A method and system for joint imaging of gravity and magnetic data based on downward continuation and gramian constraint

Abstract

This invention discloses a joint imaging method for gravity and magnetic data based on downward continuation and Gramian constraints. The method involves subdividing the subsurface space into subsurface grid cells according to the spatial scale of the target region, and calculating the magnetic and gravity inversion kernel matrices based on these cells. Preset downward continuation depth values, magnetization models, residual density models, and the maximum number of iterations are used. The predicted magnetic and gravity data fields are calculated, and the residuals of the observed and predicted fields are then calculated and converted into updates for the physical property distributions of magnetization and residual density. The gradient of the Gramian function composed of magnetization and residual density is introduced to update the magnetization and residual density models. The joint imaging model of magnetic and gravity data is then output. This invention utilizes the complementarity between different geophysical fields, reducing ambiguity and significantly improving computational speed compared to joint inversion of potential field data.

Description

Technical Field

[0001] This invention relates to the field of geophysical potential field exploration, and in particular to a joint imaging method based on downward continuation and Gramian constraint gravity and magnetic data. Background Technology

[0002] Potential field inversion is a crucial step in potential field exploration. Its significance lies in using potential field data from surface or aerial observations to infer the physical property distribution characteristics (magnetization and residual density distribution) of the subsurface medium, thus providing quantitative evidence for geological interpretation and resource exploration. One of its challenges is the strong ambiguity inherent in inversion. Multiple geophysical field observations and the addition of prior information are the main methods to address this issue. Therefore, employing a combined inversion method using gravity and magnetic data is an important approach to reducing the ambiguity of inversion. Inversion requires solving large sets of underdetermined equations. When the subsurface grid is densely subdivided, a large amount of complex mathematical calculations are required, which significantly limits the computational speed of inversion solutions. Compared to potential field inversion, potential field imaging is simpler and faster, and can achieve similar results to some extent. The principle of potential field imaging can be briefly described as follows: the potential field data is extended, and the conversion relationship between the extended field and physical property values ​​(residual density or magnetization values) is used to convert the imaging field (i.e., the extended field at different distances) into physical property distribution results. Therefore, by combining the downward extension of potential field data and applying the joint inversion approach to rapid imaging of potential field data, we can not only speed up the calculation, but also comprehensively utilize the correlation between different physical properties contained in the gravitational field and magnetic field, thereby reducing multiple solutions and enhancing resolution. Summary of the Invention

[0003] In view of the aforementioned existing problems, this invention utilizes the downward continuation of the potential field to perform downward continuation imaging of the magnetic and gravitational fields. Then, based on the frequency domain transformation relationship, the imaging field is converted into a property distribution result. Simultaneously, a Gramian constraint operator constructed from residual density and magnetization is introduced. Leveraging the complementarity between these different geophysical fields, a relatively unified physical model is constructed to reduce ambiguity. To solve the above technical problems, this invention provides the following technical solution:

[0004] A joint imaging method for gravity and magnetic data based on downward continuation and Gramian constraint is characterized by the following steps;

[0005] S1 divides the underground grid space according to the spatial scale of the target area to obtain the underground grid cells of the target area, and calculates the magnetic inversion kernel matrix and gravity inversion kernel matrix based on the underground grid cells of the target area.

[0006] S2 presets the downward extension depth, magnetization model, residual density model, and maximum number of iterations based on the underground grid cells of the target area.

[0007] S3 is based on the magnetization model and the residual density model. It combines the magnetic inversion kernel matrix and the gravity inversion kernel matrix to calculate the magnetic data prediction field and the gravity data prediction field at the observation location. It also calculates the magnetic data residual between the actual magnetic data observation field and the magnetic data prediction field, as well as the gravity data residual between the actual gravity data observation field and the gravity data prediction field.

[0008] S4 uses the Tikhonov regularization downward continuation (TRDC) method to calculate the downward continuation fields of the magnetic data residuals at different depth positions and the downward continuation fields of the gravity data residuals at different depth positions. Then, based on the frequency domain transformation relationship, the downward continuation fields of the magnetic data residuals at different depth positions are converted into the update quantities of the magnetization intensity property distribution, and the downward continuation fields of the gravity data residuals at different depth positions are converted into the update quantities of the residual density property distribution.

[0009] S5 obtains separate imaging models for magnetic data and gravity data based on the update amounts of the physical property distribution of magnetization and the physical property distribution of residual density, respectively. The gradient of the Gramian function composed of magnetization and residual density is introduced into the separate imaging models for magnetic data and gravity data to obtain the updated magnetization model and residual density model.

