Audio magnetotelluric two-dimensional deep learning inversion method integrated with physical prior

Abstract

The application discloses an audio magnetotelluric two-dimensional deep learning inversion method integrated with physical priori, and belongs to the technical field of electromagnetic data inversion processing. A parameterized modeling method is used to batch construct two-dimensional geological resistivity simulation models; then, a training set sample containing a simulation model, response data and a physical priori benchmark is formed; a deep learning network containing a heterogeneous double-path parallel encoder is constructed; a spatial self-adaptive dynamic gate aggregation module is introduced into the network; a loss function coordinated with data and physical mechanisms is constructed; and parameter iteration and optimization are performed on the deep learning network with the minimum loss function as the target. The application effectively overcomes the defects of abnormal body boundary divergence and ambiguity through a physical priori guidance and a dynamic feature self-adaptive fusion mechanism, greatly improves the recognition accuracy and noise resistance of complex underground structures and deep concealed ore bodies, and provides an efficient and accurate technical scheme for deep mineral resource exploration.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic data inversion processing technology, and in particular to a two-dimensional deep learning inversion method for audio magnetotelluric data that incorporates physical priors. Background Technology

[0002] Audio-magnetic (AMT) is a key tool in geophysical exploration, relying on the electromagnetic response caused by differences in the electrical properties of subsurface media. It infers subsurface electrical structures and the distribution of anomalies by observing natural alternating electromagnetic field data, and is widely used in deep mineral resource exploration, crustal structure analysis, and regional geological structural analysis. AMT inversion is the core step in quantitatively interpreting measured electromagnetic field data, aiming to reconstruct the location, shape, and resistivity parameters of subsurface electrical anomalies. It serves as a crucial bridge connecting physical observation and geological interpretation. In traditional AMT inversion, the optimal solution is typically found by minimizing the objective function (such as through local linearization methods) or using global optimization algorithms. However, as a typical nonlinear ill-conditioned problem, traditional methods for AMT inversion heavily rely on the initial model, are prone to getting trapped in local optima, and have limited inversion resolution. Furthermore, to finely analyze complex deep geological structures or employ global optimization algorithms, the computational complexity increases significantly. In recent years, numerous studies have focused on introducing deep learning techniques into geophysical inversion (AMT), significantly improving inversion efficiency and nonlinear representation capabilities by constructing end-to-end mapping networks. However, purely data-driven methods suffer from two major bottlenecks: first, there is a risk of deviating from physical laws (such as violating Maxwell's equations and generating non-physical solutions); second, generalization performance heavily relies on large-scale training datasets. While some existing physics-driven deep learning methods introduce physical constraints, they are computationally intensive when dealing with two-dimensional and higher-dimensional data, and they fail to establish deep interaction mechanisms across multi-scale feature spaces, resulting in insufficient resolution for anomaly boundaries in small-sample scenarios. Therefore, how to effectively coordinate physical constraints with data-driven approaches to achieve high-resolution, high-reliability AMT inversion is a problem that urgently needs to be solved. Summary of the Invention

[0003] The purpose of this invention is to address the problems of insufficient resolution in traditional audio-magnetic (AMT) inversion methods, as well as the weak physical interpretability and poor generalization of pure data-driven deep learning methods with small training sets. In this invention, a two-dimensional deep learning inversion method for audio-magnetic (PD-AMTNet) that incorporates physical priors is provided.

[0004] A two-dimensional deep learning inversion method for audio-magnetic magnetotellurics incorporating prior physical knowledge includes the following steps:

[0005] Step 1: Construct two-dimensional geological resistivity simulation models in batches using parametric modeling methods. The system covers underground targets such as low-resistivity anomalies and high-resistivity anomalies.

[0006] Step 2: Calculate the forward response data based on the finite element method, and perform traditional Occam smoothing constraint inversion on the response data to obtain the corresponding inversion results as the physical prior benchmark, thereby forming a training set sample containing "simulation model - response data - physical prior benchmark".

[0007] Step 3: Construct a deep learning network containing a heterogeneous dual-path parallel encoder, which includes an observation response feature branch and a physical prior feature branch;

[0008] Step 4: Introduce a spatially adaptive gated fusion module (GFM) into the network to concatenate the feature maps extracted from heterogeneous dual-path sources along the channel dimension. Calculate the dynamic weights of the spatial dimension using a multilayer perceptron to achieve adaptive weighted fusion of different features.

