Gravity short-range terrain correction method and system based on high-precision constraint point guidance

Abstract

The application belongs to the technical field of gravity exploration, and specifically relates to a gravity near-zone terrain correction method and system based on high-precision constraint point guidance. Low-resolution elevation data and the coordinates and elevation values of high-precision constraint points are input into a pre-trained elevation data super-resolution reconstruction model to obtain predicted high-resolution elevation data covering a correction area, and terrain correction values are calculated based on the predicted high-resolution elevation data. The application significantly reduces the acquisition cost and field workload of high-precision elevation data while ensuring the accuracy of terrain correction.

Description

Technical Field

[0001] This application relates to the field of gravity exploration technology, specifically to a gravity near-field terrain correction method and system based on high-precision constraint points. Background Technology

[0002] Gravity exploration, as a fundamental and efficient geophysical method, is widely used in mineral resource exploration, oil and gas detection, and hydrological engineering surveys. In ground-based gravity observations, topographic effects caused by terrain undulations significantly interfere with gravity values ​​at measurement points. To obtain gravity field data reflecting true underground density anomalies, rigorous topographic corrections are necessary. The gravitational effect of near-field topography (typically referring to the area within tens to hundreds of meters of the measurement point) is the most significant, and its correction accuracy directly affects the reliability of the final geological interpretation. However, widely used open-source digital elevation models (such as SRTM and ASTER GDEM) typically have a grid resolution of only 30 meters, making it difficult to accurately depict topographic details and affecting correction effectiveness. This has become a bottleneck restricting high-precision gravity exploration. SRTM stands for Space Shuttle Radar Topography Mission, and ASTER GDEM stands for Advanced Spaceborne Thermal Emission and Reflection Radiometer Global Digital Elevation Model. Although centimeter-level elevation data can be obtained through airborne lidar measurements or high-density manual ground surveys, these methods are costly and inefficient. Therefore, how to use readily available low-resolution elevation data to generate high-resolution topographic data that meets the requirements for high-precision near-field topographic correction in an economical and efficient manner has become a key technical issue in the field of gravity exploration.

[0003] Chinese Patent Publication No. CN117991393A, entitled "A Gravity Near-City Terrain Correction Method and Device Based on RTK Continuous Measurement," employs an RTK continuous measurement mode. Surveyors carry GNSS equipment while walking and automatically record the coordinates and elevations of terrain points, then calculate terrain correction values ​​through grid interpolation. Compared to traditional manual measurement, this method reduces personnel input and improves single-point measurement efficiency. However, this method is essentially still a point-by-point field measurement paradigm, requiring an RTK terrain data acquisition process to be performed near each gravity measurement point. When acquiring large-scale, high-density gravity data (such as regional gravity surveys), this method will generate a huge amount of fieldwork, time costs, and equipment investment, and is difficult to apply to areas where field RTK operations are difficult (such as dense forests, steep and dangerous terrain).

[0004] Chinese Patent Publication No. CN117474765A, entitled "DEM Super-Resolution Reconstruction System Based on Reference Image Texture Transfer," introduces high-resolution remote sensing imagery as a reference and utilizes the VGG19 network to extract multi-scale texture features, transferring the texture of the remote sensing image to the elevation data to achieve super-resolution reconstruction of the elevation data. This method alleviates the problem of inaccurate single-image super-resolution by using external remote sensing information. However, the remote sensing imagery it relies on often does not completely correspond to the terrain information, and it requires additional remote sensing data acquisition, which is difficult to obtain synchronously during gravity exploration field operations.

[0005] Chinese Patent Publication No. CN120373159A, entitled "A Residual Topography Correction Estimation Method Based on PINNs and Residual Topography Model," employs Physical Information Neural Networks (PINNs) combined with a Residual Topography Model (RTM) to directly calculate residual topography correction values. This method correlates gravity anomalies with the gravitational potential of the RTM model through physical equations as boundary conditions, using a fully connected neural network to learn the physical mapping of topography correction, thus reducing the computational load of traditional integral methods. However, this method is used to obtain residual topography correction values ​​globally, rather than for high-precision correction of near-field topography, resulting in significant errors in refined geological exploration scenarios. Furthermore, the method directly outputs topography correction values, and the calculation process relies on the black-box mapping of the neural network, leading to poor interpretability.

[0006] In summary, existing technologies either require extensive on-site measurements, rely on external remote sensing imagery, or cannot meet the needs of high-precision surveys. Summary of the Invention

[0007] This application provides a gravity-based near-field terrain correction method and system guided by high-precision constraint points, aiming to solve the problems of low near-field terrain correction accuracy due to insufficient resolution of open-source elevation data in the prior art, and high cost of acquiring high-resolution elevation data.

