Geomagnetic anomaly data stable downward continuation method based on SRGAN deep learning network

Abstract

The invention discloses a geomagnetic anomaly data stable downward continuation method based on an SRGAN deep learning network, and belongs to the field of geophysical magnetic field data continuation. According to the invention, in combination with the continuation characteristic of geomagnetic anomaly data, a CBAM space attention mechanism module is added to improve the spatial perception capability of a network model to the magnetic anomaly data, and in combination with the characteristic that the downward continuation of potential field data can amplify the noise generated by a high-frequency signal; and the deep learning model is combined with adaptive threshold multiple wavelet transform to suppress noise data so as to further improve the continuation precision. In order to enable a model to fully learn detailed information of geomagnetic anomaly data, a training data set construction method combining a Kriging super-resolution algorithm with a sliding subarea mode is provided. By designing and synthesizing a simulation model experiment and comparing actual measurement data with other three algorithms, the model is highest in calculation precision and best in magnetic anomaly detail information recovery.

Description

Technical Field

[0001] The present invention belongs to the field of geophysical magnetic field data continuation, and relates to a stable downward continuation method of geomagnetic anomaly data based on an SRGAN deep learning network. The method is widely used in the fields of potential field data continuation, further interpretation of magnetic data, and enhancement of magnetic source signals. Background Art

[0002] Downward extension of potential field data is the key to effectively utilize gravity and magnetic data, and has important application value in the field of physical geodesy. Downward extension can use the potential field data of the measurement plane to infer the lower surface potential field data at a distance multiple of the grid spacing, thereby improving the interpretability of the measurement data. Downward extension can enhance the weak signal of the plane measurement data, further improve the magnetic source characteristics, and display more detailed characteristic information. It has practical application value in resource exploration, magnetic target detection, magnetic source structure feature analysis, and combined navigation.

[0003] From the physical principle of downward extension of potential field data, the potential field can be extended to any position in space, but from the perspective of actual mathematical solution, this is an ill-posed problem, so direct extension calculation is divergent and unstable. In the frequency domain, downward extension will over-amplify some short wavelengths, resulting in the influence of noise data on the extension value. The high-frequency part is usually removed by filtering, and the maximum downward extension distance also has certain limitations. For the noise data generated by over-amplification, sampling usually adds a stability factor during calculation, but the stability factor will cause the amplitude of the extended data to attenuate and reduce the resolution of the extended data. Therefore, the downward extension distance is generally a multiple of the grid spacing, and the distance cannot be too long. To solve this problem, the extension operator can be modified, and the Tikhonov regularization method and the Wiener filtering method can be used to suppress the downward extension noise, but the selection of the optimal regularization parameter is more difficult. The parameter selection can use L-curve, Generalized cross validationand the C-normcriterion, but the parameter selection effect is poor when the curvature is relatively smooth. In addition to the transformation 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 amplify as the number of iterations increases.

[0004] As an important tool for solving many complex problems, deep learning has made great progress in different disciplines. In order to solve the problem of noise amplification in the downward extension process and the problem of long-distance downward extension accuracy, this paper proposes an improved SRGAN deep learning network, which combines the CBAM spatial attention mechanism and adaptive Bayesian threshold multiple wavelet transform to comprehensively improve the network extension accuracy; and proposes to use the Kriging super-resolution algorithm and sliding sub-area extraction technology to produce training data sets, which can effectively improve the network's learning effect on magnetic anomaly detail features. Summary of the invention

[0005] The purpose of the present invention is to solve the problem of downward extension of geomagnetic anomaly data by using an improved SRGAN deep learning network model to solve the problem of downward extension of geomagnetic anomaly data, which is prone to instability of solutions, difficulty in parameter selection, and high-frequency noise caused by rapid amplification of high-frequency signals in traditional methods. The present invention combines the characteristics of geomagnetic anomaly data extension, adds a CBAM spatial attention mechanism module to improve the spatial perception ability of the network model to magnetic anomaly data, combines the characteristics of potential field data downward extension will amplify high-frequency signals to generate noise, and combines the deep learning model 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 synthetic simulation model experiments and measuring data, and comparing with three algorithms of Tikhonov regularization, Iterationlandweber regularization and Integral iterative, the model of the present invention has the highest calculation accuracy and the best recovery of magnetic anomaly detail information.

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

[0007] A stable downward continuation method for geomagnetic anomaly data based on 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 by using Bayesian adaptive threshold multiple wavelet transform, and then the continuation calculation is performed using the Tikhonov iterative regularization method. The regularization parameter and iterative 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 are extracted by sliding sub-regions to produce a data set for training the improved SRGAN deep learning network.

