Airborne gravity correction method and system based on ground sparse constraints and storage medium
Patent Information
- Application Number
- CN202611301352.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2026-08-26
- Publication Date
- 2026-09-25
AI Technical Summary
[0007]本发明提供了一种基于地面稀疏约束的航空重力校正方法、系统及存储介质，拟解决现有技术无法完整保留研究区高频精细地质异常、无法在稀疏地面控制点条件下稳定统一全域重力基准的技术问题
1.本发明摒弃一步式空地联合等效源反演的长短波耦合同步求解、依赖正则化平滑压制病态的固有模式，采用分段两步解耦反演架构；第一步仅依托全域海量航空测点开展无正则化迭代建模，完整保留研究区矿体、断裂、浅部构造的全部中高频精细重力信号；第二步仅借助稀疏地面控制点对模型长波低频分量做限制性微调，严格锁定中高频地质单元不发生改动，从数据处理底层规避正则化约束造成的细节抹平失真。
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Abstract
Description
Technical Field
[0001] This application belongs to the field of airborne gravity measurement data correction and processing technology, and more specifically, relates to airborne gravity correction methods, systems and storage media based on ground sparse constraints. Background Technology
[0002] During airborne gravity measurements, factors such as instrument zero-point temperature drift, residual Ertworth correction, flight altitude and attitude disturbances, slow platform tilt drift, and inconsistent calibration across multiple flights can cause systemic long-wave reference shifts across the entire region. These shifts directly lead to step misalignments in survey line splicing and inaccurate gravity references throughout the area, reducing the accuracy of geological interpretation and mineral exploration results.
[0003] Currently, the industry mainly uses three types of calibration methods, but each has its own inherent limitations: The first category is pure airborne self-calibration methods, including the cross-point polynomial adjustment method and the repeated line detection and correction method. These two methods rely solely on the airborne observation data for correction. The repeated line correction is mainly used to eliminate gravimeter grid errors and linear drift of forward and reverse lines. The cross-point adjustment focuses on eliminating relative zone deviations within a single line. However, both lack high-precision ground gravity true values as absolute benchmark constraints, making it difficult to achieve a unified gravity benchmark across the entire study area. In large-area, multi-batch airborne measurement scenarios, it is still difficult to avoid the problem of global long-wavelength offset.
[0004] The second type is the one-step air-ground joint equivalent source inversion method. This method combines aerial observation data with sparse ground control points to jointly model and synchronously invert the equivalent density long, thereby anchoring the absolute gravity benchmark. However, its core drawback is that long-wave system drift and mid-to-high frequency geological signals are coupled in the solution. When the ground control points are extremely sparse, the inversion equation is highly ill-conditioned, and strong regularization constraints must be introduced to suppress the oscillation of the solution. This not only smooths out or even erases fine gravity anomalies such as ore bodies and faults, but also requires repeated manual adjustment of regularization parameters, which seriously restricts the ability of automated batch processing.
[0005] The third category is frequency domain filtering and removal-recovery reference field preprocessing methods. These methods are usually used as auxiliary means and cannot effectively distinguish between long-wave geological signals of the real regional base and false system drift introduced by the instrument. They are prone to accidentally deleting geologically significant background field information. At the same time, because they do not support absolute reference constraints, this method cannot independently complete the normalization of the global gravity reference.
[0006] In summary, the existing technology system cannot simultaneously meet the three core requirements: it cannot fully preserve the high-frequency and detailed geological anomalies of the study area, it cannot stably unify the absolute gravity benchmark across the entire region under the condition of sparse ground control points, and it cannot achieve automated batch correction without human intervention throughout the entire process. Summary of the Invention
[0007] This invention provides an airborne gravity correction method, system, and storage medium based on ground sparse constraints, aiming to solve the technical problems of existing technologies being unable to fully preserve high-frequency fine geological anomalies in the study area and unable to stably unify the global gravity benchmark under sparse ground control point conditions.