[0008] The first aspect of this application provides a gravity-guided near-field terrain correction method based on high-precision constraint points, including: Obtain low-resolution elevation data covering the near-field terrain correction area, and obtain the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points within the near-field terrain correction area; The low-resolution elevation data and the plane coordinates and elevation values ​​of the high-precision constraint points are input into a pre-trained elevation data super-resolution reconstruction model to obtain predicted high-resolution elevation data for near-field terrain correction. The near-field topographic correction value is calculated using the predicted high-resolution elevation data.

[0009] Furthermore, the elevation data super-resolution reconstruction model is a dual-branch deep learning network, comprising: The main coding branch is used to extract terrain features from the low-resolution elevation data and generate a terrain feature map. The conditional coding branch obtains a conditional feature map with the same spatial dimension as the terrain feature map based on the planar coordinates and elevation values ​​of the high-precision constraint points. The feature fusion and decoding module is used to stitch the conditional feature map and the terrain feature map together in the channel dimension to generate a fused feature map, and to decode the fused feature map to generate the predicted high-resolution elevation data.

[0010] Furthermore, the conditional coding branch performs the following steps: The planar coordinates of high-precision constraint points are converted into the corresponding index positions in low-resolution elevation data to form a sparse condition matrix. By using bilinear interpolation, the sparse conditional matrix is ​​transformed into a continuous conditional feature map with the same spatial dimension as the terrain feature map.

[0011] Furthermore, the elevation data super-resolution reconstruction model is pre-trained in the following manner: Construct a training dataset, which includes multiple sets of samples. Each set of samples contains: paired low-resolution elevation data samples and high-resolution elevation data samples, as well as the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points obtained from actual measurements. The dual-branch deep learning network is trained by using low-resolution elevation data samples and the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points as inputs, and high-resolution elevation data samples as supervision targets. The loss function used for training should include at least the following: The first reconstruction loss term is used to minimize the difference between the predicted high-resolution elevation data output during model training and the high-resolution elevation data samples used as supervision targets. The second physical constraint loss term is used to constrain the terrain gradient field of the predicted high-resolution elevation data output during model training to maintain consistency with the terrain gradient field of the high-resolution elevation data samples used as the supervision target.

[0012] Furthermore, the first reconstruction loss item adopts The loss function is calculated using the following formula: , in, For the reconstruction loss value, The high-resolution elevation data predicted during model training is the output of the model. This is a high-resolution elevation data sample. express Norm.

[0013] Furthermore, the second physical constraint loss term is expressed as the following formula: , in, This represents the physical constraint loss value. This represents the gradient computation operator. The high-resolution elevation data predicted during model training is the output of the model. This is a high-resolution elevation data sample. express Norm, The norm refers to the Euclidean norm.

[0014] A second aspect of this application provides a gravity-based near-field terrain correction system guided by high-precision constraint points, comprising: The data acquisition module is used to acquire low-resolution elevation data covering the near-field terrain correction area, and to acquire the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points within the near-field terrain correction area. The model inference module is used to input the low-resolution elevation data and the plane coordinates and elevation values ​​of the high-precision constraint points into a pre-trained elevation data super-resolution reconstruction model to obtain predicted high-resolution elevation data for near-field terrain correction. The terrain correction calculation module is used to calculate the near-field terrain correction value of the measuring point using the predicted high-resolution elevation data and the prism terrain correction algorithm.

[0015] The embodiments of this application have at least the following advantages and beneficial effects: Compared with correction methods that use low-resolution elevation data (such as high-resolution elevation data with a resolution of 30 meters), this application can utilize the elevation data to reconstruct the model at a super-resolution resolution to obtain elevation data with a resolution of 5 meters, thus improving the accuracy of near-field terrain correction. Compared with schemes that directly obtain high-precision elevation data through dense surveys (such as lidar), this application's method reduces the economic and time costs of data acquisition while ensuring accuracy. Compared with schemes that use remote sensing data as an aid, this application's method uses the plane coordinates and elevation values ​​of other nearby gravity measurement points as auxiliary information, which is more in line with actual operational scenarios. Compared with schemes that directly calculate global residual terrain correction values ​​using physically constrained neural networks, this method has stronger interpretability and is more suitable for refined gravity exploration. Attached Figure Description

[0016] Figure 1 This is a schematic diagram of the network structure of the elevation data super-resolution reconstruction model provided in the embodiments of this application; Figure 2 This is a flowchart of a gravity-guided near-field terrain correction method based on high-precision constraint points provided in an embodiment of this application; Figure 3This is a block diagram of a gravity near-field terrain correction system based on high-precision constraint points provided in an embodiment of this application; Figure 4 This is a comparison chart of the predicted high-resolution elevation data and the benchmark high-resolution elevation data output by the elevation data super-resolution reconstruction model provided in this application embodiment. (a) is the 30-meter resolution elevation data, (b) is the benchmark high-resolution elevation data, and (c) is the predicted high-resolution elevation data. Detailed Implementation

[0017] To make the objectives, technical solutions, and advantages of this application clearer, preferred embodiments of the invention are provided below in conjunction with the accompanying drawings for further detailed description. It should be noted that the specific embodiments described herein are merely illustrative and not intended to limit the scope of this application.

