Adaptive weight adjustment high-precision joint inversion method based on electromagnetic gradient data driving

Abstract

The invention discloses a self-adaptive weight-adjusting high-precision joint inversion method based on electromagnetic gradient data driving, and relates to the technical field of electromagnetic signal inversion, and the method comprises the steps: calculating the space gradient data of original electromagnetic field observation data through employing a Gaussian weighted neighborhood method; combining the conventional data residual item, the data residual item and the regularization item to construct a joint objective function; and embedding the gradient sensitive scale matrix into a data residual term of the joint objective function, establishing an inversion equation, carrying out iterative calculation on the inversion equation, updating model parameters, and obtaining a three-dimensional inversion result reflecting resistivity spatial distribution. According to the method, the classical Gaussian-Newton method is expanded, the electromagnetic field data and the residual term of the spatial gradient are utilized to perform inversion optimization, and the gradient-sensitive scale matrix is introduced into residual weighting, so that only model parameters related to the abnormal region can be updated in each inversion iteration, and the accuracy of inversion optimization is improved. And mapping to a three-dimensional finite element domain for forward modeling calculation.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic signal inversion technology, and in particular to an adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven approach. Background Technology

[0002] Methods for inverting subsurface resistivity structures based on geophysical electromagnetic data mainly fall into three categories: traditional smoothing inversion methods, 3D fine-grid inversion methods, and regularized inversion methods. While all three methods can achieve the inversion from electromagnetic data to subsurface resistivity distribution, they differ in terms of inversion accuracy, computational efficiency, and adaptability to complex geological conditions. Traditional smoothing inversion methods are based on the least squares principle and use model roughness (or smoothness) as a regularization constraint, seeking the smoothest resistivity model while fitting the observed data. This method is highly robust to noise and computationally efficient, effective in many scenarios. However, in pursuit of model smoothness, it typically smooths out sharp geological boundaries, making it difficult to accurately characterize complex geological structures or abrupt interfaces. 3D fine-grid inversion methods utilize fine grids to discretize subsurface space, reconstructing complex 3D geological structures with high resolution and unbiasedness. This method boasts extremely high resolution and strong adaptability. However, due to the need to invert millions of grid cells, it results in enormous memory consumption and computational costs, making it difficult to scale to large-scale computational domains. Furthermore, alternative regularization strategies have been developed to improve boundary preservation capabilities, including focused regularization and total variational regularization. Focused regularization recovers the well-defined geoelectric structure by introducing a minimum gradient support functional. Total variational regularization, by imposing gradient sparsity constraints, enables the inversion to produce piecewise constant solutions, preserving the discontinuities in conductivity. While these techniques effectively enhance boundary clarity, they typically increase nonlinearity and computational complexity, which can lead to slower convergence and greater sensitivity to parameter tuning.

[0003] Despite significant advancements in geophysical electromagnetic inversion techniques, existing methods struggle to simultaneously achieve physical consistency, high boundary resolution, and high computational and acquisition efficiency without multi-physics integration or repeated measurements. To address this limitation, the conventional approach involves integrating electromagnetic data residuals into the overall inversion residuals and adjusting the weights of the electromagnetic and gradient field data residuals using a single constant. This leverages the high sensitivity of electromagnetic gradients to discontinuous conductivity to enhance model convergence speed and structural clarity. However, using a uniform constant to constrain weights implies that all non-uniform gradient terms are assigned the same regularization strength. This leads to insufficient accuracy in identifying anomalous boundaries, low noise tolerance in anomaly-free regions, and susceptibility to false oscillations or anomalies, resulting in low model stability and reliability. Summary of the Invention

[0004] In view of the aforementioned existing problems, the present invention is proposed.

[0005] Therefore, this invention provides an adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method, which solves the problem of achieving high-resolution structural imaging while improving computational efficiency.

