A time-domain superconducting electromagnetic multi-effect multi-parameter extraction method and system

Abstract

The present disclosure relates to the technical field of time domain electromagnetic geological exploration, and particularly relates to a time domain superconducting electromagnetic multi-effect multi-parameter extraction method and system, which comprises the following steps: calculating a time domain superconducting electromagnetic induction-polarization-magnetization multi-effect response, constructing a data error fitting term based on the residual of the multi-effect response and measured data; constructing a constraint matrix of a multi-parameter correlation coefficient including resistivity, polarizability and magnetic susceptibility, and constructing a multi-parameter statistical constraint term for describing the statistical correlation among the multi-parameters based on the constraint matrix; constructing a regularization objective function; and using an improved Gauss-Newton optimization algorithm to iteratively solve the optimal value of the regularization objective function by minimizing the regularization objective function, so as to synchronously invert the resistivity, polarizability and magnetic susceptibility. The present disclosure realizes efficient and accurate extraction imaging of multi-parameters in the field of deep mineral exploration and geological structure identification.

Description

Technical Field

[0001] This disclosure relates to the field of time-domain electromagnetic geological exploration technology, and in particular to a time-domain superconducting electromagnetic multi-effect and multi-parameter extraction method and system. Background Technology

[0002] In time-domain electromagnetic (TDOM) exploration of metallic minerals, resistivity, as a core parameter characterizing the electrical properties of subsurface media, has long been a key basis for geological interpretation. In recent years, with the evolution of TDOM observation technology towards higher precision and multi-dimensionality, and breakthroughs in nonlinear inversion and multi-physics coupling modeling methods, polarizability and magnetic susceptibility parameters have gradually become important supplementary parameters for characterizing the induced polarization and ferromagnetic features of metallic mineral bodies. Compared to the induction coil receiving devices used in traditional TDOM systems, magnetic field measurement systems based on superconducting quantum interference (SQUID) technology have higher sensitivity and can effectively capture the weak induction-polarization-magnetization composite response signals generated by deep metallic mineral bodies. However, the multi-parameter coupling effect exhibits significant nonlinear characteristics in its time-domain attenuation characteristics, frequency dependence, and spatial distribution patterns, leading to key challenges such as complex theoretical modeling and prominent ill-conditioned inversion issues in the decoupling of multi-effect signals and the quantitative extraction of independent parameters. Summary of the Invention

[0003] This disclosure provides a time-domain superconducting electromagnetic multi-effect multi-parameter extraction method and system, which solves the problem of insufficient accuracy in existing electromagnetic multi-effect parameter extraction and interpretation.

[0004] A method for extracting multiple effects and parameters of time-domain superconducting electromagnetic fields according to an embodiment of the first aspect of this disclosure includes:

[0005] The time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response was calculated, and a data error fitting term was constructed based on the residuals between the multi-effect response and the measured data.

[0006] A constraint matrix is ​​constructed that includes the correlation coefficients of multiple parameters such as resistivity, polarizability and magnetic susceptibility, and a multi-parameter statistical constraint term is constructed based on the constraint matrix to describe the statistical correlation between multiple parameters.

[0007] A regularization objective function is constructed, which is composed of a weighted sum of the data error fitting term, the multi-parameter statistical constraint term, and the model parameter regularization term;

[0008] An improved Gauss-Newton optimization algorithm is used to iteratively solve for the optimal value of the regularization objective function by minimizing it, and the resistivity, polarizability and magnetizability are obtained simultaneously by inversion.

[0009] Furthermore, the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response is calculated, including:

[0010] Establish a Cole-Cole fractional conductivity model to characterize the induction-polarization effect of complex media, and a Cole-Cole fractional magnetic susceptibility model to characterize the magnetization effect of complex media;

[0011] Based on the Cole-Cole fractional conductivity model and the Cole-Cole fractional magnetic susceptibility model, the frequency domain superconducting vertical magnetic field response of the layered medium under the induction-polarization-magnetization multi-effect is calculated.