[0009] Step 5: Construct a loss function that coordinates data and physical mechanisms. This loss function consists of a model parameter inversion error term and a forward response matching error term. Use this loss function to constrain the deep learning network for parameter optimization training.

[0010] Step 6: With the goal of minimizing the loss function, perform parameter iteration and optimization on the deep learning network. After training, take the tested AMT response data and physical prior benchmark as input, and output a high-resolution two-dimensional resistivity prediction model through multi-scale feature splicing and restoration by the decoder.

[0011] In step one, a synthetic training dataset is constructed using a parametric modeling method. A two-dimensional geoelectric model space is established based on a structured grid system, divided into 64 equally spaced 100m cells horizontally and 32 cells vertically. The resistivity of the background region is set to 10. 3 Ω·m; By randomly generating multiple types of synthetic anomalies, the geometric shapes of the anomalies include rectangles and circles, the length and width of the rectangles and the radius of the circles are randomly determined, the number of anomalies is randomly generated between 2 and 4, and the resistivity values ​​of the anomalies are divided into two categories: low resistivity and high resistivity. 1000 sets of simulation models are generated by randomly combining different anomalies.

[0012] In step two, the two-dimensional forward modeling problem of AMT was numerically solved using the finite element method. The Maxwell equations satisfied by the AMT field can be expressed as follows:

[0013] (1)

[0014] (2)

[0015] in, It is a vector differential operator; i The imaginary unit; ω ω is the angular frequency; σ is the conductivity; μ 0 represents permeability; E represents electric field strength; H represents magnetic flux density; the time factor is set to... The Helmholtz equations can be derived from formulas (1) and (2):

[0016] (3)

[0017] (4)

[0018] in, k For wave number, ; Let be the Laplace operator; in the finite element method, the boundary value Ω problem and the variational problem can be solved equivalently. Therefore, the variational problem of the AMT two-dimensional finite element forward model can be expressed as:

[0019] (5)

[0020] Where AB is the upper boundary and CD is the lower boundary; h The magnetic field strength; G(h) Let be the energy functional; Γ be the boundary of the solution domain; It controls the strength of the diffusion term. Both are coefficients related to the polarization mode, representing the contribution of displacement current; δ is the variational operator. magnetic field Spatial gradient;

[0021] In TE mode, the following conditions are met:

[0022] ;

[0023] In TM mode, the following conditions are met:

[0024]

[0025] Where E x H is the electric field intensity in the x-direction. x Let be the magnetic flux density in the x-direction;

[0026] Discretize all the element meshes, and equation (5) becomes:

[0027] (6)

[0028] Where K is the total coefficient matrix, by finding the extreme values ​​of equation (8), the values ​​of each node can be obtained. h The corresponding apparent resistivity and impedance phase are as follows:

[0029] (7)

[0030] (8)

[0031] Among them, Z TE and Z TM The impedances are for TE and TM modes, respectively. and Apparent resistivity in TE and TM modes, respectively; and represents the impedance phase in TE and TM modes, respectively; IM and RE represent taking the imaginary and real parts, respectively; ∂ is the sign of the partial derivative; ∂ z To find the partial derivative with respect to the z-direction.

[0032] Based on the above method, the frequency range for forward modeling is set to 10. 5 A total of 38 frequency points, ranging from Hz to 1Hz and exhibiting a logarithmic uniform distribution, were used to acquire the corresponding apparent resistivity response data. Then, traditional Occam smoothing constraint inversion was performed on the response data. In AMT inversion, the objective function typically includes a data fitting term and a model constraint term. The data fitting term measures the difference between the observed data and the model prediction, while the model constraint term ensures the physical plausibility of the model. The general expression of the objective function is as follows:

[0033] (9)

[0034] Where m is the resistivity model parameter; d is the observation data of the AMT method, which is the apparent resistivity in the TM mode; Forward response of AMT; W d W is the diagonal inverse matrix of data noise error; m m is the model smoothing matrix; ref α is the reference model; α is the regularization factor.

