation feature, significantly reduces the training time, improves the integrity and accuracy of the seismic data, and significantly reduces the calculation complexity and time cost.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of seismic exploration and artificial intelligence, and particularly relates to a three-dimensional seismic data interpolation method based on cross-dimension transfer. BACKGROUND

[0002] Seismic exploration is one of the core technologies that cannot be replaced in oil and gas resource development, but still faces multiple challenges in practical application. Especially when there is missing or insufficient acquisition density of seismic data, the problem will be more prominent. These situations often result from complex topographic conditions, equipment performance limitations, and high exploration costs, etc., leading to incomplete data collected, which is difficult to fully and accurately reflect the underground geological structure. Data sparsity not only reduces the resolution of seismic profiles, but also increases the difficulty of subsequent data processing and interpretation, which may cause bias in exploration conclusions. For deep or complex structure oil and gas reservoirs, the unevenness and absence of data will significantly affect the imaging quality and reduce the accuracy of reservoir positioning. Therefore, how to use intelligent technology to efficiently process seismic data, improve data reliability and imaging accuracy while reducing exploration costs, has become an important direction of current seismic exploration research.

[0003] In the prior art, in order to effectively complete the seismic data interpolation task, a seismic data interpolation method is applied. The traditional seismic data interpolation method mainly includes the following: acoustic wave equation modeling method, prediction filter method, rank reduction method (including singular spectrum analysis, matrix completion method, principal component analysis and Cadzow filter), sparse transform-based method (including wavelet transform, Radon transform, seislet transform, curvelet transform and shearlet transform), and dictionary-based method. The above methods are based on known mathematical and physical principles, and have shown the potential to obtain good results, but their applicability is still limited by many restrictions. Usually, several prior assumptions need to be met, such as accurate underground velocity model, linear characteristics of events, low-rank structure of seismic data, and sparsity of signals. However, it is often difficult to ensure that the understanding of the underground structure is consistent with the actual situation, thereby limiting the effectiveness and adaptability of these theory-driven interpolation methods in complex real scenarios. In addition, such theory-driven methods usually involve complex and tedious operations in the parameter adjustment process, and rely heavily on professional knowledge and practical experience. Furthermore, the high computational cost is also a major obstacle, especially when dealing with large-scale seismic data sets.

[0004] In recent years, data-driven techniques have attracted extensive attention due to their ability to learn from data itself and efficiently process massive data. Deep learning is a kind of data-driven method, which automatically extracts useful features from raw data by stacking a large number of nonlinear transformation layers. In the early stage, the architecture of convolutional neural network (CNN) was the focus of research, such as U-Net, Res-Net and generative adversarial network (GAN), which were used to complete the seismic data interpolation task and showed good performance. With the in-depth research, people gradually realized that the "local perception" feature of CNN became the main bottleneck of its performance improvement. To solve this problem, researchers began to introduce Transformer because of its strong ability to model global context information. Although these deep learning-based methods have significantly outperformed traditional methods in performance, they mainly focus on two-dimensional (2D) interpolation tasks, ignoring the spatial structure correlation that can be utilized in three-dimensional (3D) interpolation processes. In addition, an extra dimension usually brings significantly higher computational burden, especially when using Transformer-based structures, whose computational complexity grows quadratically with the size of input data. Moreover, extending a two-dimensional network to a three-dimensional version will significantly increase the number of trainable parameters. Although some researchers have tried to use three-dimensional convolutional neural networks for three-dimensional seismic data interpolation in recent years, these methods still face huge computational burden. For three-dimensional Transformer networks, this problem will be more serious due to their quadratic computational complexity. Currently, there is no research trying to apply Transformer to three-dimensional seismic data interpolation tasks because training a three-dimensional Transformer network on a three-dimensional seismic data set requires extremely large computational resources. Therefore, applying Transformer to three-dimensional seismic data interpolation is still a research field that has not been explored, which has important research potential and development prospects. SUMMARY

[0005] The purpose of the present application is to provide a three-dimensional seismic data interpolation method based on cross-dimensional transfer to solve the problem of high computational cost when applying Transformer to three-dimensional seismic data interpolation.

[0006] The present application is realized by the following technical solutions:

[0007] A three-dimensional seismic data interpolation method based on cross-dimensional transfer, comprising the following steps:

[0008] S1, constructing a two-dimensional seismic data interpolation method training, verification and testing data set;

[0009] S2, constructing a two-dimensional seismic data interpolation network based on Transformer;

[0010] S3, construct a two-dimensional loss function;

[0011] S4, train the two-dimensional seismic data interpolation network based on the Transformer constructed in step S2;

[0012] S5, verify the two-dimensional seismic data interpolation network model based on the Transformer obtained after the training in step S4 is completed, and if the verification is passed, the optimal two-dimensional seismic data interpolation model is obtained; otherwise, return to step S4 to retrain the model;

[0013] S6, extract the parameters of the Transformer module in the two-dimensional seismic data interpolation network model based on the Transformer obtained in step S5;

[0014] S7, construct a three-dimensional seismic data interpolation method training, verification and testing data set;