[0012] By using sine and cosine numerical filtering coefficients to perform time-frequency conversion on the frequency domain superconducting vertical magnetic field response, the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response corresponding to the layered medium is obtained.

[0013] Furthermore, a constraint matrix is ​​constructed, comprising the correlation coefficients of multiple parameters including resistivity, polarizability, and magnetic susceptibility, including:

[0014] Determine the logarithmic expectation vector and the multi-parameter orthometric matrix based on the physical property statistics of geological models or typical mineral deposits;

[0015] A constraint matrix is ​​constructed using the Kronecker product of the multi-parameter oblique variance matrix and the N-order identity matrix;

[0016] Construct a diagonal matrix, wherein the diagonal elements of the diagonal matrix correspond to the expected vectors of each model parameter in spatial location;

[0017] Connect the diagonal matrix with The Kronecker product operation is performed on the identity matrix to obtain the reference model baseline matrix;

[0018] Subtract the reference model baseline matrix from the current model parameters to obtain the deviation of the model parameters from the statistical expectation;

[0019] The deviation is weighted and constrained using a constraint matrix.

[0020] The multi-parameter statistical constraint term is constructed by calculating the L2 norm square of the weighted constraint deviation.

[0021] Furthermore, the model parameters are expressed as follows:

[0022] ,

[0023] In the above formula, These represent the logarithmic zero-frequency resistivity, logarithmic polarizability, and logarithmic zero-frequency permeability of the first layer, respectively. They represent the first The logarithmic zero-frequency resistivity of the layer, the first Log-polarizability of the layer, the first Logarithmic zero-frequency permeability of the layer These are the model parameters.

[0024] Furthermore, the constraint matrix is ​​represented as: , For the constraint matrix, for An identity matrix of order 1. For the Kronecker product operation, It is the inverse of the multi-parameter covariance matrix.

[0025] Furthermore, the multi-parameter covariance matrix is ​​expressed as:

[0026] ,

[0027] In the above formula, the diagonal elements represent the variance, and the off-diagonal elements represent the covariance. For resistivity variance, The variance of polarizability Let Variance be the magnetic susceptibility. The covariance of resistivity and magnetic susceptibility. The covariance between polarizability and resistivity The covariance between polarizability and magnetic susceptibility. The covariance between magnetic susceptibility and resistivity. Let be the covariance between magnetic susceptibility and polarizability.

[0028] Furthermore, the regularization objective function is expressed as:

[0029] ,

[0030] in, Describes the regularization objective function. This is the data error fitting term. It is an observation data vector. This represents the multi-effect response under the current model parameters. For multi-parameter statistical constraints, For model parameters, It is a diagonal matrix. for An identity matrix of order 1. For the Kronecker product operation, These are the weighting coefficients. As a model regularization factor, for The smooth constraint matrix of the order model.

[0031] Furthermore, an improved Gauss-Newton optimization algorithm is employed to iteratively solve for the optimal value of the regularization objective function by minimizing it, including:

[0032] Acquire observation data and initialize model parameters and regularization parameters, including model regularization factors and weight coefficients; solve the regularization objective function using an improved Gauss-Newton optimization algorithm to obtain the model update amount and update the model parameters; calculate the data mismatch reduction rate of the current iteration and adaptively adjust at least one of the regularization parameters based on the data mismatch reduction rates of two adjacent iterations for constructing the regularization objective function of the next iteration; repeat the iteration until the preset convergence condition is met, and output the final model parameters.

[0033] Furthermore, at least one of the regularization parameters is adaptively adjusted using the following formula:

[0034] ,

[0035] ,

[0036] In the formula, , and The preset descent rate threshold, and For coefficients, This represents the rate of decrease in data mismatch during the k-th iteration. For the first Weight coefficients for the next iteration For the first The model regularization factor for the next iteration For the first Weight coefficients for the next iteration For the first The model regularization factor for each iteration.

