A method and device for multi-parameter airborne electromagnetic inversion combined with sparse constraints

Abstract

This invention provides a multi-parameter semi-airborne electromagnetic inversion method and apparatus with joint sparse constraints, relating to the field of geophysical exploration technology. It acquires magnetic field response data at multiple altitudes and frequencies; establishes resistivity, polarizability, and dielectric constant models; analyzes the coupling degree of parameters at each frequency point, constructs a decoupling transformation matrix, and obtains three decoupling response components; performs a sparse domain transformation on the parameter models to construct independent and joint sparse constraints; uses the decoupling response components as the fitting target and the sparse constraints as regularization conditions, introduces auxiliary variables, and sets equality constraints to construct an augmented Lagrangian function; it iteratively solves the problem using the alternating direction multiplier method, and adaptively adjusts the data fitting weights based on the residual spectrum; and outputs three-dimensional resistivity, polarizability, and dielectric constant models. This invention effectively suppresses multi-parameter coupling crosstalk, ensures the consistency of physical property boundaries, and improves inversion resolution, stability, and convergence speed.

Description

Technical Field

[0001] This invention relates to the field of geophysical exploration technology, and more specifically, to a multi-parameter semi-airborne electromagnetic inversion method and apparatus with joint sparse constraints. Background Technology

[0002] Semi-airborne frequency domain electromagnetic detection methods combine the advantages of high-power ground transmission and UAV aerial reception, and have significant application value in deep mineral resource exploration, hydrogeological surveys, and exploration of complex terrain areas. Current exploration needs have upgraded from qualitative anomaly delineation to quantitative identification of physical parameters; relying solely on resistivity as a single parameter is insufficient for the precise identification and lithological differentiation of complex geological bodies.

[0003] In existing technologies, some methods have achieved simultaneous extraction of apparent resistivity and apparent polarizability, but they have not incorporated resistivity, polarizability, and dielectric constant into a unified inversion framework, nor have they addressed the coupling interference and structural constraints among multiple parameters. Other studies, while conducting full-current numerical simulations and multi-parameter apparent parameter extraction, remain at the level of apparent parameter imaging, failing to perform quantitative inversion of true parameters and failing to address parameter coupling, structural constraints, and adaptive optimization issues, thus making it difficult to meet current exploration needs. Summary of the Invention

[0004] The purpose of this invention is to provide a multi-parameter semi-airborne electromagnetic inversion method and apparatus with joint sparse constraints to improve the aforementioned problems. To achieve the above objective, the technical solution adopted by this invention is as follows:

[0005] Firstly, this application provides a multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints, including:

[0006] Acquire raw observation data, which includes vertical components and phase information of the magnetic field at different frequencies collected at multiple altitude levels;

[0007] Establish a parametric model to be inverted, which includes a resistivity model, a polarizability model, and a dielectric constant model;

[0008] The parameter coupling degree at each frequency point is analyzed based on the original observation data to construct an adaptive decoupling transformation matrix. The original observation data is then transformed using the decoupling transformation matrix to obtain three decoupling response components corresponding to resistivity, polarizability, and dielectric constant, respectively.

[0009] The parameter model is subjected to sparse domain transformation, and sparse constraints are constructed based on the transformed coefficients;

[0010] Using three decoupled response components as the fitting objective and sparse constraints as the regularization condition, an auxiliary variable is introduced and a constraint condition is set that the model variable is equal to the auxiliary variable to construct an augmented Lagrangian function.

[0011] The augmented Lagrangian function is solved iteratively by the alternating direction multiplier method. When the change in the parameter model between two adjacent iterations meets the preset convergence condition, the iteration is terminated, and the final parameter model is obtained.

[0012] Secondly, this application also provides a multi-parameter semi-airborne electromagnetic inversion device with joint sparse constraints, comprising:

[0013] The data acquisition module is used to acquire raw observation data, which includes the vertical components and phase information of the magnetic field at different frequencies collected at multiple height levels;

[0014] The model building module is used to build the parameter model to be inverted, which includes a resistivity model, a polarizability model, and a dielectric constant model.

[0015] The decoupling transformation module is used to analyze the parameter coupling degree at each frequency point based on the original observation data, so as to construct an adaptive decoupling transformation matrix. The original observation data is then transformed using the decoupling transformation matrix to obtain three decoupling response components corresponding to resistivity, polarizability and dielectric constant, respectively.

[0016] A sparse constraint construction module is used to perform sparse domain transformation on the parameter model and construct sparse constraints based on the transformed coefficients.

[0017] The function construction module is used to construct an augmented Lagrangian function with three decoupled response components as the fitting objective, sparse constraints as the regularization condition, auxiliary variables introduced, and constraints that make the model variables equal to the auxiliary variables set.

[0018] The iterative solution module is used to iteratively solve the augmented Lagrangian function using the alternating direction multiplier method. When the change in the parameter model between two adjacent iterations meets the preset convergence condition, the iteration is terminated, and the final parameter model is obtained.

