Gravity and gravity gradient data noise reduction method and system based on U-Net network

Abstract

The invention belongs to the technical field of gravity data noise reduction, discloses a gravity data noise reduction method based on a U-Net network, and provides a U-Net network structure fusing a multi-scale feature fusion module and an attention mechanism aiming at the noise reduction problem of gravity and gravity gradient data. And a physical consistency constraint is introduced in a model training process. A Laplace equation met by the gravitational field potential in geophysics is used as prior information to be fused into a loss function, and a Laplace item is designed. The operation effectively improves the physical interpretability and generalization ability of the noise reduction result of the neural network. Meanwhile, the network structure adopts multi-scale feature fusion and an attention mechanism, and information of different spatial scale features and key spatial positions in complex geological signals is better captured.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of gravity data denoising, and particularly relates to a gravity data denoising method and system based on a U-Net network. BACKGROUND

[0002] Gravity and gravity gradient data are indispensable core information in geophysics, widely serving resource exploration, geological structure analysis and high-precision integrated navigation. Gravity data can be used to calibrate resources such as ore bodies and oil and gas reservoirs by inverting underground density anomalies, and reveal complex structures such as the crust and the upper mantle. With the support of global gravity field models and high-resolution Bouguer anomaly maps, such data are also used to predict rock properties, evaluate rift basin evolution, monitor glacier mass changes and study ocean dynamics, and the academic and engineering values are rising. As the partial derivative of the gravity field, gravity gradient has unique advantages in identifying shallow anomalies, edge detection and depth estimation in fine detection scenarios, and makes a significant contribution to improving the reliability of navigation systems in complex environments. In the future, combined with new sensing means such as satellite-borne cold atom gravimeters and quantum interferometers, the detection accuracy of the gravity field is expected to be further improved.

[0003] However, the amplitude of the gravity anomaly caused by geological bodies is usually extremely weak, and under the combined action of instrument errors, observation disturbances and data processing discrete errors, the signal-to-noise ratio of the original signal is low, which limits the accurate inversion of the position, size and shape of the geological body. Further, gravity gradient can be obtained by numerical differentiation of gravity data, or directly observed by satellite or airborne instruments, but both will amplify or introduce noise, making the reliability problem more prominent. How to retain effective spatial resolution while suppressing noise and enhancing anomaly features is a technical bottleneck for current gravity and gravity gradient data to achieve high-quality applications, and is also a key direction for subsequent algorithm and instrument development. At present, researchers have proposed multiple strategies such as time and frequency domain filtering, regularization inversion, sparse representation and deep learning denoising, but to balance noise suppression and information fidelity and achieve real-time and efficient processing, it still relies on the coordinated breakthrough of more advanced theoretical models and high-sensitivity observation technology.

[0004] Traditional data denoising methods mainly include low-pass filtering method, moving average method, wavelet transform method, etc. The traditional methods perform well in suppressing Gaussian white noise, preserving the main features of data, etc., but cannot meet the scientific application requirements of effectively extracting signals in complex and non-stationary noise environment. For example, although low-pass filtering can remove high-frequency noise, it may cause the loss of part of the useful signal, and the method depends on artificial experience in parameter adjustment and adaptability, and it is difficult to flexibly handle different types of noise. In recent years, with the rapid development of deep learning technology, intelligent denoising methods based on data driving have been gradually applied to high-precision processing of gravity and gravity gradient data. Deep learning methods have strong adaptive learning and nonlinear modeling capabilities, and can efficiently distinguish gravity anomaly signals from multiple complex noises on the basis of large-scale data training, thereby significantly improving the denoising effect and processing efficiency of gravity and gravity gradient data. This kind of method can automatically construct a nonlinear mapping model from noisy data to denoised data, and complete feature extraction and fusion without human intervention. After the model is trained and optimized, it can quickly and stably denoise new observation data, and provide high-quality basic data support for geophysical exploration, geological survey and earthquake monitoring.

[0005] Through the above analysis, the problems and defects of the prior art are: Although traditional denoising methods such as wavelet transform, moving average and low-pass filtering can suppress noise to a certain extent, they have problems such as signal loss and insufficient adaptability in the face of complex and non-stationary noise and high spatial resolution requirements. The parameter selection is complicated under different data scenarios, the processing process has low automation degree, and the denoising effect of T xx , T yy , T zz and other gravity gradient component data is poor, resulting in poor signal effective extraction effect. SUMMARY

[0006] In view of the problems existing in the prior art, the present application provides a gravity data denoising method based on a U-Net network.

[0007] The present application is implemented as follows: a gravity data denoising method based on a U-Net network comprises: Step 1, establishing a network architecture; Step 2, incorporating physical prior information; Step 3, constructing a data set; Step 4, model training and optimization.

[0008] Further, the network architecture is established as follows: The encoder and decoder network structure is applied to image denoising; the features of the encoder are transmitted to the decoder through the skip connection to better recover the detail information in the image; the training process of the neural network is a process of finding the mapping relationship between the noise data and the clean data, which can be expressed as follows:

[0009] Wherein is the expected clean data, is the input noise data, is the training parameter of the network, which is determined through the training process of the network.

[0010] Further, the physical prior information is integrated: In the model training process, the Laplace equation satisfied by the gravity field potential in geophysics is taken as the physical prior, and the Laplace term is integrated into the loss function design; The gravity field is derived from the underground density distribution, but in the area far away from the density anomaly, the gravity potential function Satisfies the Laplace equation:

[0011] Wherein Represents the two-dimensional Laplace operator, that is:

[0012] This equation reflects the physical nature of the gravity field - in the source-free area, the gravity potential distribution is smooth and has harmonic nature; The Laplace residual term (LaplacianLoss) is added to the loss function to perform soft constraint on physical consistency; specifically, after each forward propagation, in addition to calculating the conventional reconstruction loss (such as MSE+SSIM), the network output The discrete Laplace operator is calculated:

[0013] Wherein Represents the function value at grid point (i,j), h is the grid step (the distance between adjacent points); the numerator is the sum of the values of the adjacent four points minus 4 times the center point value, which approximates the second order derivative; and the final total loss is:

[0014] Wherein Is the weight hyperparameter of the physical prior; in this way, the loss of the area that "violates the Laplace condition (physical harmonic nature)" in the network output is higher, which will force the result to adjust back to the physically reasonable state during back propagation.

[0015] Further, the data set is constructed: The generation center coordinates of the object, the size (length, width, height) of the object are defined to determine the generation position and size of the object; a 200*200 grid is generated, and the grid point spacing is set to 0.1km; the generation density range is set to 1~5g / cm3 (typical rock density is 2-3g / cm3), the gravity anomaly of the object is calculated according to the center coordinates of the prism parameters; the gravity anomaly formula of the prism is calculated:

[0016] Wherein, G is the gravitational constant, and the volume contribution of the prism is determined by its geometric parameters (size, position); the output result is a two-dimensional array of grid_size*grid_size, which represents the gravity anomaly of each grid point; on the basis of generating clean noise, noise is added to generate noise data, and the added noise type is Gaussian white noise (mean value is 0, and standard deviation is noise_level*standard deviation of clean_gravity).

[0017] Further, the model training and optimization: In the model training process, the mean square error is used as a basic loss function to capture the pixel-level difference.

[0018] Optimize the model;

[0019] A mixed regularization method is adopted, combining L2 regularization and Laplace constraint; the L2 regularization adds a weight decay term in the optimization target: the L2 regularization can effectively prevent overfitting, and the Laplace constraint further enhances the physical rationality of the model; by introducing the λ coefficient, the smoothing strength can be flexibly controlled, so as to balance the complexity and generalization ability of the model;

[0020] At the same time, the early stopping strategy is optimized by using the stationarity judgment based on the validation loss; the intelligent early stopping mechanism triggers the training termination when the standard deviation of the validation loss meets:

[0021] Avoid overfitting; the early stopping strategy can stop training in advance when the validation loss no longer decreases, so as to prevent overfitting and save computing resources; finally, the spectral normalization is added after the decoder of the model, which is used to optimize the structure of the model.