[0035] In the AMT inversion process, by finding the extreme value of the objective function formula (9), we can derive the expression for the model update quantity of the k-th iteration using the Gauss-Newton method:

[0036] (10)

[0037] in, Let A be the model parameter update amount in the k-th iteration;k-1 It is a Jacobian matrix; This is the transpose of the Jacobian matrix; W is the regularization factor. d T This is the transpose of the diagonal inverse matrix of the data noise error;

[0038] The corresponding traditional Occam inversion physical prior benchmark results are obtained through the above inversion method, and then 1000 training set samples containing "simulation model-response data-physical prior benchmark" are formed.

[0039] In step three, the response data from step two is input into the observed response feature branch to extract the nonlinear response features contained in the data; the physical prior benchmark from step two is input into the physical prior feature branch to extract the construction boundary features containing physical law constraints.

[0040] A heterogeneous dual-path parallel encoder architecture is adopted. The observation response feature branch inputs AMT observation data (TM mode apparent resistivity), and this branch extracts the nonlinear response features contained in the observation data. The physical prior feature branch inputs the traditional Occam smoothing constraint inversion results, and this branch extracts the construction boundary features containing physical law constraints. The symmetric encoder realizes independent feature extraction and cross-modal association learning of multi-source heterogeneous data. Each branch adopts a four-level hierarchical coding structure. Each level consists of two 3×3 convolutional layers, BatchNorm and ReLU activation, followed by a 2×2 max pooling with a stride of 2 to form a feature compression unit. Through progressive downsampling operations, the heterogeneous dual paths respectively construct feature pyramids containing shallow high-resolution details and deep high-dimensional semantics, effectively capturing the geoelectric structure response characteristics at different scales. Each branch outputs a four-level feature map, with the resolution progressively reduced to 1 / 8 of the original image and the number of channels increasing to 8 times the original.

[0041] In step four, a spatially adaptive gated fusion module (GFM) is proposed. The feature maps of the two branches are concatenated along the channel dimension, and weights are calculated using a multilayer perceptron (MLP). This MLP consists of two 1×1 convolutional layers, a batch normalization (BN) layer, a ReLU activation function, and a sigmoid activation function. The weights are then separated, and finally, the original features are weighted and summed using these two weights to obtain the fused features. Notably, GFM adaptively adjusts the contribution of the two features because the weights are spatially dimensional, resulting in different weights at each location. This mechanism effectively captures the importance of different locations, enhancing the model's focus on key features. In summary, this module dynamically generates a weight matrix with spatial attention characteristics using 1×1 convolutional kernels, and its mathematical description is as follows:

[0042] (11)

[0043] in, F 1 and F 2 represents the feature vectors extracted from the two branches. It is a three-dimensional vector. C For the number of channels, H For height, W Width; F cat That is F 1 and F 2. Concatenate the two feature vectors. Concat Indicates a splicing operation; This represents the Sigmoid activation function. Represents the ReLU activation function; ω 1 and ω The weights are divided into two independent channels; F fusion Ä represents the feature result after fusion, and Ä represents element-wise multiplication.

[0044] This mechanism enables pixel-level dynamic weighting of feature maps and dynamic fusion of heterogeneous dual-path features. In potential anomaly regions indicated by observation response feature branches, if physical prior feature branches simultaneously detect boundary features, they are assigned higher weights, thereby injecting physically interpretable structural priors into the decoding process and suppressing the boundary ambiguity effect of purely data-driven approaches.

[0045] In step five, a loss function that coordinates data and physical mechanisms is constructed. This function enhances the model's adaptability to geoelectric structure patterns and reduces its dependence on large training data by introducing data errors from the two-dimensional forward response as physical constraints. The newly constructed loss function expression is as follows:

[0046] (12)

[0047] (13)

[0048] (14)

[0049] in, L The loss function is the collaboration between data and physical mechanisms. L m The model parameter inversion error is calculated based on the mean square error. L d The forward response matching error is calculated based on the mean square error. N For model parameters, T The number of samples used in training. For network-predicted resistivity models, m i,j For the true resistivity model, d i,j These are actual measured data. F ( m i,j ) is the forward operator, and λ1 and λ2 are the weighting coefficients; This represents a double summation, i.e., traversing all... T There are N training samples, and the N model parameters in each sample are summed; physics-driven terms L d By forced prediction model The forward modeling response approximates the observed data, ensuring that the network output satisfies the physical equations. This constraint avoids potential physical deviations (such as non-physical resistivity jumps) that may occur in purely data-driven models at the Maxwell's equations level.