[0019] Thirdly, this application also provides a multi-parameter semi-airborne electromagnetic inversion device with joint sparse constraints, comprising:

[0020] Memory, used to store computer programs;

[0021] A processor is used to implement the steps of the multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints when executing the computer program.

[0022] Fourthly, this application also provides a readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described multi-parameter semi-airborne electromagnetic inversion method based on joint sparse constraints.

[0023] The beneficial effects of this invention are as follows:

[0024] 1. This invention analyzes the parameter coupling degree at each frequency point and constructs an adaptive decoupling transformation matrix to transform the original observation data into three independent decoupling response components, effectively suppressing parameter crosstalk. At the same time, by applying independent sparsity constraints and joint sparsity constraints to the parameter models, it maintains the block uniformity of each parameter model and forces the consistency of the three parameter models on the spatial boundary, significantly improving the imaging resolution and the reliability of geological interpretation.

[0025] 2. This invention uses the alternating direction multiplier method to decompose the inversion problem into three sub-problems: parameter model update, auxiliary variable update, and Lagrange multiplier update. It also combines an adaptive weighting strategy to dynamically adjust the weights of each parameter in the data fitting, which greatly improves the convergence speed and stability of the inversion and reduces the dependence on manual parameter tuning.

[0026] Other features and advantages of the invention will be set forth in the following description, and will be apparent in part from the description, or may be learned by practicing embodiments of the invention. The objects and other advantages of the invention may be realized and obtained by means of the structures particularly pointed out in the written description, claims, and drawings. Attached Figure Description

[0027] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0028] Figure 1 This is a schematic diagram of the multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints described in this embodiment of the invention;

[0029] Figure 2 This is a schematic diagram of the structure of the multi-parameter semi-airborne electromagnetic inversion device with joint sparse constraints described in this embodiment of the invention.

[0030] Figure 3 This is a schematic diagram of the structure of the multi-parameter semi-airborne electromagnetic inversion device with joint sparse constraints as described in an embodiment of the present invention.

[0031] Marked in the image:

[0032] 800. Multi-parameter semi-airborne electromagnetic inversion device with joint sparse constraints; 801. Processor; 802. Memory; 803. Multimedia component; 804. I / O interface; 805. Communication component. Detailed Implementation

[0033] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0034] It should be noted that similar reference numerals and letters in the following figures indicate similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, terms such as "first," "second," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0035] Example 1:

[0036] This embodiment provides a multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints, including:

[0037] S1. Acquire raw observation data, which includes the vertical component and phase information of the magnetic field at different frequencies collected at multiple altitude layers;

[0038] Specifically, step S1 includes:

[0039] S11. The ground-based transmitter emits electromagnetic signals within a preset wideband range, wherein the preset wideband range is from 1Hz to 10MHz;

[0040] S12. The magnetic field sensor carried by the UAV collects the vertical component and phase data of the magnetic field at multiple altitude levels. Specifically, the multiple altitude levels include at least 50m, 80m, and 120m.

[0041] S13. Collect the vertical component of the magnetic field at each frequency point and each altitude layer. The phase data is then arranged to form the raw observation data, where f is the transmission frequency and h is the UAV flight altitude. This is the perpendicular component of the magnetic field;

[0042] Based on the above embodiments, this method further includes:

[0043] S2. Establish the parameter model to be inverted, which includes the resistivity model, polarizability model and dielectric constant model;

[0044] Specifically, the underground detection area is divided into multiple three-dimensional grid cells, each corresponding to a resistivity value, a polarizability value, and a dielectric constant value. The resistivity model is formed by the resistivity values, polarizability values, and dielectric constant values ​​of multiple three-dimensional grid cells. Polarizability model and dielectric constant model .

[0045] Based on the above embodiments, this method further includes:

[0046] S3. Analyze the parameter coupling degree at each frequency point based on the original observation data to construct an adaptive decoupling transformation matrix. Use the decoupling transformation matrix to transform the original observation data to obtain three decoupling response components corresponding to resistivity, polarizability and dielectric constant, respectively.

[0047] Specifically, step S3 includes:

[0048] S31. Calculate the Jacobian matrix of the original observation data with respect to resistivity, polarizability, and dielectric constant;

[0049] Specifically, for each transmission frequency ,in, Let represent the total number of transmitting radio points. Calculate the partial derivatives of the perpendicular component of the magnetic field with respect to resistivity, polarizability, and dielectric constant, respectively.

[0050] ;

[0051] Depend on , , Constructing the Jacobian matrix This is used to quantify the degree of influence of each parameter on the response.

[0052] S32. Based on the Jacobian matrix, quantify the coupling degree between parameters at different frequency points and construct a sensitivity matrix for the magnetic field amplitude response;

[0053] Specifically, define the coupling strength function. Used for quantization at frequency The degree of coupling between the three parameters is given by the coupling strength function, which is expressed as follows:

[0054] ;

[0055] In the formula, It is the Frobenius norm. To form a diagonal matrix that retains only the diagonal elements of J, The value ranges from 0 to 1. The closer the value is to 1, the stronger the coupling between parameters. The closer the value is to 0, the more independent the parameters are.