[0018] This application constructs a two-branch deep learning network containing a backbone coding branch and a conditional coding branch, and uses the information of measured high-precision constraint points to guide the super-resolution reconstruction of low-resolution elevation data to obtain high-resolution elevation data, thereby achieving high-precision near-field terrain correction.

[0019] like Figure 1 As shown, the elevation data super-resolution reconstruction model used in this application is a dual-branch deep learning network, which includes a backbone coding branch, a conditional coding branch, and a feature fusion and decoding module.

[0020] The backbone coding branch is used to extract terrain features from low-resolution elevation data and generate terrain feature maps, employing a residual channel attention network structure. Low-resolution elevation data refers to Digital Elevation Model (DEM) data organized in a regular grid format, where each grid cell (pixel) records the average elevation or relative elevation value of the corresponding surface area. Low resolution is relative to the reconstructed target or ground-based labeled data; in this embodiment, it specifically refers to low spatial resolution, meaning that a single pixel represents a large ground coverage area, making it unable to finely depict minute terrain undulations, but effectively reflecting the macroscopic topographic pattern, slope direction, and distribution of major landform types at the regional scale.

[0021] In a typical application scenario of this application, the spatial size of the low-resolution elevation data is 16×16 pixels, corresponding to a ground coverage area of ​​480m×480m. Therefore, its nominal spatial resolution can be calculated to be 30m, meaning each pixel represents a 30m×30m rectangular area on the ground. Resolution levels are typically provided by spaceborne or airborne radar altimetry missions, globally publicly available DEM products (such as SRTM and ASTER GDEM), or low-cost regional mapping data. These data offer advantages such as wide coverage, convenient acquisition, and small data volume, but cannot directly support fine-grained terrain classification or high-precision 3D reconstruction tasks. Therefore, feature enhancement and semantic abstraction are required through elevation data super-resolution reconstruction models.

[0022] The terrain feature extraction and feature map generation process is undertaken by the backbone coding branch, which automatically transforms the input low-resolution digital elevation model data into a structured feature map output containing rich terrain semantic information through forward propagation calculation of a deep neural network.

[0023] Low-resolution digital elevation model data enters the shallow feature extraction stage, which is performed by a convolutional layer with a stride of one and consistent padding to ensure the output size remains unchanged. This convolutional layer maps the single-channel input to a shallow feature map output. Its function is to extract primary geometric features such as elevation gradients, edge responses, and texture orientation within the local neighborhood. Simultaneously, the output shallow feature map is independently saved as a skip connection for use in the residual fusion stage of the final output.

[0024] The shallow feature maps are then processed sequentially through five residual groups. Each residual group consists of ten Residual Channel Attention Blocks (RCABs) stacked in series, resulting in a total of 50 RCABs in the deep extraction path. The working mechanism of each RCAB is as follows: First, the input shallow feature map is processed through two consecutive convolutional layers to extract local spatial context information. Each convolutional layer is followed by a rectified linear unit activation function to introduce non-linear expressive power. Second, the convolutional output feature map undergoes global average pooling to compress the spatial dimension of each channel into a single value, forming a channel description vector. This channel description vector is then input into a small network consisting of two fully connected layers. The first fully connected layer compresses the number of channels to achieve dimensionality reduction, while the second fully connected layer restores the number of channels to their original dimensions. After normalization by a sigmoid activation function, the output is a channel attention weight vector. Finally, the channel attention weight vector is multiplied back into the convolutional output feature map channel by channel to enhance key terrain response channels and suppress irrelevant channels, achieving adaptive recalibration at the channel level. Following this, the residual channel attention block introduces local residual connections, which add the original input of the residual channel attention block to the output after channel recalibration element by element, so that the gradient can bypass the convolution and attention sub-modules and propagate directly to the shallow layer, effectively alleviating the degradation problem of deep networks.

[0025] After being passed through 50 residual channel attention blocks in a stepwise manner, the network's receptive field gradually expands to cover the entire spatial range. This allows the feature vector at each spatial location to not only encode its own elevation value but also incorporate long-range dependencies with the global terrain context. At this point, the network is able to abstract high-order terrain semantic response patterns such as ridges, valleys, slopes, and flat areas from the original low-resolution numerical values. The deep outputs of these 50 residual channel attention blocks are not directly used as the final feature map. Instead, the outputs of the five residual groups are first concatenated along the channel dimension to form a fused feature tensor containing multi-level abstract information.