[0008] On the one hand, the present invention provides an airborne gravity correction method based on ground sparse constraints, comprising the following steps: S1. Acquire raw airborne gravity observation data and perform preprocessing operations to obtain standardized airborne gravity anomaly data; using only the standardized airborne gravity anomaly data as the solution input, perform iterative solution by combining depth weighting without introducing regularization constraints to construct an initial three-dimensional equivalent source reference model; S2. Obtain sparsely and discretely distributed ground measured gravity data in the study area, use the initial three-dimensional equivalent source reference model as the initial value for optimization, introduce the inversion region control matrix to limit the adjustable range of the equivalent source model, perform constrained optimization solution, and obtain the optimized three-dimensional equivalent source model. S3. Using the optimized three-dimensional equivalent source model, perform global gravity forward modeling calculations at all airborne measurement points to obtain and output corrected airborne gravity anomaly data.
[0009] Preferably, the preprocessing operation includes the following steps: The raw airborne gravity observation data were sequentially processed with Etworth correction, normal gravity correction, free air altitude correction, and high-frequency turbulence noise filtering.
[0010] Preferably, when constructing the initial three-dimensional equivalent source reference model, an airborne gravity forward modeling kernel matrix is first constructed based on the spatial geometric relationship between the equivalent source mesh and the airborne measurement points. The airborne gravity forward modeling kernel matrix is used as the calculation basis for iterative solution, and a depth weighting factor is used to complete the iterative solution without regularization conditions.
[0011] Preferably, the inversion region control matrix is used to divide the model units of the equivalent source model into adjustable units and locked units; The adjustable unit corresponds to the long-wavelength component of the equivalent source model, while the locked unit corresponds to the mid-to-high frequency component of the equivalent source model.
[0012] Preferably, when performing constrained optimization, the measured ground gravity data is used as the fitting target, and the parameters of the adjustable units in the equivalent source model are corrected only, while the parameters of the locked units remain unchanged from the initial three-dimensional equivalent source reference model.
[0013] On the other hand, the present invention provides an airborne gravity correction system based on ground sparse constraints, including a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements an airborne gravity correction method based on ground sparse constraints as described in the present invention.
[0014] On the other hand, the present invention provides a computer-readable storage medium, characterized in that the computer-readable storage medium stores a computer program, which, when executed by a processor, implements an airborne gravity correction method based on ground sparse constraints as described in the present invention.
[0015] The beneficial effects of this invention include: 1. This invention abandons the inherent mode of one-step air-ground joint equivalent source inversion, which involves simultaneous solution of long and short waves and relies on regularization to smooth out ill-conditioned phenomena. Instead, it adopts a segmented two-step decoupled inversion architecture. The first step relies solely on a massive number of airborne measurement points across the entire region to conduct unregularized iterative modeling, fully preserving all the fine mid-to-high frequency gravity signals of the ore bodies, faults, and shallow structures in the study area. The second step uses only sparse ground control points to make restrictive fine adjustments to the long-wave low-frequency components of the model, strictly locking the mid-to-high frequency geological units to remain unchanged, thus avoiding the distortion caused by regularization constraints from the bottom layer of data processing.
[0016] 2. The self-calibration methods of this invention, such as regional cross-point adjustment and repeated survey line correction, rely solely on the data of the airborne system itself. Using sparse discrete ground gravity measurement data as an absolute reference constraint, a complete global airborne equivalent source prior field is first constructed. Then, long-wave system drift is locally calibrated, and all data in the region are uniformly normalized to a unified gravity reference. This eliminates the global systematic offset caused by instrument zero-point temperature drift, residual Ertworth correction, slow platform tilt drift, and inconsistency of zero points when multiple flights are started. After correction, all survey lines are seamlessly connected without reference jumps.
[0017] 3. This invention separates airborne global modeling and ground benchmark calibration into two independent steps. It uses a complete non-regular airborne equivalent source model as a stable prior. The sparse ground control points only slightly modify the long-wavelength component of the model and will not cause global disturbance to the overall underground density. Theoretical model tests show that even in the extreme sparse case where the ratio of ground control points to airborne measurement points is as low as 1:100, the iterative solution still converges stably, and the fitting residual of sparse ground control points is much lower than that of the one-step simultaneous inversion method.