[0006] To solve the above-mentioned technical problems, the present invention provides the following technical solution: This invention provides an adaptive weighted high-precision joint inversion method based on electromagnetic gradient data. The method includes: calculating the spatial gradient data of the original electromagnetic field observation data using the Gaussian weighted neighborhood method; calculating the spatial gradient differences between adjacent frequencies to form a frequency difference spatial gradient; normalizing and combining the frequency difference spatial gradients of all measurement points to obtain a normalized matrix of the overall gradient intensity; processing the normalized matrix of the overall gradient intensity using a contrast weighting function with an adjustable exponent to construct a gradient-sensitive scale matrix; combining the conventional data residual term, the data residual term, and the regularization term to construct a joint objective function; embedding the gradient-sensitive scale matrix into the data residual term of the joint objective function to establish an inversion equation; iteratively calculating the inversion equation and updating the resistivity vector of the resistivity model at each grid point underground to obtain a three-dimensional inversion result reflecting the spatial distribution of resistivity.

[0007] As a preferred embodiment of the adaptive weighted high-precision joint inversion method based on electromagnetic gradient data driven by the present invention, the specific steps for calculating the spatial gradient data of the original electromagnetic field observation data using the Gaussian weighted neighborhood method are as follows. Acquire electromagnetic field data at the measuring point and electromagnetic field data at neighboring measuring points; Based on the electromagnetic field data under the frequency conditions at the measuring point and the spatial distance between the electromagnetic field data under the same frequency conditions at neighboring measuring points, the gradient components of each pair of neighboring points are calculated. The distance between neighboring measurement points is calculated using an exponential function and normalized to obtain normalized Gaussian weights. These normalized Gaussian weights are then used to weight the gradient components of each pair of neighboring points to generate spatial gradient data.

[0008] As a preferred embodiment of the adaptive weighted high-precision joint inversion method based on electromagnetic gradient data driven by the present invention, the specific steps for calculating the spatial gradient difference between adjacent frequencies to form a frequency difference spatial gradient are as follows. Obtain the spatial gradient between the frequency at the measurement point and the previous frequency at the measurement point, and select a frequency function that matches the frequency sampling scheme. Calculate the difference between the frequency at the measuring point and the spatial gradient at the previous frequency at the measuring point; Calculate the difference between the frequency at the measuring point and the previous frequency at the measuring point; The ratio of the difference in spatial gradients to the difference in frequency function values ​​is taken as the frequency difference spatial gradient.

[0009] As a preferred embodiment of the adaptive weighted high-precision joint inversion method based on electromagnetic gradient data driven by the present invention, the step of normalizing and combining the frequency difference spatial gradients of all measurement points to obtain the normalized gradient intensity matrix is ​​as follows: Collect the frequency differential spatial gradient at each measuring point and determine the maximum value of the frequency differential spatial gradient at all measuring points; The frequency difference space gradient of each measuring point is normalized based on the maximum value to obtain the normalized frequency difference space gradient vector of each measuring point. Combine the normalized frequency difference space gradient vectors of all measurement points to form the overall gradient intensity normalized matrix.

[0010] As a preferred embodiment of the adaptive weighted high-precision joint inversion method based on electromagnetic gradient data driven by the present invention, the specific steps for constructing the gradient-sensitive scaling matrix are as follows: The overall gradient intensity normalization matrix is ​​used as the input parameter of the contrast weighting function; Each element in the overall gradient intensity normalization matrix is ​​processed using a contrast weighting function with an adjustable exponent; The processed elements are arranged into a diagonal matrix to form a gradient-sensitive scaling matrix. This matrix is ​​then used to adjust the contribution weights of individual data points in the residual terms.

[0011] As a preferred embodiment of the adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven approach described in this invention, the specific steps for constructing a joint objective function by combining the conventional data residual term, the data residual term, and the regularization term are as follows. Based on the difference between the observed electromagnetic field data and the electromagnetic field data predicted by forward modeling, a conventional data residual term is constructed. A joint objective function is constructed by weighting and combining the regular data residuals, the data residuals, and the regularization terms.

[0012] As a preferred embodiment of the adaptive weighted high-precision joint inversion method based on electromagnetic gradient data driven by the present invention, wherein: the data residual term includes, The processing results of the differences between the weighted matrix of diagonal electromagnetic field data and the observed and predicted electromagnetic field data; The result of processing the difference between the weighted matrix of the diagonal gradient field data and the observed gradient data and the predicted gradient data; The result of adjusting the influence of the gradient-sensitive scaling matrix on the degree of influence of individual data points in the gradient data residual.

[0013] As a preferred embodiment of the adaptive weighted high-precision joint inversion method based on electromagnetic gradient data driven by the present invention, the inversion equation includes the Jacobian matrix of the predicted electromagnetic field data and the Jacobian matrix of the predicted spatial gradient data.

