Deep network based very low frequency wave propagation model resolution enhancement method and system

Abstract

The application provides a deep network-based very low frequency wave propagation model resolution enhancement method and system, and belongs to the field of very low frequency wave detection and application. First, a low-resolution and high-resolution dataset of very low frequency station signal distribution is constructed, then a CNN structure is designed, which is divided into two core modules of feature extraction and image reconstruction, wherein the feature extraction module is responsible for extracting deep features from the LR image, and the image reconstruction module improves the resolution of the output image through upsampling and super-resolution reconstruction. Then the dataset is randomly shuffled after preprocessing, and is divided into a training set and a validation set in proportion. In the model inference stage, the CNN realizes accurate reconstruction of the high-resolution signal field through deep feature analysis of the LR image, converts the complete lightweight network model into a format suitable for engineering deployment, and finally seamlessly integrates into the LWPC propagation model, thereby effectively improving the resolution of the propagation field strength distribution.

Description

Technical Field

[0001] This invention belongs to the field of very low frequency wave detection and application, and can significantly improve the resolution of very low frequency propagation simulation and the reliability of engineering applications. Background Technology

[0002] The D layer (low ionosphere) is located in the atmosphere approximately 60-100 km above the Earth's surface, where the electron density typically ranges from 1 to 1000 cm⁻³. This electron density is significantly influenced by both top-down solar radiation and cosmic rays, and bottom-up atmospheric waves and gravitational waves, exhibiting marked spatiotemporal variations. The electron density of the D layer directly determines the propagation characteristics of radio waves in this region, significantly impacting radio communication, radio wave propagation, maritime navigation and positioning, and space environment monitoring. Very Low Frequency (VLF) waves are electromagnetic waves with frequencies ranging from 3 to 30 kHz, primarily originating from global thunderstorm activity or signals emitted by artificial VLF stations. Due to their relatively long wavelengths, VLF waves are influenced by the Earth-ionospheric waveguide formed by the Earth and the D layer, propagating over long distances with low attenuation within this waveguide structure, typically with an attenuation coefficient of approximately 2-3 dB / Mm. This characteristic has led to the widespread application of VLF waves in global communications, submarine communications, and navigation and positioning. However, variations in ionospheric height and instability in electron density distribution can alter propagation characteristics, making accurate prediction of the spatial distribution of very low frequency signals a critical challenge in engineering applications.

[0003] Artificial very low frequency (VLF) stations are crucial facilities for long-range communication and navigation. Their antennas are typically large, requiring the erection of large antenna arrays in open areas such as valleys or plains, resulting in extremely high construction and maintenance costs. Currently, existing artificial VLF transmitters worldwide are primarily used for military communications, with limited publicly available information, restricting related research and engineering applications. Accurately calculating the signal distribution around artificial transmitters is a core task in VLF navigation and positioning applications. However, due to the complex multipath effects, attenuation characteristics, and ionospheric dynamics involved in VLF wave propagation in the Earth-ionospheric waveguide, traditional computational models such as Long Wave Propagation Capability (LWPC) have limitations in computational resolution and efficiency. While LWPC and similar methods based on empirical formulas and ray tracing can simulate VLF wave propagation characteristics, their low computational resolution fails to meet precise engineering requirements. Furthermore, these models typically rely on central processing units (CPUs) for computation, resulting in high computational complexity and excessively long simulation times, making it difficult to meet real-time requirements. Therefore, how to improve the resolution of very low frequency propagation calculations while accelerating the calculation speed has become an urgent problem to be solved in engineering applications. Summary of the Invention

[0004] Addressing the limitations of existing technologies, deep learning, with its powerful data-driven modeling capabilities, has demonstrated significant advantages in feature extraction, pattern recognition, and prediction of complex systems. In recent years, deep learning has gradually replaced traditional computational methods, achieving breakthroughs particularly in computer vision, speech recognition, and geophysical simulation. Compared to traditional physics-based modeling methods, deep learning can automatically learn latent patterns through large-scale data training and utilize graphics processing units (GPUs) for efficient computation, making high-resolution prediction possible. In fields such as computational mechanics, fluid dynamics, and electromagnetic propagation, deep learning has been widely applied to accelerate computation and improve prediction accuracy.