[0056] Furthermore, a sensitivity matrix is ​​constructed. The matrix focuses on the sensitivity of the magnetic field amplitude to parameters, and its elements are the logarithmic derivatives of the Jacobian matrix modulo each element, converted to the magnitude of the magnetic field. Specifically:

[0057] ;

[0058] In the formula, For the modulus of the complex number, It is the field of real numbers.

[0059] S33. Perform singular value decomposition on the sensitivity matrix to construct an adaptive weighting matrix and a decoupling transformation matrix;

[0060] Specifically, singular value decomposition is performed on the sensitivity matrix S:

[0061] ;

[0062] in, It is a left singular matrix. It is a singular value diagonal matrix. It is a right singular matrix.

[0063] Furthermore, based on the coupling strength at each frequency point Select the main sensitive frequency points based on resistivity, polarizability, and dielectric constant. Construct an adaptive weighted matrix :

[0064] ;

[0065] The adaptive weighting matrix is ​​used to suppress strong coupling directions: the stronger the coupling, the smaller the weight, and the higher the degree of decoupling.

[0066] Furthermore, a decoupling transformation matrix is ​​constructed based on the adaptive weighting matrix. :

[0067] ;

[0068] In this implementation, the decoupling transformation matrix is ​​used to project the original observation data from the frequency domain to the low-dimensional space where the three decoupling components reside.

[0069] S34. Use the decoupling transformation matrix to perform a decoupling transformation on the original observation data to obtain three decoupling response components;

[0070] Specifically, the original observation data vector is multiplied by the transpose of the decoupling transformation matrix to obtain the decoupled response vector. :

[0071] ;

[0072] In the formula, These are the decoupled response components for resistivity, polarizability, and dielectric constant, respectively.

[0073] Based on the above embodiments, this method further includes:

[0074] S4. Perform sparse domain transformation on the parameter model, and construct sparse constraints based on the transformed coefficients;

[0075] Specifically, step S4 includes:

[0076] S41. Using the wavelet transform matrix, curvelet transform matrix, or discrete cosine transform matrix as a sparse transform basis, perform sparse transforms on the resistivity model, polarizability model, and dielectric constant model respectively to obtain the sparse coefficient vector of each model in the transform domain.

[0077] In this embodiment, the sparse transformation basis The sparse transform basis employs a wavelet transform matrix. The size is ,in, This represents the total number of three-dimensional mesh cells.

[0078] For the resistivity model respectively Polarizability model and dielectric constant model Perform a sparse transformation to obtain the corresponding sparse coefficient vector:

[0079] ;

[0080] Where M is the total number of model grids, For a three-parameter model vector, This is the sparse coefficient vector in the transform domain;

[0081] S42. Apply independent sparsity constraints and joint sparsity constraints to each sparse coefficient vector respectively:

[0082] ;

[0083] In the formula, Indicates sparsity constraints. For independent sparsity constraints: for Norms promote single-parameter sparsity, i.e. express The sum of the absolute values ​​of all elements in the set. Independent sparse weights;

[0084] For joint sparsity constraints: To achieve joint sparse weights, the geological boundaries of the three parameters are forced to be consistent. The joint sparse constraint forces the sparse coefficients of the three parameter models to be either simultaneously zero or simultaneously non-zero at the same grid location, thereby ensuring that the abnormal boundary locations of resistivity, polarizability, and dielectric constant remain consistent.

[0085] Based on the above embodiments, this method further includes:

[0086] S5. Using the three decoupled response components as the fitting objective and sparse constraints as the regularization condition, an auxiliary variable is introduced and a constraint condition is set that the model variable is equal to the auxiliary variable to construct an augmented Lagrangian function.

[0087] Specifically, step S5 includes:

[0088] S51. Introduce corresponding auxiliary variables for each parameter model and set the corresponding Lagrange multipliers;

[0089] Specifically, in order to separate the joint sparse regularization term from the model variables, three auxiliary variables are introduced. Set a corresponding Lagrange multiplier vector for each equality constraint. The initial values ​​are all set to zero vectors.

[0090] S52. Establish equality constraints between each parametric model and its corresponding auxiliary variables:

[0091] ;

[0092] S53. Using the difference between the parametric model response and the decoupled response components as the error term, and the sparse constraint as the regularization term, construct the augmented Lagrangian function by constructing the difference between the model variable and the corresponding auxiliary variable as the penalty term.

[0093] Specifically, define the forward response. The forward response is obtained by forward calculation of the current parameter model and after undergoing the same decoupling transformation;

[0094] Furthermore, the multi-parameter inversion problem is transformed into a constrained optimization problem containing error terms and sparse constraint regularization terms. The original inversion problem is equivalent to:

[0095] ;

[0096] In the formula, It is the Euclidean norm; For sparse constraint regularization terms;

[0097] Furthermore, the constrained problem is transformed into an unconstrained optimization problem, and the augmented Lagrangian function is constructed:

[0098]

[0099] In the formula, This is a secondary penalty item. For linear terms of Lagrange multipliers, For penalty parameters, This is the transpose of a vector.