[0010] S6 determines whether the updated magnetization model and residual density model have reached the maximum number of iterations. If so, it outputs the joint imaging model of magnetic and gravity data.

[0011] A joint imaging system for gravity and magnetic data based on downward continuation and Gramian constraints is characterized by comprising a grid space construction module, a parameter setting module, a residual calculation module, a property distribution update module, a model update module, an iteration judgment module, and an image generation module.

[0012] The grid space construction module is used to divide the underground grid space according to the spatial scale of the target area to obtain the underground grid cells of the target area, and calculate the magnetic inversion kernel matrix and gravity inversion kernel matrix based on the underground grid cells of the target area.

[0013] The parameter setting module is used to preset the downward extension depth value, magnetization intensity model, residual density model and maximum number of iterations based on the underground grid cells of the target area.

[0014] The residual calculation module is used to calculate the magnetic data prediction field and gravity data prediction field at the observation location based on the magnetization intensity model, the residual density model, and the magnetic inversion kernel matrix and gravity inversion kernel matrix. It also calculates the magnetic data residual between the actual magnetic data observation field and the magnetic data prediction field, as well as the gravity data residual between the actual gravity data observation field and the gravity data prediction field.

[0015] The property distribution update module is used to calculate the downward extension field of the magnetic data residual at different depth positions and the downward extension field of the gravity data residual at different depth positions using the TRDC method. Then, based on the frequency domain conversion relationship, the downward extension field of the magnetic data residual at different depth positions is converted into the property distribution update amount of magnetization intensity, and the downward extension field of the gravity data residual at different depth positions is converted into the property distribution update amount of residual density.

[0016] The model update module is used to obtain separate imaging models for magnetic data and gravity data based on the update amount of the physical property distribution of magnetization intensity and the update amount of the physical property distribution of residual density, respectively. The gradient of the Gramian function composed of magnetization intensity and residual density is introduced into the separate imaging models for magnetic data and gravity data to obtain the updated magnetization intensity model and residual density model.

[0017] The iteration judgment module is used to determine whether the updated magnetization intensity model and residual density model have reached the maximum number of iterations. If so, it outputs the joint imaging model of magnetic data and gravity data.

[0018] The image generation module is used to generate images based on the joint imaging model of gravity and magnetic data to obtain the joint imaging results of magnetic data and gravity data.

[0019] The beneficial effects of this invention are as follows: By utilizing the high resolution of the downward continuation field of potential field data and the Gramian constraint operator, and employing joint imaging, it is equivalent to constraining traditional individual imaging, reducing the ambiguity of potential field imaging, and obtaining gravity and magnetic data imaging results with clear boundaries. Furthermore, compared to joint inversion of potential field data, the joint imaging technique provided by this invention, based on the frequency domain downward continuation method, avoids solving large linear equation systems, significantly reducing computation time. Attached Figure Description

[0020] Figure 1 This is a flowchart of the present invention;

[0021] Figure 2 For magnetic data models;

[0022] Figure 3 For gravity data models;

[0023] Figure 4 This is magnetic observation data;

[0024] Figure 5 This is gravity observation data;

[0025] Figure 6 This is an imaging result based solely on magnetic data;

[0026] Figure 7 This is an image result based solely on gravity data;

[0027] Figure 8 This is the result of combined magnetic data and gravity imaging.

[0028] Figure 9 This is the result of combined gravity and magnetic imaging using gravity data.

[0029] Figure 10 This is a schematic diagram of the structure of the present invention. Detailed Implementation

[0030] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the specific embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0031] Example 1

[0032] like Figure 1 As shown, this invention provides an embodiment of a joint imaging method for gravity and magnetic data based on downward continuation and Gramian constraint. Figure 2 and Figure 3 The magnetization and residual density models are shown. Rectangular block 1 (left) has a depth range of 100–300 m and an easting range of 200–400 m. Rectangular block 2 (right) has a depth range of 100–300 m and an easting range of 600–800 m. Both rectangular blocks have a magnetization of 10 A / m and a residual density of 1 g / cm³. The overall magnetization direction is aligned with the geomagnetic field direction, the geomagnetic tilt is 45°, and the geomagnetic declination is 0°. The observation data size is 51 × 51, with data intervals of 20 m × 20 m. Anomalies in the gravity and magnetic data observations are shown below. Figure 4 and Figure 5 As shown.

[0033] A joint imaging method for gravity and magnetic data based on downward continuation and Gramian constraint includes the following steps;

[0034] S1 divides the underground grid space according to the spatial scale of the target area to obtain the underground grid cells of the target area, and calculates the magnetic inversion kernel matrix and gravity inversion kernel matrix based on the underground grid cells of the target area.