[0026] The fused feature tensor is then element-wise added to the initially preserved shallow features, a process known as global residual connection. The elevation boundary locations and local abrupt changes preserved in the shallow features can bypass the fifty-layer deep network and be directly transmitted to the output, compensating for potential spatial detail loss during deep convolution. Simultaneously, the residual connections ensure that the network can utilize both low-level geometric and high-level semantic information during forward propagation, achieving complementary enhancement of multi-scale features. After global fusion, the network finally outputs a terrain feature map.

[0027] The conditional encoding branch obtains a conditional feature map with the same spatial dimension as the terrain feature map based on the planar coordinates and elevation values ​​of the high-precision constraint points.

[0028] First, the planar coordinates are converted into the corresponding index positions in the low-resolution elevation data grid, forming a sparse conditional matrix.

[0029] By using bilinear interpolation, the sparse matrix is ​​transformed into a continuous conditional feature map (size 16×16) with the same spatial dimension as the terrain feature map, containing two channels: the first channel is the interpolated elevation value, and the second channel represents whether there is a constraint point at that location.

[0030] In its implementation, the conditional coding branch receives three-dimensional spatial data of several high-precision constraint points as input. Each constraint point is fully defined by three parameters: planar coordinates and elevation value. The planar coordinates use horizontal and vertical coordinates under a unified geographic reference system for the region, typically in meters, representing the precise spatial location of the high-precision constraint point on the horizontal plane of the Earth's surface. The elevation value represents the altitude of the high-precision constraint point, also in meters, with a precision level significantly higher than the nominal precision of the original low-resolution elevation data. These high-precision constraint points can originate from in-situ GPS measurements, carefully selected ground echo points from high-precision lidar point clouds, or reliable corresponding points obtained through high-resolution stereo image pair matching. Their positioning accuracy can reach centimeter to decimeter levels, far exceeding the 30-meter grid resolution of low-resolution elevation data. Physically, each high-precision constraint point represents a reliable sample of true ground elevation observations and can be considered a precise calibration benchmark for the low-resolution elevation data at a specific spatial location.

[0031] The processing flow of the conditional coding branch begins with the grid index transformation of the planar coordinates of each high-precision constraint point. The main coding branch first needs to map the planar coordinates of each high-precision constraint point in its geographic reference system to the pixel coordinate system of the low-resolution elevation data grid through an affine transformation, calculating the row and column indices corresponding to that high-precision constraint point. This index calculation process requires precise coordinate registration based on the spatial reference range and grid division rules of the low-resolution elevation data to ensure that the high-precision constraint points can be located in the correct grid positions. Since the spatial distribution of high-precision constraint points is often discrete and non-uniform, most grid cells may not contain any constraint points, while a few grid cells may contain one or more constraint points. After the above index mapping, this discrete constraint point information constitutes a sparse condition matrix. This sparse condition matrix is ​​defined only in a few grid positions occupied by the high-precision constraint points, while remaining empty in the majority of other grid positions.

[0032] After obtaining the sparse condition matrix, the conditional encoding branch further transforms it into a continuous conditional feature map with the same spatial dimension as the terrain feature map. This transformation process employs bilinear interpolation. For each grid position in the continuous conditional feature map of the target, a weighted interpolation calculation is performed based on its distance to the known sparse constraint points adjacent to that position, thus assigning a reasonable estimate to the originally missing grid position. Bilinear interpolation performs a weighted average of the four nearest-neighbor known constraint points in a two-dimensional plane, with the weights inversely proportional to the distance. This ensures that the interpolation result smoothly reflects the spatial variation trend of the constraint points, avoiding step-like or abrupt discontinuities caused by uneven distribution of discrete points.

[0033] The conditional feature map output by this bilinear interpolation process contains two channels. The first channel stores the interpolated elevation values, providing an elevation estimate at each grid location determined by neighboring high-precision constraint points. In areas with dense constraint points, its value is close to the measured value, while in areas with sparse constraint points, it forms a smooth-transition approximation. The second channel is a spatial distribution confidence indicator channel, used to characterize whether there are real constraint points near each grid location. Specifically, during the interpolation process, the second channel assigns higher values ​​to locations closer to known constraint points, reaching its maximum value at the specific grid location of the constraint point, while its value approaches zero in areas far from all constraint points. The introduction of the second channel is crucial, enabling downstream network modules to clearly distinguish which elevation values ​​in the first channel are reliable values ​​strongly constrained by real observations, and which are merely interpolated estimates based on the spatial smoothness assumption. Thus, in subsequent feature fusion and terrain reconstruction processes, the level of trust in information at different locations can be adaptively adjusted based on confidence information. For high-confidence areas, the guidance of the conditional feature map is prioritized, while for low-confidence areas, the global terrain semantic features extracted from low-resolution elevation data by the backbone coding branch are relied upon more.