[0022] Another purpose of the present application is to provide a gravity data denoising system based on a U-Net network, comprising: A building module is configured to build a network architecture. A fusing module is configured to fuse physical prior information. A constructing module is configured to construct a data set. An optimizing module is configured to train and optimize a model.

[0023] Another object of the present application is to provide a computer device comprising a memory and a processor, wherein the memory stores a computer program, and the computer program is executed by the processor to enable the processor to perform the steps of the gravity data denoising method based on the U-Net network.

[0024] Another object of the present application is to provide a computer readable storage medium storing a computer program, and the computer program is executed by a processor to enable the processor to perform the steps of the gravity data denoising method based on the U-Net network.

[0025] Another object of the present application is to provide an information data processing terminal for implementing the gravity data denoising system based on the U-Net network.

[0026] In combination with the above technical solutions and the technical problems solved, the technical solution to be protected by the present application has the following advantages and positive effects: Firstly, the present application proposes a U-Net network structure fusing multi-scale feature fusion module and attention mechanism for the denoising problem of gravity and gravity gradient data, and introduces a physical consistency constraint in the model training process. The Laplace equation satisfied by the gravity field in geophysics is taken as prior information to be fused into the loss function, and a Laplace term is designed. This operation effectively improves the physical interpretability and generalization ability of the neural network denoising result. At the same time, the network structure adopts multi-scale feature fusion and attention mechanism, which better captures different spatial scale features and key spatial position information in complex geological signals. The specific innovations and contributions are as follows: 1. A U-Net network structure fusing multi-scale features and attention mechanism is proposed, and a physical consistency (Laplace) constraint of the gravity field is introduced into the loss function, which realizes the effective combination of physical prior and deep learning, and improves the modeling and differentiation ability of complex geological spatial features.

[0027] 2. A physically driven data expansion strategy is adopted, and a large number of underground matter distribution simulations based on random walk are introduced in the data set construction stage, so that the training samples are more consistent with the actual underground environment, and the generalization performance of the model is improved.

[0028] 3. In addition to denoising gravity data, the gravity gradient T xx , T yyAnd T zz The denoising method of three-component data expands the practical application scenarios and processing capacity of the model.

[0029] Secondly, the gravity data denoising method based on the U-Net network has certain expected benefits and commercial value in the exploration of underground resources such as oil and gas and minerals. Through efficient denoising of gravity and gravity gradient data, underground density anomalies can be accurately detected, and the accuracy and resolution of resource positioning can be significantly improved. In practical applications, it can effectively reduce the exploration cost, shorten the exploration period, and improve the resource exploitation efficiency. For example, in oil and gas exploration, accurate gravity data can help determine the location and size of oil and gas reservoirs, providing reliable basis for well site selection; in mineral exploration, it can more clearly reveal the distribution characteristics of ore bodies, and improve the exploration accuracy of mineral resources. With the continuous development of geophysical exploration technology, this method is expected to become the mainstream data processing technology in the industry, forming a new commercial growth point and bringing economic benefits to related enterprises. At the same time, this technology can also be applied to the fields of geological structure research and earthquake monitoring, and has certain market application prospects.

[0030] At present, the traditional methods such as low-pass filtering and wavelet transform have obvious limitations in complex noise environment, and the denoising effect of gravity gradient component data is poor. The U-Net network method proposed in the present application combines deep learning with physical prior information in geophysics, realizes the effective fusion of physical prior and deep learning, and introduces the physical consistency (Laplace) constraint of gravity potential field in the loss function, which improves the modeling and differentiation ability of the model to complex geological spatial features. At the same time, the denoising method of three-component data of gravity gradient Txx, Tyy and Tzz is studied, which expands the application scenarios of the model. This technology is superior to traditional methods in terms of denoising effect, physical interpretability and generalization ability, and provides a new technical idea and method for geophysical data processing.

[0031] Gravity data denoising has always been a difficult problem in geophysical research. Due to the weak gravity anomaly signal, it is easy to be disturbed by various noises, and the traditional method is difficult to effectively suppress noise in a complex and non-stationary noise environment, which may also lead to signal loss. Moreover, the parameter adjustment depends on artificial experience, and the degree of automation is low. Especially, the denoising effect of gravity gradient data is not good. The present application introduces the U-Net network structure, combines multi-scale feature fusion and attention mechanism, can automatically capture different spatial scale features and key spatial position information in complex geological signals, and realizes the nonlinear mapping from noisy data to clean data. At the same time, the Laplace equation is introduced as a physical prior into the loss function, which ensures the physical rationality of the denoising result and effectively solves the contradiction between noise suppression and signal preservation in the traditional method. The experimental results show that the method has good denoising effect under different noise levels and complex geological scenes, and successfully solves the problem of gravity data denoising, providing high-quality basic data support for geophysical research.

[0032] In the traditional field of gravity data processing, technicians generally believe that methods based on mathematical formulas and signal processing are the main way to solve the problem of denoising, and there is a certain prejudice against the application of deep learning technology in geophysical data processing, thinking that it lacks physical interpretability. The present application breaks this technical prejudice by combining deep learning with physical prior information in geophysics, proving that deep learning methods not only can efficiently denoise data, but also can improve the physical interpretability of the results by introducing physical constraints. The experimental results show that the model with physical prior constraints is superior to the model without physical constraints in terms of denoising effect and generalization ability, overcoming the prejudice that deep learning and physical laws are difficult to combine in the traditional concept. In addition, the successful application of this method in gravity gradient data denoising also breaks the limitations of traditional methods on gradient data processing effect, opening up a new way for the application of deep learning technology in the field of geophysics. BRIEF DESCRIPTION OF DRAWINGS

[0033] Figure 1 It is the gravity data denoising method flow chart based on the U-Net network provided by the embodiment of the present application.

[0034] Figure 2 It is the gravity data denoising system structure block diagram based on the U-Net network provided by the embodiment of the present application.

[0035] Figure 3 It is the U-Net network architecture diagram provided by the embodiment of the present application.

[0036] Figure 4 It is the network residual block structure diagram provided by the embodiment of the present application.

[0037] Figure 5 It is the deep attention mechanism diagram provided by the embodiment of the present application.

[0038] Figure 6 is a random generation of underground object space distribution map provided by the embodiment of the application.

[0039] Figure 7 is a full graph of U-Net model training provided by the embodiment of the application.

[0040] Figure 8 is a training round and loss function relationship graph provided by the embodiment of the application.

[0041] Figure 9 is a denoising effect comparison graph of 5% noise level provided by the embodiment of the application.

[0042] Figure 10 is a denoising effect comparison graph of 10% noise level provided by the embodiment of the application.

[0043] Figure 11 is a denoising effect comparison graph of 15% noise level provided by the embodiment of the application.

[0044] Figure 12 is an error analysis histogram provided by the embodiment of the application.

[0045] Figure 13 is a denoising effect graph of different methods provided by the embodiment of the application.

[0046] Figure 14 is a PSNR value comparison graph of different denoising methods provided by the embodiment of the application.

[0047] Figure 15 is a denoising effect graph of different methods of xx gravity gradient data provided by the embodiment of the application.

[0048] Figure 16 is a denoising effect graph of different methods of yy gravity gradient data provided by the embodiment of the application. Figure 17 is a denoising effect graph of different methods of zz gravity gradient data provided by the embodiment of the application. Figure 18 is a curve graph of physical constraint-free training provided by the embodiment of the application. Figure 19 is a curve graph of physical constraint training provided by the embodiment of the application. Figure 20 is a PSNR value comparison graph of physical constraint and physical constraint-free provided by the embodiment of the application. Figure 21 is a real data gravity denoising effect graph provided by the embodiment of the application. DETAILED DESCRIPTION

[0049] In order to make the purpose, technical scheme and advantages of the present application more clear, the present application is further described in detail below with examples. It should be understood that the specific examples described herein are only used to explain the present application and not to limit the present application.