[0018] 4. Traditional correction methods all involve a large number of manual parameter adjustments. For example, cross-point adjustment requires manually selecting the polynomial order, repeated survey line correction requires manually matching forward and backward profiles and fitting grid drift functions, and one-step air-ground joint inversion requires repeated calculation of regularization intensity coefficients. In contrast, the first step of this invention eliminates all regularization constraints, eliminating the need to adjust regularization hyperparameters. The second step relies on the depth weighting matrix and the inversion area control matrix to achieve adaptive constraints. Finally, the global forward modeling benchmark correction is a fixed difference operation, eliminating the need to fit drift functions piecewise by survey line or block.
[0019] 5. This invention uses two sets of full-coverage equivalent source models to obtain the differential drift length through global dual forward modeling, generating a seamless and continuous unified two-dimensional correction amount for the entire region. It can simultaneously eliminate all long-wavelength system deviations such as instrument zero-point drift, flight altitude / attitude disturbance error, platform tilt drift, and inconsistency of references among multiple flights. It can stably output standardized airborne gravity results in various complex terrain aerial survey scenarios such as mountains and basins, and has stronger adaptability to working conditions. Attached Figure Description
[0020] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.
[0021] Figure 1 The above is an overall flowchart provided for an embodiment of the present invention.
[0022] Figure 2 This is a schematic diagram of a three-dimensional equivalent source density model provided in an embodiment of the present invention.
[0023] Figure 3 This is a comparison diagram of measurement points provided in an embodiment of the present invention, wherein... Figure 3 Part 'a' in the diagram represents a schematic diagram of the location of airborne gravity measurement points, which will be referred to below as... Figure 3 a; Figure 3 Part b in the diagram represents a schematic diagram of the locations of sparse control points on the ground, which will be referred to hereafter as... Figure 3 b.
[0024] Figure 4 A comprehensive comparison diagram provided for embodiments of the present invention, wherein Figure 4 Part 'a' in the figure represents the theoretical airborne gravity forward model, hereinafter referred to as... Figure 4 a; Figure 4 Part 'b' in the diagram represents the long-wavelength system deviation plot, hereinafter referred to as... Figure 4 b; Figure 4 Part c in the figure represents the airborne gravity map containing systematic bias, hereinafter referred to as... Figure 4 c); Figure 4 The 'd' part in the figure represents the sparse gravity map of the ground, hereinafter referred to as... Figure 4 d; Figure 4 The 'e' part in the figure represents the ground gravity extension to the airborne gravity map, hereinafter referred to as... Figure 4 e; Figure 4 In this context, 'f' represents the modified gravity diagram of this invention, which will be referred to thereafter as... Figure 4 f; Figure 4 The 'g' part in the graph represents a comparison of gravity curves, which will be referred to as 'g' hereafter. Figure 4 g, where Figure 4 The black line in f is Figure 4 The planar position of the curve in g. Detailed Implementation
[0025] To make the technical problems, technical solutions, and beneficial effects to be solved by this application clearer, the following detailed description is provided in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this application.
[0026] Example 1 See Figure 1 As shown, this embodiment provides an airborne gravity correction method based on ground sparse constraints. Based on a piecewise two-step decoupled inversion architecture, it first iteratively constructs a high-precision reference equivalent source model using massive airborne data, then optimizes and corrects the long-wavelength reference deviation of the model using sparse ground gravity data, and finally achieves reference drift correction through global forward modeling. Specifically, it includes the following steps: S1. Acquire raw airborne gravity observation data, and sequentially perform Ertworth correction, normal gravity correction, free air altitude correction, and high-frequency turbulence noise filtering to eliminate interference from flight attitude, normal gravity field, flight altitude differences, and high-frequency random noise, thereby obtaining standardized airborne gravity anomaly data.
[0027] The three-dimensional equivalent source mesh is generated based on the study area (used only to represent the measurement area), and the steps included are exemplary: The horizontal dimension of the grid is determined based on the scale of the airborne gravity measurement map. Vertical dimension of the grid: Take 1 / 2 of the average horizontal side length of the grid; Planar subdivision range: The subdivision area of the grid should be slightly larger than the coverage area of the measured data, usually extending outward by 5 to 10 grid cells; Vertical mesh count: 1 / 2 to 1 / 3 of the number of horizontal meshes in the two sets.