[0005] In view of this, this invention proposes a method based on deep learning networks to improve the computational resolution of traditional very low frequency (VLF) propagation models. By constructing a deep convolutional neural network (CNN), this method can generate high-resolution results from low-resolution VLF signal distribution data, significantly reducing computation time while maintaining computational accuracy. Ultimately, this method can achieve a resolution enhancement from the 20km level to the 5km level, while controlling the relative computational error to ≤0.1%. This will greatly improve the engineering practicality of VLF propagation simulation, providing high-precision computational support for fields such as radio communication, navigation and positioning, and space environment monitoring.

[0006] The technical solution of this invention is a resolution enhancement method for very low frequency (VLF) wave propagation models based on deep networks, comprising:

[0007] A low-resolution LR dataset for very low frequency propagation is obtained using the LWPC model, and a high-resolution HR dataset is obtained by image processing of the LR dataset and fusion of the LMP model.

[0008] A deep convolutional neural network is constructed, including a feature extraction module and an image reconstruction module. The feature extraction module consists of several residual structures connected by dense skip connections, and the image reconstruction module consists of two sets of [convolutional layers + Leaky ReLU activation layers + pixel reorganization layers (Pixels Shuffler)].

[0009] The data sources in the LR and HR datasets are matched one-to-one, and the corresponding datasets are randomly shuffled and divided into training and validation sets according to the proportions.

[0010] During the training phase of the deep convolutional neural network, the processed data is input into the network. The feature extraction module obtains the deep feature information of the LR image, and then the image reconstruction module performs upsampling and image reconstruction to connect to the HR image, thereby realizing the mapping relationship between the LR and HR images.

[0011] During the inference phase, the very low frequency propagation (LR) data calculated by the LWPC model is directly input into the trained deep convolutional neural network to achieve resolution enhancement.

[0012] Furthermore, by inputting the same very low frequency (VLF) station's transmitted signal time, frequency, and power into the LWPC model, setting the output resolution of the LWPC model, calculating low-resolution VLF propagation distribution data, plotting the longwave amplitude distribution image obtained from the LWPC calculation, and integrating them into a low-resolution dataset labeled LR.

[0013] Furthermore, the specific implementation method for obtaining the HR dataset is as follows:

[0014] Cubic spline interpolation was used to interpolate the images in the LR dataset to improve resolution. Non-local mean filtering was used to reduce edge blurring, and oversampling was used to optimize aliasing. The dataset processed by the above image processing methods is labeled as the first high-resolution dataset HR1.

[0015] The LMP model is set with the same input parameters as the LWPC model. The output resolution is set, and high-resolution very low frequency propagation distribution data is calculated and integrated into a high-resolution dataset, which is denoted as the second high-resolution dataset HR2.

[0016] The images in HR1 and HR2 are linearly composited pixel by pixel. The composite image is generated by performing the linearly composited pixel operation on the two images. The composite image forms a new dataset, which is denoted as the high-resolution HR dataset.

[0017] Furthermore, the formula for pixel linear composite is as follows:

[0018] HR(x,y)=0.5×HR1(x,y)+0.5×HR2(x,y)

[0019] Where x and y are the pixel coordinates in the image.

[0020] Furthermore, the mean absolute error (MAE) is used as the loss function for the deep convolutional neural network.

[0021] Furthermore, the specific formula for the Mean Absolute Error (MAE) is as follows:

[0022]

[0023] Where T is the actual VLF propagation image, P is the network prediction result, N is the total number of pixels in the image, and x and y are the pixel coordinates in the image.

[0024] Furthermore, the training phase of a deep convolutional neural network includes:

[0025] The training set is input into the network according to the set number of training iterations and the maximum number of input samples.

[0026] The feature extraction module of the network acquires deep feature information of the LR image during training; the reconstruction module achieves ×4 image super-resolution reconstruction through two upsampling steps and then connects it to the HR image to train the mapping relationship between the LR and HR images.

[0027] The results of super-resolution of LR images to HR images by each training iteration of the network are visualized and compared using the loss function. The loss value between the simulated amplitude and the predicted amplitude is calculated by the loss function MAE. The network is trained iteratively, and the loss value is observed to decrease. The iterative training is completed when the loss value tends to stabilize.