[0015] S8, construct a three-dimensional seismic data interpolation network based on cross-dimension migration;

[0016] S9, construct a three-dimensional loss function;

[0017] S10, load the parameters extracted in step S6 into the Transformer module in the three-dimensional seismic data interpolation network based on cross-dimension migration constructed in step S8, and freeze it;

[0018] S11, fine-tune the three-dimensional seismic data interpolation network based on cross-dimension migration obtained in step S10;

[0019] S12, verify the three-dimensional seismic data interpolation network based on cross-dimension migration obtained after the fine-tuning in step S11 is completed, and if the verification is passed, the optimal three-dimensional seismic data interpolation model is obtained; otherwise, return to step S10 to retrain the model;

[0020] S13, randomly delete traces from the real seismic profile and input them into the optimal interpolation model obtained in step S12 to obtain the interpolated seismic profile.

[0021] Further, step S1 specifically includes the following steps:

[0022] S1.1, obtain a public data set from a public website, and obtain multiple two-dimensional slices from the data set by a sliding window method, and divide the obtained slices into three parts in proportion, respectively as a training set, a verification set and a test set;

[0023] S1.2, randomly delete traces in the slices in the training set, the verification set and the test set in step S1.1 to form a two-dimensional data set containing missing data and complete data one-to-one corresponding, and complete the construction of the data set.

[0024] Further, step S2, specifically: the two-dimensional seismic data interpolation network based on the Transformer mainly consists of two 3x3 convolutional layers, a head module, a global feature extraction module, a tail module, and two residual connections; the data slices containing missing data in the training set first pass through a 3x3 convolutional layer to expand the dimension, and then pass through the head module to extract shallow features; after passing through the global feature extraction module, the features are finally optimized by the tail module; the output of the tail module is added to the output of the head module through a residual connection, and the sum is then passed through a 3x3 convolutional layer to reduce the feature dimension; the final feature output is added to the initial input through a residual connection, thereby obtaining the interpolated seismic profile;

[0025] The head module consists of two repeated sub-modules composed of a 3x3 convolutional layer, a linear rectifier unit, a 3x3 convolutional layer, and a residual connection; the residual connection is used to add the output of the second convolutional layer of each sub-module to the input of the sub-module; the output of the second sub-module is the extracted shallow feature;

[0026] The global feature extraction module consists of four Transformer modules; the input feature map first passes through a Transformer module, and then is spliced with itself in the channel dimension, and the channel number is reduced to the same as the input feature map using a 3x3 convolutional layer; the outputs of the subsequent three Transformer modules are all spliced with the output of each previous Transformer module in the channel dimension, and then the channel is reduced using a 3x3 convolutional layer; after the last channel reduction, the output feature map of the global feature extraction module is obtained;

[0027] The tail module is composed of three 3x3 convolutional layers and two linear rectifier units with leakage alternately stacked, with the first 3x3 convolutional layer as the head and the third 3x3 convolutional layer as the tail; the output of the third 3x3 convolutional layer is the optimized feature.

[0028] Further, in step S3, the two-dimensional loss function is an L2 loss function, i.e., a root mean square error loss function, and its mathematical expression is:

[0029] ;

[0030] In the formula, is the input seismic data containing missing data, is the corresponding complete seismic data in the training set, and and are the number of time sampling points and the number of traces of a two-dimensional seismic profile, respectively.

[0031] Further, step S4, specifically: training the two-dimensional seismic data interpolation network based on Transformer constructed by step S2, through the mapping from the data containing missing data to the complete data, optimizing the two-dimensional loss function constructed in step S3 according to the mapping result, obtaining the optimal network model parameters within a specified number of training rounds, at this time, the training is completed;

[0032] Step S11, specifically: fine-tuning the three-dimensional seismic data interpolation network based on cross-dimension migration obtained by step S10, through the mapping from the data containing missing data to the complete data, optimizing the three-dimensional loss function constructed in step S9 according to the mapping result, obtaining the optimal network model parameters within a specified number of training rounds, at this time the training is completed.

[0033] Further, in step S5, network model verification, specifically including the following steps:

[0034] S5.1, input the paired missing-complete seismic profile in the verification set into the trained two-dimensional seismic data interpolation network based on Transformer for verification;

[0035] S5.2, when the evaluation index of the verification result, the peak signal-to-noise ratio and the structural similarity, does not meet the set index threshold, then continue to return to step S4, optimize and adjust the parameters, and then retrain the two-dimensional seismic data interpolation network based on Transformer;

[0036] S5.3, when the evaluation index of the verification result, the peak signal-to-noise ratio and the structural similarity, meets the set index threshold, then stop training, and then the trained two-dimensional seismic data interpolation network based on Transformer is used as the optimal pre-training model.

[0037] Further, step S7, specifically including the following steps:

[0038] S7.1, obtain a plurality of three-dimensional cutouts from the data set by the sliding window method, and divide the obtained cutouts into three parts in proportion, respectively as the training set, the verification set and the test set;

[0039] S7.2, randomly delete the cutouts in the training set, the verification set and the test set in step S7.1, forming a three-dimensional data set corresponding to the data containing missing data and the complete data one by one, thus completing the whole process of constructing the data set.