[0050] In the traditional gravity data processing flow, the terrain factor, instrument noise and signal superimposed by the complex structure of the underground often lead to the difficulty in distinguishing noise and target signal. When the existing filtering algorithm is simply cut in the frequency domain or time domain, the weak abnormal information is lost or the artifact is introduced, which is difficult to meet the needs of high-resolution remote sensing imaging. In order to overcome the above defects, the present technology adopts the U-Net architecture based on deep convolutional network, which can effectively recover the detail information while preserving the low-frequency large-scale structure through multi-scale feature extraction and cross-layer skip connection, thereby solving the deficiency of the traditional method in weak anomaly recovery. The overall process firstly extracts multi-level features in the gravity anomaly image through the encoder, and then reconstructs these features back to high-resolution output layer by layer through the decoder, plus the skip connection mechanism, which avoids the loss of gravity detail information in the network propagation process.

[0051] In order to further enhance the physical rationality of the model, the prior knowledge that the gravity field potential satisfies Laplace equation in geophysics is introduced, and the discrete Laplace operator is taken as a soft constraint term and integrated into the loss function. After the forward propagation of the network, the discrete Laplace operator is calculated on the two-dimensional grid for the output gravity potential function, and the second derivative approximation is realized through adjacent sampling, so as to measure whether the point deviates from the harmonic state. When the physical constraint term is back propagated together with the reconstruction loss, the network can automatically adjust the parameters, so that the output result is not only minimized in pixel level error, but also tends to the harmonic state of the source-free area in the physical field distribution, thereby reducing the interference of the noise of the field data on the final gravity anomaly interpretation.

[0052] In the training data construction link, the center coordinates and size of the prism model under different geometric parameters are pre-set, the theoretical gravity anomaly value of each grid point is calculated based on the universal gravitation formula, and the two-dimensional gravity anomaly atlas with grid resolution of 200x200 and grid spacing of 0.1 km is generated. These clean data essentially conform to the harmonic distribution characteristics of the geophysical field; on this basis, white noise conforming to 0 mean value and Gaussian distribution is added, and the standard deviation of the white noise is proportionally related to the standard deviation of the clean data, which simulates the random noise generated by the instrument error and terrain interference in the field. The training set contains both the internal structure of the physical field and the typical noise form, which provides sufficient samples for subsequent model learning.

[0053] In the network training and optimization stage, a composite loss function is constructed by combining the mean square error (MSE) as the basic reconstruction loss, the L2 regularization as the weight attenuation, and the Laplace physical constraint term, and multi-objective optimization is achieved through continuous iteration. The learning rate of the training process is gradually reduced according to the decay factor, which can quickly converge in the early stage while refining the network weights in the later stage. At the same time, an early stopping mechanism based on the loss stability judgment of the validation set is introduced to avoid noise misinterpretation caused by overfitting and reduce unnecessary computational resource consumption. In addition, a spectral normalization technique is used at the end of the decoder to control the spectral norm of the network weight matrix, thereby stabilizing the training process, preventing gradient explosion or disappearance, and ensuring the continuity and realism of the output gravity image.

[0054] In the model inference and application stage, the input noisy gravity data is first extracted through the encoder to extract multi-scale features, and then gradually restores the difference signal through the decoder combined with the skip connection. At the same time, the physical constraint term does not participate in gradient update in inference, but can be used for post-processing to check the physical consistency of the output image. When the network output deviates from the discrete solution of the Laplace equation, the abnormal area can be identified according to the deviation degree, and then combined with traditional inversion technology for secondary refinement. This mechanism not only improves the adaptability of the model to complex geological bodies in real scenarios, but also makes the output results more interpretable than traditional black box networks.

[0055] At the system level, by integrating the above functional modules, a gravity data denoising system with full-process functions such as data preprocessing, network inference, physical consistency verification, and post-processing feedback is formed. This system can be deployed on multiple computing platforms and dynamically adjust network hyperparameters and physical constraint weights for input data of different resolutions and noise levels, thereby ensuring reconstruction accuracy while considering computational efficiency. In practical exploration and monitoring applications, engineers can identify faults, evaluate reservoirs, and locate abnormal bodies based on the output results to improve the reliability of geological analysis.

[0056] As shown in Figure 1 The gravity data denoising method based on the U-Net network provided by the embodiment of the present application comprises the following steps: S101, establishing a network architecture; S102, incorporating physical prior information; S103, constructing a data set; S104, model training and optimization.

[0057] The measured gravity sequence is preprocessed: the original time sequence is divided into blocks according to the measuring point, instrument drift correction, tide and solid earth tide subtraction are completed, and the trend item is eliminated by using a cubic spline; subsequently, the latitude-longitude-elevation coordinate is uniformly converted into a geodetic rectangular coordinate system, is cut into a two-dimensional tensor according to a fixed time window (such as 256 or 512 sampling points), and then the tensors are subjected to Z-score normalization, so that the network input remains stable within a numerical range.

[0058] The physical prior is integrated into the network: based on the Newtonian gravity integral equation, a three-dimensional geological body forward operator is constructed to obtain the theoretical gravity response caused by different depths and density disturbances; the forward result is encoded as a channel weight or an additional input layer to guide the convolution kernel to maintain the morphological boundary at a low frequency and suppress short-period noise at a high frequency; at the same time, a forward residual term is introduced into the loss function to constrain the network output to be consistent with the physical field.

[0059] The training data set is constructed: a “measured-simulated” dual-source strategy is adopted to superimpose Gaussian white noise, instrument 1 / f noise and cultural noise on the field measured denoising residual to generate paired (noisy, clean) samples; the samples are subjected to translation, mirroring, amplitude scaling, random spectrum disturbance and other enhancement operations to improve the network's generalization ability to different noise scenarios; finally, a training set, a validation set and a test set containing 10 4 level patches are formed.

[0060] The model training and optimization are completed: residual blocks and attention gate modules are embedded in a typical U-Net backbone, a dual loss of MSE + spectral consistency is used, an Adam optimizer is used and a cosine annealing learning rate is enabled; after each training round, the signal-to-noise ratio improvement and the structural similarity are evaluated on the validation set, and the best weight is saved according to the early stopping strategy; in the inference stage, the gravity profile is reconstructed by sliding window-overlapping splicing to realize high-resolution and artifact-free denoising output.

[0061] The network architecture provided by the embodiment of the present application is established: The encoder and decoder network structure is applied to image denoising; the features of the encoder are transmitted to the decoder through a skip connection to better recover the detail information in the image; the training process of the neural network is a process of finding the mapping relationship between the noise data and the clean data, which can be represented as follows:

[0062] Wherein is the desired clean data, is the input noise data, is the training parameter of the network, which is determined through the training process of the network.

[0063] The physical prior information provided by the embodiment of the application is integrated as follows: In the model training process, the Laplace equation satisfied by the gravity field potential in geophysics is taken as a physical prior, and a Laplace term is integrated into the loss function design; The gravity field is derived from the underground density distribution, but in the area far away from the density anomaly, the gravity potential function satisfies the Laplace equation:

[0064] wherein represents a two-dimensional Laplace operator, that is:

[0065] This equation reflects the physical nature of the gravity field - in the source-free area, the gravity potential distribution is smooth and has a harmonic nature; The Laplace residual term is added to the loss function to perform soft constraint on the physical consistency; specifically, after each forward propagation, in addition to calculating the conventional reconstruction loss (such as MSE+SSIM), the network output The discrete Laplace operator is calculated as follows:

[0066] wherein represents the function value at the grid point (i, j), and h is the grid step (the distance between adjacent points); the numerator part is the sum of the values of the adjacent four points minus 4 times the center point value, which approximates the second-order derivative; and the final total loss is:

[0067] wherein is a weight hyperparameter of the physical prior; in this way, the loss of the area in the network output that “violates the Laplace condition (physical harmonic nature)” is higher, and the result will be forced to adjust back to the physically reasonable state during back propagation.