[0028] Then, combining the spatial coordinates of all airborne measurement points, and based on the spatial geometric relationship between the equivalent source grid cells and the airborne measurement points, an airborne gravity forward modeling kernel matrix is constructed as the computational basis for equivalent source inversion. The specific steps for constructing the airborne gravity forward modeling kernel matrix are as follows: In a Cartesian coordinate system, the X and Y axes are defined as horizontal, and the Z axis is vertically downward, representing east, north, and underground depth, respectively; let... For arbitrary volume units within an abnormal body The coordinates of the mass unit are then... At any point in space Gravitational potential formula : ; In the formula: Let gravitational constant be denoted as , and its magnitude is . , For mass element to any point in space The distance; among which These represent the values corresponding to the X, Y, and Z axis coordinates, respectively. These represent the values corresponding to the X, Y, and Z axis coordinates, respectively. Gravitational potential formula The formula for gravitational potential is obtained by integrating the subsurface half-space using a prism. : ; In the formula: This indicates the spatial density distribution of the underground semi-space; and They are single-layer dielectrics along direction and along Half the length of the direction; The thickness of the underground semi-space; Indicates the depth of the top surface.
[0029] Finally, based on the prism formula, the forward modeling coefficients for each measurement point corresponding to each grid are calculated to obtain the airborne gravity forward modeling kernel matrix.
[0030] In this embodiment, only airborne gravity anomaly data is used as the sole observation constraint. An unregularized iterative solution algorithm based on depth-weighted constraints is employed to construct the initial three-dimensional equivalent source reference model, where the solution equations are as follows: ; In the formula: Represents the forward modeling kernel matrix of airborne gravity; This represents the three-dimensional equivalent source density vector to be solved; This represents the preprocessed airborne gravity anomaly data; This represents the depth-weighted matrix that matches airborne gravity data. For a diagonal matrix, the elements on its diagonal are... Depth-weighted function In the formula: This indicates finding the absolute value. Indicates the depth of the grid in space. This represents the average height of the measuring point; then, the above formula is solved using the conjugate gradient. .
[0031] Traditional equivalent source inversion methods are limited by insufficient observation data and ill-conditioned equations, necessitating the introduction of regularization constraints to suppress solution oscillations. However, regularization smooths out mid-to-high frequency gravity anomalies corresponding to ore bodies, faults, and local structures, leading to the loss of geological details. In this embodiment, relying on the massive, high-density, and spatially comprehensive characteristics of airborne gravity measurement points, the spatial completeness of the observation data supports the stable solution of the equations. Therefore, regularization constraints are completely eliminated, preserving all mid-to-high frequency geological anomaly information in the study area. Simultaneously, a depth-weighted mechanism is introduced to offset the inherent physical characteristic of rapid attenuation of the potential field signal with increasing depth, ensuring the stability of deep source solutions while maintaining the detail fidelity of shallow geological anomalies. The initial three-dimensional equivalent source reference model obtained in this embodiment fully preserves the mid-to-high frequency geological anomalies in the study area, but it also carries a systematic benchmark deviation of the entire longwave system caused by factors such as instrument zero-point temperature drift, residual Ertworth correction, and inconsistent calibration across multiple flights. This deviation needs to be corrected in subsequent steps.
[0032] S2. Obtain high-precision ground-measured gravity data with sparse and discrete distribution within the study area. After unifying the coordinate system and elevation datum, coarse discrepancies are eliminated; the initial three-dimensional equivalent source reference model vector obtained in step S1 is used. As the initial model for conjugate gradient inversion, ground coefficient gravity anomaly data are used as the sole observation constraint. A modified equivalent source model is constructed using an unregularized iterative solution algorithm based on depth-weighted constraints. The solution equations are as follows: ; In the formula: This is the ground gravity forward modeling kernel matrix; The three-dimensional equivalent source density model to be corrected; To match the depth weighting matrix of ground gravity data; The inversion region control matrix is used to correct low-frequency anomalies by fine-tuning the control model. It is a diagonal matrix, with diagonal elements set to 1 by default. Only the terms corresponding to the shallow part of the model are set to 0, typically constraining only the 2-5 layers of the model closest to the surface. Then, the above formula is solved using the conjugate gradient. .