[0035] S2 presets the downward extension depth, magnetization model, residual density model, and maximum number of iterations based on the underground grid cells of the target area.

[0036] S3 is based on the magnetization model and the residual density model. It combines the magnetic inversion kernel matrix and the gravity inversion kernel matrix to calculate the magnetic data prediction field and the gravity data prediction field at the observation location. It also calculates the magnetic data residual between the actual magnetic data observation field and the magnetic data prediction field, as well as the gravity data residual between the actual gravity data observation field and the gravity data prediction field.

[0037] S4 uses the Tikhonov regularization downward continuation (TRDC) method to calculate the downward continuation fields of the magnetic data residuals at different depth positions and the downward continuation fields of the gravity data residuals at different depth positions. Then, based on the frequency domain transformation relationship, the downward continuation fields of the magnetic data residuals at different depth positions are converted into the update quantities of the magnetization intensity property distribution, and the downward continuation fields of the gravity data residuals at different depth positions are converted into the update quantities of the residual density property distribution.

[0038] S5 obtains separate imaging models for magnetic data and gravity data based on the update amounts of the physical property distribution of magnetization and the physical property distribution of residual density, respectively. The gradient of the Gramian function composed of magnetization and residual density is introduced into the separate imaging models for magnetic data and gravity data to obtain the updated magnetization model and residual density model.

[0039] S6 determines whether the updated magnetization model and residual density model have reached the maximum number of iterations. If so, outputs the joint imaging model of magnetic data and gravity data; otherwise, returns to step S3.

[0040] S7 inputs the joint imaging model of magnetic and gravity data into the image generation module to obtain the joint imaging results of magnetic data and gravity data.

[0041] A joint imaging method for gravity and magnetic data based on downward continuation and Gramian constraints, wherein the subsurface grid space is subdivided according to the spatial scale of the target area to obtain subsurface grid cells of the target area, and the specific method for calculating the magnetic inversion kernel matrix and gravity inversion kernel matrix based on the subsurface grid cells of the target area is as follows:

[0042] Based on the spatial scale of the target area, the three-dimensional range of the underground grid is defined, and the grid size is set to obtain the underground grid cells of the target area. Based on the underground grid cells of the target area, the magnetic inversion kernel matrix is ​​calculated according to the gravity and magnetic anomaly response of the cuboid cells. and gravity inversion kernel matrix ;

[0043] In this embodiment, the underground grid is divided into 1000(x-)×1000(y-)×500(z-) m sections, with a grid size of 20(x-)×20(y-)×20(z-) m. x- represents the easting axis, y- represents the northing axis, z- represents the depth axis, and m represents the unit meter. There are a total of 51×51×25 = 65025 grids. The magnetic inversion kernel matrix is ​​calculated based on the gravity and magnetic anomaly response of the cuboid elements. and gravity inversion kernel matrix ;

[0044] The core function of this step is to build the mathematical foundation for forward modeling. Its purpose is to discretize the continuous underground space into regular three-dimensional grid cells and calculate the physical response of each cell to the surface observation point (i.e., the kernel matrix) to provide underground physical parameters (magnetization intensity, residual density) for subsequent inversion calculations.

[0045] A joint imaging method for gravity and magnetic data based on downward continuation and Gramian constraints, which predetermines the downward continuation depth, initial magnetization model, initial residual density model, and maximum number of iterations for the subsurface grid cells of the target area, is as follows:

[0046] The downward extension depth is preset based on the underground grid cells of the target area, and an initial magnetization model is preset. Initial residual density model And the maximum number of iterations, n.

[0047] This invention uses a subsurface grid of the target area, extending downwards at depths ranging from 10 to 490 m, with each 20 m interval, for a total of 25 downward extensions. An initial magnetization model is then established. and the initial residual density model All values ​​are 0, and the maximum number of iterations is set to n=30.

[0048] The core function of setting initialization parameters is to transform the static mathematical foundation output from step S1 into a dynamically iterative inversion system by scientifically defining the initial physical property model, the extended depth sequence, and the iterative control parameters. Specifically: This step first initializes the magnetization and residual density models based on the zero-value assumption (e.g., setting the global initial value to zero), providing an iterative starting point for subsequent Gramian-constrained joint updates. Simultaneously, by setting the downward extended depth sequence, it defines the depth and resolution gradient of the residual field's downward propagation, ensuring the recovery of physical property distributions at different depths. Furthermore, setting the maximum number of iterations (e.g., n=30) provides a balance between computational efficiency and convergence accuracy in the inversion process. Ultimately, it provides an updatable physical property model and iterative control conditions for subsequent steps, enabling the system to gradually approximate the real underground structure through iterative iterations.