[0034] After the above processing, the conditional feature map output by the conditional coding branch has a spatial size of 16×16 and two channels, which is perfectly aligned spatially with the 64-channel terrain feature map output by the backbone coding branch. Therefore, the two can achieve pixel-by-pixel feature stitching or adaptive weighted fusion in the subsequent fusion module. In this way, the precise ground control information carried by the planar coordinates and elevation values ​​of high-precision constraint points is efficiently encoded into a conditional feature expression consistent with the spatial structure of the terrain feature map. The aforementioned high-precision constraint points refer to discrete ground control sample points whose spatial location and elevation values ​​are obtained by measurement methods with a precision significantly higher than that of the input low-resolution elevation data, for example, an order of magnitude higher than the low-resolution elevation data.

[0035] The feature fusion and decoding module first concatenates the terrain feature map (16×16) output by the backbone coding branch and the conditional feature map (16×16) output by the conditional coding branch along the channel dimension, and then uses a convolutional layer to complete feature fusion to obtain a fused feature map. Subsequently, the fused feature map is enlarged by 6 times through subpixel convolution, restoring the spatial resolution from 16×16 to the target high-resolution size of 96×96. Finally, a convolutional layer is used to output the predicted high-resolution elevation data, which corresponds to a spatial resolution of 480m×480m on the ground, with a resolution of 5 meters.

[0036] The elevation data super-resolution reconstruction model is pre-trained in the following way: Construct a training dataset, which includes multiple sets of samples. Each set of samples contains: paired low-resolution elevation data samples and high-resolution elevation data samples, as well as the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points obtained from actual measurements. The dual-branch deep learning network is trained by using low-resolution elevation data samples and the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points as inputs, and high-resolution elevation data samples as supervision targets. The training dataset is drawn from geographical regions different from the target correction area to ensure the model's generalization ability. Each training sample includes: Low-resolution elevation data samples serve as the input for model training; high-resolution elevation data samples serve as the supervised targets for model training; sparsely distributed high-precision constraint point information, with each constraint point containing its planar coordinates and elevation value. The training dataset contains a total of 9600 samples, covering various terrain types such as plains, hills, and mountains, to ensure the model's adaptability to different terrains.

[0037] The model training employs a composite loss function to simultaneously ensure the accuracy of elevation values ​​and the physical plausibility of terrain features. Composite Loss Function Defined as: , in, To balance the weighting coefficients of the two losses, a value of 0.05 is used in this embodiment.

[0038] The first reconstruction loss item adopts The loss function is used to minimize the predicted high-resolution elevation data output by the model training output. With high-resolution elevation data samples as the monitoring target The absolute error between them is calculated using the following formula: ; in, To reconstruct the loss value, The high-resolution elevation data predicted during model training is the output of the model. This is a high-resolution elevation data sample. express Norm.

[0039] The second physical constraint loss term is used to ensure that the terrain gradient field of the predicted high-resolution elevation data output by the model training is consistent with the terrain gradient field of the high-resolution elevation data used as the supervision target, so that the reconstruction result maintains the natural continuity of the terrain. The calculation formula is as follows: , in, This represents the gradient computation operator. Represents norm calculation, express Norm, The norm refers to the Euclidean norm.

[0040] The model was trained using the Adam optimizer with an initial learning rate of 0.0001, which decreased to 0.5 times every 25 training epochs. The total training duration was 100 epochs, with a batch size of 16. An early stopping strategy was employed: training was terminated and the optimal model parameters were saved when the validation set loss did not decrease for five consecutive epochs.

[0041] Combination Figure 2 The flowchart shown illustrates the gravity-guided near-field terrain correction method based on high-precision constraint points provided in this application. This method utilizes the aforementioned elevation data super-resolution reconstruction model and includes the following steps: S101, acquire low-resolution elevation data covering the near-field terrain correction area, and acquire the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points within the near-field terrain correction area. S102, input the low-resolution elevation data and the plane coordinates and elevation values ​​of the high-precision constraint points into the pre-trained elevation data super-resolution reconstruction model to obtain predicted high-resolution elevation data for near-field terrain correction; S103, calculate the near-area terrain correction value using the predicted high-resolution elevation data.

[0042] In step S101, the near-field topographic correction area refers to the spatial range within a certain radial distance around the target measuring point that needs to be quantitatively corrected when performing gravity near-field topographic correction or geophysical exploration data processing. In one example, for the gravity measuring point to be corrected, 30-meter resolution elevation data is acquired within a 480m×480m range around it; The low-resolution elevation data refers to a regular gridded digital elevation model covering the near-field terrain correction area. In one example, the spatial resolution is 30 meters, meaning each grid cell represents a 30-meter × 30-meter rectangular area on the ground, with a data size of 16 × 16 pixels, corresponding to a total ground area of ​​480 meters × 480 meters. This data can be obtained through various means, including but not limited to publicly available global digital elevation model products, such as the 30-meter resolution DEM data released by the Space Shuttle Radar Topography Mission, the advanced spaceborne thermal emission and reflection radiometer global digital elevation model data, or 30-meter gridded DEM products provided by regional surveying departments. After data acquisition, basic quality checks and preprocessing are required. Specifically, this includes checking whether the data coverage completely encompasses the target's near-field terrain correction area, identifying and marking null values ​​or anomalous elevation jumps in the data, and filling a small number of missing pixels using neighborhood interpolation based on actual conditions. After the above preprocessing, the low-resolution elevation data will be organized into a single-channel floating-point tensor with a spatial size of 16 × 16, serving as the standard input format for the backbone coding branch.