[0068] The data set construction provided by the embodiment of the application is as follows: The generation center coordinates of the object and the size (length, width and height) of the object are defined to determine the generation position and size of the object; a 200*200 grid is generated, and the grid point spacing is set to 0.1 km; the generated density range is set to 1-5 g / cm3 (typical rock density is 2-3 g / cm3), and the gravity anomaly of the object is calculated according to the center coordinates of the prism parameter; the gravity anomaly formula based on the prism is calculated as follows:

[0069] Wherein, G is the gravitational constant, p is the density, the volume contribution of the prism is determined by its geometric parameters (size, position); the output result is a two-dimensional array of grid_size*grid_size, which represents the gravity anomaly of each grid point; on the basis of generating clean noise, add noise to generate noisy data, and the added noise type is Gaussian white noise (mean is 0, standard deviation is noise_level*standard deviation of clean_gravity).

[0070] The model training and optimization provided by the embodiment of the application has the advantages that: In the model training process, mean square error is used as a basic loss function to capture pixel-level differences.

[0071] Optimize the model.

[0072] In the optimization target, L2 regularization adds a weight decay term: L2 regularization can effectively prevent overfitting, and Laplace constraint can further enhance the physical rationality of the model; by introducing a lambda coefficient, the smoothing strength can be flexibly controlled, so as to balance the complexity and generalization ability of the model.

[0073] At the same time, the early stopping strategy is optimized by using the stationarity judgment based on the validation loss, and the intelligent early stopping mechanism is triggered when the standard deviation of the validation loss satisfies:

[0074] The training termination is triggered to avoid overfitting; the early stopping strategy can stop training in advance when the validation loss no longer decreases, so as to prevent overfitting and save computing resources; finally, spectral normalization is added after the decoder of the model to optimize the structure of the model.

[0075] As shown in Figure 2 The gravity data denoising system based on the U-Net network provided by the embodiment of the application includes: The establishment module is configured to establish a network architecture. The fusion module is configured to fuse physical prior information. The construction module is configured to construct a data set. The optimization module is configured to train and optimize the model.

[0076] Another purpose of the application is to provide an information data processing terminal for realizing the gravity data denoising system based on the U-Net network.

[0077] The present application is embodied: 1、 The present application is aimed at the noise reduction problem of gravity and gravity gradient data, a U-Net network structure is proposed which fuses multi-scale feature fusion module and attention mechanism, and physical consistency constraint is introduced in the model training process. The Laplace equation satisfied by the gravity field potential in geophysics is taken as prior information and fused into the loss function to design the Laplace term. This operation effectively improves the physical interpretability and generalization ability of the neural network noise reduction result. At the same time, the network structure adopts multi-scale feature fusion and attention mechanism, which better captures the different spatial scale features and key spatial position information in the complex geological signal. The specific innovations and contributions are as follows: The U-Net network structure fusing multi-scale features and attention mechanism is proposed, and the physical consistency (Laplace) constraint of gravity potential field is introduced in the loss function, which realizes the effective combination of physical prior and deep learning, and improves the modeling and differentiation ability of complex geological spatial features.

[0078] A physically driven data expansion strategy is adopted, and a large number of underground matter distribution simulations based on random walk are introduced in the data set construction stage, so that the training samples are more consistent with the actual underground environment, and the generalization performance of the model is improved.

[0079] In addition to noise reduction of gravity data, the noise reduction method of gravity gradient T xx , T yy and T zz three-component data is also systematically studied, which expands the practical application scene and processing capacity of the model.

[0080] Convolutional Nerural Network (CNN) is designed from the visual system in biology, which aims to simulate the way of biological visual information processing, imitate the mechanism of "local perception" and "parameter sharing", and efficiently extract the key features in the image. In the past few years, CNN has made significant progress in image recognition, object detection, image generation and many other fields. The limitation of traditional neural network is the control of input dimension and the lack of translation invariance. CNN helps neurons to perceive the local input in the visual field by introducing convolution operation, and effectively reduces the parameter amount in the operation process by reusing the parameters of the same convolution kernel in different positions. The encoder-decoder network framework in the convolutional neural network is an end-to-end learning algorithm, and this structure is very suitable for image denoising task. Mao, Shen and Yang first applied the encoder and decoder network structure to image denoising. Through the skip connection, the features of the encoder are transmitted to the decoder to better restore the detailed information in the image. The training process of neural network is to find the mapping relationship between noisy data and clean data, which can be expressed as follows:

[0081] wherein is the expected clean data, is the input noisy data, is the training parameter of the network, which is determined through the training process of the network. The network structure proposed in the present application is based on the improved U-Net architecture, and the U-Net network architecture built is as shown in Figure 3

[0082] ​The function of the network is mainly optimized for the end-to-end denoising task of single-channel images. The network input is a single-channel image with a size of 200x200, and the output maintains the same dimension and channel configuration as the input. The multi-scale feature fusion module and attention mechanism module are integrated to improve the network's ability to learn and extract features from data. The training dataset uses randomly generated three cuboid underground object models to improve data diversity and help the model achieve better generalization. The encoder part of the network uses a typical step-down sampling structure, which is stacked by multiple 3x3 convolution blocks. Each convolution block contains two layers of convolution and activation operations (ReLU), and the number of feature channels increases with depth (64, 128, 256, 512) to enhance the ability to abstract complex high-order features. After the convolution module, 2x2 max pooling is applied to realize spatial down-sampling and gradually extract representative spatial information. To improve the model's generalization performance and suppress overfitting, increasing Dropout (0.1, 0.2, 0.3) is introduced in the down-sampling layer. The deepest network bottleneck aggregates global semantic information, laying the foundation for subsequent high-quality feature reconstruction. The decoder uses a symmetric structure, with 2x2 up-sampling to restore spatial resolution. Each level is connected to the encoder of the same layer through a skip connection to effectively preserve high-resolution spatial details and significantly improve the decoder's ability to recover target edges and fine-grained structures.

[0083] Figure 4Two convolutional neural network structure modules are shown. The left module is a classic standard convolutional block, and the right module is a new module that introduces a gating mechanism on this basis. The module accepts an input feature map with a size of HxWxC1. First, it passes through two 3x3 convolution layers in turn. After each convolution operation, batch normalization and linear rectifier activation are performed to realize local feature extraction and nonlinear mapping. The module finally outputs further to the subsequent network layer. This structure is a deep convolutional neural network unit that can effectively extract hierarchical feature representation. Based on the standard block, the structure maps the input features through a 1x1 convolution branch to adapt the channel number (dimension reduction or dimension increase), and sets up a shortcut connection to realize cross-layer residual fusion. The convolution output on the main branch enters the gating module. The module first calculates the importance weight of each channel through global feature aggregation, and then re-labels the features in the channel dimension to realize fine adjustment of the information flow. After gating, the features are added to the shortcut branch output and passed through ReLU nonlinear activation to finally obtain a feature map with an output size of (H / 2)x(W / 2)xC2. The output spatial resolution is halved compared to the input, and the channel number increases, usually through convolution or pooling with a stride of 2 to realize downsampling. Compared with the standard convolution block on the left, the gating residual block on the right further integrates the SE channel attention mechanism on the basis of the residual connection, significantly enhances the feature expression ability and selectivity, and improves the discriminant performance of the model, with better adaptive emphasis on key features.

[0084] In order to improve the learning effect of the network, the attention mechanism is integrated into the network structure. The attention mechanism can solve the problem of insufficient convolution, and the attention mechanism can be added to the U-Net network as a module. In order to further strengthen the modeling of multi-scale information, a multi-scale feature fusion module is integrated into the decoder to aggregate features at different resolution levels and promote the sensitivity of the model to multi-scale spatial structures such as geological anomalies. Figure 5 An attention mechanism module structure integrated in a deep neural network is shown. The module first performs global context perception on the input feature map, and through feature re-labeling, it significantly improves the model's attention to key information. After a series of convolution and nonlinear activation operations, the attention unit performs adaptive weighting on the features, significantly enhancing the response of key regions while suppressing redundant information. This mechanism can effectively focus on task-related areas during feature encoding, thereby effectively improving the overall feature expression ability and downstream task performance.