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

[0012] By setting a sub-area 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 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 data set 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 data sets. Double convolutional layers are used in the deep residual network to extract the features of magnetic anomaly data, and batch normalization and parameterization (PReLU) activation functions are used to process the data after the double convolutional layers. Then, the data after all the deep residual networks are input into two convolutional layers and one pixel-level convolutional layer (PixelShuffle) to map the features back to the extended magnetic anomaly data. At the same time, the CBAM (Convolutional Block Attention Module) attention mechanism is added to the pixel-level convolutional layer. The attention mechanism extracts the spatial information and spatial dimensional features in the extended magnetic anomaly data, and returns the spatial information and spatial dimensional features of the magnetic anomaly data to 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 extension 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 L-curve graph and curvature graph. (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 This is a graph of the loss function for model training.

[0023] Figure 8 The images are extended by different methods. Among them, (a) this invention, (b) Integral iterative, (c) Iteration landweber regularization, (d) Tikhonov regularization, and (e) 900m real data.

[0024] Fig. 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] Fig.10The data of the present invention are extended to different heights at different positions. Among them, (a) data of different heights at y = 530m, (b) data of different heights at y = 930m, (c) data of different heights at y = 1330m, (d) data of different heights at y = 1730m, (e) data of different heights at y = 2130m, (f) data of different heights at y = 2530m, (g) data of different heights at y = 2930m, (h) data of different heights at y = 3330m, (i) data of different heights at y = 3730m.

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

[0027] Fig.12 The residual image of the filtering effect. (a) The model does not have a denoising module, and (b) The model has a denoising module.

[0028] Fig.13 The extended images are obtained by different algorithms. Among them, (a) this invention, (b) Integral iterative, (c) Iteration landweber regularization, (d) Tikhonov regularization, and (e) 300 real data.

[0029] Fig.14 The residual graphs are extended by different methods. Among them, (a) the present invention, (b) Integral iterative, (c) Iteration landweber regularization, and (d) Tikhonov regularization.

[0030] Fig.15 The profiles and residuals of the extension results of different algorithms. (a) The profile data of each algorithm, (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, and the point (x, y, z h ) is the observation point data, and point (x, y, z0) is the desired point. The downward extension expression can be obtained by using Fourier transform to sort out equation (1):

[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 Improved SRGAN deep learning model

[0040] Tikhonov regularization has a saturation effect, and it is difficult to improve the smoothness of the solution and the calculation accuracy of the solution at the same time; the Iteration Landweber regularization algorithm has a slow convergence speed and is sensitive to noise. When the noise level is high, the quality of the solution will decrease; the integral iteration method has a high computational complexity and will also cause unstable solutions when processing data with high noise. The above three algorithms are all sensitive to the selection of parameters, and it is difficult to effectively determine the appropriate regularization parameters to obtain a stable solution, and their robustness is poor.

[0041] In order to make the extension of magnetic data more accurate, reduce the influence of parameters on the extension 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 true and false 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 network training data sets, in order to improve the effectiveness and sufficiency of deep learning network learning of training data, the Kriging interpolation method is used to increase the resolution of the original grid geomagnetic anomaly data by 3 times, and obtain super-resolution geomagnetic anomaly data. Based on the super-resolution, Bayesian adaptive threshold multiple wavelet transform is used for denoising, further expanding the size of the training sample data set and reducing the influence of the original data measurement and collection noise. The Kriging interpolation method is a commonly used interpolation method in geophysical neighborhoods. Based on the principle of minimum mean square error, it gives 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, more samples are sampled 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-data sets 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 in the corresponding coordinate area by setting a sub-area of ​​a certain size and sliding. 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 more detailed the data feature characterization. The sliding sub-area moving path is shown in the figure. Figure 3 As shown, the sliding modes are left-right translation and downward translation, which can be understood as a convolution mode, but this mode only extracts data and does not perform convolution calculations on it. This method can fully cover the extension area and improve the training effect of the deep learning model. Preferably, the sliding sub-area moves in steps of 1 grid point spacing each time, and the size of the sliding sub-area is 128×128 grid points.

[0046] The selection of Tikhonov iteration parameters is determined by the L-curve method. a -f and regular solution g a The relationship between the norm of and the change of the regularization parameter is plotted, and the curves of the two as the parameters change are drawn, and the parameter at the point with the maximum curvature change is taken 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, and 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] In order to reduce the edge effect in the extension process, the sub-area output by the network uses the nearest point principle to take the extension sub-area closest to the grid point as the extension calculation value of the grid point for sub-area splicing. Since the downward extension result of magnetic data is ill-posed, it will amplify the high-frequency part of the observation error. Therefore, the network model should have the ability to suppress high-frequency noise and restore the real extension image to a large extent. Therefore, Bayesian adaptive threshold multiple wavelet analysis is used to adaptively filter high-frequency noise in the network output stage. Compared with traditional wavelet analysis technology, multiple wavelet analysis has multiple wavelet basis functions, which can capture more feature information; and it can 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 improve the accuracy and flexibility of data filtering.