[0049] A joint imaging method for gravity and magnetic data based on downward continuation and Gramian constraints is proposed. This method calculates the predicted magnetic and gravity data fields at the observation location using a magnetization model and a residual density model, combined with magnetic and gravity inversion kernel matrices. The specific method for calculating the magnetic data residuals between the observed and predicted magnetic data fields, and the gravity data residuals between the observed and predicted gravity data fields at the actual location, is as follows:

[0050] Calculate magnetic data to predict the field ;

[0051] (1)

[0052] Calculate gravity data to predict the field ;

[0053] (2)

[0054] In the formula, j is the iteration number. For the magnetization model of the j-th iteration, Let n be the residual density model for the j-th iteration, and n be the maximum number of iterations.

[0055] The residual of the magnetic data is obtained by subtracting the observed field from the predicted field of the actual magnetic data. ;

[0056] (3)

[0057] The residual of the gravity data is obtained by subtracting the observed gravity data field from the predicted gravity data field. ;

[0058] (4)

[0059] In the formula The observation field for actual location magnetic data, This is the actual location gravity data observation field.

[0060] The core function of calculating the residuals of magnetic and gravity data is to quantify the difference between the current model and the actual observation data, and to provide input for the downward extension of this difference through forward modeling. Specifically, this step first calculates the predicted field based on the current property model and kernel matrix, and then generates the residual field by subtracting the predicted field from the observed field. Its purpose is to provide an accurate input source for the downward extension of subsequent steps, and ultimately improve the convergence speed and accuracy of joint imaging.

[0061] A joint imaging method for gravity and magnetic data based on downward continuation and Gramian constraints is proposed. The method utilizes the Tikhonov regularized downward continuation method to calculate the downward continuation field of the magnetic data residuals at different depth locations. The specific method for calculating the downward continuation field of the gravity data residuals at different depth locations is as follows:

[0062] Based on the residuals of the magnetic data Based on the Tikhonov regularized downward continuation method, the frequency domain downward continuation field of magnetic data at depth h is obtained. for:

[0063] (5)

[0064] Based on the residuals of gravity data Based on the Tikhonov regularized downward continuation method, the frequency domain downward continuation field of gravity data at depth h is obtained. for:

[0065] (6)

[0066] Where u and v are the wave numbers in the x and y directions, respectively. It is the angular frequency. These are the downward extension filter coefficients for the magnetic data. These are the downward extension filtering coefficients for gravity data; all of these coefficients are determined based on the grid spacing of the measurement data. For the residuals of magnetic data The frequency domain response is obtained by calculating using a two-dimensional Fourier transform. Residuals of gravity data The frequency domain response is obtained by calculating using a two-dimensional Fourier transform. It is a natural constant.

[0067] The core function of calculating the downward continuation fields of magnetic data residuals and gravity data residuals at different depths is to map the residual fields output by S3 to different depths underground through frequency domain downward continuation technology and convert them into updated quantities of physical property parameters (magnetization and residual density). The purpose is to provide incremental information that directly reflects the location and physical property parameters of underground anomalies for subsequent steps, and to gradually approximate the real physical property model through iterative optimization, ultimately improving the depth resolution of joint imaging.

[0068] A joint imaging method for gravity and magnetic data based on downward continuation and Gramian constraints, according to the frequency domain transformation relationship, converts the downward continuation field of the magnetic data residual at different depth positions into the update quantity of the magnetization intensity property distribution, and converts the downward continuation field of the gravity data residual at different depth positions into the update quantity of the residual density property distribution. The specific method is as follows:

[0069] Based on the Tikhonov regularized downward continuation method, the response of the downward continuation residual field in the frequency domain at different depths can be obtained. Then, according to the following conversion formula between the frequency domain potential field and the property values, the imaging results composed of the continuation fields at different depths are converted into property distribution results:

[0070] The downward continuation field of the magnetic data residual at different depth locations is converted into the update quantity of the physical property distribution of magnetization intensity;

[0071] (7)

[0072] The gravity data residuals at different depth locations are converted into the physical property distribution update of the residual density by the downward extension field.