[0037] The second aspect of this disclosure provides a time-domain superconducting electromagnetic multi-effect multi-parameter extraction system for performing the aforementioned time-domain superconducting electromagnetic multi-effect multi-parameter extraction method, comprising:

[0038] The response calculation and residual construction module calculates the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response, and constructs a data error fitting term based on the residual between the multi-effect response and the measured data;

[0039] The statistical constraint construction module constructs a constraint matrix including the correlation coefficients of multiple parameters such as resistivity, polarizability and magnetic susceptibility, and constructs a multi-parameter statistical constraint term to describe the statistical correlation between multiple parameters based on the constraint matrix.

[0040] The objective function construction module constructs a regularized objective function, which is composed of a weighted sum of the data error fitting term, the multi-parameter statistical constraint term, and the model parameter regularization term.

[0041] The optimization module employs an improved Gauss-Newton optimization algorithm. By minimizing the regularized objective function, it iteratively solves for the optimal value of the regularized objective function and simultaneously inverts to obtain resistivity, polarizability, and magnetizability.

[0042] Beneficial effects: Compared with existing technologies, this disclosure achieves multi-parameter extraction of the time-domain superconducting electromagnetic multi-effect response. Applied to a three-layered medium theoretical model, the extracted resistivity, polarizability, and magnetic susceptibility parameters are basically consistent with the set theoretical parameters. The superconducting time-domain electromagnetic response shows good fitting, with a root mean square error (RMS) of less than 5%. This method provides new technical support for mineral resource exploration and is conducive to the practical application of time-domain superconducting electromagnetic detection. Attached Figure Description

[0043] Figure 1 This is a flowchart of a time-domain superconducting electromagnetic multi-effect and multi-parameter extraction method provided in an embodiment of this disclosure;

[0044] Figure 2 This is a schematic diagram of the theoretical layered model parameter settings and the time-domain airborne superconducting electromagnetic detection and observation system provided in the embodiments of this disclosure;

[0045] Figure 3 This is a comparison of the fitting results of the noisy fitted time-domain airborne superconducting multi-effect response and the parameter-extracted time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response provided in the embodiments of this disclosure;

[0046] Figure 4 This is a comparison of multiple parameters, including resistivity, polarizability, and magnetic susceptibility, provided in the embodiments of this disclosure, between setting a layered formation model and extracting parameters from the layered model. Detailed Implementation

[0047] To make the objectives, technical solutions, and advantages of this disclosure clearer, the following detailed description is provided in conjunction with the accompanying drawings and specific embodiments. It should be understood that the specific embodiments described herein are merely illustrative and are not intended to limit the scope of this disclosure.

[0048] Based on the fractional polarizability and magnetic susceptibility model, this disclosure uses the statistical correlation constraint relationship of resistivity, polarizability, and magnetic susceptibility to construct a regularization objective function by weighted summation of the data error fitting term, the multi-parameter statistical constraint term, and the model parameter regularization term. The regularization objective function is optimized using an improved Gauss-Newton algorithm to complete the multi-parameter extraction and imaging of underground media.

[0049] Combination Figure 1 As shown, a method for extracting multiple effects and parameters of time-domain superconducting electromagnetics includes:

[0050] S101, Calculate the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response, and construct a data error fitting term based on the residuals of the multi-effect coupled response and the measured data;

[0051] S102, construct a constraint matrix including the multi-parameter correlation coefficients of resistivity, polarizability and magnetic susceptibility, and construct a multi-parameter statistical constraint term to describe the statistical correlation between the multi-parameters based on the constraint matrix;

[0052] S103, Construct a regularization objective function, which is composed of a weighted sum of the data error fitting term, the multi-parameter statistical constraint term, and the model parameter regularization term;

[0053] S104 employs an improved Gauss-Newton optimization algorithm. By minimizing the regularization objective function, it iteratively solves for the optimal value of the regularization objective function, and simultaneously inverts to obtain resistivity, polarizability, and magnetizability.