[0028] Furthermore, during the training process of the deep convolutional neural network, the optimizer is Adam, the learning rate and weight decay are set, and Tensorflow is selected as the training platform.

[0029] Furthermore, it also includes using root mean square error, peak signal-to-noise ratio, structural similarity, and correlation to evaluate the difference between the prediction results and the original high-resolution image.

[0030] This invention also provides a resolution enhancement system for very low frequency wave propagation models based on deep networks, comprising:

[0031] The processor and memory are used to store program instructions, and the processor is used to call the stored instructions in the memory to execute a resolution enhancement method for a very low frequency wave propagation model based on deep networks as described in the above technical solution.

[0032] This invention provides a resolution enhancement method for very low frequency (VLF) wave propagation models based on deep convolutional neural networks (CNNs), belonging to the field of VLF wave detection and application. Existing VLF propagation capability (LWPC) models are widely used due to their fast computation speed, but their accuracy is limited. In contrast, long-wave modal propagation (LMP) models, while having higher accuracy, require significant computational resources, making them unsuitable for efficient engineering applications. This invention innovatively introduces deep learning methods, using a high-precision LMP model as an auxiliary, to construct a CNN-based super-resolution enhancement framework, significantly improving the resolution and accuracy of the LWPC model while ensuring computational speed. First, low-resolution (LR) and high-resolution (HR) datasets of VLF station signal distribution are constructed to support the training of the deep learning model. Subsequently, a CNN architecture was designed, consisting of two core modules: feature extraction and image reconstruction. The feature extraction module is responsible for extracting deep features from LR images, while the image reconstruction module improves the resolution of the output image through upsampling and super-resolution reconstruction. To enhance the model's generalization ability and improve training efficiency, the dataset was randomly shuffled after preprocessing and proportionally divided into training and validation sets to optimize the network's input-output matching. During the model inference stage, the CNN achieves accurate reconstruction of the high-resolution signal field through deep feature analysis of LR images. The fully trained lightweight network model is then converted into a format suitable for engineering deployment and seamlessly integrated into the LWPC propagation model, effectively improving the resolution of the propagation field strength distribution. This method can improve the resolution from the 20km level to the 5km level while ensuring real-time computation and controlling the relative computational error to ≤0.1%. This method can be used to construct high-precision very low frequency (VLF) signal distribution maps, providing strong support for propagation characteristic research, precise positioning, and navigation assurance, further expanding the application value of VLF waves in radio communication, space environment monitoring, and remote detection. Attached Figure Description

[0033] Figure 1 This is a flowchart of a method according to an embodiment of the present invention;

[0034] Figure 2 This is a diagram of the deep convolutional neural network structure in an embodiment of the present invention;

[0035] Figure 3 This is a comparison diagram of the prediction results and the original HR and LR images in an embodiment of the present invention;

[0036] Figure 4 for Figure 3 A magnified comparison of the area within the dashed box at the top;

[0037] Figure 5 for Figure 3 A magnified comparison of the area within the dashed box below;

[0038] Figure 6 This is a comparison chart of the prediction results and LMP results in an embodiment of the present invention. Detailed Implementation

[0039] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0040] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0041] Figure 1 This is a flowchart of the method. An embodiment of the present invention provides a method for enhancing the resolution of a very low frequency (VLF) wave propagation model based on a deep convolutional neural network, the specific steps of which include:

[0042] Step 1: Use the low-resolution output LWPC model to simulate and calculate the propagation distribution of very low frequency waves, and draw the LR dataset of very low frequency propagation. Obtain the HR1 dataset by processing the LR data. At the same time, use the high-resolution output LMP model, select the same input parameters, and simulate and calculate to obtain the HR2 dataset. Perform pixel linear composite of HR1 and HR2 images to obtain a new dataset denoted as HR.

[0043] Step 11: Input the same very low frequency station's transmission time, frequency, power, and other parameters into LWPC. Set the LWPC output resolution to 20km and calculate the low-resolution very low frequency propagation distribution data.

[0044] Step 12: Use MATLAB R2021a to plot the long-wavelength amplitude distribution image obtained from LWPC calculation, and integrate it into a low-resolution dataset labeled LR;

[0045] Step 13: Use cubic spline interpolation to interpolate the images in the LR dataset to improve the resolution to 5km. Use nonlocal mean filtering to reduce edge blurring and oversampling to optimize aliasing. The dataset processed using the above image processing methods is labeled HR1.