[0085] After building the U-Net network architecture, physical prior information is integrated to improve model performance. The multi-scale feature fusion module and the Laplace constraint are complementary. The former captures the multi-scale spatial features of geological bodies, and the latter ensures that different scale features conform to physical laws through gravity field harmonicity constraints, avoiding non-physical artifacts. Specifically, during model training, the Laplace equation satisfied by the gravity field potential in geophysics is used as a physical prior to design the Laplace term in the loss function. This physical consistency constraint not only effectively suppresses the generation of non-physical artifacts, ensuring the consistency of the denoising result with the actual physical law, but also enhances the model's adaptability and generalization ability to different noise levels and complex geological scenarios. The overall structure realizes high-precision physical consistency restoration of gravity or gravity gradient data, improving the scientific interpretability and practical application value of the model.

[0086] In classical geophysics, the gravity field is derived from the underground density distribution, but in areas far from density anomalies, the gravity potential function satisfies the Laplace equation:

[0087] where represents the Laplacian operator, i.e.:

[0088] This equation reflects the physical nature of the gravity field - in the source-free region, the gravity potential distribution is smooth and has harmonicity. Based on this, any observation data derived from physical processes and its reconstruction results should (at least in the main area) obey the constraint of the Laplace equation. Noise, measurement error or unreasonable fitting of neural networks may lead to reconstruction results that violate this physical law. Therefore, introducing the Laplace equation as a prior in the network training process helps to ensure the physical reasonableness of the output results.

[0089] To integrate the above physical law into deep network training, we add a Laplace residual term to the loss function to perform soft constraint on physical consistency. Specifically, after each forward propagation, in addition to calculating the regular reconstruction loss (such as MSE+SSIM), the network output is also calculated to calculate the discrete Laplacian:

[0090] where represents the function value at grid point (i,j), and h is the grid step (the distance between adjacent points). The numerator is the sum of the values of the four adjacent points minus 4 times the center point value, which approximates the second-order derivative. The final total loss is:

[0091] where The weight hyper-parameter is a physical prior. In this way, the areas that "violate the Laplace condition (physical harmonicity)" in the network output have higher loss, and when backpropagating, the results will be forced to adjust back to a physically reasonable state. Traditional purely data-driven neural networks may overfit to out-of-distribution noise or sampling changes, producing outputs that do not conform to physical laws. As a soft constraint, the Laplace prior can constrain the output to satisfy the harmonic characteristics of the real physical field even with limited training data, effectively preventing the emergence of non-physical artifacts. Regardless of the nature and amplitude of the input noise, as long as the gravity field itself is harmonic, the network output will naturally approach the physical "true solution", showing strong cross-distribution generalization ability and achieving the compatibility of "physically reasonable + detail fidelity".

[0092] The process of deep learning requires a large training data set to improve the training effect of the network. In order to provide a large amount of gravity data for network model learning, a modeling method is adopted to construct a randomly generated object model underground. The density disturbance range is set to ±20% of the typical rock density, and three prisms are randomly selected to simulate the distribution of real underground non-uniform medium and enhance data diversity. The generation center coordinates of the object and the size (length, width, and height) of the object are defined to determine the generation position and size of the object. A 200*200 grid is generated, and the grid point spacing is set to 0.1 km. The density range is set to 1~5 g / cm3 (typical rock density is 2-3 g / cm3), and the gravity anomaly of the object is calculated according to the center coordinates of the prism parameters. The gravity anomaly formula based on the prism is calculated as follows:

[0093] where G is the gravitational constant, and the density is the volume contribution of the prism determined by its geometric parameters (size, position). The output result is represented by a two-dimensional array of grid_size*grid_size, indicating the gravity anomaly of each grid point. On the basis of generating clean noise, noise data is generated by adding noise. The added noise type is Gaussian white noise (mean value is 0, and standard deviation is noise_level*standard deviation of clean_gravity). The spatial distribution of randomly generated underground objects is shown in Figure 6 , where the darkness of the object color represents the size of the object density, and different points represent the center positions of different objects. The physical information of the randomly generated objects is shown in Table 1.

[0094] Table 1 Randomly generated underground object data

[0095] The generated data is divided according to the ratio of 80% training set + 20% test set, and the data is standardized for preprocessing. The input and output are separated and standardized to prevent abnormal values in noisy data from affecting the distribution of clean data, so that the network focuses more on learning the mapping relationship from noise to clean signal. Save the standardization parameters to a file to ensure that the same standardization parameters are used in the training and inference stages to maintain data processing consistency.

[0096] During the training and optimization of the model, in order to improve the noise reduction effect of the model, various optimization methods are used, including input data enhancement processing, optimization of the loss function, use of the Adam optimizer combined with an exponential learning rate decay strategy to improve the stability and convergence speed of the training, and use of L2 regularization and spectral normalization techniques to prevent overfitting of the model. The entire process of training the U-Net model is shown in Figure 7 .

[0097] During the model training process, mean squared error is used as the basic loss function to capture pixel-level differences. To further enhance the physical reasonableness and robustness of the model, a Laplace constraint is introduced to calculate the gradient field difference through a discrete Laplace operator. The Laplace operator can effectively enhance edge consistency, while the second-order derivative constraint can suppress high-frequency noise, which is consistent with the smoothing characteristics of the gravity field data. In this way, the model can be optimized while maintaining the physical characteristics and smoothness of the data.

[0098]

[0099] To optimize the model effect, the Adam optimizer is selected, which is an adaptive learning rate optimization algorithm that can dynamically adjust the learning rate based on the first and second moments of the gradient, thereby improving the convergence speed and stability of the model. At the same time, implicit regularization is achieved through Batch Norm, which normalizes the input. This not only stabilizes and accelerates the training process of the model, but also has certain regularization effects, which helps to prevent overfitting. In terms of hyperparameter adjustment, a dynamic learning rate is introduced and an exponential decay strategy is adopted. This strategy can use a larger learning rate in the early stages of training to speed up convergence, and gradually reduce the learning rate as the training progresses to improve the stability of the model.

[0100]

[0101] In addition, a hybrid regularization method is adopted, combining L2 regularization and Laplacian constraint. L2 regularization adds a weight decay term in the optimization objective: L2 regularization can effectively prevent overfitting, while Laplacian constraint further enhances the physical reasonableness of the model. By introducing the λ coefficient, the smoothing strength can be flexibly controlled, so as to balance the complexity and generalization ability of the model. In order to improve the learning ability of the model, random rotation and random flip are used to enhance the experimental data in the data preparation stage. Data augmentation can increase the diversity of data and expand the size of the training data set, thereby improving the generalization ability and robustness of the model.

[0102]

[0103] At the same time, the early stopping strategy is optimized by using the stationarity judgment based on the validation loss. The intelligent early stopping mechanism triggers when the standard deviation of the validation loss satisfies:

[0104] The training is terminated to avoid overfitting. The early stopping strategy can stop training in advance when the validation loss no longer decreases, to prevent overfitting and save computing resources. Finally, spectral normalization is added after the decoder of the model to optimize the structure of the model. Spectral normalization can effectively control the continuity of the model by limiting the spectral norm of the model weight matrix, thereby improving the stability and generalization ability of the model.

[0105] In terms of data set design, it includes clean data obtained by gravity forward calculation and noise data obtained by adding Gaussian noise to clean data. The data generation process is based on the gravity field calculation formula of the prism, simulating the gravity contribution of multiple underground objects. Gaussian noise is added to the clean data, and the standard deviation of the noise is proportional to the standard deviation of the clean data to control the signal-to-noise ratio (SNR). The training set contains 20000 samples and the validation set contains 5000 samples, ensuring the diversity and representativeness of data distribution.