[0100] Based on the above embodiments, this method further includes:

[0101] S6. The augmented Lagrangian function is solved iteratively by the alternating direction multiplier method. When the change in the parameter model between two adjacent iterations meets the preset convergence condition, the iteration is terminated to obtain the final parameter model.

[0102] In this embodiment, the alternating direction multiplier method (ADMM) is used to iteratively solve the augmented Lagrange function. Each iteration sequentially performs parameter model updates, auxiliary variable updates, and Lagrange multiplier updates, while an adaptive weighting strategy is introduced to dynamically adjust the weights of the data fitting error term.

[0103] Specifically, step S6 includes:

[0104] S61. In each iteration, the Gauss-Newton method is used to update the parameter model. Specifically, in the k-th iteration, the auxiliary variables and Lagrange multipliers obtained in the previous iteration are fixed, and the unconstrained minimization subproblem of the parameter model is solved.

[0105] Specifically, step S61 includes:

[0106] S611. Construct an objective function with the auxiliary variable of the current iteration as a reference benchmark. The objective function includes an error term for the parametric model response and the decoupled response components, as well as a proximal constraint term for the difference between the parametric model and the auxiliary variable.

[0107] Specifically, the objective function is:

[0108] ;

[0109] In the formula, Let represent the auxiliary variables in the k-th iteration.

[0110] S612. The optimization problem of the objective function is transformed into a linear least squares problem;

[0111] Specifically, a first-order linear approximation is made to the forward response at the current model parameters, so that the original nonlinear least squares problem is approximated as a linear least squares problem in each Gauss-Newton iteration.

[0112] S613. Solve the linear least squares problem to obtain the correction values ​​for each parameter model, and then add the current parameter model to the correction values ​​to obtain the updated parameter model. ;

[0113] S62. Transform the updated parameter model using the proximal operator of the joint sparse constraint to obtain the updated auxiliary variables;

[0114] Specifically, the proximal operator is defined as:

[0115] ;

[0116] In the formula, Denotes the joint sparse regularization term, by Norm and The norm is composed of x, which represents the input variable, such as resistivity model, polarizability model, or dielectric constant model. Let μ represent the auxiliary variable and μ represent the penalty parameter.

[0117] Furthermore, the updated parameter model is fixed. Update auxiliary variables using proximal operators:

[0118] ;

[0119] In the formula, , , Let represent the auxiliary variables in the (k+1)th iteration.

[0120] S63. Update the Lagrange multipliers using the updated parameter model and auxiliary variables:

[0121] ;

[0122] In the formula, , , Let represent the Lagrange multipliers in the (k+1)th iteration.

[0123] Specifically, step S6 further includes dynamically adjusting the weights:

[0124] S64. In each iteration, calculate the residual spectrum between the current model response and the three decoupled response components at each frequency point;

[0125] In this embodiment, to achieve adaptive regularization adjustment, the residual between the model response and the decoupled data is calculated in each iteration. Specifically, the residual at frequency f is defined as:

[0126] ;

[0127] The residuals at all frequency points are calculated sequentially using the above formula to form the residual spectrum.

[0128] S65. Divide the residual spectrum into multiple frequency bands according to the main sensitive frequency bands of each parameter, and calculate the average residual of each frequency band;

[0129] Specifically, based on prior knowledge, the dominant sensitive frequency bands for the three parameters are determined: the dominant sensitive frequency band for resistivity is the low-frequency band. Specifically, the frequency range is 1-100Hz, with the main sensitive frequency band for polarization being the mid-frequency band. Specifically, the main sensitive frequency band for dielectric constant is the high-frequency band, which is 100Hz-1kHz. Specifically, for the frequency range of 1kHz-10MHz, the average residual within each frequency band was calculated:

[0130] ;

[0131] In the formula, , , This indicates the number of frequency points within the corresponding frequency band.

[0132] S66. Dynamically adjust the weights of each parameter in the error term based on the average residual;

[0133] In this embodiment, an exponential function is used to update the weight of each parameter in the data fitting term. The larger the residual, the greater the weight. Parameters with large fitting errors are optimized first.

[0134] ;

[0135] In the formula, For learning rate, , where are the weights of resistivity, polarizability, and dielectric constant, respectively, and t and t+1 are the iteration numbers, respectively. These are the average residuals of resistivity, polarizability, and dielectric constant within their main sensitive frequency bands, respectively.

[0136] Furthermore, update the Gauss-Newton curve using the updated weights:

[0137] ;

[0138] In the formula, These are the decoupled response components corresponding to resistivity, polarizability, and dielectric constant. The response components are obtained after forward modeling and decoupling of the current parameter model.