[0050] In step six, the network is optimized and trained using a loss function that combines data and physical mechanisms. The parameters include the weights, biases, and other information of each layer of the network. After training, new AMT response data for testing and physical prior benchmarks are used as inputs. The saved optimal model parameters are loaded, and the model is constructed according to the predetermined network structure and parameter settings. Through multi-scale feature splicing and reconstruction by the decoder, a high-resolution two-dimensional resistivity prediction model is finally output, enabling accurate assessment of the location attributes of underground anomalies.

[0051] The beneficial effects of this invention are:

[0052] 1. Noise Resistance and Generalization Mechanism Guided by Physical Priors: This invention innovatively introduces the physical prior benchmark obtained from traditional Occam smoothing constraint inversion as the input to the physical prior feature branch, extracting subsurface structural boundary information (such as the location trend of anomalies) that conforms to the laws of electromagnetic field propagation. When facing noisy data, traditional Occam smoothing constraint inversion preprocessing can effectively filter out high-frequency random noise; when facing complex models not covered by the training set, this physical prior feature branch can provide physically interpretable guidance, significantly reducing the network's dependence on the distribution of large-scale training samples.

[0053] 2. Data-Physical Adaptive Fusion, Significantly Improving Boundary Resolution: This invention designs a Dynamic Gated Aggregation Module (GFM) that dynamically adjusts the weights of the original response data features and physical prior features in the spatial dimension. In potential anomaly boundary regions, physical prior features are given higher weights, successfully overcoming the divergence and ambiguity defects of anomaly boundaries caused by pure data-driven approaches, and achieving refined reconstruction of shallow and deep structures.

[0054] 3. Physically Driven Joint Optimization: This invention constructs a loss function that combines data and physical mechanisms, including a forward response matching term. This forces the network output model to approximate the observed data, thus avoiding non-physical resistivity jump solutions that might arise from purely data-driven approaches at the Maxwell's equations level. This mechanism ensures both inversion accuracy and deep structural recovery while endowing the inversion results with strong physical interpretability. Attached Figure Description

[0055] Figure 1 This is a flowchart of the present invention;

[0056] Figure 2 This is a diagram of the deep learning inversion network architecture of the present invention;

[0057] Figure 3 This is a schematic diagram of the spatially adaptive dynamic gating aggregation module structure in an embodiment of the invention;

[0058] Figure 4 This is the loss function curve for network training in this invention;

[0059] Figure 5 This is a schematic diagram of the deep learning network inversion result model of the present invention. Detailed Implementation

[0060] Please see Figures 1 to 5 The image shown is an embodiment of the present invention.

[0061] A two-dimensional deep learning inversion method for audio-magnetic magnetotellurics incorporating prior physical knowledge includes the following steps:

[0062] Step 1: Using parametric modeling methods, construct two-dimensional geological resistivity simulation models in batches. The system covers underground targets such as low-resistivity anomalies and high-resistivity anomalies.

[0063] In step one, a parametric modeling method is used to construct a synthetic training dataset. A two-dimensional geoelectric model space is established based on a structured grid system. The horizontal direction (x) is divided into 64 equally spaced cells of 100m each (total length 6.4km), and the vertical direction (z) is divided into 32 cells (maximum detection depth 3.2km). The resistivity of the background region is set to 10. 3 Ω·m; Multiple types of synthetic anomalies are randomly generated. The geometry of the anomalies includes rectangles and circles, with the length and width of the rectangles and the radius of the circles randomly determined. The number of anomalies is randomly generated between 2 and 4. The resistivity values ​​of the anomalies are divided into low resistivity (10~10 Ω·m). 2 Ω·m) and high resistivity (10 4 ~10 5 Two categories (Ω·m) are used to generate 1000 sets of simulation models by randomly combining different anomalies.

[0064] Step 2: Calculate the forward response data based on the finite element method, and perform traditional Occam smoothing constraint inversion on the response data to obtain the corresponding inversion results as physical prior benchmarks, thereby forming a training set sample containing "simulation model - response data - physical prior benchmarks".