[0014] As a preferred embodiment of the adaptive weighted high-precision joint inversion method based on electromagnetic gradient data driven by the present invention, the specific steps for establishing the inversion equation by embedding the gradient-sensitive scaling matrix into the data residual term of the joint objective function are as follows. The coefficient matrix of the inversion equation is constructed based on the Jacobian matrix of the predicted electromagnetic field data, the Jacobian matrix of the predicted spatial gradient data, and the gradient-sensitive scale matrix. Based on the Jacobian matrix of the predicted electromagnetic field data, the Jacobian matrix of the predicted spatial gradient data, the data residual terms, and the regularization terms, the gradient direction of the inversion equation is constructed. By combining the coefficient matrix with the gradient direction, an inversion equation is established.

[0015] As a preferred embodiment of the adaptive weighted high-precision joint inversion method based on electromagnetic gradient data driven by the present invention, the specific steps for iteratively calculating the inversion equation and updating the model parameters to obtain a three-dimensional inversion result reflecting the spatial distribution of resistivity are as follows. Calculate the resistivity model update step value for the current iteration, and correct the resistivity model parameters based on the resistivity model update step value; Based on the corrected resistivity model parameters, the output is a three-dimensional inversion result reflecting the spatial distribution of resistivity.

[0016] The beneficial effects of this invention are as follows: By extending the classical Gauss-Newton method, while utilizing the residual terms of electromagnetic field data and spatial gradients for inversion optimization, a gradient-sensitive scaling matrix is ​​introduced into the residual weighting. This allows each inversion iteration to update only the model parameters related to the anomalous region and map them to the three-dimensional finite element domain for forward modeling. This mechanism improves boundary resolution while significantly reducing computational costs and fully capturing the three-dimensional physical response. It overcomes the limitations of traditional constant-constrained gradient residual term methods in terms of anomalous region boundary identification accuracy and background region stability caused by neglecting mesh non-uniformity and spatial heterogeneity of physical properties. This provides a practical solution for electromagnetic detection in complex geological environments. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 The flowchart shows the adaptive weighted high-precision joint inversion method based on electromagnetic gradient data.

[0019] Figure 2 To compare the responses of electromagnetic gradient data and electromagnetic field data and their sensitivity to boundary changes, among which, Figure 2 (a) A true three-dimensional model of the electromagnetic gradient field containing conduction band anomalies; Figure 2 (b) indicates compared to Figure 2 (a) A three-dimensional model diagram showing slight displacement and dimensional changes in the model; Figure 2 (c) is Figure 2 (a) and Figure 2 (b) Plot showing the relative differences in electromagnetic field data responses between models; Figure 2 (d) is Figure 2 (a) and Figure 2 (b) Plot showing the relative differences in spatial gradient data responses between models; Figure 2 (e) shows the relative differences between the two models in terms of electromagnetic field and gradient field response. Detailed Implementation

[0020] 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.

[0021] Many specific details are set forth in the following description in order to provide a full understanding of the invention. However, the invention may also be practiced in other ways different from those described herein, and those skilled in the art can make similar extensions without departing from the spirit of the invention. Therefore, the invention is not limited to the specific embodiments disclosed below.

[0022] Secondly, the term "one embodiment" or "embodiment" as used herein refers to a specific feature, structure, or characteristic that may be included in at least one implementation of the present invention. The phrase "in one embodiment" appearing in different places in this specification does not necessarily refer to the same embodiment, nor is it a single or selective embodiment that is mutually exclusive with other embodiments.

[0023] Reference Figures 1-2 This is one embodiment of the present invention, which provides an adaptive weighted high-precision joint inversion method based on electromagnetic gradient data driving, comprising the following steps: S1. Calculate the spatial gradient data of the original electromagnetic field observation data using the Gaussian weighted neighborhood method.

[0024] S1.1: Obtain electromagnetic field data at the measuring point and electromagnetic field data at neighboring measuring points; It should be noted that the resistivity model response is obtained through forward modeling or through actual detection, and electromagnetic field data at the measuring point and the electromagnetic field data at neighboring measuring points are obtained.