[0073] (8)

[0074] In the formula, This is a two-dimensional inverse Fourier transform. This represents the update amount of the physical property distribution of magnetization. This is the update amount for the physical property distribution of the remaining density. Where i is the vacuum permeability, and i is the imaginary unit. The wave number in the depth direction, P is the unit vector representing the direction of the geomagnetic field. M is the unit vector of the total magnetization direction. ,in It is the geomagnetic tilt angle. It is the magnetic declination. The total magnetization tilt angle, θ is the total magnetization deflection, and p is the gravitational constant.

[0075] The purpose of calculating the update of the physical property distribution of magnetic and gravity data is to provide directional correction guidance for iterative inversion. Its purpose is to convert the data residual (the difference between the observed field and the predicted field) into the adjustment range of physical property parameters (such as magnetization and residual density) by quantifying the deviation between the current model and the actual underground structure. This drives the model to gradually approach the true solution. At the same time, the incremental update strategy significantly reduces the computational cost and ensures that the inversion process converges to a high-precision solution while taking efficiency into account.

[0076] A joint imaging method for gravity and magnetic data based on downward continuation and Gramian constraints is proposed. This method derives separate imaging models for magnetic data and gravity data based on the updates of the magnetization and residual density property distributions, respectively. The gradient of the Gramian function composed of magnetization and residual density is then introduced into these separate imaging models to obtain the updated magnetization and residual density models. The specific method is as follows:

[0077] Magnetic data separate imaging model The calculation formula is:

[0078] (9)

[0079] Gravity data separate imaging model The calculation formula is:

[0080] (10)

[0081] In the formula Compression matrix in the magnetic data iteration process The compression matrices in the gravity data iteration process are diagonal matrices that depend only on the property values ​​of the previous iteration. This is the first coefficient of the model update term during the gravity and magnetic imaging iteration process. Its value is in the range of greater than 0 and less than or equal to 1, and it is usually set to 1. This is the second coefficient of the model update term during the gravity and magnetic imaging iteration process. Its value is in the range of greater than 0 and less than or equal to 1, and it is usually taken as 1.

[0082] By introducing the gradient of the Gramian function composed of magnetization and residual density into the separate imaging models of magnetic data and gravity data, an updated magnetization model is obtained. and the updated residual density model The process is as follows:

[0083] (11)

[0084] (12)

[0085] In the above formula is the coefficient of the magnetic data joint term in the joint imaging of magnetic data and gravity data, is the coefficient of the gravity data joint term in the joint imaging of magnetic data and gravity data. The magnitude of the joint term coefficient is usually taken as the ratio of the two-norms of the joint term and the physical property conversion term; is the Gramian function composed of the residual density and magnetization intensity in the j-th iteration, is the partial derivative symbol.

[0086] The role of calculating the updated magnetization intensity model and residual density model is to introduce the Gramian function as a joint constraint term, integrate the individual update amounts of magnetization intensity and residual density into a synergistically optimized physical property model, so as to solve the non-unique solution problem of single physical property inversion and enhance the geological correlation between gravity and magnetic data. Its core purpose is to force the distribution patterns of magnetization intensity and residual density to tend to be consistent through Gramian constraints, thereby reducing the common equivalent defects in geophysical inversion and ensuring that the output model simultaneously satisfies the observational constraints of gravity and magnetic data and geological prior knowledge.

[0087] A joint imaging method of gravity and magnetic data based on downward continuation and Gramian constraint. In step S6, it is judged whether the maximum number of iterations is reached. If so, the joint imaging model of gravity and magnetic data is output; if not, return to step S3; the specific method is;

[0088] Check the number of iterations. When the number of iterations is equal to the preset number, that is, j = n, output the magnetization intensity model and the residual density model as the joint imaging model of gravity and magnetic data; when the number of iterations is less than the preset number, that is, j < n, input the iterated magnetization intensity model and residual density model into step S3, and repeat steps S3 - S6.

[0089] The role of checking the number of iterations is to ensure an optimal balance between computational efficiency and result reliability in the inversion process, preventing unlimited consumption of computing resources caused by non-convergence or oscillation; if the upper limit is not reached, return to step S3 to continue iterating, and further optimize the model using residual calculation and physical property update. This design not only avoids the risk of infinite loop but also ensures that the inversion has sufficient opportunities to approach the true solution, and finally outputs a geologically reasonable joint imaging result within a controllable time.

[0090] Embodiment 2

[0091] A joint imaging system of gravity and magnetic data based on downward continuation and Gramian constraint, as Figure 10 shown, it includes a grid space construction module, a parameter setting module, a residual calculation module, a physical property distribution update module, a model update module, an iteration judgment module and an image generation module;

[0092] The grid space construction module is used to divide the underground grid space according to the spatial scale of the target area to obtain the underground grid cells of the target area, and calculate the magnetic inversion kernel matrix and gravity inversion kernel matrix based on the underground grid cells of the target area.