[0054] By calculating the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response, and addressing the difficulty of separating the coupling of resistivity, polarizability, and magnetic susceptibility in traditional electromagnetic parameter extraction techniques, a multi-parameter correlation coefficient constraint matrix for resistivity, polarizability, and magnetic susceptibility is constructed to achieve statistical distribution correlation constraints on physical property parameters. This constraint matrix is ​​introduced into a regularization objective function, and an improved Gauss-Newton iterative optimization algorithm, combined with an adaptive regularization strategy, is used to solve for the minimum value of the regularization objective function, thus achieving the extraction of multiple parameters (resistivity, polarizability, and magnetic susceptibility). This disclosure achieves efficient and accurate extraction and imaging of multiple parameters (resistivity, polarizability, and magnetic susceptibility) of subsurface anomalous media in the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response using the Gauss-Newton optimization algorithm, combined with regularization theory and the concept of multi-parameter structural constraints.

[0055] In step S101, a Cole-Cole fractional-order conductivity and susceptibility model is established, and a polarization current density correction term and a magnetization vector correction term are introduced into Maxwell's equations to calculate the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response;

[0056] First, a Cole-Cole fractional-order complex resistivity model characterizing the induced-polarization effect of complex media is established:

[0057] ,

[0058] And the Cole-Cole fractional-order magnetic susceptibility model characterizing the magnetization effect of complex media:

[0059] ,

[0060] in Zero-frequency resistivity, Polarizability It is a time constant. The frequency correlation coefficient, Angular frequency is resistivity, Zero-frequency magnetic susceptibility, For infinite frequency magnetic susceptibility, Let be the relaxation time constant. The dispersion coefficient is... Angular frequency, The imaginary unit, Angular frequency is Magnetic susceptibility.

[0061] Based on the aforementioned Cole-Cole fractional conductivity model and Cole-Cole fractional magnetic susceptibility model, the frequency-domain superconducting vertical magnetic field response of the layered medium under induction-polarization-magnetization multi-effects was calculated. ;

[0062] Its expression is: ;

[0063] In the above formula, The magnitude of the transmitting coil current, The radius of the transmitting coil, Let z be the vertical coordinate of the receiving coil (z = -h when the receiving coil is above the ground), and h be the depth of the receiving coil below the ground. It is a first-order Bessel function. The reflection coefficient, It is an integral variable; the reflection coefficient calculation depends on the wavenumber. :

[0064] , is the vacuum permeability.

[0065] Using sine and cosine numerical filtering coefficients, time-frequency conversion is performed on the frequency domain superconducting vertical magnetic field response to obtain the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response corresponding to the layered medium:

[0066] ,

[0067] In the above formula For the time of collection, These are the sine and cosine transform filter coefficients. For sampling interval, This represents the index of the sine and cosine numerical filter coefficients. The above steps yield the time-domain response of the induction-polarization-magnetization multi-effects in the layered medium. This step realizes the forward modeling of the multi-effect response of the layered medium in multi-parameter extraction. A data error fitting term is constructed based on the residuals between the multi-effect response and the measured data, including:

[0068] Based on the forward modeling results, a forward modeling function of the time-domain response of the induction-polarization-magnetization multi-effects in layered media can be established, representing the multi-effect response under the current model parameters.

[0069] The residuals between the multi-effect response and the measured data are calculated, and the data error fitting term is constructed using the L2 norm, as follows: ,in It is an observation data vector. This represents the multi-effect response under the current model parameters.

[0070] In step S102, a constraint matrix including the correlation coefficients of multiple parameters such as resistivity, polarizability and magnetic susceptibility is constructed, and a multi-parameter statistical constraint term describing the statistical correlation between multiple parameters is constructed based on the constraint matrix; including: determining the logarithmic expectation vector and the multi-parameter oblique variance matrix of multiple parameters according to the physical property statistical table of geological model or typical mineral deposit;

[0071] A constraint matrix is ​​constructed using the Kronecker product of the multi-parameter oblique variance matrix and the N-order identity matrix;

[0072] Construct a diagonal matrix, wherein the diagonal elements of the diagonal matrix correspond to the expected vectors of each model parameter in spatial location;

[0073] Connect the diagonal matrix with The Kronecker product operation is performed on the identity matrix to obtain the reference model baseline matrix;

[0074] Subtract the reference model baseline matrix from the current model parameters to obtain the deviation of the model parameters from the statistical expectation;

[0075] The deviation is weighted and constrained using a constraint matrix.