[0046] Step 14: Use the LMP model for assistance. Set the same input parameters in the LMP model, including signal transmission time, VLF transmitter station frequency, power, etc., and set the output resolution to 5km to calculate high-resolution VLF propagation distribution data.

[0047] Step 15: Similarly, use MALTBA to draw the very low frequency propagation image calculated by LMP, and integrate it into a high-resolution dataset denoted as HR2;

[0048] Step 16: Perform pixel-wise linear composite on the images in HR1 and HR2, and perform proportional weighted fusion on the two images to generate a composite image with each image having a 50% weight; the composite image forms a new dataset denoted as HR; LR and HR are the datasets input for training the neural network; the formula for pixel-wise linear composite is as follows:

[0049] HR(x,y)=0.5×HR1(x,y)+0.5×HR2(x,y)

[0050] Where x and y are the pixel coordinates in the image;

[0051] Step 2: Construct a deep convolutional neural network, including a feature extraction module and an image reconstruction module. Use the mean absolute error (MAE) as the loss function of the neural network, select Adam as the optimizer, set the learning rate to 0.001, and set the weight decay to 0.00001.

[0052] Step 21: Construct a deep convolutional neural network, the specific structure of which is as follows: Figure 1 As shown, it includes a feature extraction module and an image reconstruction module; the data processing module consists of 6 residual structures connected by dense skip connections, used to extract deep feature information of LR images; the image reconstruction module consists of two sets of [convolutional layers + Leaky ReLU activation layers + Pixels Shuffler layers], used for two ×2 upsampling to achieve ×4 image super-resolution reconstruction;

[0053] Residual structure: The front end of the previous convolutional layer and the back end of the next convolutional layer are stacked to enhance the nonlinearity and feature extraction capabilities of the network;

[0054] Dense jump connection: The connection method is shown in the attached diagram. Figure 2 The image shows existing methods for mitigating network gradient vanishing and improving information flow.

[0055] Pixels Shuffler Layer: An upsampling method that effectively enlarges the feature map, replacing interpolation or deconvolution methods to achieve upsampling; using a single pixel shuffler layer can achieve upsampling of ×2, and two layers can achieve ×4; [Convolutional Layer + Leaky ReLU Activation Layer] does not have upsampling functionality, but is used to enhance network nonlinearity and stability, as well as increase network depth;

[0056] Step 22: Use MAE as the loss function. The specific formula is as follows:

[0057]

[0058] Where T is the actual VLF propagation image, P is the network prediction result, and N is the total number of pixels in the image;

[0059] Step 23: Select Adam as the network optimizer, set the learning rate to 0.001, and the weight decay to 0.00001; select Tensorflow as the training platform.

[0060] Step 3: Preprocess the dataset. Match the data sources of LR and HR one by one, randomly shuffle the corresponding datasets and split them into training and validation sets according to the proportions to enhance the generalization ability of the model and speed up the training rate.

[0061] Step 31: After establishing a one-to-one correspondence between the LR and HR datasets obtained in Step 1, randomly shuffle them to enhance the generalization ability of the model and accelerate the training gradient descent rate.

[0062] Step 32: Divide the data into a dataset and a validation set in an 8:2 ratio to test the model configuration and training results, and to determine whether the validation results are overfitting or underfitting, so as to make adjustments and retrain.

[0063] Step 4: During the training phase of the neural network, the preprocessed data is input into the CNN network. The feature extraction module obtains the deep feature information of the LR image, and then the image reconstruction module performs upsampling and image reconstruction to connect to the HR image, thereby realizing the mapping relationship between the LR and HR images.

[0064] Step 41: Input the training data into the network according to the set number of training epochs and maximum number of input samples (batch size);

[0065] Step 42: The feature extraction module of the network acquires deep feature information of the LR image during training; the reconstruction module achieves ×4 image super-resolution reconstruction through two upsampling steps and then connects it to the HR image to train the mapping relationship between the LR and HR images.

[0066] Step 43: Visualize and compare the results of each training iteration of the network super-resolution from the LR image to the HR image using the loss function. Calculate the loss value between the simulated amplitude and the predicted amplitude using the loss function MAE. Iterate through the training of the network and observe whether the loss value decreases. Complete the iterative training when the loss value tends to stabilize.