[0025] S1.2: Based on the electromagnetic field data at the measurement point under the same frequency conditions and the spatial distance between the electromagnetic field data at neighboring measurement points under the same frequency conditions, calculate the gradient components of each pair of neighboring points, defined as: ; in, Indicates at the measuring point frequency Electromagnetic fields under certain conditions; Indicates at the measuring point Frequency conditions Electromagnetic field under; This represents the x-coordinate of measurement point j in the three-dimensional coordinate system; This represents the x-coordinate of the measuring point p in the three-dimensional coordinate system.

[0026] S1.3: The distance between neighboring measurement points is calculated and normalized using an exponential function to obtain normalized Gaussian weights. The gradient components of each neighboring point pair are weighted using the normalized Gaussian weights to generate spatial gradient data.

[0027] Spatial gradient data is defined as: ; in, For measuring points frequency Spatial gradient below; Indicates at the measuring point frequency Electromagnetic fields under certain conditions; Indicates at the measuring point Frequency conditions Electromagnetic field under; It is a measuring point The set of adjacent measuring points; For normalized Gaussian weights.

[0028] To simultaneously preserve the high noise suppression capability and high boundary clarity of the resistivity model, the normalized Gaussian weight expression is as follows: ; in, Normalized Gaussian weights; Indicates the measurement point in the three-dimensional coordinate system The x-direction vector at that location; Indicates the measurement point in the three-dimensional coordinate system The x-direction vector at that location; It is a weighting factor used to adjust noise suppression capability and boundary sensitivity when calculating the electromagnetic field gradient. When the Gaussian function broadens to a maximum, the differences in weights at different points are smoothed out, thus the weights approach a uniform average, and the noise suppression capability is enhanced; when When the Gaussian function broadens minimally, it has significant weight only at local near points, thus greatly emphasizing local sensitivity and enhancing boundary sensitivity and clarity.

[0029] S2. Calculate the spatial gradient difference between adjacent frequencies to form a frequency difference spatial gradient. Normalize and combine the frequency difference spatial gradients of all measurement points to obtain the overall gradient intensity normalization matrix. Then, use a contrast weighting function with an adjustable exponent to process the overall gradient intensity normalization matrix and construct a gradient sensitive scale matrix.

[0030] S2.1: Set the transmission frequency according to the measurement requirements, and use the Gaussian weighted neighborhood method to calculate the electromagnetic field data, obtain the spatial gradient between the frequency at the measurement point and the previous frequency at the measurement point, and select a mathematical function that matches the frequency sampling scheme as the frequency function according to the frequency sampling method and analysis purpose (such as accuracy and resolution). S2.2: Calculate the difference between the frequency at the measuring point and the spatial gradient at the previous frequency at the measuring point, defined as: ; in, For measuring points frequency Spatial gradient below; It should be noted that, The spatial gradient of frequency at the measurement point. This represents the spatial gradient at the previous frequency at the measurement point.

[0031] S2.3: Calculate the difference between the frequency at the measuring point and the previous frequency at the measuring point, defined as: ; in, It is a function of frequency; It should be noted that, The frequency function value at the measuring point. This is the frequency function value of the previous frequency at the measurement point.

[0032] S2.4: The ratio of the difference in spatial gradients to the difference in frequency function values ​​is taken as the frequency difference spatial gradient, expressed as: ; in, For measuring points frequency The gradient in the difference space below, For measuring points frequency Spatial gradient below; The function is a function of frequency. The appropriate function is selected based on the chosen frequency sampling scheme and the requirements for accuracy and resolution (e.g., when using a logarithmic interval sampling frequency). = ).

[0033] It should be noted that frequency normalization suppresses background response, significantly improving boundary sensitivity.

[0034] S2.5: Collect the frequency differential spatial gradient at each measuring point, and determine the maximum value of the frequency differential spatial gradient at all measuring points. The expression is: ; in, Indicates the measuring point Located in the vertical direction Spatial gradient vectors at each grid point ; This is set to a minimum value to avoid division by zero errors. Let j be the total number of grid cells in the longitudinal direction.

[0035] S2.6: Based on the maximum value, the frequency difference spatial gradient of each measuring point is normalized to obtain the normalized frequency difference spatial gradient vector of each measuring point, expressed as: ; It should be noted that the frequency difference spatial gradient at each measurement point is... The ratio to the maximum value is normalized to generate a normalized frequency difference space gradient vector.

[0036] S2.7: Combine the normalized frequency difference space gradient vectors of all measurement points to form the overall gradient intensity normalized matrix.