[0040] Further, step S8, specifically: the three-dimensional seismic data interpolation network based on cross-dimension migration mainly consists of two 3x3 convolutional layers, a head module, a cross-dimension migration module, a tail module, and two residual connections; the data body containing missing data in the training set first combines the crossline dimension in advance with the batch dimension to be compatible with the two-dimensional module in the network; secondly, the dimension is expanded through a 3x3 convolutional layer, and then the shallow features are extracted through the head module; after passing through the cross-dimension migration module, the tail module optimizes the features; the output of the tail module is added to the output of the head module through a residual connection, and the sum is then reduced in dimension through a 3x3 convolutional layer; finally, the last feature output is added to the initial input through a residual connection, thereby obtaining the interpolated seismic profile;

[0041] Wherein, the cross-dimension migration module is composed of four Transformer modules and four seismic dimension adapters; wherein, each Transformer module is placed in front of an SDA to perform cross-dimension adaptation; the input feature map first restores the dimension to the same shape as the input; after passing through an SDA module, the dimension is further converted into a batch-crossline combination collision, then the input Transformer module is input, then it is spliced with itself in the channel dimension, and the channel number is reduced to the same as the input feature map using a 3x3 convolutional layer; then, the output of the three SDA-Transformer modules is spliced with the output of each previous SDA-Transformer module in the channel dimension, and then the channel is reduced using a 3x3 convolutional layer; after the last channel reduction, the output feature map of the cross-dimension migration module is obtained;

[0042] The seismic dimension adapter is composed of two linear layers and a deep convolution; the input feature map first passes through a linear layer to map the channel number to a high-dimensional space; then, the spatial correlation information is learned through a deep convolution; finally, the channel number is mapped back to the same as the input through another linear layer.

[0043] Further, in step S9, the three-dimensional loss function is an L2 loss function, i.e., a root mean square error loss function, and its mathematical expression is:

[0044] ;

[0045] In the formula, is the input seismic data containing missing data, is the corresponding complete seismic data in the training set, , , and The number of time sampling points, inline numbers and crossline numbers of a three-dimensional seismic volume respectively.

[0046] Further, in step S12, network model verification, specifically comprising the following steps:

[0047] S12.1, input the pairs of missing-complete seismic volumes in the verification set into the trained three-dimensional seismic data interpolation network based on cross-dimensional migration for verification;

[0048] S12.2, when the evaluation indicators of the verification results, peak signal-to-noise ratio and structural similarity, do not meet the set indicator threshold, then continue to return to step S11, optimize and adjust the parameters, and then re-tune the three-dimensional seismic data interpolation network based on cross-dimensional migration;

[0049] S12.3, when the evaluation indicators of the verification results, peak signal-to-noise ratio and structural similarity, meet the set indicator threshold, then stop fine-tuning, and then take the trained three-dimensional seismic data interpolation network based on cross-dimensional migration as the optimal training model.

[0050] Compared with the prior art, the beneficial effects of the present application are:

[0051] 1, the network structure is designed in combination with the cross-dimensional migration method, so that the network captures global features at the same time, has smaller calculation burden compared with the pure three-dimensional Transformer network, and reduces a large amount of training and testing time;

[0052] 2, the present application designs a cross-dimensional migration module, which effectively extracts the spatial information of the seismic volume by adopting multiple Transformer modules based on SDA adaptation, and adopts dense connection to enrich the feature interaction between layers and better plan the information of each layer;

[0053] 3, the present application adopts a two-dimensional pre-training plus three-dimensional fine-tuning training strategy, which effectively simplifies the training process and reduces the calculation time and memory requirement. BRIEF DESCRIPTION OF DRAWINGS

[0054] In order to more clearly illustrate the technical solutions of the embodiments of the present application, the following will briefly introduce the drawings needed to be used in the embodiments, and it should be understood that the following drawings only show some embodiments of the present application, and therefore should not be regarded as a limitation on the scope, and for those skilled in the art, other related drawings can also be obtained without creative labor on the basis of these drawings.

[0055] Figure 1The diagram shows a two-dimensional seismic data interpolation network structure based on Transformer, where (a) is the two-dimensional seismic data interpolation network structure based on Transformer, (b) is the head module in (a), and (c) is the tail module in (a).

[0056] Figure 2 The diagram shows a three-dimensional seismic data interpolation network structure based on cross-dimensional transfer, where (a) is the three-dimensional seismic data interpolation network structure based on cross-dimensional transfer, and (b) is the seismic dimension adapter (SDA) in (a).

[0057] Figure 3 The flowchart shows a three-dimensional seismic data interpolation method based on cross-dimensional transfer.

