Stable downward continuation method of geomagnetic anomaly data based on SRGAN deep learning network

Abstract

The method for stable downward extension of geomagnetic anomaly data based on the SRGAN deep learning network belongs to the field of geophysical magnetic field data extension. The present invention combines the characteristics of geomagnetic anomaly data extension and adds a CBAM spatial attention mechanism module to improve the network model's spatial perception of magnetic anomaly data. In combination with the characteristics that the downward extension of potential field data will amplify high-frequency signals and generate noise, the deep learning model is combined with adaptive threshold multiple wavelet transform to suppress noise data and further improve the extension accuracy. In order to enable the model to fully learn the detailed information of geomagnetic anomaly data, a training data set construction method combining a Kriging super-resolution algorithm with a sliding sub-area mode is proposed. By designing a synthetic simulation model experiment and comparing the measured data with the other three algorithms, the model of the present invention has the highest calculation accuracy and the best recovery of magnetic anomaly details.

Description

Technical Field

[0001] The present invention belongs to the field of geophysical magnetic field data extension, and relates to a stable downward extension method for geomagnetic anomaly data based on the SRGAN deep learning network. The method has wide applications in the fields of potential field data extension, further interpretation of magnetic data, and magnetic source signal enhancement. Background Art

[0002] Downward continuation of potential field data is key to effectively utilizing gravity and magnetic data and holds significant application value in physical geodesy. Downward continuation utilizes the potential field data of the measured plane to infer the underlying surface potential field data at distances multiples of the grid spacing, thereby improving the interpretability of the measured data. Downward continuation enhances weak signals in planar measurement data, further enhancing magnetic source characteristics and revealing more detailed information. This approach has practical applications in resource exploration, magnetic target detection, magnetic source structure analysis, and integrated navigation.

[0003] From the physical principle of downward continuation of potential field data, the potential field can be extended to any position in space. However, from a practical mathematical perspective, this is an ill-posed problem, and direct continuation calculations are therefore divergent and unstable. In the frequency domain, downward continuation can over-amplify some short wavelengths, causing noise to affect the extended values. Filtering is often used to remove high-frequency components, but the maximum downward continuation distance is also limited. To address this noise caused by over-amplification, a stabilization factor is often added during sampling calculations. However, this factor attenuates the amplitude of the extended data, reducing the resolution of the extended data. Therefore, the downward continuation distance is generally a multiple of the grid spacing and should not be too long. To address this issue, the continuation operator can be modified, using Tikhonov regularization and Wiener filtering to suppress downward continuation noise. However, selecting the optimal regularization parameter is difficult. L-curve, Generalized cross validation, and the C-norm criterion can be used, but these parameters are less effective when the curvature is smooth. In addition to the modification of the extension operator, the extension can also be performed in an iterative manner. The integral iteration method can improve the accuracy of the downward extension by continuously calculating the upward extension residual in an iterative manner, but the noise will gradually be amplified as the number of iterations increases.

[0004] Deep learning, as an important tool for solving numerous complex problems, has made significant progress across various disciplines. To address the issues of noise amplification during downward continuation and the accuracy of long-distance downward continuation, this paper proposes an improved SRGAN deep learning network. This network combines the CBAM spatial attention mechanism and adaptive Bayesian threshold multiple wavelet transform to comprehensively improve the network's continuation accuracy. Furthermore, the paper proposes using the Kriging super-resolution algorithm and sliding sub-region extraction technology to create a training dataset, which effectively improves the network's learning of detailed magnetic anomaly features. Summary of the Invention

[0005] The present invention addresses the problems of solution instability, parameter selection difficulties, and high-frequency noise caused by rapid amplification of high-frequency signals in traditional methods for downward continuation of geomagnetic anomaly data. This paper proposes an improved SRGAN deep learning network model to solve the downward continuation problem of geomagnetic anomaly data. Taking into account the characteristics of geomagnetic anomaly data continuation, the present invention adds a CBAM spatial attention mechanism module to enhance the network model's spatial perception of magnetic anomaly data. Furthermore, considering that downward continuation of potential field data amplifies high-frequency signals and generates noise, the deep learning model is combined with an adaptive threshold multiple wavelet transform to suppress noise data and further improve continuation accuracy. To enable the model to fully learn the detailed information of geomagnetic anomaly data, a training dataset construction method combining a Kriging super-resolution algorithm with a sliding sub-region model is proposed. Experiments with synthetic simulation models and measured data were compared with three algorithms: Tikhonov regularization, Iterationlandweber regularization, and Integral iterative regularization. The proposed model achieves the highest accuracy and best recovers magnetic anomaly details.