[0037] Combining the frequency difference spatial gradients of all measurement points, the normalized matrix of gradient intensity at all measurement points is obtained as follows: ; Where r is the global gradient intensity normalization matrix, These represent the normalized frequency difference space gradient vectors at measurement points 1, 2, j, and N2, respectively. This represents the total number of measurement points.

[0038] S2.8: Use the overall gradient intensity normalization matrix as the input parameter of the contrast weighting function; ; in, This is an adjustable index used to control the weighting between boundary sensitivity and smooth region stability; S2.9: Use a contrast weighting function with an adjustable exponent to process each element in the overall gradient intensity normalization matrix; Introducing a contrast-weighted function with an adjustable exponent, each element in the overall gradient intensity normalization matrix is ​​calculated and defined as: ; S2.10: Arrange the processed elements into a diagonal matrix to form a gradient-sensitive scaling matrix. Use the gradient-sensitive scaling matrix to adjust the contribution weight of individual data in the data residual term.

[0039] It should be noted that the gradient-sensitive scaling matrix is ​​used to adjust the contribution weight of individual data in the electromagnetic data residual term, enhancing sensitivity at electrical boundaries to improve resolution, and maintaining smooth constraints in uniform regions to suppress noise.

[0040] S3. Combine the regular data residual term, the data residual term, and the regularization term to construct a joint objective function.

[0041] S3.1: Based on the difference between the observed electromagnetic field data and the electromagnetic field data predicted by forward modeling, the conventional data residual term is constructed as follows: ; in, This is a weighting matrix for diagonal electromagnetic field data; For the observed electromagnetic field data, For predicted electromagnetic field data; For the observed electromagnetic gradient data, For the predicted electromagnetic gradient data; This is the weighting matrix for the diagonal gradient field data; It should be noted that each element of the diagonal electromagnetic field data weighting matrix corresponds to the reciprocal of the standard deviation of the noise at each observed electromagnetic field data location; and each element of the diagonal gradient field data weighting matrix corresponds to the reciprocal of the standard deviation of the noise at each observed electromagnetic gradient data location. Both the predicted electromagnetic field data and the predicted electromagnetic gradient data are obtained through forward modeling. Forward modeling refers to generating the predicted electromagnetic field data by simulating the physical laws in the resistivity model of the current iteration, and further deriving the predicted electromagnetic gradient data.

[0042] S3.2: Construct a joint objective function by weighting the regular data residuals, data residuals, and regularization terms.

[0043] The joint objective function expression is: ; in, For resistivity model vectors; For data residuals; This is a regularization term used to impose prior constraints and enhance the smoothness of the resistivity model. Used to balance the two weights.

[0044] To address the issues of weak resistivity model updates and slow convergence in traditional EM inversion, this paper leverages the sensitivity of the gradient field to small perturbations at the boundary locations. An additional term explaining the spatial electromagnetic field gradient is introduced into the data residual term to restore the convergence speed and structural clarity of the resistivity model. The data residual term after introducing the spatial electromagnetic field gradient additional term is defined as follows: ; in, This is a weighting matrix for diagonal electromagnetic field data; For the observed electromagnetic field data, For predicted electromagnetic field data; For the observed electromagnetic gradient data, For the predicted electromagnetic gradient data; This is the weighting matrix for the diagonal gradient field data; This is a weighting parameter used to adjust the weight of the overall contribution of the electromagnetic data residual to the data residual; This is the gradient-sensitive scaling matrix, used to adjust the weights of individual data points contributing to the electromagnetic data residuals.

[0045] S3.3: The result of processing the differences between the weighted matrix of the diagonal electromagnetic field data and the observed and predicted electromagnetic field data is as follows: ; It should be noted that the further detailed description of the composition of the residual terms of conventional data explicitly points out that the residual terms of conventional data are weighted matrices of diagonal electromagnetic field data. right and The result of the processing.

[0046] S3.4: The result of processing the differences between the diagonal gradient field data constraint matrix and the observed and predicted gradient data is as follows: ; It should be noted that, The core components of the residual term for conventional data are described, and it is clearly pointed out that the residual term for conventional data is a weighted matrix of diagonal gradient field data. right and The result of the processing.

[0047] S3.5: The result of adjusting the influence of the gradient-sensitive scaling matrix on the degree of influence of individual data in the gradient data residual.