[0139] After each iteration, the changes in the parameter models between two adjacent iterations are calculated. The iteration terminates when the changes in the resistivity, polarizability, and dielectric constant models obtained from two adjacent iterations are less than a preset threshold, or when the current iteration count reaches the preset maximum iteration count. The result from the last iteration is then used. As the final inversion result, images of the distribution of resistivity, polarizability, and dielectric constant in three-dimensional space are generated.

[0140] Example 2:

[0141] This embodiment takes a complex geological model containing anomalies as an example and uses the same steps and procedures as in Embodiment 1 to further illustrate the implementation process and effects of the method of the present invention.

[0142] S1. Acquire raw observation data, which includes the vertical component and phase information of the magnetic field at different frequencies collected at multiple altitude layers;

[0143] Specifically, the transmission system is a ground-based long-wire power source, with a transmission frequency band of 100Hz-50000Hz, selecting 10 frequency points;

[0144] The receiving system is a quadcopter drone equipped with a three-axis magnetic probe, which collects the vertical component and phase of the magnetic field at three altitude levels: 50m, 80m and 120m.

[0145] The target model is a three-layer model. The second layer is a low-resistivity, high-polarization, and high-dielectric anomaly with a resistivity of 15 Ω·m, a polarizability of 0.7, and a dielectric constant that is 18 times that of the vacuum dielectric constant. The background surrounding rock has a resistivity of 100 Ω·m, a polarizability of 0.1, and a dielectric constant that is 6 times that of the vacuum dielectric constant.

[0146] The data collected at each frequency point and each altitude level are arranged in ascending order of frequency and ascending order of altitude to form the original observation data.

[0147] S2. Establish the parameter model to be inverted, which includes the resistivity model, polarizability model and dielectric constant model;

[0148] S3. Analyze the parameter coupling degree at each frequency point based on the original observation data to construct an adaptive decoupling transformation matrix. Use the decoupling transformation matrix to transform the original observation data to obtain three decoupling response components corresponding to resistivity, polarizability and dielectric constant, respectively.

[0149] Specifically, the Jacobian matrix and coupling strength spectrum are calculated, yielding coupling strengths of approximately 0.1 to 0.25 in the low-frequency band, approximately 0.3 to 0.55 in the mid-frequency band, and approximately 0.55 to 0.75 in the high-frequency band. Based on these coupling strengths, an adaptive decoupling matrix is ​​constructed, transforming the original data into three decoupling response components. .

[0150] S4. Perform sparse domain transformation on the parameter model, and construct sparse constraints based on the transformed coefficients;

[0151] Specifically, the Daubechies wavelet basis is used as the sparse transform basis. Sparse transformations were performed on the resistivity model, polarizability model, and dielectric constant model respectively to obtain sparse coefficient vectors. Furthermore, set independent sparse weights. Joint sparse weights To construct joint sparse regularization terms .

[0152] S5. Using the three decoupled response components as the fitting objective and sparse constraints as the regularization condition, an auxiliary variable is introduced and a constraint condition is set that the model variable is equal to the auxiliary variable to construct an augmented Lagrangian function.

[0153] Specifically, auxiliary variables are introduced for the resistivity model, polarizability model, and dielectric constant model, respectively. and Lagrange multipliers Establish equality constraints The difference between the parametric model response and the three decoupled response components is used as the error term, the joint sparse constraint is used as the regularization term, and the difference between the model variable and the corresponding auxiliary variable is used as the penalty term to construct the augmented Lagrangian function.

[0154] S6. The augmented Lagrangian function is solved iteratively by the alternating direction multiplier method. When the change in the parameter model between two adjacent iterations meets the preset convergence condition, the iteration is terminated to obtain the final parameter model.

[0155] Specifically, an iterative solution is performed using the alternating direction multiplier method, updating the three-parameter model, auxiliary variables, and Lagrange multipliers sequentially in each iteration. Simultaneously, the residual spectrum of the model response and decoupled response components is calculated in each iteration, divided according to the dominant sensitive frequency band of each parameter, and the average residual is calculated. An exponential function is used to dynamically adjust the weights of each parameter in the data fitting term; preferably, the learning rate is 0.15.

[0156] During the iteration process, the model is rapidly adjusted in the first 3 iterations, tends to stabilize after the 5th iteration, and the model change is less than the preset threshold after the 8th iteration, thus terminating the iteration.

[0157] In the inversion results, the inverted resistivity value of the anomalous volume is approximately The polarizability is approximately 0.57, and the relative permittivity is approximately... .

[0158] The final resistivity model, polarizability model, and dielectric constant model are then visualized in three dimensions to generate three-dimensional resistivity distribution maps, three-dimensional polarizability distribution maps, and three-dimensional dielectric constant distribution maps, respectively.

[0159] Example 3:

[0160] like Figure 2 As shown, this embodiment provides a multi-parameter semi-airborne electromagnetic inversion device with joint sparse constraints, the device comprising:

[0161] The data acquisition module is used to acquire raw observation data, which includes the vertical components and phase information of the magnetic field at different frequencies collected at multiple height levels;

[0162] The model building module is used to build the parameter model to be inverted, which includes a resistivity model, a polarizability model, and a dielectric constant model.