[0053] The selection of multiple wavelet transform thresholds has a great influence on the filtering effect, so it is necessary to estimate the noise of the geomagnetic anomaly extension data to set a suitable threshold for filtering. The Bayesian estimation threshold principle is a signal processing method based on Bayesian theory, which 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 after magnetic data extension 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), we can get the variance of noise wavelet coefficients:

[0058]

[0059] Where s = 1, 2, 3 represents the horizontal decomposition coefficient 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 coefficients of the real magnetic anomaly data is The variance of the noise wavelet coefficients 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] In order to verify the feasibility of the model method of the present invention, a synthetic simulation model is established for verification. The synthetic simulation model consists of magnetic anomalies generated by four different cuboids, and the setting parameters of the four cuboids are shown in Table 1. The magnetization intensity is set to 15A / m, the magnetic inclination is set to 90°, the magnetic declination is set to 90°, the generated grid data size is 4000×4000m, the grid spacing size is 40m, and the generated simulation data resolution is 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 plane schematic diagram of the magnetic anomaly values ​​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] Firstly, the geomagnetic anomaly data of the synthetic simulation model at an altitude of Z = 1260m was extracted, and the initial grid spacing was 40m and the resolution was 100×100. The Kriging super-resolution algorithm was used to reconstruct the geomagnetic anomaly data of Z = 1260m with super resolution, and the grid resolution was increased to 300×300 to prepare for the next step of making a deep learning dataset. The Tikhonov iteration and sliding sub-area data extraction method were combined to produce a total of 1225 data with a resolution of 128×128 each. The constructed training dataset was put into the deep learning model for training and the extended data was output. Finally, the adaptive Bayesian threshold multi-wavelet algorithm was used to remove the noise data generated in the extension process, further improving the extension accuracy of the model. RMSE (Root Mean Square Error) was used as the loss function for model training, the number of training times was set to 500 times, the learning rate was set to 0.001, and the number of model processing samples in each training iteration was 16.

[0076] In order to verify the influence of super-resolution, network structure optimization and denoising on the deep learning model of the present invention, a series of ablation experiments were conducted, and the results are shown in Table 2. The ablation experiment results show that on the basis of the baseline model, the basic extension model is improved by 2 through the optimization model. 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) The Kriging super-resolution algorithm is introduced to improve the model's learning of detailed features of magnetic anomaly data, and the sliding sub-area extraction data set method is combined to further increase the data set size, making the model learning more comprehensive, which is 0.0741nT higher than the baseline model.

[0079] 3) In order to solve the problem that extension will amplify the noise data, the extended data is adaptively denoised in the output stage of the model by introducing adaptive Bayesian threshold multiple wavelet transform, which is 0.0078nT higher than the model that introduces CBAM attention mechanism and Kriging super-resolution algorithm. Since the noise content of the simulated data constructed in this experiment is relatively small, the improvement effect is not obvious. Experimental verification shows that if 5% Gaussian noise is added when constructing the data, the accuracy of the model can be improved 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 the training rounds. The RMSE calculated in the figure is the normalized value. It can be seen that the RMSE value of the loss function of the model is close to convergence at 115 rounds.

[0083] The present invention is compared with three methods, namely, Integral iterative, Iteration landweber regularization and Tikhonov regularization, to illustrate the algorithm advantages of the present invention.

[0084] Depend on Figure 8 As shown in the figure, after the magnetic anomaly generated by the synthetic simulation model is extended by 9 times using four algorithms, the calculation results of the present invention are more similar to the magnetic anomaly data generated by the synthetic simulation model at 900m in terms of morphology and have higher accuracy than the other three algorithms, which reflects the advantage 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 model of the present invention is 2.7827nT.

[0085] Fig. 9 This is the profile data of different algorithms. The profile runs from north to south, passes through the area with large changes in magnetic anomaly, and passes through cuboids 1, 2 and 3. Fig. 9 In (a), it can be seen that the extended values ​​calculated by the four algorithms are consistent in the general trend terms, but the present invention can better restore the original data form and is more consistent with the waveform of the real data. Fig. 9 In the profile error analysis of (b), the error of the proposed method is relatively stable and has higher accuracy than the other three algorithms. By comparing and analyzing the extension accuracy of the four algorithms, the error sources are mainly concentrated in Fig. 9 The peak of (a) in the figure is where it is difficult to depict the high-frequency information of the data.