[0076] The multi-parameter statistical constraint term is constructed by calculating the L2 norm square of the weighted constraint deviation.

[0077] Based on the geological background of the exploration area and the known types of mineral deposits, relevant physical property statistics are collected and organized. Generally, a statistical table can be obtained by querying the data. The statistical table includes parameters such as resistivity, polarizability, magnetic susceptibility, and time constant.

[0078] The resulting multi-parameter logarithmic expectation vector is: ,

[0079] In the above formula, This represents the logarithmic prior expectation of the zero-frequency resistivity. This represents the logarithmic prior expectation of the polarizability. This represents the logarithmic prior expectation of the zero-frequency magnetic susceptibility.

[0080] Multiparameter orthometric matrix It can be represented as: ,

[0081] In the above formula, the diagonal elements represent the variance. For resistivity variance, The variance of polarizability This represents the variance of magnetic susceptibility.

[0082] like , For the number of model layers, This represents the logarithm of the zero-frequency resistivity of the i-th layer;

[0083] , Let be the logarithm of the polarizability of the i-th layer;

[0084] , The logarithm of the zero-frequency magnetic susceptibility of the i-th layer.

[0085] The off-diagonal elements are the covariance, such as , Let represent the logarithm of the polarizability of the i-th layer, and be the covariance between resistivity and polarizability. The covariance of resistivity and magnetic susceptibility. The covariance between polarizability and resistivity The covariance between polarizability and magnetic susceptibility. The covariance between magnetic susceptibility and resistivity. This represents the covariance of magnetic susceptibility and polarizability. It's important to note the multi-parameter orthometric matrix. It is a symmetric matrix, that is and equal, and equal, and equal.

[0086] Multiparameter orthometric matrix Describe the statistical correlation between different parameters.

[0087] The constraint matrix is ​​constructed using the Kronecker product of the multi-parameter orthometric variance matrix and the N-order identity matrix, and is expressed as follows: , For the constraint matrix, for An identity matrix of order 1. This is the Kronecker product operation.

[0088] Construct a diagonal matrix, where the diagonal elements correspond to the expected vectors of each model parameter in space; the diagonal matrix for A 3D diagonal matrix, consisting of multi-parameter expectation vectors for its diagonal elements.

[0089] Connect the diagonal matrix with The Kronecker product operation is performed on the identity matrix to obtain the reference model baseline matrix;

[0090] Subtracting the reference model baseline matrix from the current model parameters yields the deviation of the model parameters from the statistical expectation. The model parameters are:

[0091] ,

[0092] In the above formula, These represent the logarithmic zero-frequency resistivity, logarithmic polarizability, and logarithmic zero-frequency permeability of the first layer, respectively. They represent the first The logarithmic zero-frequency resistivity of the layer, the first Log-polarizability of the layer, the first Logarithmic zero-frequency permeability of the layer These are the model parameters.

[0093] The deviation is weighted using a constraint matrix to form a multi-parameter statistical constraint term. The format is: .

[0094] The model parameter regularization term is established as follows: ,in As a model regularization factor, for The smoothing constraint matrix of the model has values ​​only on the main diagonal and second diagonal, with elements having values ​​of 1 or -1, and all other elements having values ​​of 0. These are the model parameters.

[0095] In step S103, a regularization objective function is constructed that includes a data fitting term, a model regularization term, and a multi-parameter statistical constraint term:

[0096] .

[0097] Based on the regularization objective function established in step 103, an improved Gauss-Newton iterative optimization method is used to solve for the regularization objective function. The optimal value is determined to ensure the stability of iterative convergence.

[0098] The improved Gauss-Newton iterative optimization method employs the Gauss-Newton algorithm combined with an adaptive weight factor update strategy.