[0163] The decoupling transformation module is used to analyze the parameter coupling degree at each frequency point based on the original observation data, so as to construct an adaptive decoupling transformation matrix. The original observation data is then transformed using the decoupling transformation matrix to obtain three decoupling response components corresponding to resistivity, polarizability and dielectric constant, respectively.

[0164] A sparse constraint construction module is used to perform sparse domain transformation on the parameter model and construct sparse constraints based on the transformed coefficients.

[0165] The function construction module is used to construct an augmented Lagrangian function with three decoupled response components as the fitting objective, sparse constraints as the regularization condition, auxiliary variables introduced, and constraints that make the model variables equal to the auxiliary variables set.

[0166] The iterative solution module is used to iteratively solve the augmented Lagrangian function using the alternating direction multiplier method. When the change in the parameter model between two adjacent iterations meets the preset convergence condition, the iteration is terminated, and the final parameter model is obtained.

[0167] Based on the above embodiments, the data acquisition module includes:

[0168] A signal transmitting unit is used to control a ground-based transmitter to transmit electromagnetic signals within a preset wideband range, wherein the preset wideband range is from 1Hz to 10MHz.

[0169] The data acquisition unit is used to control the magnetic field sensor carried by the UAV to collect the vertical component and phase data of the magnetic field at multiple altitude levels.

[0170] The data arrangement unit is used to arrange the vertical component and phase data of the magnetic field collected at each frequency point and each altitude layer to form the raw observation data.

[0171] Based on the above embodiments, the decoupling transformation module includes:

[0172] The Jacobian matrix calculation unit is used to calculate the Jacobian matrix of the original observation data with respect to resistivity, polarizability, and dielectric constant.

[0173] A matrix construction unit is used to quantify the coupling degree between parameters at different frequency points based on the Jacobian matrix and construct a sensitivity matrix for the magnetic field amplitude response.

[0174] A singular value decomposition unit is used to perform singular value decomposition on the sensitivity matrix to construct an adaptive weighting matrix and a decoupling transformation matrix;

[0175] The decoupling transformation unit is used to decouple the original observation data using the decoupling transformation matrix to obtain three decoupled response components.

[0176] Based on the above embodiments, the sparse constraint construction module includes:

[0177] The sparse transform unit is used to take the wavelet transform matrix, curvelet transform matrix or discrete cosine transform matrix as sparse transform basis, and perform sparse transform on resistivity model, polarizability model and dielectric constant model respectively to obtain the sparse coefficient vector of each model in the transform domain.

[0178] The constraint application unit is used to apply independent sparse constraints and joint sparse constraints to each sparse coefficient vector, respectively.

[0179] Based on the above embodiments, the function construction module includes:

[0180] The auxiliary variable introduction unit is used to introduce corresponding auxiliary variables for each parameter model and set the corresponding Lagrange multipliers;

[0181] The equality constraint establishment unit is used to establish equality constraint relationships between each parameter model and its corresponding auxiliary variables;

[0182] The function building unit is used to construct an augmented Lagrangian function by using the difference between the parametric model response and the decoupled response components as the error term, the sparse constraint as the regularization term, and the difference between the model variables and the corresponding auxiliary variables as the penalty term.

[0183] Based on the above embodiments, the iterative solution module includes:

[0184] The parameter model update unit is used to update the parameter model using the Gauss-Newton method in each iteration;

[0185] The variable update unit is used to transform the updated parameter model using the proximal operator of the joint sparse constraint to obtain the updated auxiliary variables;

[0186] The multiplier update unit is used to update the Lagrange multipliers using the updated parameter model and auxiliary variables.

[0187] The parameter model update unit includes:

[0188] The objective function construction sub-unit is used to construct the objective function with the auxiliary variable of the current iteration as a reference. The objective function includes the error term of the parametric model response and the decoupled response component, as well as the proximal constraint term of the difference between the parametric model and the auxiliary variable.

[0189] An optimization transformation subunit is used to transform the optimization problem of the objective function into a linear least squares problem;

[0190] The model correction subunit is used to solve the linear least squares problem to obtain the correction amount of each parameter model, and to superimpose the current parameter model with the correction amount to obtain the updated parameter model.

[0191] The iterative solution module further includes an adaptive weighting unit, which is used for:

[0192] In each iteration, the residual spectrum between the current model response and the three decoupled response components at each frequency point is calculated.

[0193] The residual spectrum is divided into multiple frequency bands according to the main sensitive frequency bands of each parameter, and the average residual of each frequency band is calculated.

[0194] The weights of each parameter in the error term are dynamically adjusted based on the average residual.

[0195] It should be noted that the specific manner in which each module performs its operation in the apparatus described in the above embodiments has been described in detail in the embodiments of the method, and will not be elaborated here.