[0093] The parameter setting module is used to preset the downward extension depth value, magnetization intensity model, residual density model and maximum number of iterations based on the underground grid cells of the target area.

[0094] The residual calculation module is used to calculate the magnetic data prediction field and gravity data prediction field at the observation location based on the magnetization intensity model, the residual density model, and the magnetic inversion kernel matrix and gravity inversion kernel matrix. It also calculates the magnetic data residual between the actual magnetic data observation field and the magnetic data prediction field, as well as the gravity data residual between the actual gravity data observation field and the gravity data prediction field.

[0095] The property distribution update module is used to calculate the downward continuation field of the magnetic data residual at different depth positions and the downward continuation field of the gravity data residual at different depth positions using the Tikhonov regularized downward continuation method. Then, based on the frequency domain conversion relationship, the downward continuation field of the magnetic data residual at different depth positions is converted into the property distribution update amount of magnetization intensity, and the downward continuation field of the gravity data residual at different depth positions is converted into the property distribution update amount of residual density.

[0096] The model update module is used to obtain separate imaging models for magnetic data and gravity data based on the update amount of the physical property distribution of magnetization intensity and the update amount of the physical property distribution of residual density, respectively. The gradient of the Gramian function composed of magnetization intensity and residual density is introduced into the separate imaging models for magnetic data and gravity data to obtain the updated magnetization intensity model and residual density model.

[0097] The iteration judgment module is used to determine whether the updated magnetization intensity model and residual density model have reached the maximum number of iterations. If so, it outputs the joint imaging model of magnetic data and gravity data.

[0098] The image generation module is used to generate images based on the joint imaging model of gravity and magnetic data to obtain the joint imaging results of magnetic data and gravity data.

[0099] Ultimately, this invention demonstrates gravity and magnetism imaging results separately, such as... Figure 6 and Figure 7 As shown, the combined imaging results are as follows: Figure 8 and Figure 9 As shown (all sections are taken at y = 500 m, and the white boxes represent the actual positions of the rectangular blocks). Figure 6 Magnetic data alone, when imaged, shows the size of the block. Figure 8It is far less than the actual situation. Figure 7 The individual imaging results of the gravity data shown indicate that the block position is shifted downwards. After processing the gravity and magnetic data using the joint imaging method proposed in this patent, Figure 9 The combined imaging results better match the distribution range of the actual block. Therefore, it can be seen that, by employing combined imaging of gravity and magnetic data based on downward continuation and Gramian constraints, this invention achieves imaging results with clear boundaries and high consistency compared to unconstrained methods, demonstrating the advantages of the proposed method.

[0100] Example 3

[0101] A computer-readable storage medium, the computer-readable storage medium including a memory and a processor;

[0102] The memory is used to store computer instructions;

[0103] The processor is configured to execute a combined gravity and magnetic data imaging method based on downward continuation and Gramian constraints when executing the computer instructions.

[0104] This invention first utilizes the downward continuation of the potential field to perform downward continuation imaging of the residual fields of the magnetic and gravitational fields. Then, based on the frequency domain transformation relationship, the imaging field is converted into a property distribution result. Simultaneously, a Gramian constraint operator constructed from residual density and magnetization is introduced to update and constrain the property model. By leveraging the complementarity between these different geophysical fields, the ambiguity of solutions is reduced, and the computational speed is significantly improved compared to joint inversion of potential field data.