[0043] The high-precision constraint points refer to a set of three-dimensional ground control points with known planar coordinates and elevation values ​​obtained through high-precision measurement methods within the same near-field topographic correction area. The planar coordinates of these high-precision constraint points use a geographic reference system and projection method completely consistent with the low-resolution elevation data, typically expressed in meters to represent their precise spatial location on the horizontal plane of the Earth's surface; their elevation values ​​represent the altitude at the location of the high-precision constraint point, also recorded in meters. The main methods for obtaining high-precision constraint points include the following: Control points collected in the field using real-time dynamic differential GPS or GPS static measurement methods, achieving centimeter-level horizontal positioning accuracy and centimeter-to-decimeter-level vertical elevation accuracy; Utilizing airborne lidar point cloud data, after filtering the ground point cloud to remove surface vegetation and artificial structures, reliable ground echo points are extracted as constraint points, with accuracy depending on the nominal accuracy of the lidar system and the point cloud density; High-precision corresponding ground points are generated from high-resolution stereo remote sensing image pairs through dense matching and forward intersection calculations, and then high-confidence matching points are retained after manual editing or automatic quality screening. Regardless of the acquisition method, all high-precision constraint points must undergo spatial reference consistency verification, meaning their planar coordinates must be strictly aligned with the spatial reference system of the low-resolution elevation data. If necessary, coordinate transformation should be performed to achieve benchmark unification.

[0044] In step S102, the backbone encoding branch of the pre-trained elevation data super-resolution reconstruction model receives low-resolution elevation data as input. Using a residual channel attention network structure, it extracts the macroscopic terrain features contained in the low-resolution elevation data and outputs a terrain feature map with the same spatial dimension. The terrain feature map condenses deep semantic information such as terrain undulation, slope direction, and landform type within the region, serving as the terrain prior for the entire reconstruction process. Simultaneously, the conditional encoding branch receives the planar coordinates and elevation values ​​of sparsely distributed high-precision constraint points in the same area as input. These discrete, precise constraint points are registered to the pixel coordinate system of the low-resolution grid through affine transformation, forming a sparse conditional matrix. This matrix is ​​then expanded through bilinear interpolation into a two-channel continuous conditional feature map with the same spatial dimension as the terrain feature map. The first channel of this conditional feature map stores the interpolated elevation estimate, and the second channel stores the confidence level of the existence of a true constraint point at each location, thus encoding the high-precision measured information into a conditional constraint tensor usable by the network.

[0045] The feature fusion and reconstruction branch receives the 64-channel terrain feature map output from the backbone coding branch and the two-channel conditional feature map output from the conditional coding branch, and concatenates them along the channel dimension to form a fused feature tensor. This fused tensor then passes through multiple upsampling modules, each consisting of a pixel rearrangement convolutional layer and a residual convolutional layer, progressively increasing the spatial resolution. The specific target output resolution is pre-set based on the actual accuracy requirements of near-field terrain correction. During each upsampling stage, the constraint information carried by the conditional feature channels in the fused feature tensor is repeatedly passed to each decoding sub-layer through cross-layer connections, ensuring that the guiding effect of high-precision constraint points remains effective throughout the resolution improvement process. After progressive upsampling and feature refinement, the final layer of the reconstruction branch compresses the multi-channel features into a single-channel output through a 3×3 convolution; this output is the predicted high-resolution elevation data.

[0046] The predicted high-resolution elevation data is spatially much larger than the input low-resolution data, with a significantly reduced ground coverage area for each pixel, thus enabling the depiction of finer terrain undulation details. More importantly, because the conditional coding branch continuously injects measured elevation information of high-precision constraint points during reconstruction, the predicted result not only possesses statistically similar texture and structural features to the real high-resolution terrain, but also achieves precise matching with measured values ​​at the location of the constraint points and their vicinity, effectively overcoming the inherent defect of pure data-driven super-resolution methods with large deviations at sparse measured points. The predicted data is quantitatively expressed as a two-dimensional floating-point raster matrix, with the spatial reference frame consistent with the input low-resolution elevation data and high-precision constraint points. Therefore, it can be directly used for subsequent near-field terrain correction calculations, serving as a high-precision terrain undulation field in the integral calculation of gravity terrain correction, thereby significantly improving the accuracy and reliability of near-field terrain correction.