[0058] Figure 4 The three-dimensional seismic data volumes in the test set are: the missing three-dimensional seismic data volume, the corresponding complete three-dimensional seismic data volume, the three-dimensional seismic data volume interpolated by the three-dimensional seismic data interpolation method based on cross-dimensional transfer, and the difference between the prediction result and the complete data. Among them, (a) is the missing three-dimensional seismic data volume in the test set, (b) is the corresponding complete three-dimensional seismic data volume, (c) is the three-dimensional seismic data volume interpolated by the three-dimensional seismic data interpolation method based on cross-dimensional transfer, and (d) is the difference between the prediction result and the complete data.

[0059] Figure 5 The values ​​are: (a) a 2D seismic profile with missing data in the test set; (b) a 2D seismic profile with corresponding complete data; (c) a 2D seismic profile interpolated by a 3D seismic data interpolation method based on cross-dimensional transfer; and (d) the difference between the prediction result and the complete data. Detailed Implementation

[0060] The present invention will be further described below with reference to embodiments:

[0061] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and not intended to limit it. Furthermore, it should be noted that, for ease of description, the accompanying drawings show only the parts relevant to the present invention, and not all of the structures.

[0062] It should be noted that similar reference numerals and letters refer to like items in the accompanying drawings, and once an item is defined in one drawing, it is not necessary to further define and explain it in subsequent drawings. Meanwhile, in the description of the present application, the terms "first", "second", and the like are only used to distinguish the description, and cannot be understood as indicating or implying relative importance.

[0063] The present application is implemented on the Python language compiler Anaconda platform, the operating system is Ubuntu 22.04, the GPU is 1 NVIDIA L20 graphics card, and the deep learning framework is Pytorch 2.5.1. The core of the application is to propose a three-dimensional seismic data interpolation method based on cross-dimension migration. Due to environmental and budgetary constraints, three-dimensional seismic data often faces challenges such as missing and sparsity. The existing three-dimensional deep learning-based seismic data interpolation method is difficult to well balance globality and efficiency. Therefore, the present application designs a three-dimensional seismic data interpolation network based on cross-dimension migration, which effectively restores missing traces through global information, and has lower cost and higher efficiency than pure three-dimensional Transformer network. By constructing a one-to-one missing-complete seismic profile dataset to train and verify the invented network. When the evaluation index of the verification result meets the set index threshold, the trained three-dimensional seismic data interpolation network based on cross-dimension migration is used as the optimal seismic data interpolation model.

[0064] As shown in Figure 3 The three-dimensional seismic data interpolation method based on cross-dimension migration of the present application includes the following steps: constructing a two-dimensional seismic data interpolation model dataset; constructing a two-dimensional seismic data interpolation network based on Transformer; constructing a loss function of the two-dimensional seismic data interpolation network based on Transformer; training the two-dimensional seismic data interpolation network based on Transformer; determining whether the model effect meets the threshold requirement, if not, optimizing the network model and parameters, retraining, if it meets the requirement, extracting the parameters of the Transformer module in the two-dimensional seismic data interpolation network based on Transformer; constructing a three-dimensional seismic data interpolation model dataset; constructing a three-dimensional seismic data interpolation network based on cross-dimension migration; importing the parameters into the Transformer module of the three-dimensional seismic data interpolation network based on cross-dimension migration; constructing a loss function of the three-dimensional seismic data interpolation network based on cross-dimension migration; fine-tuning the three-dimensional seismic data interpolation network based on cross-dimension migration; determining whether the model effect meets the threshold requirement, if not, optimizing the network model and parameters, re-tuning, if it meets the requirement, applying the three-dimensional seismic data interpolation network based on cross-dimension migration to test data. Specifically, the steps include:

[0065] S1. Construct the dataset required for training, validating, and testing the two-dimensional seismic data interpolation method.

[0066] S1.1 Obtain a public dataset from a public website, and obtain multiple two-dimensional slices from the dataset using the sliding window method. Divide the obtained slices into three parts according to the proportion, and use them as the training set, validation set and test set respectively.

[0067] S1.2. Randomly delete slices from the training set, validation set, and test set in step S1.1 to form a two-dimensional dataset with a one-to-one correspondence between missing data and complete data. This completes the entire process of constructing the dataset.

[0068] Through this process, the present invention generated 6000 pairs of two-dimensional slices containing missing seismic profiles and complete seismic profiles for use as a training set, and 1500 such pairs of two-dimensional slices for use as a validation set. The slice size was 40×40. A slice with a size of 224×224×16 was used for testing.

[0069] S2. Construct a Transformer-based 2D seismic data interpolation network to recover missing traces in 2D seismic data.

[0070] The Transformer-based 2D seismic data interpolation network mainly consists of two 3×3 convolutional layers, a head module, a global feature extraction module, a tail module, and two residual connections, such as... Figure 1 As shown in (a), the missing data slices in the training set are first expanded in dimension by a 3×3 convolutional layer, and then shallow features are extracted by the head module. After the global feature extraction module, the tail module performs the final feature optimization. The output of the tail module is added to the output of the head module through a residual connection, and the sum is then passed through a 3×3 convolutional layer to reduce the feature dimension. The final feature output is added to the initial input through a residual connection to obtain the interpolated seismic profile.