[0006] The technical solution adopted in the present invention:

[0007] A stable downward continuation method for geomagnetic anomaly data based on the SRGAN deep learning network, the steps are as follows:

[0008] Step 1: Use the Kriging interpolation algorithm to improve the resolution of the original grid geomagnetic anomaly data to obtain super-resolution geomagnetic anomaly data.

[0009] Step 2: The obtained super-resolution geomagnetic anomaly data is denoised using Bayesian adaptive threshold multiple wavelet transform, and then the continuation calculation is performed using the Tikhonov iterative regularization method. The regularization parameter and iteration parameter in the continuation calculation are calculated using the L-curve curve method.

[0010] Step 3: The data obtained by the extended calculation is further denoised using Bayesian adaptive threshold multiple wavelet transform, and the data after the two denoising processes are extracted using sliding sub-regions to create a dataset for training the improved SRGAN deep learning network.

[0011] Furthermore, the steps for extracting the two denoised data using sliding sub-regions to create an improved dataset for training the SRGAN deep learning network are as follows:

[0012] By setting sub-areas of a certain size, the data on the geomagnetic anomaly map in the corresponding coordinate area are extracted by sliding. The step size of each sliding can control the degree of change and overlap rate of adjacent sub-areas. The smaller the step size, the more detailed the data feature description; the movement path of the sliding sub-area includes left and right translation and downward translation, which can cover all areas of the entire map.

[0013] Step 4: Input the dataset into the improved SRGAN deep learning network. Five deep residual networks (DRNs) are first used to learn the residual mapping between the datasets. Double convolutional layers are used within the DRNs to extract magnetic anomaly data features. Batch normalization and a parameterized (PReLU) activation function are used to process the data after the double convolutional layers. The data after all the DRNs are then input into two convolutional layers and a pixel-level convolutional layer (PixelShuffle) to map the features back to the extended magnetic anomaly data. A Convolutional Block Attention Module (CBAM) attention mechanism is also added to the pixel-level convolutional layer to extract spatial information and spatial dimensional features from the extended magnetic anomaly data. These information and spatial dimensional features are then fed back into the improved SRGAN deep learning network for iterative training.

[0014] Step 5. For the sliding sub-area results output by the improved SRGAN deep learning network trained in step 5, the sliding sub-area results closest to the grid point are used as the extended value of the grid point using the nearest point principle. The extended values ​​of the grid points obtained from different sliding sub-areas are spliced ​​and further denoised using the Bayesian adaptive threshold multiple wavelet transform to obtain the final extended magnetic anomaly data.

[0015] The beneficial effects of the present invention are as follows: the present invention has higher magnetic anomaly extension accuracy than traditional extension algorithms, has stronger magnetic anomaly detail feature recovery capability for extended data, reduces the influence of regularization parameters on accuracy, and has higher robustness; the present invention adopts a Bayesian adaptive threshold multiple wavelet transform dual noise reduction mode, which not only reduces the noise level of the original measurement data, but also removes the amplified noise generated by the extension, thereby improving the anti-noise capability of the present invention and further improving the extension accuracy and detail feature recovery capability. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 This is a schematic diagram of the extension of magnetic data.

[0017] Figure 2 This is a flow chart of the deep learning model of the present invention.

[0018] Figure 3 Schematic diagram of data extraction for the sliding sub-area.

[0019] Figure 4 The L-curve graph and curvature graph are shown in Figure 1. (a) L-curve graph, (b) curvature change graph.

[0020] Figure 5 Schematic diagram of the simulation model.