[0048] It should be noted that, This is a gradient-sensitive scaling matrix used to adjust the weights of individual data points contributing to the data residuals in the regular data residuals.

[0049] S4. The gradient-sensitive scale matrix is ​​embedded in the data residual term of the joint objective function to establish the inversion equation. The inversion equation is iteratively calculated and the resistivity model parameters are updated to obtain the three-dimensional inversion result reflecting the spatial distribution of resistivity.

[0050] S4.1: The inversion equation contains the Jacobian matrix of the predicted electromagnetic field data and the Jacobian matrix of the predicted spatial gradient data.

[0051] It should be noted that, Let be the Jacobian matrix of the predicted electromagnetic field data corresponding to the k-th iteration resistivity model; Let be the Jacobian matrix of the predicted spatial gradient data corresponding to the resistivity model in the k-th iteration.

[0052] S4.2: Construct the coefficient matrix of the inversion equation based on the Jacobian matrix of the predicted electromagnetic field data, the Jacobian matrix of the predicted spatial gradient data, and the gradient-sensitive scale matrix; ; ; in, This represents the left-hand side of the k-th iteration inversion equation, i.e., the coefficient matrix; Let be the regularization parameter for the k-th iteration; This is the weighting matrix for the small constraints of the resistivity model; The Laplace operator represents the controllable smoothness of the resistivity model; and These are scalar weighting coefficients used to control the balance of small constraints and smooth constraints, respectively.

[0053] It should be noted that in the process of constructing the coefficient matrix of the inversion equation, the data fitting, gradient data and prior information of the resistivity model are integrated to determine the direction and step size of the resistivity model update, and to ensure the stability and rationality of the inversion.

[0054] S4.3: Construct the gradient direction of the inversion equation based on the Jacobian matrix of the predicted electromagnetic field data, the Jacobian matrix of the predicted spatial gradient data, the data residuals and regularization terms; ; ; in, This is the right-hand side term of the k-th iteration inversion equation, i.e., the gradient direction; For the current resistivity model; Use the reference resistivity model; It should be noted that in the process of constructing the gradient direction of the inversion equation, the right-hand side term... The negative gradient of the objective function with respect to the resistivity model parameters determines the direction of resistivity model updates during iterative inversion. The data residuals reflect the impact of the difference between observed and predicted data on the direction of resistivity model updates. The regularization term, constrained by prior information about the resistivity model, adjusts the direction of resistivity model updates. Together, these factors make the resistivity model updates closer to the observed data, guiding the inversion process towards a direction closer to the true resistivity distribution.

[0055] S4.4: Combine the coefficient matrix with the gradient direction to establish the inversion equation.

[0056] ; in, This represents the left-hand side of the k-th iteration inversion equation, i.e., the coefficient matrix; This represents the difference between the resistivity model calculated in step k and the resistivity model obtained in step (k-1). This is the right-hand side term of the k-th iteration inversion equation, i.e., the gradient direction; S4.5: Calculate the resistivity model update step value for the current iteration, and correct the resistivity model parameters based on the resistivity model update step value; ; It should be noted that, The difference between the resistivity model calculated in step k and the resistivity model obtained in step (k-1) is the resistivity model update step value. The current resistivity model is corrected by the resistivity model update step value to obtain the corrected resistivity model parameters.

[0057] S4.6: Based on the corrected resistivity model parameters, output the three-dimensional inversion results reflecting the spatial distribution of resistivity.

[0058] It should be noted that the corrected resistivity model parameters obtained from the last iteration are used as the three-dimensional inversion result reflecting the spatial distribution of resistivity.

[0059] It should be noted that, referring to Figure 2 , Figure 2 This is a schematic diagram illustrating the sensitivity of electromagnetic gradient data to boundary changes. Figure 2 (a) Represents a true three-dimensional model of the electromagnetic gradient field containing conduction band anomalies; Figure 2 (b) indicates compared to Figure 2 (a) is a three-dimensional model that has undergone slight displacement and dimensional changes; Figure 2 (c) Reflection Figure 2 (a) and Figure 2 (b) The relative differences in electromagnetic field data responses between models; Figure 2(d) Reflection Figure 2 (a) and Figure 2 (b) The relative differences in spatial gradient data responses between models; Figure 2 (e) reflects the relative differences between the two models in terms of electromagnetic field and gradient field response; the ordinate represents the logarithm of the relative difference (the pink curve represents...). Figure 2 (c) Subtract the relative differences between the two curves, divide by one of them, and then take the logarithm of 10; the blue curve is... Figure 2 (d) Subtract the relative differences between the two curves and divide by one of them, then take the logarithm of 10); the x-coordinate reflects the coordinate value of the measuring point on the measuring line relative to the midpoint of the transmitter source, and the origin X=0 is the midpoint of the transmitter source.