[0086] Fig.10 The paper describes the extension of the model of the present invention from the Z=1260m plane to four heights of Z=1140m, Z=1020m, Z=900m and Z=800m, and observes the extension effect from 9 profile data. Fig.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] Fig.11 The RMSE bar graph of all sliding sub-areas calculated by the model of the present invention shows that the calculated RMSE of more than 80% of the sub-areas is less than 2.72nT. The calculated RMSE value of the sliding extraction sub-area varies with the position, but the error difference is small, with the maximum difference 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 Fig.12 It can be seen that the extension residuals are mainly concentrated in the complex change area. Fig.12 (a) and Fig.12 From (b) in the figure, the adaptive Bayesian threshold multiple wavelet transform can effectively reduce the influence of high-frequency noise in the extension process, and from the amplitude of the residual, adding a denoising module reduces the maximum residual amplitude, and the Bayesian adaptive threshold selection is more appropriate, which is 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, the aerial measured magnetic data at a certain sea area altitude and 300m altitude were used to carry out downward extension experiments. The magnetic measurement data at an altitude of 600m were extended downward by 300m using the present invention, Integral iterative, Iteration landweber regularization and Tikhonov regularization, and compared and analyzed with the measured data at an altitude 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 is added to the magnetic measurement data at an altitude of 600m. The calculation results of the extension of each algorithm are shown as follows. Fig.13 shown.

[0091] Fig.13For each extension algorithm, 600m aeromagnetic data is used to extend 3 times the grid spacing 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 Tikhonovregularization. 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] It can be seen from Table 3 that 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 in the continuation process.

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

[0096] Fig.15 The profile data of different algorithm extension results and real results at the experimental area X = 18km. Fig.15 In (a), it can be seen that the profile data of the model of the present invention is more consistent with the real data, has higher accuracy, and has better anti-noise ability; Fig.15In the profile residual information shown in (b), the model of the present invention has higher accuracy and no obvious noise fluctuation. In the profile residual information calculated by the integral iterative, there is a large fluctuation and the degree of interference from the noise information is greater.

[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] In order to solve the problem of the influence of noise data on the extension accuracy in the extension process of the traditional method, the model of the present invention uses adaptive threshold multiple wavelet transform to denoise the extension data, and uses Bayesian estimation to determine the threshold of the multiple wavelet transform, thereby improving the denoising accuracy. The plane magnetic anomaly data of Z=1260m is extended to 4 different heights through the model of the present invention, and 9 profile data corresponding to different heights are taken for analysis. In all 9 profile data, the closer the distance to the magnetic source, the more drastic the change of the magnetic anomaly value with the distance. Therefore, for the preparation of deep learning training sets, 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 extension of potential field data using deep learning is an important development trend. Compared with traditional algorithms, it has higher accuracy and more accurate description of magnetic anomaly data, and has important application value for the extension of gravity data and magnetic data. How to use the deep learning model for the extension of potential field data is the key to the algorithm. By modifying the model, the algorithm accuracy and adaptability to the description of the changing characteristics of potential field data can be further improved. This paper introduces the SRGAN deep learning model into the field of potential field data extension, and optimizes it in combination with the characteristics of potential field data extension. Through simulation experiments and measured data, it is verified that it has certain advantages over traditional algorithms and has certain practical application value.

Claims

1. A method for stable downward extension of geomagnetic anomaly data based on SRGAN deep learning network, characterized in that: 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, the obtained super-resolution geomagnetic anomaly data is denoised by using Bayesian adaptive threshold multiple wavelet transform, and then the continuation calculation is performed using the Tikhonov iterative regularization method, and the regularization parameter and iterative 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 data after the two denoising are extracted by sliding sub-areas to prepare a data set for training the improved SRGAN deep learning network; Step 4: Input the data set into the improved SRGAN deep learning network. In the improved SRGAN deep learning network, firstly, five deep residual networks are used to learn the residual mapping between data sets. Double convolutional layers are used in the deep residual network to extract the features of magnetic anomaly data, and batch normalization and parameterized activation functions are used to process the data after the double convolutional layers. Then, the data after all the deep residual networks are input into two convolutional layers and one pixel-level convolutional 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 convolutional layer. The attention mechanism extracts the spatial information and spatial dimensional features in the extended magnetic anomaly data, and returns the spatial information and spatial dimensional features of the magnetic anomaly data 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. According to claim 1, a method for stable downward extension of geomagnetic anomaly data based on SRGAN deep learning network is characterized in that: The steps of extracting the data after two denoising by sliding sub-areas to make an improved dataset for training the SRGAN deep learning network are as follows: by setting a sub-area of ​​a certain size, extracting the data on the geomagnetic anomaly map in the corresponding coordinate area by sliding, the step size of each sliding can control the degree of change and overlap rate of adjacent sub-areas, and the smaller the step size, the finer the description of data features; 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.

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