Claims

1. A joint imaging method for gravity and magnetic data based on downward continuation and Gramian constraint, characterized in that: It includes the following steps; S1 divides the underground grid space according to the spatial scale of the target area to obtain the underground grid cells of the target area, and calculates the magnetic inversion kernel matrix and gravity inversion kernel matrix based on the underground grid cells of the target area. S2 presets the downward extension depth, magnetization model, residual density model, and maximum number of iterations based on the underground grid cells of the target area. S3 is based on the magnetization model and the residual density model. It combines the magnetic inversion kernel matrix and the gravity inversion kernel matrix to calculate the magnetic data prediction field and the gravity data prediction field at the observation location. It also calculates the magnetic data residual between the actual magnetic data observation field and the magnetic data prediction field, as well as the gravity data residual between the actual gravity data observation field and the gravity data prediction field. S4 uses the Tikhonov regularized downward continuation method to calculate the downward continuation field of the magnetic data residual at different depth positions and the downward continuation field of the gravity data residual at different depth positions. Then, based on the frequency domain transformation relationship, the downward continuation field of the magnetic data residual at different depth positions is converted into the update amount of the magnetization intensity property distribution, and the downward continuation field of the gravity data residual at different depth positions is converted into the update amount of the residual density property distribution. S5 obtains separate imaging models for magnetic data and gravity data based on the update amounts of the physical property distribution of magnetization and the physical property distribution of residual density, respectively. The gradient of the Gramian function composed of magnetization and residual density is introduced into the separate imaging models for magnetic data and gravity data to obtain the updated magnetization model and residual density model. S6 determines whether the updated magnetization model and residual density model have reached the maximum number of iterations. If so, it outputs the joint imaging model of magnetic data and gravity data. Based on the frequency domain transformation relationship, the downward extension field of the magnetic data residual at different depth locations is... The specific method for converting the physical property distribution update of the gravity data residuals at different depth locations into the residual density physical property distribution update is as follows: The downward continuation field of the magnetic data residual at different depth locations is converted into the update quantity of the physical property distribution of magnetization intensity; （7） The downward extension field of gravity data residuals at different depth locations The updated physical property distribution converted to residual density; （8） In the formula, This is a two-dimensional inverse Fourier transform. This represents the update amount of the physical property distribution of magnetization. This is the update amount for the physical property distribution of the remaining density. Where i is the vacuum permeability, and i is the imaginary unit. The wave number in the depth direction. ; P is the unit vector representing the direction of the Earth's magnetic field. M is the unit vector of the total magnetization direction. ,in It is the geomagnetic tilt angle. It is the magnetic declination. The total magnetization tilt angle, θ is the total magnetization deflection, and p is the gravitational constant.

2. The method for joint imaging of gravity and magnetic data based on downward continuation and Gramian constraint according to claim 1, characterized in that: The magnetic data and gravity data joint imaging model is input into the image generation module to obtain the magnetic data and gravity-magnetic joint imaging results and the gravity data and gravity-magnetic joint imaging results.

3. The method for joint imaging of gravity and magnetic data based on downward continuation and Gramian constraint according to claim 1, characterized in that: The underground grid space is divided according to the spatial scale of the target area to obtain the underground grid cells of the target area. The specific method for calculating the magnetic inversion kernel matrix and gravity inversion kernel matrix based on the underground grid cells of the target area is as follows: Based on the spatial scale of the target area, the three-dimensional range of the underground grid is defined, and the grid size is set to obtain the underground grid cells of the target area. Based on the underground grid cells of the target area, the magnetic inversion kernel matrix is ​​calculated according to the gravity and magnetic anomaly response of the cuboid cells. and gravity inversion kernel matrix .

4. The method for joint imaging of gravity and magnetic data based on downward continuation and Gramian constraint according to claim 3, characterized in that: Based on the magnetization model and residual density model, and combining the magnetic inversion kernel matrix and gravity inversion kernel matrix, the predicted magnetic and gravity data fields at the observation location are calculated. The specific methods for calculating the magnetic data residuals between the observed magnetic data field and the predicted magnetic data field, and the gravity data residuals between the observed gravity data field and the predicted gravity data field at the actual location are as follows: Calculate magnetic data to predict the field ; （1） Calculate gravity data to predict the field ; （2） In the formula, j is the iteration number. For the magnetization model of the j-th iteration, Let n be the residual density model for the j-th iteration, and n be the maximum number of iterations. The residual of the magnetic data is obtained by subtracting the observed field from the predicted field of the actual magnetic data. ; （3） The residual of the gravity data is obtained by subtracting the observed gravity data field from the predicted gravity data field. ; （4） In the formula The observation field for actual location magnetic data, This is the actual location gravity data observation field.

5. The method for joint imaging of gravity and magnetic data based on downward continuation and Gramian constraint according to claim 4, characterized in that: The specific method for calculating the downward continuation field of magnetic data residuals at different depths using the Tikhonov regularized downward continuation method is as follows: Based on the residuals of the magnetic data Based on the Tikhonov regularized downward continuation method, the frequency domain downward continuation field of magnetic data at depth h is obtained. for: （5） Based on the residuals of gravity data Based on the Tikhonov regularized downward continuation method, the frequency domain downward continuation field of gravity data at depth h is obtained. for: （6） Where u is the wave number in the x-direction and v is the wave number in the y-direction. It is the angular frequency. These are the downward extension filter coefficients for the magnetic data. These are the downward extension filter coefficients for gravity data; For the residuals of magnetic data The frequency domain response is calculated using a two-dimensional Fourier transform. Residuals of gravity data The frequency domain response is calculated using a two-dimensional Fourier transform. It is a natural constant.