[0071] The header module includes:

[0072] The head module consists of two repeating sub-modules, each composed of a 3×3 convolutional layer, a linear rectified unit (ReLU), another 3×3 convolutional layer, and a residual connection. Figure 1 As shown in (b), the residual connection is used to add the output of the second convolutional layer of each submodule to the input of that submodule; the output of the second submodule is the extracted shallow features.

[0073] The global feature extraction module includes:

[0074] The global feature extraction module consists of four Transformer modules, such as... Figure 1(a) shows; the input feature map first passes through a Transformer module, then is spliced with itself in the channel dimension, and the channel number is reduced to the same as the input feature map by a 3x3 convolution layer; then, the output of the three Transformer modules is spliced with the output of each previous Transformer module in the channel dimension, and then the channel is reduced by a 3x3 convolution layer; after the last channel reduction, the output feature map of the global feature extraction module is obtained.

[0075] The tail module comprises:

[0076] The tail module is composed of three 3x3 convolution layers and two leaky rectified linear units (Leaky ReLU) alternately stacked, starting with the first 3x3 convolution layer and ending with the third 3x3 convolution layer, as shown in Figure 1 (c) shows; the output of the third 3x3 convolution layer is the optimized feature.

[0077] S3, a two-dimensional loss function is constructed to measure the performance of the two-dimensional seismic data interpolation network based on Transformer.

[0078] The two-dimensional loss function is an L2 loss function, that is, a root mean square error loss function, and its mathematical expression is:

[0079] ;

[0080] In the formula, is the input seismic data containing missing data, is the complete seismic data corresponding to in the training set, and are the number of time sampling points and the number of channels of a two-dimensional seismic profile, respectively.

[0081] S4, two-dimensional network model pre-training: the two-dimensional seismic data interpolation network based on Transformer constructed in step S2 is trained, the mapping from the data containing missing data to the complete data is performed, the loss function constructed in step S3 is optimized according to the mapping result, and the optimal network model parameters are obtained within a specified number of training rounds, at which time the training is completed.

[0082] S5, two-dimensional network model verification:

[0083] The trained two-dimensional seismic data interpolation network model based on the Transformer obtained in step S4 is verified, and if the evaluation indexes of the verification result meet the set index threshold, the two-dimensional seismic data interpolation network model based on the Transformer obtained in step S4 is taken as the optimal two-dimensional seismic data interpolation model; otherwise, the model is retrained by adjusting the network training parameters in step S4.

[0084] Specifically, the following steps are included:

[0085] S5.1, input the pairs of missing-intact seismic profiles in the verification set into the trained two-dimensional seismic data interpolation network based on the Transformer for testing.

[0086] S5.2, when the evaluation indexes of the verification result, i.e., the peak signal-to-noise ratio and the structural similarity, do not meet the set index threshold, the two-dimensional seismic data interpolation network based on the Transformer is retrained in step S4 after the parameters are optimized and adjusted.

[0087] S5.3, when the evaluation indexes of the verification result, i.e., the peak signal-to-noise ratio and the structural similarity, meet the set index threshold, the training is stopped, and then the trained two-dimensional seismic data interpolation network model based on the Transformer is taken as the optimal pre-training model, as shown in the left flowchart. Figure 3

[0088] S6, network parameter extraction: the parameters of the Transformer module in the two-dimensional seismic data interpolation network pre-training model based on the Transformer obtained in step S5 are extracted for subsequent loading.

[0089] S7, constructing a three-dimensional seismic data interpolation method training, verification and testing data set.

[0090] S7.1, obtaining a public data set from a public website, and obtaining multiple three-dimensional cutouts from the data set by a sliding window method, and dividing the obtained cutouts into three parts in proportion, respectively, as a training set, a verification set and a test set;

[0091] S7.2, randomly deleting traces in the cutouts in the training set, the verification set and the test set in step S7.1 to form a three-dimensional data set with missing data and complete data one-to-one corresponding, and thus the whole process of constructing the data set is completed.

[0092] Through the process, the application generates 6000 pairs of three-dimensional data bodies of missing seismic profiles and complete seismic profiles for training set, 1500 pairs of such three-dimensional data bodies for verification set, and the size of the data body is 40x40x16. A slice with a size of 224x224x16 is used for testing.​

[0093] S8, constructing a three-dimensional seismic data interpolation network based on cross-dimension migration, for recovering missing traces in three-dimensional seismic data.

[0094] The three-dimensional seismic data interpolation network based on cross-dimension migration mainly consists of two 3x3 convolutional layers, a head module, a cross-dimension migration module, a tail module, and two residual connections, as shown in Figure 2 (a); the data body containing missing data in the training set first combines the crossline dimension in advance with the batch dimension to be compatible with the two-dimensional module in the network; secondly, the dimension is expanded through a 3x3 convolutional layer, then the shallow features are extracted through the head module; after passing through the cross-dimension migration module, the features are finally optimized by the tail module; the output of the tail module is added to the output of the head module through a residual connection, and the sum is then reduced through a 3x3 convolutional layer to reduce the feature dimension; finally, the feature output is added to the initial input through a residual connection, thereby obtaining the interpolated seismic profile;

[0095] The head module has the same structure as the head module in step S2, as shown in Figure 1 (b).