[0067] Step 5: Select a suitable format part network model and output it, connect it to the LWPC model, and further integrate the obtained network into the low frequency signal amplitude calculation system to improve the resolution of the LWPC model's calculation results while ensuring the calculation speed.

[0068] Step 51: Store the trained network model parameters in Torch Script format, select the LibTorch extension package that is compatible with the C / C++ environment for code porting, and realize the operation of the deep learning model in the C / C++ integrated system;

[0069] Step 52: Further integrate the obtained network into the calculation system of very low frequency signal amplitude containing the LWPC model for fast calculation of high resolution very low frequency signal amplitude distribution.

[0070] Specifically, in this embodiment of the invention, MATLAB is used to plot the very low frequency wave propagation images calculated by LWPC and LMP, the transmitter location is set to (20°N, 100°E), the frequency is set to 20kHz, the power is set to 1000kW, and other parameters are left as default; and the LR and HR images are obtained through image processing. Figure 3 The image on the left is a low-resolution image, and the image on the right is a high-resolution image; a deep learning network was used to train the dataset, and the network architecture is as follows. Figure 2 As shown; the network prediction results are as follows Figure 3 As shown in the second image from the left; Figure 4 , 5 for Figure 3 The magnified images within the two dashed rectangles are compared with the LR, HR, and prediction results using evaluation metrics. The evaluation metrics between the prediction results and the original HR images are as follows: MAE value is 0.002, Root Mean Squared Error (RMSE) value is 0.0023, Peak Signal-to-Noise Ratio (PSNR) value is 0.9998, Structural Similarity Index (SSIM) is 0.9997, and Correlation Coefficient (CC) is 0.999. These metrics clearly demonstrate the superior performance of images trained using deep networks. Figure 6The figure shows a comparison between the prediction results of this method and the LMP results. It can be seen that the results of this method and LMP are in high agreement, proving that this method has a certain degree of scientific validity and reliability.

[0071] After network training is complete, the deep convolutional neural network (CNN) can be deployed to the very low frequency (VLF) wave propagation computing system to achieve rapid resolution enhancement of the computation results. In actual computation, users only need to quickly generate low-resolution (LR, 20km level) propagation field results using the LWPC model, convert them into LR images, input them into the CNN network, and after model processing, quickly obtain high-resolution (HR, 5km level) propagation field results. Compared to the traditional LWPC model, this method can significantly improve the resolution of the computation results while maintaining the high computational speed of LWPC; compared to the high-precision LMP model, this method significantly reduces computation time while ensuring computational accuracy. Figure 6 As shown, the results calculated using LWPC combined with the method presented in this paper achieve resolution and accuracy comparable to the LMP model, thus providing a solution for very low frequency (VLF) wave propagation simulation that balances computational efficiency and high accuracy. Since the CNN only performs super-resolution enhancement on the LWPC calculation results, its final accuracy depends on the calculation results of the LWPC and LMP propagation models used to construct the training dataset. Furthermore, this method has a significantly lower computational complexity than directly using LMP, enabling high-resolution VLF propagation calculations with higher real-time performance and wide applicability in long-wave communication and navigation, remote sensing, and space environment monitoring. However, it is important to note that although this method optimizes the accuracy of LWPC calculations through deep learning, the model's output still depends on the LWPC and LMP calculation results. The actual propagation characteristics of VLF signals may be affected by complex factors such as dynamic changes in the ionosphere and differences in the surface medium, leading to some errors between the model's calculation results and the actual propagation situation. Therefore, in the future, we can combine measured data to further optimize the deep learning model, use data assimilation technology to correct propagation errors, or improve the accuracy of very low frequency wave propagation modeling through multi-source telemetry, so as to further improve the adaptability and reliability of the calculation results to the real environment, and make this method more widely applicable to the calculation and engineering application of very low frequency signal propagation in complex environments.

[0072] On the other hand, embodiments of the present invention also provide a resolution enhancement system for very low frequency wave propagation models based on deep networks, comprising:

[0073] The processor and memory are used to store program instructions, and the processor is used to call the stored instructions in the memory to execute a resolution enhancement method for a very low frequency wave propagation model based on deep networks as described in the above technical solution.