[0021] Figure 6 The data forms of the synthetic simulation model in and . Among them, (a) magnetic anomaly data form, (b) magnetic anomaly data form.

[0022] Figure 7 Graph of the loss function for model training.

[0023] Figure 8 Different methods for image continuation. (a) This invention, (b) Integral iterative, (c) Iteration Landweber regularization, (d) Tikhonov regularization, and (e) 900m real data.

[0024] Figure 9 The following are the cross-sectional analysis diagrams of the extended data using different algorithms. (a) The cross-sectional calculation results of different algorithms, and (b) The cross-sectional errors of different algorithms.

[0025] Figure 10The data of the present invention are extended to different heights at different positions. Among them, (a) y = 530m at different heights, (b) y = 930m at different heights, (c) y = 1330m at different heights, (d) y = 1730m at different heights, (e) y = 2130m at different heights, (f) y = 2530m at different heights, (g) y = 2930m at different heights, (h) y = 3330m at different heights, (i) y = 3730m at different heights.

[0026] Figure 11 This is the RMSE distribution diagram of the sliding sub-area.

[0027] Figure 12 The residual graph of the filtering effect. (a) Model without denoising module, (b) Model with denoising module.

[0028] Figure 13 The extended images are obtained using different algorithms. (a) This invention, (b) Integral iterative, (c) Iteration Landweber regularization, (d) Tikhonov regularization, and (e) 300 real data.

[0029] Figure 14 The residual graphs of different extended methods are shown in Figure 1. (a) The present invention, (b) Integral iterative, (c) Iteration landweber regularization, and (d) Tikhonov regularization.

[0030] Figure 15 The profiles and residuals of the extension results of different algorithms are shown in Figure 1. (a) The profile data of each algorithm, and (b) the residual information of the profile. DETAILED DESCRIPTION

[0031] The technical solution of the present invention will be further described below in conjunction with specific embodiments and drawings.

[0032] 1. Methods

[0033] 1.1 Principle of Bit Field Data Extension

[0034] like Figure 1 As shown, the extension model coordinate system is established. The center of the area of ​​the extension surface is taken as the center of the coordinate circle. A three-dimensional coordinate system is established on the plane formed by taking any direction as the X axis, the Y axis perpendicular to the X axis, and the Z axis perpendicular to the XY coordinate axis. h) means at point (x,y,z h ), u(ξ,η,z0) represents the extended surface potential field data at point (ξ,η,z0). According to the Dirichlet variance, the upward extension formula of the potential field data can be obtained:

[0035]

[0036] In formula (1), h is the extension height, point (x, y, z h ) is the observation point data, and point (x, y, z0) is the point to be found. Using Fourier transform to sort out equation (1), we can get the downward extension expression:

[0037]

[0038] In formula (2), n and v correspond to the frequency domain variables of x and y, U corresponds to the frequency domain potential field data of u, and R -1 is the downward continuation operator. As n and v change exponentially, high-frequency noise will increase sharply during the downward continuation process, resulting in instability of the continuation solution.

[0039] 1.2 Improving the SRGAN deep learning model

[0040] Tikhonov regularization suffers from a saturation effect, making it difficult to simultaneously achieve both smooth and accurate solutions. The Iteration Landweber regularization algorithm suffers from slow convergence and is sensitive to noise, leading to a decrease in solution quality in high-noise scenarios. The integral iteration method also suffers from high computational complexity and can lead to unstable solutions when processing noisy data. All three algorithms are sensitive to parameter selection, making it difficult to effectively determine the appropriate regularization parameters to obtain stable solutions, resulting in poor robustness.

[0041] In order to make the extension of magnetic data more accurate, reduce the influence of parameters on the extended data, and improve the stability of the solution, the present invention proposes a deep learning model for magnetic data extension based on the SRGAN network structure. SRGAN is an image reconstruction algorithm using a GAN network, which uses a tanh activation function to limit the output range, outputs the authenticity probability of the image through a sigmoid function, and generates a better image by minimizing the root mean square error between the generated image and the actual image. The present invention uses the generator model of the SRGAN network. In order to make the network have a stronger perception ability for the extension of magnetic data, a CBAM (Convolutional Block Attention Module) is added to the last layer. The attention mechanism is a convolutional neural network module. CBAM integrates the channel attention mechanism and the spatial attention mechanism, which can enable the network model to enhance the key features in the channel and spatial dimensions, and realize the learning of the key features of the magnetic data and the filtering of non-critical information.