[0047] In step S103, the near-field terrain correction value is calculated using a prism terrain correction algorithm. Based on predicted high-resolution elevation data with a 5-meter resolution, the near-field terrain correction value for the measuring point is calculated. The near-field terrain correction value is the change in gravity field at the measuring point caused by adjusting the terrain mass within a certain radial range around the measuring point from its actual undulation state to the reference plane, using the target measuring point's location as a reference. In geophysical gravity exploration, terrain correction is a crucial step in eliminating the influence of terrain undulation on gravity observation data; its accuracy directly determines the reliability of the final Bouguer gravity anomaly.

[0048] In this embodiment, the calculation of the near-field terrain correction value is based on the prism terrain correction algorithm. The basic idea of ​​this algorithm is to divide the terrain around the measuring point into several regular upright prism units. The base of each upright prism unit is a rectangular grid unit, and the height of the top surface is determined by the elevation value at the grid unit. The height of the base surface is uniformly taken as the elevation of the measuring point or the elevation of the reference plane. Then, the vertical gravity attraction component generated by each prism at the measuring point is calculated. The contributions of all upright prism units are accumulated and summed to obtain the total terrain correction value.

[0049] In one example, the resolution of the predicted high-resolution elevation data is 5 meters, meaning each raster cell corresponds to a 5×5 rectangular area on the ground. This resolution level provides sufficient detail for near-field topographic correction calculations, effectively characterizing subtle variations in local topographic relief, including micro-topographic features such as small valleys, mounds, road embankments, and foundations of man-made structures—features completely invisible in the original 30-meter resolution low-resolution elevation data. The calculation process is performed in the following steps: First, the calculation radius for the near-field topographic correction is defined with the plane coordinates of the target measuring point as the origin. The value of the calculation radius is predetermined based on the accuracy requirements of gravity exploration and the complexity of the terrain. Second, all 5-meter resolution grid cells with their centers located within the radial range are selected to form a set of prisms for calculation. Subsequently, for each upright prism cell, the gravitational effect generated at the measuring point is calculated using the horizontal distance between its center point and the measuring point, the relative height difference, and the base area of ​​the upright prism cell, based on the analytical expression of the vertical component of the universal gravitation formula. Finally, the gravitational effects of all upright prism cells are summed to obtain the near-field topographic correction value for the measuring point.

[0050] In the specific implementation of analytical calculations for upright prism elements, the geometric parameters of each upright prism element are determined by the elevation and planar coordinates of its four corner points. To balance computational accuracy and efficiency, the standard analytical formula for upright prisms is adopted. This formula is obtained by analytically solving the closed-form of the three-dimensional gravitational integral over a finite volume. This allows for accurate calculation of the vertical gravitational component generated by an upright prism element of arbitrary size at any point in space, without the need for numerical integration approximation. For upright prism elements located directly below the measuring point, i.e., the grid element where the measuring point's projection point is located, the gravitational effect is specially treated using a disk approximation or a point mass approximation to avoid singularities in the analytical formula caused by zero horizontal distance.

[0051] After completing the calculation for a single measuring point, the same calculation process is repeated for all measuring points within the entire near-field terrain correction area to obtain the terrain correction value sequence for each measuring point. Because the 5-meter resolution elevation data used in the calculation process significantly improves spatial detail compared to the original input, the calculated near-field terrain correction values ​​are more smoothly distributed in space and more reliable in numerical accuracy, effectively avoiding systematic biases in correction values ​​caused by the inability of low-resolution data to distinguish micro-topography.

[0052] See Figure 3 As shown, another embodiment of this application provides a gravity near-field terrain correction system based on high-precision constraint points, comprising: The data acquisition module is used to acquire low-resolution elevation data covering the near-field terrain correction area, and to acquire the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points within the near-field terrain correction area. The model inference module integrates a pre-trained and fixed network parameter elevation data super-resolution reconstruction model, which is used to input the low-resolution elevation data and the plane coordinates and elevation values ​​of the high-precision constraint points into the pre-trained elevation data super-resolution reconstruction model to obtain predicted high-resolution elevation data for near-field terrain correction. The terrain correction calculation module is used to calculate the near-field terrain correction value of the measuring point using the predicted high-resolution elevation data and the prism terrain correction algorithm.

[0053] To further verify the effectiveness of the method proposed in actual production, a field test was conducted at a gravity measuring point in a metal mining area. The area where the measuring point is located has a large topographic relief and complex conditions.

[0054] The area was generated using oblique photogrammetry by drones, resulting in 5-meter resolution elevation data as a reference for the actual terrain.

[0055] By inputting 30-meter resolution elevation data and the plane coordinates and elevation values ​​of 16 constraint points into a trained elevation data super-resolution reconstruction model, we obtain predicted high-resolution elevation data with a resolution of 5 meters.