[0196] Example 4:

[0197] Corresponding to the above method embodiments, this embodiment also provides a multi-parameter semi-airborne electromagnetic inversion device with joint sparse constraints. The multi-parameter semi-airborne electromagnetic inversion device with joint sparse constraints described below and the multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints described above can be referred to each other.

[0198] Figure 3 This is a block diagram illustrating a multi-parameter semi-airborne electromagnetic inversion device 800 with joint sparse constraints, according to an exemplary embodiment. Figure 3As shown, the multi-parameter semi-airborne electromagnetic inversion device 800 with joint sparse constraints may include: a processor 801 and a memory 802. The multi-parameter semi-airborne electromagnetic inversion device 800 with joint sparse constraints may also include one or more of the following: a multimedia component 803, an I / O interface 804, and a communication component 805.

[0199] The processor 801 controls the overall operation of the joint sparse constraint multi-parameter semi-airborne electromagnetic inversion device 800 to complete all or part of the steps in the aforementioned joint sparse constraint multi-parameter semi-airborne electromagnetic inversion method. The memory 802 stores various types of data to support the operation of the joint sparse constraint multi-parameter semi-airborne electromagnetic inversion device 800. This data may include, for example, instructions for any application or method operating on the joint sparse constraint multi-parameter semi-airborne electromagnetic inversion device 800, as well as application-related data such as contact data, sent and received messages, images, audio, video, etc. The memory 802 can be implemented using 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 Read-Only Memory (PROM), Read-Only Memory (ROM), magnetic storage, flash memory, magnetic disk, or optical disk. The multimedia component 803 may include a screen and an audio component. The screen may be, for example, a touchscreen, and the audio component is used to output and / or input audio signals. For example, the audio component may include a microphone for receiving external audio signals. The received audio signals may be further stored in the memory 802 or transmitted via the communication component 805. The audio component also includes at least one speaker for outputting audio signals. I / O interface 804 provides an interface between processor 801 and other interface modules, such as keyboards, mice, and buttons. These buttons can be virtual or physical. Communication component 805 is used for wired or wireless communication between the joint sparse-constrained multi-parameter semi-airborne electromagnetic inversion device 800 and other devices. Wireless communication includes, for example, Wi-Fi, Bluetooth, Near Field Communication (NFC), 2G, 3G, or 4G, or a combination thereof. Therefore, the corresponding communication component 805 may include a Wi-Fi module, a Bluetooth module, and an NFC module.

[0200] In an exemplary embodiment, the multi-parameter semi-airborne electromagnetic inversion device 800 with joint sparse constraints can be implemented by one or more application-specific integrated circuits (ASICs), digital signal processors (DSPs), digital signal processing devices (DSPDs), programmable logic devices (PLDs), field-programmable gate arrays (FPGAs), controllers, microcontrollers, microprocessors, or other electronic components to perform the multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints described above.

[0201] In another exemplary embodiment, a computer-readable storage medium including program instructions is also provided, which, when executed by a processor, implement the steps of the aforementioned joint sparse constraint multi-parameter semi-airborne electromagnetic inversion method. For example, the computer-readable storage medium may be the aforementioned memory 802 including program instructions, which may be executed by the processor 801 of the joint sparse constraint multi-parameter semi-airborne electromagnetic inversion device 800 to complete the aforementioned joint sparse constraint multi-parameter semi-airborne electromagnetic inversion method.

[0202] Example 5:

[0203] Corresponding to the above method embodiments, this embodiment also provides a readable storage medium. The readable storage medium described below can be referred to in relation to the multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints described above.

[0204] A readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints described in the above method embodiments.

[0205] The readable storage medium can specifically be a USB flash drive, external hard drive, read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk, or any other readable storage medium capable of storing program code.

[0206] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

[0207] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints, characterized in that, include: Acquire raw observation data, which includes vertical components and phase information of the magnetic field at different frequencies collected at multiple altitude levels; Establish a parametric model to be inverted, which includes a resistivity model, a polarizability model, and a dielectric constant model; The parameter coupling degree at each frequency point is analyzed based on the original observation data to construct an adaptive decoupling transformation matrix. The original observation data is then transformed using the decoupling transformation matrix to obtain three decoupling response components corresponding to resistivity, polarizability, and dielectric constant, respectively. The parameter model is subjected to sparse domain transformation, and sparse constraints are constructed based on the transformed coefficients; Using three decoupled response components as the fitting objective and sparse constraints as the regularization condition, an auxiliary variable is introduced and a constraint condition is set that the model variable is equal to the auxiliary variable to construct an augmented Lagrangian function. The augmented Lagrangian function is solved iteratively by the alternating direction multiplier method. When the change in the parameter model between two adjacent iterations meets the preset convergence condition, the iteration is terminated, and the final parameter model is obtained.

2. The multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints according to claim 1, characterized in that, Obtain raw observation data, including: The ground-based transmitter emits electromagnetic signals within a preset wideband range, which is 1Hz to 10MHz. The magnetic field sensor carried by the drone collects the vertical component and phase data of the magnetic field at multiple altitude levels; The vertical component and phase data of the magnetic field collected at each frequency and at each altitude layer are arranged to form the original observation data.