[0106] The performance of the model is quantified by the following indicators: root mean square error (RMSE) and signal-to-noise ratio (SNR):

[0107] where, and represent the true value and the predicted value, respectively.

[0108] Signal-to-noise ratio (SNR):

[0109] where, is the variance of the clean data, is the variance of the residual.

[0110] The training loss and validation loss of the training process are shown in FIG. 6. In the early stage of training, both loss values decrease significantly, reflecting the rapid learning of the model on the data features. As the training progresses, the loss gradually stabilizes and maintains at a low level, indicating that the model gradually converges. Although the overall trend is downward and stable, there are still small fluctuations, which may be caused by the randomness of the batch data used in each training. The training loss and validation loss are almost coincident in the later training, which shows that the model performs consistently on the training set and validation set without obvious overfitting phenomenon, and the overall training process is relatively stable. Figure 8

[0111] The experiment is designed to evaluate the effectiveness of the proposed denoising method in gravity data inversion. Three different underground prism distribution models are selected as experimental objects, and each row corresponds to an underground geological structure. Each set of experiments shows, from left to right: a distribution diagram of the underground prism, a noise-free gravity anomaly field generated by the distribution theory, observed gravity data with random noise added, and gravity anomaly results processed by the denoising algorithm. The experimental results show that the proposed method can effectively remove random noise in the observed data and significantly restore the true gravity anomaly characteristics caused by the underground structure. The denoised results are consistent with the theoretical model and show strong robustness and generalization ability under different geological models and noise types, thereby verifying the practicality and superiority of the denoising method in gravity data preprocessing. The experimental results under the conditions of adding 5%, 10%, and 15% Gaussian noise are shown in FIG. 5. Figure 9

[0112] Figure 9 The experimental results for three different underground prism distribution models are shown. Each row corresponds to an underground geological structure: the first column (a) is a distribution diagram of the underground prism, which identifies the planar position of the target structure; the second column (b) is a noise-free gravity anomaly field generated by the distribution theory, which shows the gravity effect under ideal conditions; the third column (c) is the observed gravity data with Gaussian random noise added, which highlights the degree of interference of noise on the signal; the fourth column (d) is the gravity anomaly result processed by the proposed denoising algorithm, which shows the recovered gravity features after denoising. By comparing (c) and (d), the effectiveness of the denoising algorithm in removing random noise and the closeness to the noise-free theoretical model can be visually observed, and the data shown in the figure verify the robustness of the method under different noise levels.

[0113] ​​To more intuitively illustrate the denoising effect of the improved U-Net network, it is compared with the traditional wavelet transform method, moving average method and low-pass filtering method. In this experimental case, three existing superimposed cuboids are constructed to verify the model's denoising processing capability in dealing with complex situations caused by superimposed bodies. The gravity anomaly is calculated on a 200*200 grid with a spacing of 0.1 km.

[0114] Table 2 Comparison of PSNR values of different denoising methods

[0115] Table 2 compares the peak signal-to-noise ratio (PSNR) performance of various denoising methods in restoring images under different noise levels. For noise levels of 5%, 10%, 15% and 30%, the table lists the PSNR values of the original noisy data and the data processed by the denoising method. The larger the PSNR value, the better the denoising effect. From the table, it can be analyzed that under the same noise level, the denoising effect of the U-Net network is the best, and as the noise level increases, the denoising effect of the U-Net network is more obvious. The horizontal and vertical comparison of the data shows that the proposed denoising algorithm significantly improves the PSNR value under each noise level, and compared with other methods, it shows a more superior denoising effect, especially under high noise level. This shows that the denoising strategy can effectively suppress noise while better preserving the details of the original image.

[0116] To further analyze the differences between several denoising methods, a histogram is drawn. Figure 10 The comparison histogram of the estimation effect of different methods on the earth's gravity anomaly (in mGal) is shown, including U-Net, wavelet transform method, moving average method and low-pass filtering.

[0117] In Figure 10In each subplot, the green bar represents the true value, while the bars of other colors represent the estimated values of the corresponding algorithm. As can be seen from the top-left U-Net result, the estimated values of this algorithm coincide with the true values most, implying its excellent performance in gravity anomaly detection. The frequency distribution of U-Net almost completely covers the true values, especially showing excellent fitting ability in the range of low gravity anomaly values. In contrast, the top-right wavelet transform method shows a significant deviation between the estimated values and the true values, mainly concentrated in a small range of low-frequency gravity anomalies, failing to capture the changes of medium and high amplitude anomalies well. The bottom-left moving average method shows poor consistency, especially in the high-frequency region. The bottom-right low-pass filter method is only accurate in part of the range, indicating its significant deficiency in capturing medium and high-frequency anomalies. U-Net performs particularly well in detecting and frequency matching of various gravity anomalies, reflecting its advantages in the application of gravity data denoising.

[0118] Figure 11 The processing effects of different denoising methods on gravity field data under the condition of 5% noise level are shown. The first column (a) in the figure is the true gravity anomaly field before adding noise, serving as an ideal benchmark; the second column (b) shows the observed data after adding noise, illustrating the interference of noise on the gravity field signal; the third to sixth columns (c-f) are the denoising results processed by U-Net neural network, wavelet transform, moving average, and low-pass filter, respectively. As can be seen, the U-Net method (c) is the most effective in restoring the main features of the gravity field, being closest to the true field (a) with clear waveforms and good details. The denoising effects of other methods are inferior, each with its own characteristics. This figure directly reveals the applicability of each denoising method to gravity data and their different performances in noise suppression.

[0119] The gravity gradient tensor has multiple components (such as T xx , T yy , T zz , etc.), which can reflect structural information such as the shape and trend of the anomaly body. Since gravity gradient is essentially a spatial differentiation of gravity signal, denoising is more difficult than conventional gravity data, and the differentiation operation not only enhances the local changes of the signal, but also greatly amplifies the high-frequency noise in the observation process. Traditional linear filtering often has difficulty in balancing signal edge preservation and effective noise suppression, and the improved U-Net network can better solve this problem. The attention mechanism effectively suppresses the amplified high-frequency noise in the gradient data differentiation process by enhancing the feature weight of the edge region, while the multi-scale feature fusion preserves the gradient details of different scales, avoiding the boundary blurring problem of traditional filtering. Based on the construction of underground objects and grids mentioned in the previous section, the gravity gradient values of the three components T xx , T yy , and T zzThe computed gradient data is added with different levels of Gaussian noise and denoised using the U-Net network and traditional methods.

[0120] Figure 12 The comparative analysis of PSNR values of different denoising methods under different noise levels is presented. The evaluated methods include noise images, U-Net-based denoising methods, wavelet transform, moving average filtering, and low-pass filtering. At a noise level of 0.05, the PSNR value of U-Net reaches 59.13 dB, which is significantly higher than that of the untreated data (41.31 dB) and other methods. As the noise level increases, the advantage of U-Net becomes more apparent. At a noise level of 30%, U-Net still maintains a PSNR value of 48.82 dB, while the performance of wavelet transform and low-pass filtering decreases significantly. Although the moving average filter performs well at lower noise levels, its PSNR value decreases significantly as the noise intensity increases. The results show that the U-Net architecture can effectively maintain image quality under different noise conditions, demonstrating its robustness and denoising ability. Especially at high noise levels, the performance of U-Net far exceeds that of traditional methods.

[0121] Figure 13 The effects of different denoising methods on gravity gradient data are compared. Each row corresponds to the processing results of a component, showing the denoising effects of U-Net neural network, moving average, low-pass filter, and wavelet transform from left to right. In the T xx , T yy , T zz component, the U-Net method exhibits a smooth and clear feature recovery ability, and can better maintain the integrity and details of the target structure; although other methods also effectively reduce noise, they perform slightly less well in detail and boundary processing. This shows that U-Net has a leading comprehensive performance in the denoising task of gravity gradient data, especially in complex geological structures, showing higher resolution.