[0065] In step two, the two-dimensional forward modeling problem of AMT was numerically solved using the finite element method. The Maxwell equations satisfied by the AMT field can be expressed as follows:

[0066] (1)

[0067] (2)

[0068] in, It is a vector differential operator; i The imaginary unit; ω ω is the angular frequency; σ is the conductivity; μ 0 represents permeability; E represents electric field strength; H represents magnetic flux density; the time factor is set to... The Helmholtz equations can be derived from formulas (1) and (2):

[0069] (3)

[0070] (4)

[0071] in, k For wave number, ; Let be the Laplace operator; in the finite element method, the boundary value Ω problem and the variational problem can be solved equivalently. Therefore, the variational problem of the AMT two-dimensional finite element forward model can be expressed as:

[0072] (5)

[0073] Where AB is the upper boundary and CD is the lower boundary; h The magnetic field strength; G(h) Let be the energy functional; Γ be the boundary of the solution domain; It controls the strength of the diffusion term. Both are coefficients related to the polarization mode, representing the contribution of displacement current; δ is the variational operator. magnetic field Spatial gradient.

[0074] In TE mode, the following conditions are met:

[0075] ;

[0076] In TM mode, the following conditions are met:

[0077] ;

[0078] Where E x H is the electric field intensity in the x-direction. x Let be the magnetic flux density in the x-direction;

[0079] Discretize all the element meshes, and equation (5) becomes:

[0080] (6)

[0081] Where K is the total coefficient matrix, by finding the extreme value of equation (8), the h of each node can be obtained, and the corresponding apparent resistivity and impedance phase are as follows:

[0082] (7)

[0083] (8)

[0084] Among them, Z TE and Z TM The impedances are for TE and TM modes, respectively. and Apparent resistivity in TE and TM modes, respectively; and represents the impedance phase in TE and TM modes, respectively; IM and RE represent taking the imaginary and real parts, respectively; ∂ is the sign of the partial derivative; ∂ z To find the partial derivative with respect to the z-direction.

[0085] Based on the above method, the frequency range for forward modeling is set to 10. 5 A total of 38 frequency points, ranging from Hz to 1Hz and exhibiting a logarithmic uniform distribution, were used to acquire the corresponding apparent resistivity response data. Then, traditional Occam smoothing constraint inversion was performed on the response data. In AMT inversion, the objective function typically includes a data fitting term and a model constraint term. The data fitting term measures the difference between the observed data and the model prediction, while the model constraint term ensures the physical plausibility of the model. The general expression of the objective function is as follows:

[0086] (9)

[0087] Where m is the resistivity model parameter; d is the observation data of the AMT method, which is the apparent resistivity in the TM mode; Forward response of AMT; W d W is the diagonal inverse matrix of data noise error; m m is the model smoothing matrix;ref α is the reference model; α is the regularization factor.

[0088] In the AMT inversion process, by finding the extreme value of the objective function formula (9), we can derive the expression for the model update quantity of the k-th iteration using the Gauss-Newton method:

[0089] (10)

[0090] in, Let A be the model parameter update amount in the k-th iteration; k-1 It is a Jacobian matrix; This is the transpose of the Jacobian matrix; W is the regularization factor. d T This is the transpose of the diagonal inverse matrix of the data noise error;

[0091] The corresponding traditional Occam inversion physical prior benchmark results are obtained through the above inversion method, and then 1000 training set samples containing "simulation model-response data-physical prior benchmark" are formed.

[0092] Step 3: Construct a deep learning network containing a heterogeneous dual-path parallel encoder, which includes an observation response feature branch and a physical prior feature branch.

[0093] In step three, the response data from step two is input into the observed response feature branch to extract the nonlinear response features contained in the data; the physical prior benchmark from step two is input into the physical prior feature branch to extract the structural boundary features containing physical law constraints.

[0094] A heterogeneous dual-path parallel encoder architecture is adopted. The observation response feature branch inputs AMT observation data (TM mode apparent resistivity), and this branch extracts the nonlinear response features contained in the observation data. The physical prior feature branch inputs the traditional Occam smoothing constraint inversion results, and this branch extracts the construction boundary features containing physical law constraints. The symmetric encoder realizes independent feature extraction and cross-modal association learning of multi-source heterogeneous data. Each branch adopts a four-level hierarchical coding structure. Each level consists of two 3×3 convolutional layers, BatchNorm and ReLU activation, followed by a 2×2 max pooling with a stride of 2 to form a feature compression unit. Through progressive downsampling operations, the heterogeneous dual paths respectively construct feature pyramids containing shallow high-resolution details and deep high-dimensional semantics, effectively capturing the geoelectric structure response characteristics at different scales. Each branch outputs a four-level feature map, with the resolution progressively reduced to 1 / 8 of the original image and the number of channels increasing to 8 times the original.