[0099] The Gauss-Newton optimization algorithm was used to regularize the objective function. Optimize the process by using an adaptive weight factor update strategy to iteratively update the first... Sub-model parameters Below is a detailed derivation of the model parameter iteration formula:

[0100] In the In the next iteration, the regularization objective function In the Sub-model parameters Perform a Taylor expansion nearby to obtain information about the model update amount. Approximate quadratic function:

[0101] ,

[0102] In the above formula, =m- , k For the first The Jacobian matrix of the next iteration can be calculated using the finite difference method. For the first The residual vector of the next iteration =dF( ), for the above formula Taking the derivative and setting it to zero, we obtain the iterative equation:

[0103] ,

[0104] Simplifying the above formula, we obtain the model parameter iteration formula as follows:

[0105] ,

[0106] in, It is a Jacobian matrix. For the first Weight coefficients for the next iteration For the first The model regularization factor for the next iteration For the residual vector, It is a diagonal matrix. For the first Model parameters for the next iteration.

[0107] The iteration stops when the regularization objective function reaches the minimum threshold, and the model parameters at this point are the extracted results.

[0108] In one embodiment, an improved Gauss-Newton optimization algorithm is employed to iteratively solve for the optimal value of the regularization objective function by minimizing it, including:

[0109] Acquire observation data and initialize model parameters and regularization parameters, including model regularization factors and weight coefficients; solve the regularization objective function using an improved Gauss-Newton optimization algorithm to obtain the model update amount and update the model parameters; calculate the data mismatch reduction rate of the current iteration and adaptively adjust at least one of the regularization parameters based on the data mismatch reduction rates of two adjacent iterations for constructing the regularization objective function of the next iteration; repeat the iteration until the preset convergence condition is met, and output the final model parameters.

[0110] The adaptive weight factor update strategy in this disclosure is explained in detail below. Each iteration requires dynamic adjustment of the model regularization factor and weight coefficients. For the k-th iteration, the data mismatch reduction rate between adjacent iterations is calculated based on the data error fitting term of the objective function.

[0111] ,

[0112] In the above, This represents the rate of decrease in data mismatch during the k-th iteration. For the data error fitting term in the (k-1)th iteration, This is the data error fitting term for the k-th iteration.

[0113] In the kth iteration, the model regularization factor and weight coefficients are adjusted according to the data mismatch reduction rate:

[0114] ,

[0115] ,

[0116] In the above formula, , The preset minimum threshold for the rate of decline, The preset maximum threshold for the rate of decline, For the first Weight coefficients for the next iteration For the first The model regularization factor for the next iteration. When the data error fitting term decreases slowly ( When the regularization factor is relatively small, it indicates that the iteration direction may be unstable or affected by noise, and the model regularization factor and weight coefficient should be increased; when the data error fitting term decreases rapidly, it indicates that the model parameters are effectively approaching the optimal solution, and the regularization constraint can be appropriately reduced to enhance the resolution.

[0117] Finally, by minimizing the objective function, multiple parameters such as resistivity, polarizability, and magnetic susceptibility are extracted simultaneously, and the spatial distribution imaging results of the physical properties of the underground anomalous medium are finally output.

[0118] Another aspect of this disclosure provides a time-domain superconducting electromagnetic multi-effect and multi-parameter extraction system. The airborne superconducting time-domain electromagnetic observation system used in the embodiments of this disclosure is as follows: Figure 2 As shown, it includes:

[0119] The response calculation and residual construction module calculates the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response, and constructs a data error fitting term based on the residual between the multi-effect response and the measured data;

[0120] The statistical constraint construction module constructs a constraint matrix including the correlation coefficients of multiple parameters such as resistivity, polarizability and magnetic susceptibility, and constructs a multi-parameter statistical constraint term to describe the statistical correlation between multiple parameters based on the constraint matrix.

[0121] The objective function construction module constructs a regularized objective function, which is composed of a weighted sum of the data error fitting term, the multi-parameter statistical constraint term, and the model parameter regularization term.

[0122] The optimization module employs an improved Gauss-Newton optimization algorithm. By minimizing the regularized objective function, it iteratively solves for the optimal value of the regularized objective function and simultaneously inverts to obtain resistivity, polarizability, and magnetizability.