[0042] The implementation process is as follows Figure 2 shown.

[0043] Depend on Figure 2 As shown in the figure, in the preparation of the network training dataset, to improve the effectiveness and sufficiency of the deep learning network's learning of the training data, the Kriging interpolation method was used to triple the resolution of the original gridded geomagnetic anomaly data, generating super-resolution geomagnetic anomaly data. Based on the super-resolution, Bayesian adaptive threshold multiple wavelet transform was used for denoising, further expanding the size of the training sample dataset and reducing the impact of the original data measurement and acquisition noise. Kriging interpolation is a commonly used interpolation method in geophysical neighborhoods. Based on the principle of minimum mean square error, it provides the optimal estimate of spatial data.

[0044] After the original data is super-resolution-enhanced, the data volume is further increased, providing data support for the subsequent sliding extraction of training subsets. At the same time, in order to reduce the impact of noise data caused by measurement in the original data, Bayesian adaptive threshold multiple wavelet transform is used to denoise it. The construction of the training set uses the Tikhonov iteration method. In order to accurately depict the characteristics of magnetic anomalies at different locations in the geomagnetic anomaly map and improve the feature learning of the extended area by the deep learning model, the geomagnetic data is extracted by sliding sub-areas to produce a training data set. Compared with the data set produced by direct data segmentation, the sampling of samples is more, and the detailed information is learned more fully. The sliding sub-area data extraction method is as follows Figure 3 shown.

[0045] like Figure 3As shown in the figure, the data set is produced by using the sliding sub-area extraction method to produce multiple sub-datasets to accurately characterize the magnetic anomaly characteristic information of the target area. The sliding sub-area extraction method is to extract the data on the geomagnetic anomaly map under the corresponding coordinate area by setting a sub-area of ​​a certain size. The change degree of two adjacent sliding sub-areas is small and the overlap rate is high. The step size of each sliding can control the change degree and overlap rate of adjacent sub-areas. The smaller the step size, the finer the data feature characterization. The sliding sub-area movement path is shown in the figure. Figure 3 As shown, the sliding mode is two-way translation and downward translation. It can be understood as a convolution mode, but this mode only extracts data without performing convolution calculations on it. This method can fully cover the extended area and improve the training effect of deep learning models. Preferably, the sliding sub-area moves in steps of 1 grid point each time, and the sliding sub-area size is 128×128 grid points.

[0046] The selection of Tikhonov iteration parameters is determined by the L-curve method. The L-curve is determined by analyzing the Ag a -f and regular solution g a The relationship between the norm of and as the regularization parameter changes, draw the curve of the two as the parameter changes, and take the parameter at the position with the maximum curvature change as the optimal regularization parameter. The calculation formula is as follows:

[0047]

[0048] In formula (3), f is the observation vector, A is the design matrix, g a Regular solution.

[0049] According to formula (3), α and β are obtained, and the curvature calculation formula is as follows:

[0050]

[0051] Depend on Figure 4 As shown, Figure 4 (a) is the L-curve graph for solving the optimal regularization parameter. The position of the maximum curvature of the curve is usually selected as the optimal regularization parameter selection point. Figure 4 (b) in the figure is the corresponding curvature calculation change diagram. It can be seen that the extreme point is the maximum curvature point, which is also the optimal regularization parameter selection point.

[0052] To reduce edge effects during the continuation process, the sub-areas output by the network use the nearest point principle to take the continuation sub-area closest to the grid point as the continuation calculation value of the grid point for sub-area splicing. Since the downward continuation results of magnetic data are ill-posed and will amplify the high-frequency portion of the observation error, the network model should have the ability to suppress high-frequency noise and restore the true continuation image to a large extent. Therefore, Bayesian adaptive threshold multiple wavelet analysis is used in the network output stage to adaptively filter high-frequency noise. Compared with traditional wavelet analysis technology, multiple wavelet analysis has multiple wavelet basis functions, which can capture more feature information; it can also extract data information at multiple levels and resolutions, which helps to reveal deeper details in the data, enabling it to process more complex data and improving the accuracy and flexibility of data filtering.