[0095] Step 4: Introduce a spatially adaptive dynamic gating aggregation module (GFM) into the network to stitch the feature maps extracted from heterogeneous dual paths together in the channel dimension. Then, use a multilayer perceptron to calculate the dynamic weights of the spatial dimension to achieve adaptive weighted fusion of different features.

[0096] In step four, a spatially adaptive dynamic gated aggregation module (GFM) is proposed. The feature maps of the two branches are concatenated along the channel dimension, and weights are calculated using a multilayer perceptron (MLP). This MLP consists of two 1×1 convolutional layers, a batch normalization (BN) layer, a ReLU activation function, and a sigmoid activation function. These weights are then separated, and finally, the original features are weighted and summed using these two weights to obtain the fused features, such as... Figure 2 As shown. It's worth noting that GFM adaptively adjusts the contributions of the two features because the weights are spatially dimensional, so each position has a different weight. This mechanism effectively captures the importance of different positions, enhancing the model's focus on key features. In summary, this module dynamically generates a weight matrix with spatial attention properties through a 1×1 convolutional kernel, and its mathematical description is as follows:

[0097] (11)

[0098] in, F 1 and F 2 represents the feature vectors extracted from the two branches. It is a three-dimensional vector. C For the number of channels, H For height, W Width; F cat That is F 1 and F 2. Concatenate the two feature vectors. Concat Indicates a splicing operation; This represents the Sigmoid activation function. Represents the ReLU activation function; ω 1 and ω The weights are divided into two independent channels; F fusion The result is the fused feature set, and Ä represents element-wise multiplication. This mechanism enables pixel-level dynamic weighting of feature maps and dynamic fusion of heterogeneous dual-path features. In potential anomaly regions indicated by the observation response feature branch, if the physical prior feature branch also detects boundary features, it is assigned a higher weight, thereby injecting physically interpretable structural priors into the decoding process and suppressing the boundary ambiguity effect of purely data-driven approaches.

[0099] Step 5: Construct a loss function that coordinates data and physical mechanisms. This loss function consists of a model parameter inversion error term and a forward response matching error term. Use this loss function to constrain the deep learning network for parameter optimization training.

[0100] In step five, a loss function that coordinates data and physical mechanisms is constructed. This function enhances the model's adaptability to geoelectric structure patterns and reduces its dependence on large training data by introducing data errors from the two-dimensional forward response as physical constraints. The newly constructed loss function expression is as follows:

[0101] (12)

[0102] (13)

[0103] (14)

[0104] in, L The loss function is the collaboration between data and physical mechanisms. L m The model parameter inversion error is calculated based on the mean square error. L d The forward response matching error is calculated based on the mean square error. N For model parameters, T The number of samples used in training. For network-predicted resistivity models, m i,j For the true resistivity model, d i,j These are actual measured data. F ( m i,j ) is the forward operator, and λ1 and λ2 are the weighting coefficients; This represents a double summation, i.e., traversing all... T There are N training samples, and the N model parameters in each sample are summed; physics-driven terms L d By forced prediction model The forward modeling response approximates the observed data, ensuring that the network output satisfies the physical equations. This constraint avoids potential physical deviations (such as non-physical resistivity jumps) that may occur in purely data-driven models at the Maxwell's equations level.

[0105] Step 6: With the goal of minimizing the loss function, perform parameter iteration and optimization on the deep learning network. After training, take the tested AMT response data and physical prior benchmark as input, and output a high-resolution two-dimensional resistivity prediction model through multi-scale feature splicing and restoration by the decoder.

[0106] In step six, the network is optimized and trained using a loss function that combines data and physical mechanisms. The parameters cover information such as weights and biases of each layer of the network. After training, new AMT response data for testing and physical prior benchmarks are used as inputs, and the saved optimal model parameters are loaded. The model follows the predetermined network structure and parameter settings. Through multi-scale feature splicing and restoration by the decoder, a high-resolution two-dimensional resistivity prediction model is finally output, which enables accurate assessment of the location attributes of underground anomalies.