[0123] To verify the accuracy of the method and system provided in this embodiment, a three-layer model is set up, with an air layer preceding the three layers. Data is collected by a receiving coil carried by an aircraft. The resistivity of the first layer is... 100 First-layer polarization The first layer magnetic susceptibility is 0.1. The thickness is 0.1. The resistivity is 60m. The second layer resistivity... The second-layer polarizability is 50 Ω·m. The magnetic susceptibility of the second layer is 0.4. The thickness is 0.3. It is 90m. The resistivity of the third layer. The third-layer polarizability is 200 Ω·m. The magnetic susceptibility of the third layer is 0.1. To a value of 0.1, 5% Gaussian random noise was added to the forward modeling data of the three-layer layered model to represent the measured data. The results of resistivity, polarizability, and magnetic susceptibility parameter extraction are as follows: Figure 4 As shown, for the 3-layered model, the extracted multi-parameter results (inversion model) are basically consistent with the actual stratigraphic parameter values ​​(real model). From Figure 3As can be seen, BZ in the vertical axis represents the vertical component of the actual multi-effect response, and the horizontal axis represents time. The actual multi-effect response of the noisy airborne superconducting system, i.e., the measured data, is very consistent with the fitting results of the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response extracted from the parameters, i.e., the inversion data. The root mean square error (RMS) is less than 5%, which verifies the accuracy of this disclosure.

[0124] The above description is merely a preferred embodiment of this disclosure and is not intended to limit this disclosure. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of this disclosure should be included within the scope of protection of this disclosure.

Claims

1. A method for extracting multiple effects and parameters of time-domain superconducting electromagnetics, characterized in that, include: The time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response was calculated, and a data error fitting term was constructed based on the residuals between the multi-effect response and the measured data. A constraint matrix is ​​constructed that includes the correlation coefficients of multiple parameters such as resistivity, polarizability and magnetic susceptibility, and a multi-parameter statistical constraint term is constructed based on the constraint matrix to describe the statistical correlation between multiple parameters. A regularization objective function is constructed, which is composed of a weighted sum of the data error fitting term, the multi-parameter statistical constraint term, and the model parameter regularization term; An improved Gauss-Newton optimization algorithm is used to iteratively solve for the optimal value of the regularization objective function by minimizing it, and the resistivity, polarizability and magnetizability are obtained simultaneously by inversion.

2. The method for extracting multiple effects and parameters of time-domain superconducting electromagnetic fields according to claim 1, characterized in that, Calculate the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response, including: Establish a Cole-Cole fractional conductivity model to characterize the induction-polarization effect of complex media, and a Cole-Cole fractional magnetic susceptibility model to characterize the magnetization effect of complex media; Based on the Cole-Cole fractional conductivity model and the Cole-Cole fractional magnetic susceptibility model, the frequency domain superconducting vertical magnetic field response of the layered medium under the induction-polarization-magnetization multi-effect is calculated. By using sine and cosine numerical filtering coefficients to perform time-frequency conversion on the frequency domain superconducting vertical magnetic field response, the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response corresponding to the layered medium is obtained.

3. The method for extracting multiple effects and parameters of time-domain superconducting electromagnetic fields according to claim 1, characterized in that, Construct a constraint matrix including the multi-parameter correlation coefficients of resistivity, polarizability, and magnetic susceptibility, including: Determine the logarithmic expectation vector and the multi-parameter orthometric matrix based on the physical property statistics of geological models or typical mineral deposits; A constraint matrix is ​​constructed using the Kronecker product of the multi-parameter oblique variance matrix and the N-order identity matrix; Construct a diagonal matrix, wherein the diagonal elements of the diagonal matrix correspond to the expected vectors of each model parameter in spatial location; Connect the diagonal matrix with The Kronecker product operation is performed on the identity matrix to obtain the reference model baseline matrix; Subtract the reference model baseline matrix from the current model parameters to obtain the deviation of the model parameters from the statistical expectation; The deviation is weighted and constrained using a constraint matrix. The multi-parameter statistical constraint term is constructed by calculating the L2 norm square of the weighted constraint deviation.