[0060] By comparison Figure 2 (a) and Figure 2 The difference between the electromagnetic field data response and the spatial gradient data response in (b) indicates that the spatial gradient data response is far more sensitive to changes in the boundary of the anomalous body than the original electromagnetic field. Even a small boundary displacement can cause a relative change in the spatial gradient data response of more than an order of magnitude, thus enabling a clearer depiction of the target body's outline.

[0061] This embodiment also provides a computer device applicable to the case of an adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method, comprising: a memory and a processor; the memory is used to store computer-executable instructions, and the processor is used to execute the computer-executable instructions to implement the adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method proposed in the above embodiment.

[0062] The computer device can be a terminal, comprising a processor, memory, communication interface, display screen, and input devices connected via a system bus. The processor provides computing and control capabilities. The memory includes non-volatile storage media and internal memory. The non-volatile storage media stores the operating system and computer programs. The internal memory provides an environment for the operation of the operating system and computer programs stored in the non-volatile storage media. The communication interface is used for wired or wireless communication with external terminals; wireless communication can be achieved through Wi-Fi, carrier networks, NFC (Near Field Communication), or other technologies. The display screen can be an LCD screen or an e-ink screen. The input devices can be a touch layer covering the display screen, buttons, a trackball, or a touchpad on the computer device's casing, or an external keyboard, touchpad, or mouse.

[0063] This embodiment also provides a storage medium storing a computer program that, when executed by a processor, implements the adaptive weighting high-precision joint inversion method based on electromagnetic gradient data driven as proposed in the above embodiments. The storage medium can be implemented by any type of volatile or non-volatile storage device or a combination thereof, such as Static Random Access Memory (SRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read Only Memory (EPROM), Programmable Red-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk.

[0064] In summary, this invention extends the classical Gauss-Newton method by introducing a gradient-sensitive scaling matrix into the residual weighting of electromagnetic field data and spatial gradients for inversion optimization. This allows each inversion iteration to update only the model parameters related to the anomalous region and map them to the three-dimensional finite element domain for forward modeling. This mechanism improves boundary resolution while significantly reducing computational costs and fully capturing the three-dimensional physical response. It overcomes the limitations of traditional constant-constrained gradient residual methods in terms of anomalous region boundary identification accuracy and background region stability caused by neglecting mesh non-uniformity and spatial heterogeneity of physical properties. This provides a practical solution for electromagnetic detection in complex geological environments.

[0065] It should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit it. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can be made to the technical solutions of the present invention without departing from the spirit and scope of the technical solutions of the present invention, and all such modifications or substitutions should be covered within the scope of the claims of the present invention.

Claims

1. A high-precision joint inversion method based on adaptive weighting driven by electromagnetic gradient data, characterized in that: include, Spatial gradient data of the original electromagnetic field observation data were calculated using the Gaussian weighted neighborhood method. The spatial gradient difference between adjacent frequencies is calculated to form a frequency difference spatial gradient. The frequency difference spatial gradients of all measurement points are normalized and combined to obtain the overall gradient intensity normalization matrix. The overall gradient intensity normalization matrix is ​​then processed using a contrast weighting function with an adjustable exponent to construct a gradient sensitive scale matrix. By combining the regular data residual term, the data residual term, and the regularization term, a joint objective function is constructed. By embedding the gradient-sensitive scale matrix into the data residual term of the joint objective function, an inversion equation is established. The inversion equation is iteratively calculated and the resistivity vector of the resistivity model at each grid in the subsurface is updated to obtain a three-dimensional inversion result that reflects the spatial distribution of resistivity.