[0096] The cross-dimension migration module consists of four Transformer modules and four seismic dimension adapters (SDA), wherein each Transformer module has an SDA placed in front of it for cross-dimension adaptation, as shown in Figure 1 (a); the input feature map first restores the dimension to the same shape as the input; after passing through an SDA module, the dimension is further converted to a batch-crossline combination collision, then the input Transformer module is input, then it is concatenated with itself in the channel dimension, and the channel number is reduced to the same as the input feature map using a 3x3 convolutional layer; the output of the subsequent three SDA-Transformer modules is all concatenated with the output of each previous SDA-Transformer module in the channel dimension, and then the channel is reduced using a 3x3 convolutional layer; after the last channel reduction, the output feature map of the cross-dimension migration module is obtained.

[0097] The seismic dimension adapter consists of two linear layers and a depth convolution, as shown in Figure 2 (b); the input feature map first passes through a linear layer to map the channel number to a high-dimensional space; then the spatial correlation information is learned through a depth convolution; finally, the channel number is mapped back to the same as the input through another linear layer.

[0098] The tail module is the same as the tail module structure in step S2, as shown in Figure 1 (c) shown.

[0099] S9, a three-dimensional loss function is constructed for measuring the performance of the three-dimensional seismic data interpolation network based on cross-dimensional transfer.

[0100] The three-dimensional loss function is an L2 loss function, i.e., a root mean square error loss function, and its mathematical expression is:

[0101] ;

[0102] In the formula, is the input seismic data containing missing data, is the corresponding complete seismic data in the training set, , , and are the number of time sampling points, inline and crossline of a three-dimensional seismic body, respectively.

[0103] S10, three-dimensional network parameter loading and freezing: the parameters extracted in step S6 are loaded into the Transformer module of the three-dimensional seismic data interpolation network based on cross-dimensional transfer constructed in step S8, and are frozen and do not participate in new training.

[0104] S11, three-dimensional network model fine-tuning: fine-tuning the three-dimensional seismic data interpolation network based on cross-dimensional transfer obtained in step S10. Through the mapping from the missing data to the complete data, the loss function constructed in step S9 is optimized according to the mapping result, and the optimal network model parameter is obtained within the specified training number of rounds, and the training is ended at this time.

[0105] S12, three-dimensional network model verification: verifying the three-dimensional seismic data interpolation network based on cross-dimensional transfer obtained by fine-tuning in step S11. If the evaluation index of the verification result meets the set index threshold, the three-dimensional seismic data interpolation network based on cross-dimensional transfer obtained by training in step S11 is taken as the optimal three-dimensional seismic data interpolation model; otherwise, return to step S10 and fine-tune the model again by adjusting the network fine-tuning parameters.

[0106] Specifically, the network model verification specifically includes the following steps:

[0107] S12.1, input the pairs of missing-complete seismic bodies in the verification set into the trained three-dimensional seismic data interpolation network based on cross-dimensional transfer for verification;

[0108] S12.2 When the evaluation indicators of the verification results—peak signal-to-noise ratio and structural similarity—do not meet the set indicator thresholds, return to step S11, optimize and adjust the parameters, and then fine-tune the three-dimensional seismic data interpolation network based on cross-dimensional migration.

[0109] S12.3 When the evaluation metrics of the verification results—peak signal-to-noise ratio and structural similarity—meet the set threshold values, fine-tuning stops, and the trained 3D seismic data interpolation network model based on cross-dimensional transfer is used as the optimal training model, such as... Figure 3 The flowchart is shown on the right.

[0110] S13. Network Model Application: Randomly delete traces from the test data obtained in step S7, and input them into the optimal three-dimensional interpolation model obtained in step S12 to obtain the interpolated seismic profile, i.e., the three-dimensional seismic body.

[0111] This invention employs multiple Seismic Dimension Adapters (SDAs) to learn spatially relevant information from 3D data, addressing the issues of missing data and low density caused by sparse acquisition in 3D seismic data. The SDAs introduced in this invention not only assist the Transformer in capturing spatial correlation features, resulting in higher quality interpolated data, but also significantly reduce training time compared to a pure 3D Transformer network due to their lightweight design. Therefore, this invention can significantly reduce computational complexity and time costs while improving the completeness and accuracy of seismic data.