[0033] By solving the constraint optimization problem, only the long-wave systematic deviations caused by instrument zero drift and flight reference offset in the initial three-dimensional equivalent source reference model are corrected, while the inherent mid-to-high frequency geological anomaly information of the airborne data is preserved, resulting in the optimized three-dimensional equivalent source model. .
[0034] S3. Using the corrected three-dimensional equivalent source model obtained in step S2. Gravity forward modeling was performed at all airborne measurement points to obtain optimized forward modeling results, i.e., corrected airborne gravity anomaly data. The calculation formula is as follows: ; In the formula: This is the final corrected airborne gravity anomaly data.
[0035] This invention separates airborne global modeling and ground benchmark calibration into two independent steps. A complete, non-regular airborne equivalent source model serves as a stable prior. Sparse ground control points only slightly modify the long-wavelength components of the model, without causing global disturbances to the overall subsurface density. Theoretical model tests show that even in extremely sparse conditions where the ratio of ground control points to airborne measurement points is as low as 1:100, the iterative solution still converges stably, and the fitting residuals of sparse ground control points are significantly lower than those of the one-step simultaneous inversion method. Specific model test examples are as follows: See Figure 2 As shown in Table 1, the theoretical model for this numerical experiment was constructed using a single rectangular density anomaly. The spatial distribution of the magnetic body and its magnetic susceptibility parameters are shown in Table 1. Table 1 Parameters of the Inclined Plate-like Body Model
[0036] In this embodiment, the underground space of the study area was finely divided using a grid scheme of 81×99×30, resulting in 240,570 cubic computational cells. The cuboid anomaly in the model has dimensions of 500m×500m×250m; see [link / reference] Figure 3 As shown, the experimental observation points are divided into aerial observation (see...). Figure 3 (as shown in a) and sparse ground observations (see...) Figure 3 (as shown in b) There are two categories. Among them, there are a total of 8,020 airborne gravity observation points with a plane spacing of 500m×500m and a uniform observation elevation of 500m. There are a total of 61 ground sparse control points with a plane spacing of 5,000m×7,500m and an observation elevation of 0m. According to statistics, the ratio of ground control points to airborne measurement points is only 1:131, which is better than the extreme sparse observation condition of 1:100. It can effectively simulate the actual operation scenario of extremely sparse ground reference points.
[0037] See Figure 4As shown, this embodiment obtains the theoretical airborne gravity anomaly field (e.g., by forward modeling the theoretical model constructed above) through the above-constructed method. Figure 4 As shown in a), the result represents the standard theoretical gravity field, and the anomaly exhibits a central ring-shaped distribution characteristic, matching the preset theoretical model; the systematic deviation field of the airborne gravity system (as shown in a) was obtained through simulation calculations. Figure 4 As shown in b), this deviation field exhibits an east-west wavy undulation characteristic, with no obvious anomalous response in the north-south direction. It can effectively simulate the systematic errors generated by different operation cycles and different survey lines of airborne gravity. By superimposing and fusing this systematic deviation field with the theoretical gravity field, airborne gravity anomaly data containing the systematic deviation can be constructed (e.g., Figure 4 (as shown in c), thus restoring the true data state of actual airborne gravity field measurements.
[0038] Meanwhile, this invention obtains sparse ground gravity anomaly data by calculating them separately. Figure 4 As shown in d), and airborne gravity anomaly data obtained by extending the ground gravity anomaly upwards by 500m (see d). Figure 4 As shown in e), a comparison with the standard theoretical airborne gravity anomaly reveals significant differences in the anomaly morphology and field value characteristics between the two sets of data. They cannot be directly used for constraint correction and accuracy optimization of airborne gravity data, exhibiting obvious application limitations.