2. The adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method as described in claim 1, characterized in that: The specific steps for calculating the spatial gradient data of the original electromagnetic field observation data using the Gaussian weighted neighborhood method are as follows. Acquire electromagnetic field data at the measuring point and electromagnetic field data at neighboring measuring points; Based on the electromagnetic field data under the frequency conditions at the measuring point and the spatial distance between the electromagnetic field data under the same frequency conditions at neighboring measuring points, the gradient components of each pair of neighboring points are calculated. The distance between neighboring measurement points is calculated using an exponential function and normalized to obtain normalized Gaussian weights. These normalized Gaussian weights are then used to weight the gradient components of each pair of neighboring points to generate spatial gradient data.

3. The adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method as described in claim 1, characterized in that: The specific steps for calculating the spatial gradient difference between adjacent frequencies to form a frequency difference spatial gradient are as follows. Obtain the spatial gradient between the frequency at the measurement point and the previous frequency at the measurement point, and select a frequency function that matches the frequency sampling scheme. Calculate the difference between the frequency at the measuring point and the spatial gradient at the previous frequency at the measuring point; Calculate the difference between the frequency at the measuring point and the previous frequency at the measuring point; The ratio of the difference in spatial gradients to the difference in frequency function values ​​is taken as the frequency difference spatial gradient.

4. The adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method as described in claim 1, characterized in that: The normalized combination of the frequency difference spatial gradients of all measurement points yields the normalized gradient intensity matrix. The specific steps are as follows: Collect the frequency differential spatial gradient at each measuring point and determine the maximum value of the frequency differential spatial gradient at all measuring points; The frequency difference space gradient of each measuring point is normalized based on the maximum value to obtain the normalized frequency difference space gradient vector of each measuring point. Combine the normalized frequency difference space gradient vectors of all measurement points to form the overall gradient intensity normalized matrix.

5. The adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method as described in claim 1, characterized in that: The specific steps for constructing the gradient-sensitive scaling matrix are as follows: The overall gradient intensity normalization matrix is ​​used as the input parameter of the contrast weighting function; Each element in the overall gradient intensity normalization matrix is ​​processed using a contrast weighting function with an adjustable exponent; The processed elements are arranged into a diagonal matrix to form a gradient-sensitive scaling matrix. This matrix is ​​then used to adjust the contribution weights of individual data points in the residual terms.

6. The adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method as described in claim 1, characterized in that: The steps for constructing a joint objective function by combining the conventional data residual term, the data residual term, and the regularization term are as follows: Based on the difference between the observed electromagnetic field data and the electromagnetic field data predicted by forward modeling, a conventional data residual term is constructed. A joint objective function is constructed by weighting and combining the regular data residuals, the data residuals, and the regularization terms.

7. The adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method as described in claim 6, characterized in that: The data residuals include, The processing results of the differences between the weighted matrix of diagonal electromagnetic field data and the observed and predicted electromagnetic field data; The result of processing the difference between the weighted matrix of the diagonal gradient field data and the observed gradient data and the predicted gradient data; The result of adjusting the influence of the gradient-sensitive scaling matrix on the degree of influence of individual data points in the gradient data residual.

8. The adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method as described in claim 1, characterized in that: The inversion equation includes the Jacobian matrix for predicting electromagnetic field data and the Jacobian matrix for predicting spatial gradient data.

9. The adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method as described in claim 1, characterized in that: The specific steps for embedding the gradient-sensitive scaling matrix into the data residual term of the joint objective function to establish the inversion equation are as follows: The coefficient matrix of the inversion equation is constructed based on the Jacobian matrix of the predicted electromagnetic field data, the Jacobian matrix of the predicted spatial gradient data, and the gradient-sensitive scale matrix. Based on the Jacobian matrix of the predicted electromagnetic field data, the Jacobian matrix of the predicted spatial gradient data, the data residual terms, and the regularization terms, the gradient direction of the inversion equation is constructed. By combining the coefficient matrix with the gradient direction, an inversion equation is established.

10. The adaptive weighted high-precision joint inversion method based on electromagnetic gradient data-driven method as described in claim 1, characterized in that: The iterative calculation of the inversion equation and the updating of the resistivity model parameters yield a three-dimensional inversion result reflecting the spatial distribution of resistivity. The specific steps are as follows: Calculate the resistivity model update step value for the current iteration, and correct the resistivity model parameters based on the resistivity model update step value; Based on the corrected resistivity model parameters, the output is a three-dimensional inversion result reflecting the spatial distribution of resistivity.

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