[0056] Comparison of predicted high-resolution elevation data with baseline high-resolution elevation data generated by UAVs, for example Figure 4 As shown, where Figure 4 (a) in the figure represents elevation data with a resolution of 30 meters. Figure 4 (b) in the figure represents the baseline high-resolution elevation data. Figure 4 (c) in the figure represents the predicted high-resolution elevation data. It can be seen that the predicted high-resolution elevation data and the baseline high-resolution elevation data are highly consistent, and the local details are well restored.

[0057] The near-field topographic correction value calculated using predicted high-resolution elevation data is 0.47 mGal, while the near-field topographic correction value calculated directly using 30-meter resolution elevation data is 0.38 mGal, a difference of 0.09 mGal. Using the near-field topographic correction value of 0.63 mGal calculated from baseline elevation data as a reference, the error of the method in this application is 0.16 mGal, while the error of the traditional method is 0.25 mGal. The method in this application reduces the near-field topographic correction error by 36%, significantly improving the accuracy of near-field topographic correction.

[0058] The method proposed in this application requires only a small number of constraint points, which can significantly reduce the workload of traditional high-precision topographic surveying while ensuring accuracy.

[0059] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this application should be included within the protection scope of this application.

Claims

1. A gravity-based near-field terrain correction method guided by high-precision constraint points, characterized in that, include: Obtain low-resolution elevation data covering the near-field terrain correction area, and obtain the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points within the near-field terrain correction area; The low-resolution elevation data and the plane coordinates and elevation values ​​of the high-precision constraint points are input into a pre-trained elevation data super-resolution reconstruction model to obtain predicted high-resolution elevation data for near-field terrain correction. The near-field topographic correction value is calculated using the predicted high-resolution elevation data.

2. The gravity-guided near-field terrain correction method based on high-precision constraint points according to claim 1, characterized in that, The elevation data super-resolution reconstruction model is a two-branch deep learning network, including: The main coding branch is used to extract terrain features from the low-resolution elevation data and generate a terrain feature map. The conditional coding branch obtains a conditional feature map with the same spatial dimension as the terrain feature map based on the planar coordinates and elevation values ​​of the high-precision constraint points. The feature fusion and decoding module is used to stitch the conditional feature map and the terrain feature map together in the channel dimension to generate a fused feature map, and to decode the fused feature map to generate the predicted high-resolution elevation data.

3. The gravity-guided near-field terrain correction method based on high-precision constraint points according to claim 2, characterized in that, The conditional coding branch performs the following steps: The planar coordinates of high-precision constraint points are converted into the corresponding index positions in low-resolution elevation data to form a sparse condition matrix. By using bilinear interpolation, the sparse conditional matrix is ​​transformed into a continuous conditional feature map with the same spatial dimension as the terrain feature map.

4. The gravity-guided near-field terrain correction method based on high-precision constraint points according to claim 2, characterized in that, The elevation data super-resolution reconstruction model is pre-trained in the following manner: Construct a training dataset, which includes multiple sets of samples. Each set of samples contains: paired low-resolution elevation data samples and high-resolution elevation data samples, as well as the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points obtained from actual measurements. The dual-branch deep learning network is trained by using low-resolution elevation data samples and the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points as inputs, and high-resolution elevation data samples as supervision targets. The loss function used for training should include at least the following: The first reconstruction loss term is used to minimize the difference between the predicted high-resolution elevation data output during model training and the high-resolution elevation data samples used as supervision targets. The second physical constraint loss term is used to constrain the terrain gradient field of the predicted high-resolution elevation data output during model training to maintain consistency with the terrain gradient field of the high-resolution elevation data samples used as the supervision target.

5. The gravity-guided near-field terrain correction method based on high-precision constraint points according to claim 4, characterized in that, The first reconstruction loss item adopts The loss function is calculated using the following formula: , in, For the reconstruction loss value, The high-resolution elevation data predicted during model training is the output of the model. This is a high-resolution elevation data sample. express Norm.

6. The gravity-guided near-field terrain correction method based on high-precision constraint points according to claim 4, characterized in that, The second physical constraint loss term is expressed by the following formula: ， in, This represents the physical constraint loss value. This represents the gradient computation operator. The high-resolution elevation data predicted during model training is the output of the model. This is a high-resolution elevation data sample. express Norm, The norm refers to the Euclidean norm.

7. A gravity-based near-field terrain correction system guided by high-precision constraint points, characterized in that, include: The data acquisition module is used to acquire low-resolution elevation data covering the near-field terrain correction area, and to acquire the plane coordinates and elevation values ​​of sparsely distributed high-precision constraint points within the near-field terrain correction area. The model inference module is used to input the low-resolution elevation data and the plane coordinates and elevation values ​​of the high-precision constraint points into a pre-trained elevation data super-resolution reconstruction model to obtain predicted high-resolution elevation data for near-field terrain correction. The terrain correction calculation module is used to calculate the near-field terrain correction value of the measuring point using the predicted high-resolution elevation data and the prism terrain correction algorithm.

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