[0039] This invention utilizes sparse ground gravity anomalies (such as...) Figure 4 (as shown in d) is high-precision reference data. For airborne gravity data containing systematic biases (such as...) Figure 4 c) Perform deviation correction processing to obtain the optimized airborne gravity anomaly results (e.g., Figure 4 f、 Figure 4 As shown in g), based on the optimized airborne gravity anomaly results, it can be seen that the optimized airborne gravity anomaly field (i.e. the corrected airborne gravity anomaly field) is in high agreement with the theoretical gravity field, effectively eliminating false anomalies introduced by systematic errors in the airborne gravity system, and significantly improving the accuracy and reliability of airborne gravity observation data.
[0040] Example 2 This embodiment provides an airborne gravity correction system based on ground sparse constraints, including a memory, a processor, and a computer program stored in the memory and executable on the processor; when the processor executes the computer program, it implements all the steps of the airborne gravity correction method based on ground sparse constraints described in Embodiment 1 above.
[0041] Optionally, the system also includes a data input interface and a data output interface: the data input interface is used to import raw airborne gravity observation data and ground-measured gravity data; the data output interface is used to output corrected airborne gravity anomaly data; the system can be deployed on various hardware devices with numerical computing capabilities, such as desktop computers and industrial servers, to meet the batch processing needs of airborne gravity data in research areas of different sizes.
[0042] Example 3 This embodiment provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements all the steps of the airborne gravity correction method based on ground sparse constraints described in Embodiment 1 above.
[0043] The computer-readable storage media include, but are not limited to, physical storage media such as hard disks, optical disks, flash memory, and solid-state drives, as well as distributed storage media in network servers.
[0044] The above are merely preferred embodiments of this application and are 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. An airborne gravity correction method based on ground sparse constraints, characterized in that, Includes the following steps: S1. Acquire raw airborne gravity observation data and perform preprocessing operations to obtain standardized airborne gravity anomaly data; use only the standardized airborne gravity anomaly data as the solution input, combine depth weighting to perform iterative solution, and construct an initial three-dimensional equivalent source reference model; S2. Obtain sparsely and discretely distributed ground measured gravity data in the study area, use the initial three-dimensional equivalent source reference model as the initial value for optimization, introduce the inversion region control matrix to limit the adjustable range of the equivalent source model, perform constrained optimization solution, and obtain the optimized three-dimensional equivalent source model. S3. Using the optimized three-dimensional equivalent source model, perform global gravity forward modeling calculations at all airborne measurement points to obtain and output corrected airborne gravity anomaly data.
2. The airborne gravity correction method based on ground sparse constraints according to claim 1, characterized in that, The preprocessing operation includes the following steps: The raw airborne gravity observation data were sequentially processed with Etworth correction, normal gravity correction, free air altitude correction, and high-frequency turbulence noise filtering.
3. The airborne gravity correction method based on ground sparse constraints according to claim 1, characterized in that, When constructing the initial three-dimensional equivalent source reference model, the airborne gravity forward modeling kernel matrix is first constructed based on the spatial geometric relationship between the equivalent source mesh and the airborne measurement points. The airborne gravity forward modeling kernel matrix is used as the calculation basis for iterative solution, and the iterative solution without regularization conditions is completed in conjunction with the depth weighting factor.
4. The airborne gravity correction method based on ground sparse constraints according to claim 1, characterized in that, The inversion region control matrix is used to divide the model units of the equivalent source model into adjustable units and locked units; The adjustable unit corresponds to the long-wavelength component of the equivalent source model, while the locked unit corresponds to the mid-to-high frequency component of the equivalent source model.
5. The airborne gravity correction method based on ground sparse constraints according to claim 4, characterized in that, When performing constrained optimization, the measured ground gravity data is used as the fitting target. Only the adjustable elements in the equivalent source model are modified, while the parameters of the locked elements remain unchanged from the initial three-dimensional equivalent source reference model.
6. An airborne gravity correction system based on ground sparse constraints, characterized in that, It includes a memory and a processor, wherein the memory stores a computer program, and the processor executes the computer program to implement the airborne gravity correction method based on ground sparse constraints as described in any one of claims 1 to 5.
7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the airborne gravity correction method based on ground sparse constraints as described in any one of claims 1 to 5.