3. The multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints according to claim 1, characterized in that, Based on the analysis of the parameter coupling degree at each frequency point using the original observation data, an adaptive decoupling transformation matrix is ​​constructed. This decoupling transformation matrix is ​​then used to transform the original observation data, yielding three decoupling response components corresponding to resistivity, polarizability, and dielectric constant, respectively. Calculate the Jacobian matrix of the original observation data with respect to resistivity, polarizability, and dielectric constant; Based on the Jacobian matrix, the degree of coupling between parameters at different frequency points is quantified, and a sensitivity matrix for the magnetic field amplitude response is constructed. Singular value decomposition is performed on the sensitivity matrix to construct an adaptive weighting matrix and a decoupling transformation matrix; The original observation data is decoupled using the decoupling transformation matrix to obtain three decoupled response components.

4. The multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints according to claim 1, characterized in that, The parameter model is subjected to sparse domain transformation, and sparse constraints are constructed based on the transformed coefficients, including: Using wavelet transform matrix, curvilinear transform matrix or discrete cosine transform matrix as sparse transform basis, sparse transform is performed on resistivity model, polarizability model and dielectric constant model respectively to obtain sparse coefficient vector of each model in the transform domain. Apply independent sparsity constraints and joint sparsity constraints to each sparse coefficient vector respectively.

5. The multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints according to claim 1, characterized in that, Using three decoupled response components as the fitting objective and sparse constraints as the regularization condition, an auxiliary variable is introduced, and a constraint condition is set that the model variable is equal to the auxiliary variable. An augmented Lagrangian function is constructed, including: For each parameter model, introduce corresponding auxiliary variables and set corresponding Lagrange multipliers; Establish equality constraints between each parameter model and its corresponding auxiliary variables; Using the difference between the parametric model response and the decoupled response components as the error term, and the sparse constraint as the regularization term, the difference between the model variable and the corresponding auxiliary variable is used as the penalty term to construct the augmented Lagrangian function.

6. The multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints according to claim 1, characterized in that, The augmented Lagrangian function is solved iteratively using the alternating direction multiplier method, including: In each iteration, the Gauss-Newton method is used to update the parameter model; The updated parameter model is transformed using the proximal operator of joint sparse constraints to obtain the updated auxiliary variables; Update the Lagrange multipliers using the updated parameter model and auxiliary variables.

7. The multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints according to claim 6, characterized in that, The Gauss-Newton method is used to update the parameter model, including: A target function is constructed using the auxiliary variable of the current iteration as a reference benchmark. The target function includes an error term for the parametric model response and the decoupled response components, as well as a proximal constraint term for the difference between the parametric model and the auxiliary variable. The optimization problem of the objective function is transformed into a linear least squares problem; Solving the linear least squares problem yields the correction values ​​for each parameter model, and the current parameter model is superimposed with the correction values ​​to obtain the updated parameter model.

8. The multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints according to claim 1, characterized in that, The iterative solution of the augmented Lagrangian function using the alternating direction multiplier method also includes: In each iteration, the residual spectrum between the current model response and the three decoupled response components at each frequency point is calculated. The residual spectrum is divided into multiple frequency bands according to the main sensitive frequency bands of each parameter, and the average residual of each frequency band is calculated. The weights of each parameter in the error term are dynamically adjusted based on the average residual.

9. The multi-parameter semi-airborne electromagnetic inversion method with joint sparse constraints according to claim 1, characterized in that, The preset convergence condition is: the change in the resistivity model, polarizability model, and dielectric constant model obtained from two adjacent iterations is less than a preset threshold, or the current iteration number reaches the preset maximum iteration number.

10. A multi-parameter semi-airborne electromagnetic inversion device with joint sparse constraints, characterized in that, include: The data acquisition module is used to acquire raw observation data, which includes the vertical components and phase information of the magnetic field at different frequencies collected at multiple height levels; The model building module is used to build the parameter model to be inverted, which includes a resistivity model, a polarizability model, and a dielectric constant model. The decoupling transformation module is used to analyze the parameter coupling degree at each frequency point based on the original observation data, so as to construct an adaptive decoupling transformation matrix. The original observation data is then transformed using the decoupling transformation matrix to obtain three decoupling response components corresponding to resistivity, polarizability and dielectric constant, respectively. A sparse constraint construction module is used to perform sparse domain transformation on the parameter model and construct sparse constraints based on the transformed coefficients. The function construction module is used to construct an augmented Lagrangian function with three decoupled response components as the fitting objective, sparse constraints as the regularization condition, auxiliary variables introduced, and constraints that make the model variables equal to the auxiliary variables set. The iterative solution module is used to iteratively solve the augmented Lagrangian function using the alternating direction multiplier method. When the change in the parameter model between two adjacent iterations meets the preset convergence condition, the iteration is terminated, and the final parameter model is obtained.

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