4. The method for extracting multiple effects and parameters of time-domain superconducting electromagnetic fields according to claim 3, characterized in that, The model parameters are expressed as follows: ， In the above formula, These represent the logarithmic zero-frequency resistivity, logarithmic polarizability, and logarithmic zero-frequency permeability of the first layer, respectively. They represent the first The logarithmic zero-frequency resistivity of the layer, the first Log-polarizability of the layer, the first Logarithmic zero-frequency permeability of the layer These are the model parameters.

5. The method for extracting multiple effects and parameters of time-domain superconducting electromagnetic fields according to claim 3, characterized in that, The constraint matrix is ​​represented as: , For the constraint matrix, for An identity matrix of order 1. For the Kronecker product operation, It is the inverse of the multi-parameter covariance matrix.

6. The method for extracting multiple effects and parameters of time-domain superconducting electromagnetic fields according to claim 3, characterized in that, The multi-parameter covariance matrix is ​​represented as: ， In the above formula, the diagonal elements represent the variance, and the off-diagonal elements represent the covariance. For resistivity variance, The variance of polarizability Let Variance be the magnetic susceptibility. The covariance of resistivity and magnetic susceptibility. The covariance between polarizability and resistivity The covariance between polarizability and magnetic susceptibility. The covariance between magnetic susceptibility and resistivity. Let be the covariance between magnetic susceptibility and polarizability.

7. The method for extracting multiple effects and parameters of time-domain superconducting electromagnetic fields according to claim 1, characterized in that, The regularization objective function is expressed as: ， in, Describes the regularization objective function. This is the data error fitting term. It is an observation data vector. This represents the multi-effect response under the current model parameters. For multi-parameter statistical constraints, For model parameters, It is a diagonal matrix. for An identity matrix of order 1. For the Kronecker product operation, These are the weighting coefficients. As a model regularization factor, for The smooth constraint matrix of the order model.

8. The method for extracting multiple effects and parameters of time-domain superconducting electromagnetic fields according to claim 7, characterized in that, An improved Gauss-Newton optimization algorithm is employed to iteratively solve for the optimal value of the regularization objective function by minimizing it, including: Acquire observation data and initialize model parameters and regularization parameters, including model regularization factors and weight coefficients; solve the regularization objective function using an improved Gauss-Newton optimization algorithm to obtain the model update amount and update the model parameters; calculate the data mismatch reduction rate of the current iteration and adaptively adjust at least one of the regularization parameters based on the data mismatch reduction rates of two adjacent iterations for constructing the regularization objective function of the next iteration; repeat the iteration until the preset convergence condition is met, and output the final model parameters.

9. The method for extracting multiple effects and parameters of time-domain superconducting electromagnetic fields according to claim 8, characterized in that, At least one of the regularization parameters is adaptively adjusted using the following formula: ， ， In the formula, , and The preset descent rate threshold, and For coefficients, This represents the rate of decrease in data mismatch during the k-th iteration. For the first Weight coefficients for the next iteration For the first The model regularization factor for the next iteration For the first Weight coefficients for the next iteration For the first The model regularization factor for each iteration.

10. A time-domain superconducting electromagnetic multi-effect multi-parameter extraction system, used to execute the time-domain superconducting electromagnetic multi-effect multi-parameter extraction method according to any one of claims 1-9, characterized in that, The response calculation and residual construction module calculates the time-domain superconducting electromagnetic induction-polarization-magnetization multi-effect response, and constructs a data error fitting term based on the residual between the multi-effect response and the measured data; The statistical constraint construction module constructs a constraint matrix including the correlation coefficients of multiple parameters such as resistivity, polarizability and magnetic susceptibility, and constructs a multi-parameter statistical constraint term to describe the statistical correlation between multiple parameters based on the constraint matrix. The objective function construction module constructs a regularized objective function, which is composed of a weighted sum of the data error fitting term, the multi-parameter statistical constraint term, and the model parameter regularization term. The optimization module employs an improved Gauss-Newton optimization algorithm. By minimizing the regularized objective function, it iteratively solves for the optimal value of the regularized objective function and simultaneously inverts to obtain resistivity, polarizability, and magnetizability.

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