[0074] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for resolution enhancement of a very low frequency wave propagation model based on deep network, characterized in that, The application comprises the following steps: a low-resolution LR data set of very low frequency propagation is obtained by using a LWPC model, a high-resolution HR data set is obtained by image processing based on the LR data set and fusion of an LMP model; the specific implementation mode of obtaining the HR data set is as follows: a cubic spline interpolation method is used to perform interpolation processing on the images in the LR data set to improve the resolution, a non-local mean filter is used to reduce the edge blur of the images, and oversampling is used to optimize the aliasing phenomenon of the images; the data set processed by the above image processing means is marked as a first high-resolution data set HR1; the same input parameters as the LWPC model are set for the LMP model, the output resolution is set, the high-resolution very low frequency propagation distribution data is calculated and integrated into a high-resolution data set, which is marked as a second high-resolution data set HR2; the images in HR1 and HR2 are subjected to pixel linear composition, pixel linear composition is performed on the two images to generate a composite image, and a new data set composed of the composite image is marked as a high-resolution HR data set; a deep convolutional neural network is constructed, including a feature extraction module and an image reconstruction module, the feature extraction module is connected by a plurality of layers of residual structures through a dense jump connection mode, and the image reconstruction module is composed of two groups of [convolutional layer + Leaky ReLU activation layer + pixel recombination layer Pixels Shuffler]; the data sources in the LR data set and the HR data set are one-to-one corresponding, the corresponding data sets are subjected to random shuffling and divided into a training set and a validation set according to a proportion; in the training stage of the deep convolutional neural network, the processed data are input into the network, the feature extraction module obtains deep feature information of the LR image, and then the image reconstruction module is connected to the HR image through upsampling and image reconstruction to realize the mapping relationship between the LR and HR images; in the inference stage, the LR data of very low frequency propagation calculated by the LWPC model are directly input into the trained deep convolutional neural network to realize resolution enhancement. 2.The method of claim 1, wherein: the same very low frequency station transmitting signal time as the LWPC model input, as well as the frequency and power of the station, the output resolution of the LWPC model is set, the low-resolution very low frequency propagation distribution data is calculated, the long-wave amplitude distribution image calculated by the LWPC is drawn, and the low-resolution data set is integrated and marked as LR. 3.The method of claim 1, wherein: The formula of pixel linear composition is as follows: wherein x , y are pixel coordinates in the image. 4.The method of claim 1, wherein: the mean absolute error MAE is used as the loss function of the deep convolutional neural network.

5. The deep network based very low frequency wave propagation model resolution enhancement method of claim 4, wherein: The specific formula of the mean absolute error MAE is as follows: wherein, T is the actual VLF propagation image, P is the network prediction, N is the sum of the number of pixels in the image, x , y is the pixel coordinate in the image.

6. The deep network based very low frequency wave propagation model resolution enhancement method of claim 1, wherein: the training stage of the deep convolutional neural network comprises the following steps: according to the set training times and the maximum input sample quantity, the training set is input into the network; the feature extraction module of the network obtains deep feature information of the LR image in the training process; the reconstruction module is connected to the HR image after image super-resolution reconstruction through twice upsampling, so as to realize the training of the mapping relationship between the LR and HR images; The results of super-resolution of the LR image to the HR image by the network of each single training are visualized by the loss function, the loss value between the simulated amplitude and the predicted amplitude is calculated by the loss function MAE, the network is iteratively trained, and whether the loss value is reduced is observed; when the loss value tends to be stable, the iterative training is completed.

7. The deep network based very low frequency wave propagation model resolution enhancement method of claim 1, wherein: In the training process of the deep convolutional neural network, the optimizer is selected as Adam, the learning rate and weight decay are set, and Tensorflow is selected as the training platform. 8.The method of claim 1, wherein: Further comprising, using the root mean square error, the peak signal-to-noise ratio, the structural similarity, and the correlation to evaluate the difference between the predicted results and the original high-resolution image.

9. A deep network based very low frequency wave propagation model resolution enhancement system, characterized in that, Comprise: A processor and a memory, the memory is used to store program instructions, and the processor is used to call the stored instructions in the memory to execute a very low frequency wave propagation model resolution enhancement method based on a deep network as claimed in any one of claims 1-8.

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