[0053] The selection of multiple wavelet transform thresholds has a significant impact on the filtering effect, so it is necessary to estimate the noise of the geomagnetic anomaly extension data to set an appropriate threshold for filtering. The Bayesian estimation threshold principle is a signal processing method based on Bayesian theory. It is used to determine the appropriate signal threshold in the process of wavelet transform denoising. Its basic idea is to determine the optimal threshold by maximizing the posterior probability or minimizing the expected loss. Compared with other threshold selection methods, the Bayesian threshold method can better consider the noise statistical characteristics of the geomagnetic anomaly map. The Bayesian threshold calculation formula is as follows:

[0054] Assume that the noise model of the extended magnetic data is as follows:

[0055] Y=X+S(5)

[0056] In formula (5), Y is the extended data, X is the real magnetic anomaly data, and S is the noise data of the extended parameters.

[0057] After performing multiple wavelet transform on equation (5), the variance of noise wavelet coefficients is obtained:

[0058]

[0059] Where s=1, 2, 3 represent the horizontal decomposition coefficients HL after wavelet transform j , vertical decomposition coefficient LH j and the diagonal direction coefficient HH j j=1,2… represents the number of decomposition layers of multiple wavelet transform. Suppose the variance of the extended data wavelet coefficients is The variance of the wavelet coefficient of the real magnetic anomaly data is The variance of the noise wavelet coefficient is Since the wavelet coefficients of the real magnetic anomaly data and the noise are independent of each other, we can get:

[0060]

[0061] From formula (7) and formula (8), we can get:

[0062]

[0063] The Bayesian threshold expression can be obtained as:

[0064]

[0065] T(i,j) is the desired Bayesian threshold.

[0066] 2. Experimental Verification

[0067] 2.1 Simulation Data Verification

[0068] To verify the feasibility of the proposed modeling method, a synthetic simulation model was established. This synthetic simulation model consists of magnetic anomalies generated by four different rectangular blocks, with the parameters set as shown in Table 1. The magnetization intensity was set to 15 A / m, the magnetic inclination was set to 90°, and the magnetic declination was set to 90°. The generated grid data size was 4000 × 4000 m, the grid spacing was 40 m, and the generated simulation data resolution was 100 × 100.

[0069] Table 1 Synthetic simulation model parameters

[0070]

[0071] Table 1 gives the model parameters of the four cuboids and the coordinates of the center points of various models.

[0072] Figure 5 It is a schematic diagram of the simulation model. The magnetic field environment is simulated by setting four rectangular blocks. Above it is a schematic diagram of the magnetic anomaly value plane of the synthetic simulation model at a height of 300m.

[0073] 2.2 Extension experiment

[0074] The experiment selected the magnetic anomaly plane data generated by the synthetic simulation model at a height of Z = 1260m as the initial data for downward extension, and extended it to a height of Z = 900m with 9 times the point spacing. The magnetic anomaly data at Z = 900m was taken as the verification value. The morphology of the two data is as follows: Figure 6 shown.

[0075] First, geomagnetic anomaly data for the synthetic simulation model at an altitude of Z = 1260 m was extracted. The initial grid spacing was 40 m, and the grid resolution was 100 × 100. Kriging super-resolution was used to reconstruct the Z = 1260 m geomagnetic anomaly data at super-resolution, increasing the grid resolution to 300 × 300 to prepare for the next step of deep learning dataset generation. Tikhonov iteration and sliding sub-area extraction were combined to generate a total of 1225 datasets, each with a resolution of 128 × 128. This constructed training dataset was fed into the deep learning model for training, and the extended data was output. Finally, an adaptive Bayesian threshold multiwavelet algorithm was used to remove noise generated during the extension process, further improving the model's extension accuracy. Root Mean Square Error (RMSE) was used as the loss function for model training. The training epochs were set to 500, the learning rate was 0.001, and the number of samples processed in each training iteration was 16.