6. The method for joint imaging of gravity and magnetic data based on downward continuation and Gramian constraint according to claim 1, characterized in that: The specific method for obtaining the updated magnetization intensity model and residual density model by separately obtaining the magnetic data independent imaging model and the gravity data independent imaging model according to the physical property distribution update amount of magnetization intensity and the physical property distribution update amount of residual density, and introducing the gradient of the Gramian function composed of magnetization intensity and residual density in the magnetic data independent imaging model and the gravity data independent imaging model is as follows: Magnetic data separate imaging model The calculation formula is: （9） Gravity data separate imaging model The calculation formula is: （10） In the formula Compression matrix in the magnetic data iteration process Compression matrix during gravity data iteration; This is the first coefficient of the model update term during the gravity and magnetic imaging iteration process, and its value is in the range of greater than 0 and less than or equal to 1. This is the second coefficient of the model update term during the gravity and magnetic imaging iteration process, and its value is in the range of greater than 0 and less than or equal to 1. By introducing the gradient of the Gramian function composed of magnetization and residual density into the separate imaging models of magnetic data and gravity data, an updated magnetization model is obtained. and the updated residual density model The process is as follows: （11） （12） In the above formula These are the joint coefficients of the magnetic data term in joint imaging of magnetic and gravity data. These are the joint coefficients of the gravity data term in joint imaging of magnetic and gravity data. Let be the Gramian function composed of the residual density and magnetization in the j-th iteration. This is the sign for the partial derivative.

7. The method for joint imaging of gravity and magnetic data based on downward continuation and Gramian constraint according to claim 1, characterized in that: In step S6, it is judged whether the maximum number of iterations is reached. If so, the joint imaging model of gravity and magnetic data is output; if not, return to step S3; the specific method is as follows; Check the number of iterations. When the number of iterations is equal to the preset number, that is, j = n, the magnetization intensity model and the residual density model are output as the joint imaging model of gravity and magnetic data; when the number of iterations is less than the preset number, that is, j < n, the iterated magnetization intensity model and residual density model are input into step S3, and steps S3 - S6 are repeated.

8. A joint imaging system for gravity and magnetic data based on downward continuation and Gramian constraint according to the method of claim 1, characterized in that: It includes a grid space construction module, a parameter setting module, a residual calculation module, a physical property distribution update module, a model update module, an iteration judgment module and an image generation module; The grid space construction module is used to divide the underground grid space according to the spatial scale of the target area to obtain the underground grid units of the target area, and calculate the magnetic inversion kernel matrix and the gravity inversion kernel matrix based on the underground grid units of the target area; The parameter setting module is used to preset the downward continuation depth value, the magnetization intensity model, the residual density model and the maximum number of iterations according to the underground grid units of the target area; The residual calculation module is used to calculate the predicted magnetic field of magnetic data and the predicted gravitational field of gravitational data at the observation position based on the magnetization intensity model and the residual density model, combined with the magnetic inversion kernel matrix and the gravity inversion kernel matrix, calculate the magnetic data residual between the actual position magnetic data observation field and the magnetic data predicted field, and the gravitational data residual between the actual position gravitational data observation field and the gravitational data predicted field; The physical property distribution update module is used to calculate the downward continuation field of the magnetic data residual at different depth positions and the downward continuation field of the gravitational data residual at different depth positions by using the Tikhonov regularization downward continuation method, and then convert the downward continuation field of the magnetic data residual at different depth positions into the physical property distribution update amount of magnetization intensity according to the frequency domain conversion relationship, and convert the downward continuation field of the gravitational data residual at different depth positions into the physical property distribution update amount of residual density; The model update module is used to separately obtain the magnetic data independent imaging model and the gravity data independent imaging model according to the physical property distribution update amount of magnetization intensity and the physical property distribution update amount of residual density, and introduce the gradient of the Gramian function composed of magnetization intensity and residual density in the magnetic data independent imaging model and the gravity data independent imaging model to obtain the updated magnetization intensity model and residual density model; The iteration judgment module is used to judge whether the updated magnetization intensity model and residual density model reach the maximum number of iterations. If so, the joint imaging model of magnetic data and gravity data is output; The image generation module is used to generate images based on the joint imaging model of gravity and magnetic data to obtain the joint imaging results of magnetic data and gravity data.

9. A computer-readable storage medium, characterized in that, The computer-readable storage medium includes a memory and a processor; The memory is used to store computer instructions; The processor is configured to execute the gravity and magnetic data joint imaging method based on downward continuation and Gramian constraint as described in claim 1 when executing the computer instructions.

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