[0112] Example 1:

[0113] This embodiment provides an application of seismic data interpolation using a cross-dimensional transfer-based 3D seismic data interpolation network for 3D seismic volumes containing missing data, as detailed below:

[0114] This invention inputs missing data from the test set into a pre-trained 3D seismic data interpolation network model based on cross-dimensional transfer, and the output results are as follows: Figure 4 As shown, Figure 4 The interpolation result in (c) is the same as Figure 4 (b) shows a complete match of the data signal, effectively recovering the original signal. Figure 4 (a) shows that the randomly missing signals result in a more complete and smoother interpolated 3D data volume compared to the 3D data volume containing the missing signals. Meanwhile, as shown in [the original text]... Figure 4 As shown in (d), the difference between the interpolated data and the complete data does not contain signal leakage, further verifying the interpolation performance of the present invention. Figure 5 For the interpolation in this invention, a survey line is extracted from the three-dimensional seismic body for two-dimensional comparison. Figure 5 (a) shows the extracted two-dimensional seismic profile containing missing data, and the result after interpolation using this invention is as follows. Figure 5(c) the shown, and Figure 5 (b) is very close to the full 2D profile, which proves that the present application has effective interpolation performance and detail recovery, while, in Figure 5 (d) the difference between the interpolated data and the full data further proves that the interpolated data has good amplitude preservation, which further proves that the present application has excellent interpolation performance for 3D seismic data and potential for more practical seismic data.

[0115] Note that the above only describes the preferred embodiments of the present application and the technical principles used. Those skilled in the art will understand that the present application is not limited to the specific embodiments described herein, and those skilled in the art can make various obvious changes, re-adjustments and substitutions without departing from the scope of the present application. Therefore, although the present application has been described in more detail through the above embodiments, the present application is not limited to the above embodiments, and can include more other equivalent embodiments without departing from the concept of the present application, and the scope of the present application is determined by the scope of the appended claims.

Claims

1. A method for 3D seismic data interpolation based on cross-dimension migration, characterized in that, The method comprises the following steps: S1, constructing a two-dimensional seismic data interpolation method training, verification and testing dataset; S2, constructing a two-dimensional seismic data interpolation network based on Transformer; S3, constructing a two-dimensional loss function; S4, training the two-dimensional seismic data interpolation network based on Transformer constructed in step S2; S5, verifying the two-dimensional seismic data interpolation network model based on Transformer obtained after the training in step S4, and if the verification is passed, the optimal two-dimensional seismic data interpolation model is obtained; otherwise, return to step S4 to retrain the model; S6, extracting the parameters of the Transformer module in the two-dimensional seismic data interpolation network model based on Transformer obtained in step S5; S7, constructing a three-dimensional seismic data interpolation method training, verification and testing dataset; S8, constructing a three-dimensional seismic data interpolation network based on cross-dimensional migration; S9, constructing a three-dimensional loss function; S10, loading the parameters extracted in step S6 into the Transformer module in the three-dimensional seismic data interpolation network based on cross-dimensional migration constructed in step S8, and freezing the Transformer module; S11, fine-tuning the three-dimensional seismic data interpolation network based on cross-dimensional migration obtained in step S10; S12, verifying the three-dimensional seismic data interpolation network model based on cross-dimensional migration obtained after the fine-tuning in step S11, and if the verification is passed, the optimal three-dimensional seismic data interpolation model is obtained; otherwise, return to step S10 to retrain the model; S13, randomly deleting traces of a real seismic profile and inputting the real seismic profile into the optimal interpolation model obtained in step S12 to obtain an interpolated seismic profile. 2.The method of claim 1, wherein, Step S1 specifically comprises the following steps: S1.1, obtaining a public dataset from a public website, and obtaining a plurality of two-dimensional slices from the dataset by a sliding window method, the obtained slices being divided into three parts in proportion, and being used as a training set, a verification set and a test set respectively; S1.2, randomly deleting traces in the slices in the training set, the verification set and the test set in step S1.1 to form a two-dimensional dataset containing missing data and complete data one-to-one, and completing the construction of the dataset.

3. The method of claim 2, wherein, Step S2 specifically comprises: the two-dimensional seismic data interpolation network based on Transformer mainly comprises two 3x3 convolution layers, a head module, a global feature extraction module, a tail module and two residual connections; the data slice containing missing data in the training set is first expanded in dimension by a 3x3 convolution layer, and then shallow features are extracted by the head module; After passing through the global feature extraction module, the features are finally optimized by the tail module; the output of the tail module is added to the output of the head module through a residual connection, and the sum is then reduced in dimension by a 3x3 convolution layer; finally, the feature output is added to the initial input through a residual connection, thereby obtaining an interpolated seismic profile; The head module is composed of two repeated sub-modules composed of a 3*3 convolution layer, a linear rectifier unit, a 3*3 convolution layer, and a residual connection; the residual connection is used to add the output of the second convolution layer of each sub-module to the input of the sub-module; the output of the second sub-module is the extracted shallow layer feature; The global feature extraction module is composed of four Transformer modules; the input feature map is first passed through a Transformer module, then concatenated with itself in the channel dimension, and the channel number is reduced to the same as the input feature map by a 3*3 convolution layer; subsequently, the output of the three Transformer modules is all concatenated with the output of each previous Transformer module in the channel dimension, and then the channel is reduced by a 3*3 convolution layer; after the last channel reduction, the output feature map of the global feature extraction module is obtained; The tail module is composed of three 3*3 convolution layers and two linear rectifier units with leakage alternately stacked, with the first 3*3 convolution layer as the head and the third 3*3 convolution layer as the tail; the output of the third 3*3 convolution layer is the optimized feature.