[0076] To verify the effects of super-resolution, network structure optimization, and denoising on the deep learning model of this invention, a series of ablation experiments were conducted, and the results are shown in Table 2. The ablation experiment results show that, based on the baseline model, the optimization model improves the basic extension model by 2. The specific results are as follows:

[0077] 1) By introducing the CBAM attention mechanism to enhance the model's spatial feature learning ability, the RMSE of the extended model is improved by 0.0479nT compared with the baseline model.

[0078] 2) By introducing the Kriging super-resolution algorithm to improve the model's learning of the detailed features of magnetic anomaly data, and combining the sliding sub-area extraction data set method to further increase the data set size, the model learning is more comprehensive, and the improvement is 0.0741nT compared with the baseline model.

[0079] 3) To address the issue of continuation amplifying noisy data, the extended data is adaptively denoised at the output stage of the model by introducing an adaptive Bayesian threshold multiple wavelet transform. This improves the accuracy by 0.0078nT compared to the model that introduces the CBAM attention mechanism and the Kriging super-resolution algorithm. Since the noise content of the simulated data constructed in this experiment is relatively low, the improvement effect is not obvious. Experimental verification shows that adding 5% Gaussian noise when constructing the data can improve the accuracy of the model by 0.0148nT.

[0080] Table 2 Ablation experiment of extension model

[0081]

[0082] Figure 7The RMSE value of the model training loss function changes with training rounds. The calculated RMSE in the figure is the normalized value. It can be seen that the RMSE value of the loss function of this model approaches convergence after 115 rounds.

[0083] The algorithm advantages of the present invention are illustrated by comparing the present invention with three methods: Integral iterative, Iteration landweber regularization and Tikhonov regularization.

[0084] Depend on Figure 8 As shown, after extending the magnetic anomaly generated by the synthetic simulation model by 9 times the spacing using the four algorithms, the calculation results of the present invention are more similar in morphology to the magnetic anomaly data generated by the synthetic simulation model at 900 meters, and have higher accuracy than the other three algorithms, demonstrating the advantages of the present invention in extending magnetic anomaly data. The RMSE calculated by Tikhonov regularization is 4.7247nT, the RMSE calculated by Iteration Landweber regularization is 6.1540nT, the RMSE calculated by Integral Iterative is 3.0590nT, and the RMSE calculated by the present model is 2.7827nT.

[0085] Figure 9 This is the profile data of different algorithms. The profile is in the north-south direction, passing through the area with large changes in magnetic anomaly, and passing through the No. 1, 2 and 3 cuboids. Figure 9 In (a), it can be seen that the extension values ​​calculated by the four algorithms are consistent in terms of general trend items, but the present invention can better restore the original data form and is more consistent with the waveform of the real data. Figure 9 In the cross-section error analysis of (b), the error of the present invention is relatively stable and has higher accuracy than the other three algorithms. Figure 9 The peak of (a) in the figure is where it is difficult to depict the high-frequency information of the data.

[0086] Figure 10 The paper describes the extension of the model of the present invention to the data of the Z=1260m plane downward to four heights of Z=1140m, Z=1020m, Z=900m and Z=800m, and observes the extension effect from 9 profile data. Figure 10It can be seen that the change patterns of geomagnetic anomaly data at different altitudes are not consistent, especially the numerical difference between Z = 900m and Z = 800m is large, while the change from Z = 1140m to Z = 900m is relatively gentle. It can be seen that the extension of magnetic anomaly data at different altitudes is not consistent. Therefore, the deep learning model cannot use the training data set with different altitudes but the same height difference to extend the data at other altitudes but the same height difference. It is necessary to re-establish the deep training training set.

[0087] Figure 11 The RMSE histogram of all sliding sub-areas calculated by the model of the present invention shows that the RMSE calculated for more than 80% of the sub-areas is less than 2.72nT. The RMSE calculated values ​​of the sliding extraction sub-areas vary with different positions, but the error gap is small, with the maximum gap being 1.1264nT, indicating that the calculated values ​​of the model of the present invention are relatively stable in different complex areas.