[0122] To further evaluate the proposed algorithm, we use global satellite gravity data for verification. The global gravity data is divided into a 3°x3° grid, and noise data with noise levels ranging from [0.05, 0.08, 0.10, 0.13, 0.15, 0.18, 0.20, 0.23, 0.25, 0.28, 0.30] are added to expand the training sample size. The data is divided into 80% training set + 20% test set, and trained for 300 rounds.

[0123] To compare the effects before and after adding the physical constraint term, an ablation experiment is added for comparative analysis, Figure 14The comparison results of two different neural network training schemes are shown, the baseline model without using physical constraints and the model introducing physical constraints. Figure 14 The training process is divided into four sub-plots, showing the trend of the loss function, mean square error and structural similarity index. The left two plots show the training loss and validation loss of the two models with the number of iterations. It can be seen that the training loss of the two models decreases rapidly at the beginning, and the physical constraint model reaches a lower training loss value and remains stable. The validation loss in the physical constraint model shows smaller volatility, indicating that its performance on the validation set is more stable. The right two plots show the MSE and SSIM on the training set and validation set with the number of iterations. Although the physical constraint-free model also achieves rapid decline of MSE at the beginning, its validation error shows greater volatility compared with the physical constraint model, especially after a long time of training. The SSIM curve shows that the physical constraint model has higher validation stability, which may indicate that the physical constraint enhances the model's ability to maintain visual quality. The low volatility and high SSIM value of the physical constraint method on the validation set show that introducing physical constraints during training helps to improve the generalization performance and visual perception quality of the model.

[0124] Figure 15 The peak signal-to-noise ratio (PSNR) comparison between the physical constraint model and the baseline model without physical constraints under different noise levels is shown in the middle. The horizontal axis represents the added Gaussian noise level, ranging from 3% to 11%; the vertical axis represents the PSNR value, which aims to evaluate the reconstruction quality of the model. From the figure, it can be observed that the PSNR of the physical constraint model is significantly higher than that of the baseline model without physical constraints, and it presents relatively stable performance at all noise levels, with the PSNR value always remaining around 26. This indicates that the physical constraint helps to improve the robustness and reconstruction accuracy of the model under noise interference. In contrast, the PSNR value of the baseline model without physical constraints is significantly lower, about 24.2, and its reconstruction quality does not improve significantly with the increase of noise level. This highlights the effectiveness and necessity of physical constraints in dealing with noise effects.

[0125] The gravity denoising effect of real data is shown in Figure 16As shown, three regions with different geological distribution characteristics are selected for comparative analysis. In the study, we use the U-Net network with physical prior information (physical consistency constraint based on Laplace equation) for gravity data denoising. As can be seen from the figure, the U-Net network has a significant effect on real gravity data denoising. Due to the addition of physical prior information constraint during training, the network can not only remove noise, but also process data more reasonably according to the physical properties of the gravity field. Specifically, the left subgraph shows the original gravity field data of each region, and the geological features are clear. After introducing noise, the image clarity is significantly reduced, seriously interfering with the identification of geological structures. The right subgraph after U-Net denoising, compared with the original data, not only effectively suppresses the noise, but also restores many detailed features, and reconstructs a more realistic geological structure. It is worth noting that the U-Net network with physical prior information constraint has better denoising effect in marine areas than in land areas. This also shows that the U-Net network with physical prior information constraint can provide more robust and accurate denoising capability in different geographical areas in the gravity data denoising task.

[0126] The present application proposes an improved U-Net network method that fuses multi-scale features, attention mechanisms, and physical prior constraints for gravity and gravity gradient data denoising. 1) The multi-scale feature fusion module introduced in this study effectively captures the multi-scale spatial features of geological anomalies by aggregating features at different depths of the encoder, accurately modeling from shallow edges to deep semantic information. Combined with the spatial attention mechanism, the network can adaptively focus on key areas in the gravity field. This design improves the PSNR index by 10%-20% compared to traditional methods, demonstrating its superiority in feature learning. 2) The Laplace equation in geophysics is incorporated into the loss function to build a physical consistency constraint, which is an important theoretical innovation of this study. Especially in passive areas such as the ocean, the physical smoothness of the denoised data improves by more than 30% compared to the theoretical model. 3) This study extends the improved U-Net network to the multi-component field (T xx , T yy , T zz ). Through the synergistic effect of multi-scale features and attention mechanisms, the network can not only preserve high-frequency details but also suppress noise amplification during differentiation, avoiding the boundary blurring problem caused by traditional filtering methods. The structure similarity (SSIM) of the gradient component after denoising is improved by 15%-25% compared to wavelet transform.

[0127] As for the limitations of this work, the model may face performance limitations when dealing with extremely complex or special physical properties of geological structures. The complexity and irregularity of these special data may exceed the learning ability of the model, resulting in poor noise reduction effect. Therefore, in future research, efforts will be made to expand the combination of physical constraints and deep learning to further improve the ability to handle high-dimensional complex geological scenarios.

[0128] This study focuses on the core problem of gravity data denoising in geophysical exploration, and proposes an improved U-Net method that combines deep learning and physical priors. Through the design of multi-scale feature fusion, attention mechanism and Laplace constraint, the dual improvement of denoising performance and physical interpretability is achieved. Experimental results show that this method is significantly better than traditional filtering techniques in both synthetic and real data, especially in high-noise scenarios and gradient component processing, providing a new technical path for high-precision geophysical data processing.

[0129] The gravity data denoising method based on U-Net network proposed in this invention focuses on the core application fields of geophysical exploration, geological structure research and navigation, and related products can be extended to data processing software, exploration equipment and industry services. In geophysical exploration, efficient denoising of gravity and gravity gradient data can accurately detect the location and size of underground oil and gas reservoirs, ore bodies and other density anomalies, such as using the generated 200x200 grid gravity anomaly data (grid point spacing 0.1 km, density range 1~5 g / cm 3 ) to simulate real underground environment, significantly improve the accuracy of resource positioning after denoising, and reduce the blindness of drilling. In geological structure research, this method can reveal the density distribution of crust and mantle and the characteristics of complex geological bodies such as fault zones by analyzing the denoised gravity data (such as combining Laplace equation constraints to ensure physical reasonableness), especially for the denoising of gravity gradient T xx , T yy , T zz three components, which can achieve fine detection of shallow geological structure. In the field of navigation, the integration of gravity gradient data and inertial navigation system can improve the navigation accuracy and robustness in complex environments. Related products can integrate the algorithm of this invention into Geosoft and other geophysical data processing software to develop intelligent denoising modules, cooperate with equipment manufacturers such as superconducting gravity meters to embed data preprocessing into a "hardware + software" integrated solution, and provide customized data denoising services for exploration companies to output high-precision geological interpretation results, promoting the development of geophysical data processing towards automation and intelligence.

[0130] To further evaluate the proposed algorithm, we used global satellite gravity data for validation. The global gravity data was divided into a 3°x3° grid, and noise data with noise levels ranging from [0.05, 0.08, 0.10, 0.13, 0.15, 0.18, 0.20, 0.23, 0.25, 0.28, 0.30] was added to expand the training sample size. The data was divided into 80% training set + 20% test set, and trained for 300 rounds.

[0131] To compare the effect of adding physical constraint terms before and after, an ablation experiment is added for comparative analysis, Figure 14 The comparison results of two different neural network training schemes are shown, the baseline model without using physical constraints and the model with introducing physical constraints. Figure 14 The four subgraphs respectively show the trend of loss function, mean square error and structural similarity index during training. The left two graphs are the change curves of training loss and validation loss of the two models with iteration number. By comparison, the training loss of the two models decreases rapidly in the early stage, and the physical constraint model reaches a lower training loss value and remains stable. The validation loss in the physical constraint model shows smaller volatility, indicating that its performance on the validation set is more stable. The right two graphs respectively show the change of MSE and SSIM on the training set and validation set with iteration. Although the physical constraint-free model also realizes the rapid decrease of MSE in the early stage, its validation error shows greater fluctuation compared with the physical constraint, especially after a long time of training. The SSIM curve shows that the physical constraint model has higher validation stability, which may indicate that the physical constraint enhances the model's ability to maintain visual quality. The low volatility and high SSIM value of the physical constraint method on the validation set show that introducing physical constraint in the training process helps to improve the generalization performance and visual perception quality of the model.