4. The method of claim 1, wherein: In step S3, the two-dimensional loss function is an L2 loss function, i.e., a root mean square error loss function, and its mathematical expression is: ； wherein is the input missing seismic data, is the corresponding complete seismic data in the training set, is the corresponding complete seismic data in the training set, and are the number of time samples and traces of a two-dimensional seismic profile, respectively.

5. The method of claim 1, wherein: In step S4, the Transformer-based two-dimensional seismic data interpolation network constructed in step S2 is trained, the mapping from the data with missing data to the complete data is performed, the two-dimensional loss function constructed in step S3 is optimized according to the mapping result, and the optimal network model parameters are obtained within a specified number of training rounds, at which point the training is completed. In step S11, the three-dimensional seismic data interpolation network based on cross-dimension migration obtained in step S10 is fine-tuned, the mapping from the data with missing data to the complete data is performed, the three-dimensional loss function constructed in step S9 is optimized according to the mapping result, and the optimal network model parameters are obtained within a specified number of training rounds, at which point the training is completed.

6. The method of claim 1, wherein, In step S5, the network model is verified, specifically including the following steps: S5.1, input the paired missing-complete seismic profiles in the verification set into the trained Transformer-based two-dimensional seismic data interpolation network for verification; S5.2, when the evaluation indicators of the verification result, i.e., the peak signal-to-noise ratio and the structural similarity, do not meet the set indicator threshold, the Transformer-based two-dimensional seismic data interpolation network is retrained after optimization and parameter adjustment in step S4; S5.3, when the evaluation indicators of the verification result, i.e., the peak signal-to-noise ratio and the structural similarity, meet the set indicator threshold, the training is stopped, and the trained Transformer-based two-dimensional seismic data interpolation network model is used as the optimal pre-training model.

7. The method of claim 1, wherein, In step S7, the following steps are included: S7.1, obtain a public data set from a public website, and obtain multiple three-dimensional cutouts from the data set by a sliding window method; the obtained cutouts are divided into three parts in proportion, which are used as the training set, the verification set, and the test set, respectively; S7.2, randomly delete the patches in the training set, validation set and test set in step S7.1, form a three-dimensional data set containing missing data and complete data one by one, and complete the whole process of building the data set. 8.The method of claim 1, wherein, Step S8, specifically: the three-dimensional seismic data interpolation network based on cross-dimensional migration mainly consists of two 3*3 convolution layers, a head module, a cross-dimensional migration module, a tail module and two residual connections; the data body containing missing data in the training set is first combined with the batch dimension to be compatible with the two-dimensional module in the network; secondly, the dimension is expanded through a 3*3 convolution layer, and then the shallow features are extracted through the head module; After the cross-dimensional migration module, the tail module optimizes the features; the output of the tail module is added to the output of the head module through a residual connection, and the sum is then reduced through a 3*3 convolution layer to reduce the feature dimension; finally, the feature output is added to the initial input through a residual connection, thereby obtaining the interpolated seismic profile; Wherein, the cross-dimensional migration module consists of four Transformer modules and four seismic dimension adapters; each Transformer module is placed in front of an SDA to perform cross-dimensional adaptation; the input feature map first restores the dimension to the same shape as the input; after passing through an SDA module, the dimension is further converted into a batch-crossline combination; then, the input Transformer module is input, then it is spliced with itself in the channel dimension, and the channel number is reduced to the same as the input feature map using a 3*3 convolution layer; then, the output of the three SDA-Transformer modules is spliced with the output of each previous SDA-Transformer module in the channel dimension, and then the channel is reduced using a 3*3 convolution layer; after the last channel reduction, the output feature map of the cross-dimensional migration module is obtained; The seismic dimension adapter consists of two linear layers and a deep convolution; the input feature map is first mapped to a high-dimensional space through a linear layer; then, the spatial correlation information is learned through a deep convolution; finally, the channel number is mapped back to the same as the input through another linear layer.

9. The method of claim 1, wherein, In step S9, the three-dimensional loss function is an L2 loss function, i.e. a root mean square error loss function, and its mathematical expression is: ； wherein, is the input missing seismic data, is the corresponding complete seismic data in the training set, is the corresponding complete seismic data in the training set, , and are the number of time samples, inline and crossline, respectively, of a three-dimensional seismic volume.

10. The method of claim 1, wherein, In step S12, the network model is verified, specifically including the following steps: S12.1, input the paired missing-complete seismic body in the validation set into the trained three-dimensional seismic data interpolation network based on cross-dimensional migration for verification; S12.2, when the evaluation index of the verification result, the peak signal-to-noise ratio and the structural similarity, does not meet the set index threshold, then return to step S11, optimize and adjust the parameters, and then fine-tune the three-dimensional seismic data interpolation network based on cross-dimensional migration. S12.3, when the evaluation index of the verification result: peak signal-to-noise ratio, structural similarity meets the set index threshold, stop fine tuning, then the trained three-dimensional seismic data interpolation network model based on cross-dimensional migration is used as the optimal training model.

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