[0088] Depend on Figure 12 It can be seen that the extension residuals are mainly concentrated in the complex change area. Figure 12 (a) and Figure 12 As shown in (b), the adaptive Bayesian threshold multiple wavelet transform can effectively reduce the influence of high-frequency noise during the continuation process. From the amplitude of the residual, the addition of the denoising module reduces the maximum residual amplitude, and the Bayesian adaptive threshold is more appropriate, making it more suitable for denoising geomagnetic anomaly data.

[0089] 2.3 Measured data verification

[0090] In order to verify the advantages of the model of the present invention, a downward extension experiment was carried out using aerial measured magnetic data at a certain sea area height and a height of 300m. The magnetic measurement data at a height of 600m was extended downward by 300m using the present invention, Integral iterative, Iteration landweber regularization and Tikhonov regularization, and compared with the measured data at a height of 300m. The survey line spacing of the aerial measured data is 100m, and the area size is 50km×50km. In order to reflect the anti-noise ability of each algorithm, Gaussian noise with a standard deviation of 1 and a mean of 0 was added to the magnetic measurement data at a height of 600m. The calculation results of the extension of each algorithm are shown as follows: Figure 13 shown.

[0091] Figure 13For each extension algorithm, 600m aeromagnetic data is used to extend the grid spacing by 3 times to 300m height. Due to the addition of Gaussian noise in the aeromagnetic data, the calculation results of the three traditional algorithms all have obvious traces of noise interference. Compared with the three traditional algorithms, the extension results of the model of the present invention have the highest similarity with the 300m real aerial survey data and are least affected by noise. Compared with the other three traditional algorithms, the Integral iterative algorithm is most seriously affected by noise interference. Judging from the degree of interference on the contour lines, the Iteration landweber regularization has better noise resistance than Tikhonov regularization. In order to study the calculation accuracy of each algorithm and the noise suppression problem of magnetic data, the present invention uses RMSE and PSNR (Peak Signal-to-Noise Ratio) to quantify the extension calculation results:

[0092] Table 3 Statistics of continuation calculation indicators of different algorithms

[0093]

[0094] As can be seen from Table 3, the RMSE of the continuation calculation result of the present invention is the smallest and the accuracy is the highest; the PSNR calculation result is the highest, indicating that it can effectively suppress the noise amplification problem of magnetic data during the continuation process.

[0095] Figure 14 The residual graphs of the extension results of different algorithms show that the residual amplitude calculated by the present invention is smaller, more accurate, and less affected by noise. Figure 14 (b) is the residual information calculated by Integral iterative, and its extended calculation result is most affected by noise interference and is difficult to reflect the residual feature information. Figure 14 (a), Iteration landweber regularization Figure 14 (c) and Tikhonov regularization Figure 14 From the residual information in the rectangular area and the elliptical area in (d), it can be seen that the model of the present invention has stronger noise resistance under the same noise intensity in the downward extension calculation.

[0096] Figure 15 The cross-sectional data of the extended results of different algorithms and the actual results at the experimental area X = 18 km are shown in Figure 15 In (a), it can be seen that the cross-sectional data of the model of the present invention is more consistent with the real data, has higher accuracy, and has better anti-noise ability; Figure 15In the profile residual information shown in (b), the model of the present invention has higher accuracy and no obvious noise fluctuation. The profile residual information calculated by the integral iterative method has large fluctuations and is more affected by noise information.

[0097] 3 Discussions

[0098] From the principle of the algorithm, it can be seen that the traditional method is an unstable process for solving the downward extension of magnetic anomaly data. It is very sensitive to the selection of extension parameters and is easily affected by the noise of the original data, resulting in further amplification of the error. The present invention introduces the SRGAN deep learning network to fully learn the extension principle, and proposes to use the Kriging super-resolution algorithm and the sliding sub-area method to construct a data set to improve the learning of the detailed features of the original data. In order to enable the deep learning network to fully learn the original features, the present invention adds a CBAM attention mechanism to the last layer of the SRGAN network to enhance the network's learning of the key features of the original data in the spatial dimension. From the simulation case and the measured data analysis, it can be seen that the morphological characteristics of the extension results of the model of the present invention are closer to the real data.