[0132] Figure 15 The comparison of peak signal-to-noise ratio (PSNR) between the physical constraint model and the baseline model without physical constraint is shown in the middle. The horizontal axis represents the added Gaussian noise level, ranging from 3% to 11%; the vertical axis represents the PSNR value, which aims to evaluate the reconstruction quality of the model. From the figure, it can be observed that the PSNR of the physical constraint model is significantly higher than that of the baseline model without physical constraint, and it presents relatively stable performance at all noise levels, with the PSNR value always remaining around 26. This indicates that the physical constraint helps to improve the robustness and reconstruction accuracy of the model under noise interference. In contrast, the PSNR value of the baseline model without physical constraint is significantly lower, about 24.2, and its reconstruction quality does not improve significantly with the increase of noise level. This highlights the effectiveness and necessity of physical constraint in dealing with noise influence.

[0133] The gravity denoising effect of real data is as follows Figure 16 As shown, three regions with distinct geological distribution characteristics were selected for comparative analysis. In this study, we used a U-Net network incorporating physical prior information (based on physical consistency constraints of the Laplace equation) to denoise gravity data. The figure clearly demonstrates the remarkable denoising effect of the U-Net network on real gravity data. Due to the incorporation of physical prior information during training, the network not only removes noise but also performs more rational processing of the data based on the physical properties of the gravity field. Specifically, the left sub-image shows the original gravity field data for each region, showcasing clear geological features. The introduction of noise in the middle sub-image significantly reduces image clarity, severely interfering with the identification of geological structures. The right sub-image, after denoising using the U-Net, shows effective noise suppression compared to the original data while also restoring many detailed features, reconstructing a more realistic geological structure. Notably, the U-Net network, with the incorporation of physical prior information, performs better in denoising ocean regions than over land. This also shows that U-Net, which incorporates physical prior information constraints, can provide more robust and accurate denoising capabilities in different geographical regions in the denoising task of gravity data.

[0134] It should be noted that the embodiments of the present invention can be implemented by hardware, software, or a combination of software and hardware. The hardware portion can be implemented using dedicated logic; the software portion can be stored in a memory and executed by an appropriate instruction execution system, such as a microprocessor or dedicated design hardware. Those skilled in the art will appreciate that the above-mentioned devices and methods can be implemented using computer-executable instructions and / or contained in processor control code, for example, such as a carrier medium such as a disk, CD or DVD-ROM, a programmable memory such as a read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuits such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field programmable gate arrays, programmable logic devices, etc., can also be implemented by software executed by various types of processors, or can be implemented by a combination of the above-mentioned hardware circuits and software, such as firmware.

[0135] The above description is only a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with this technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered by the scope of protection of the present invention.

Claims

1. A gravity data denoising method based on U-Net network, characterized in that: The following steps are involved: Step 1: Establish the network architecture: Use the encoder and decoder network structure for gravity data denoising. Transmit the features extracted by the encoder to the decoder through skip connections to better restore image details. The network training process determines the network parameters by finding the mapping relationship between noisy data and clean data. Step 2: Incorporate physical prior information: Add a physical constraint term based on the Laplace equation to the loss function to impose a soft constraint on the physical consistency of the network output. Specifically, the discrete Laplace operator value is calculated at each grid point of the network output data and added to the overall loss. Step 3: Construct a training dataset: Generate a two-dimensional grid based on the preset prism parameters and calculate the gravity anomaly at each grid point as clean data. Add Gaussian white noise to the clean data to generate noisy data. Step 4: Model training and optimization: Use mean square error as the basic reconstruction loss, combine L2 regularization term and Laplace physical constraint term for joint optimization, adopt learning rate decay strategy and early stopping mechanism based on validation set loss stability, and apply spectral normalization at the end of the decoder to optimize the network structure.

2. The gravity data denoising method based on the U-Net network according to claim 1, characterized in that: The network training objective in step 1 is to determine the network parameters by minimizing the pixel-wise squared difference between the network output and the expected clean data, and to directly transfer the feature maps extracted from each layer in the encoder to the corresponding decoder layer through skip connections to effectively recover the detailed information of the gravity data.

3. The gravity data denoising method based on the U-Net network according to claim 1, characterized in that: The physical constraint term based on the Laplace equation in step 2 further includes: calculating the discrete Laplace operator value obtained by subtracting four times the center point data from the sum of the four directions of the neighborhood data at each grid point of the network output and then dividing it by the square of the grid spacing, and multiplying the discrete Laplace operator value by the physical prior weight and adding it to the overall loss function to ensure that the network output satisfies physical harmony in the passive area.

4. The gravity data denoising method based on the U-Net network according to claim 1, characterized in that: The dataset construction in step three includes: generating multiple prism models according to preset center coordinates and size parameters, calculating the gravity anomaly value of each grid point under a given grid size and spacing, and the gravity anomaly calculation is based on the universal gravitational constant and the prism density value, which together with the prism geometric parameters determine the gravity contribution; then, adding Gaussian white noise with zero mean and a standard deviation equal to the noise level multiplied by the standard deviation of the clean data to each clean gravity data point to construct a noisy training sample.

5. The gravity data denoising method based on the U-Net network according to claim 1, characterized in that: In the optimization process of step 4, the basic loss is the average of the squared differences between the pixel-level reconstruction results of all samples and the clean data. The L2 regularization term uses half of the sum of the squares of all network weights multiplied by the regularization coefficient. The learning rate is decayed by multiplying a fixed decay factor at each iteration. The early stopping mechanism determines whether training should be terminated by calculating the standard deviation of the loss value of the validation set over the past ten iterations and comparing it with a preset threshold. In addition, the network weights are spectrally normalized at the end of the decoder to stabilize training.

6. A gravity data denoising system based on U-Net network, characterized in that: include: A building module for building a network architecture including an encoder and a decoder with skip connections; Integration module, used to use the physical prior information of Laplace equation to impose physical consistency constraints on the output results during network training; A construction module is used to generate clean gravity data based on a preset prismatic model and grid parameters and add Gaussian white noise thereto to construct a training dataset; The optimization module is used to optimize network parameters based on the mean square error loss combined with L2 regularization and Laplace physical constraints, and adopts a learning rate decay and an early stopping strategy based on the stability of the validation set loss, while applying spectral normalization at the decoder backend.

7. A computer device, characterized in that: The method comprises a memory and a processor, wherein the memory stores computer-executable instructions, and after the processor executes the computer-executable instructions, the processor performs the steps of the gravity data denoising method based on the U-Net network as claimed in claim 1.

8. The system according to claim 6, wherein: The construction module generates a two-dimensional grid based on the preset prism center coordinates and size parameters, where the grid size is 200ths of a thousand meters and the density ranges from one to five grams per cubic centimeter. The construction module calculates the gravity anomaly of each grid point based on the universal gravitational constant, the prism density value and the geometric parameters, and adds Gaussian white noise to this basis to generate noisy training data.

9. A non-volatile computer-readable storage medium storing instruction codes for executing the gravity data denoising method based on the U-Net network as described in any one of claims 1 to 5, wherein when the instruction codes are executed by a processor, the processor executes each step of the method.

10. The computer device according to claim 7, wherein: When the computer-executable instructions described in claim 7 are executed by a processor, the processor is further caused to detect the standard deviation of the validation set loss value during the model training process, and when the standard deviation is less than one times the fifth power of one tenth, an early stopping strategy is triggered to terminate the training.

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