[0099] To address the impact of noise data on the extension accuracy during the extension process of traditional methods, the model of the present invention uses adaptive threshold multiple wavelet transform to denoise the extended data, and uses Bayesian estimation to determine the threshold of the multiple wavelet transform, thereby improving the accuracy of denoising. The model of the present invention extends the plane magnetic anomaly data of Z = 1260m to four different heights, and takes 9 profile data corresponding to different heights for analysis. In all 9 profile data, the closer the distance to the magnetic source, the more dramatic the change in magnetic anomaly value with distance. Therefore, for the purpose of making a deep learning training set, the model trained with the same height difference cannot be applied to data at different heights, and the model data needs to be retrained.

[0100] The application of deep learning to extend potential field data is an important development trend. Compared with traditional algorithms, it offers higher accuracy and more precise depiction of magnetic anomaly data, and has important application value in the extension of gravity and magnetic data. The key to this algorithm is how to apply deep learning models to the characteristics of potential field data extension. Modifying the model can further improve the algorithm's accuracy and adaptability to depicting the changing characteristics of potential field data. This paper introduces the SRGAN deep learning model to the field of potential field data extension and optimizes it based on its characteristics. Simulation experiments and measured data verify its advantages over traditional algorithms and its practical application value.

Claims

1. A method for stable downward extension of geomagnetic anomaly data based on SRGAN deep learning network, characterized by: The steps are as follows: Step 1: Use the Kriging interpolation algorithm to improve the resolution of the original grid geomagnetic anomaly data to obtain super-resolution geomagnetic anomaly data; Step 2: Denoise the obtained super-resolution geomagnetic anomaly data using Bayesian adaptive threshold multiple wavelet transform, and then use the Tikhonov iterative regularization method to perform continuation calculation. The regularization parameter and iteration parameter in the continuation calculation are calculated using the L-curve curve method; Step 3: The data obtained by the extended calculation is further denoised using Bayesian adaptive threshold multiple wavelet transform, and the two denoised data are extracted using sliding sub-regions to create datasets for training the improved SRGAN deep learning network; Step 4. Input the dataset into the improved SRGAN deep learning network. In the improved SRGAN deep learning network, five deep residual networks are first used to learn the residual mapping between the datasets. A double convolution layer is used in the deep residual network to extract the features of the magnetic anomaly data, and the data after the double convolution layer is processed by batch normalization and parameterized activation function. The data after all the deep residual networks are then input into two convolution layers and one pixel-level convolution layer to map the features back to the extended magnetic anomaly data. At the same time, a CBAM attention mechanism is added to the pixel-level convolution layer to extract the spatial information and spatial dimensional features in the extended magnetic anomaly data. The spatial information and spatial dimensional features of the magnetic anomaly data are returned to the improved SRGAN deep learning network for iterative training. Step 5. For the sliding sub-area results output by the improved SRGAN deep learning network trained in step 5, the sliding sub-area results closest to the grid point are used as the extended value of the grid point using the nearest point principle. The extended values ​​of the grid points obtained from different sliding sub-areas are spliced ​​and further denoised using the Bayesian adaptive threshold multiple wavelet transform to obtain the final extended magnetic anomaly data.

2. The method for stable downward extension of geomagnetic anomaly data based on the SRGAN deep learning network according to claim 1 is characterized in that: The steps for extracting the two denoised data using sliding subregions to create an improved dataset for training the SRGAN deep learning network are as follows: by setting subregions of a certain size, the data on the geomagnetic anomaly map in the corresponding coordinate area is extracted by sliding. The step size of each sliding can control the degree of change and overlap rate of adjacent subregions. The smaller the step size, the more detailed the data feature characterization. The movement path of the sliding sub-area includes left and right translation and downward translation, which can cover all areas of the entire map.

Images