Claims

1. A two-dimensional deep learning inversion method for audio-magnetic resonance incorporating prior physical knowledge, characterized in that, Includes the following steps: Step 1: Construct two-dimensional geological resistivity simulation models in batches using parametric modeling methods. The system covers underground targets such as low-resistivity anomalies and high-resistivity anomalies. Step 2: Calculate the forward response data based on the finite element method, and perform traditional Occam smoothing constraint inversion on the response data to obtain the corresponding inversion results as the physical prior benchmark, thereby forming a training set sample containing "simulation model - response data - physical prior benchmark"; Step 3: Construct a deep learning network containing a heterogeneous dual-path parallel encoder, which includes an observation response feature branch and a physical prior feature branch; Step 4: Introduce a spatially adaptive dynamic gating aggregation module into the network to stitch the feature maps extracted from heterogeneous dual paths together in the channel dimension. Calculate the dynamic weights of the spatial dimension through a multilayer perceptron to achieve adaptive weighted fusion of different features. Step 5: Construct a loss function that coordinates data and physical mechanisms. This loss function consists of a model parameter inversion error term and a forward response matching error term. Use this loss function to constrain the deep learning network for parameter optimization training. Step 6: With the goal of minimizing the loss function, perform parameter iteration and optimization on the deep learning network. After training, take the tested AMT response data and physical prior benchmark as input, and output a high-resolution two-dimensional resistivity prediction model through multi-scale feature splicing and restoration by the decoder.

2. The two-dimensional deep learning inversion method for audio-magnetic resonance based on physical priors as described in claim 1, characterized in that: In step one, a synthetic training dataset is constructed using a parametric modeling method. A two-dimensional geoelectric model space is established based on a structured grid system, divided into 64 equally spaced 100m cells horizontally and 32 cells vertically. The resistivity of the background region is set to 10. 3 Ω·m; By randomly generating multiple types of synthetic anomalies, the geometric shapes of the anomalies include rectangles and circles, the length and width of the rectangles and the radius of the circles are randomly determined, the number of anomalies is randomly generated between 2 and 4, and the resistivity values ​​of the anomalies are divided into two categories: low resistivity and high resistivity. 1000 sets of simulation models are generated by randomly combining different anomalies.

3. The two-dimensional deep learning inversion method for audio-magnetic resonance based on physical priors as described in claim 1, characterized in that: In step two, the two-dimensional forward modeling problem of AMT was numerically solved using the finite element method. The Maxwell equations satisfied by the AMT field can be expressed as follows: （1） （2） in, It is a vector differential operator; i The imaginary unit; ω ω is the angular frequency; σ is the conductivity; μ 0 represents permeability; E represents electric field strength; H represents magnetic flux density; the time factor is set to... The Helmholtz equations can be derived from formulas (1) and (2): （3） （4） in, k For wave number, ; Let be the Laplace operator; in the finite element method, the boundary value Ω problem and the variational problem can be solved equivalently. Therefore, the variational problem of the AMT two-dimensional finite element forward model can be expressed as: （5） Where AB is the upper boundary and CD is the lower boundary; h The magnetic field strength; G(h) Let be the energy functional; Γ be the boundary of the solution domain; It controls the strength of the diffusion term. Both are coefficients related to the polarization mode, representing the contribution of displacement current; δ is the variational operator. magnetic field Spatial gradient; In TE mode, the following conditions are met: ； In TM mode, the following conditions are met: ； Where E x H is the electric field intensity in the x-direction. x Let be the magnetic flux density in the x-direction; Discretize all the element meshes, and equation (5) becomes: （6） Where K is the total coefficient matrix, by finding the extreme values ​​of equation (8), the values ​​of each node can be obtained. h The corresponding apparent resistivity and impedance phase are as follows: （7） （8） Among them, Z TE and Z TM The impedances are for TE and TM modes, respectively. and Do not specify the apparent resistivity in TE and TM modes; and represents the impedance phase in TE and TM modes, respectively; IM and RE represent taking the imaginary and real parts, respectively; ∂ is the sign of the partial derivative; ∂ z To find the partial derivative with respect to the z-direction; Based on the above method, the frequency range for forward modeling is set to 10. 5 A total of 38 frequency points, ranging from Hz to 1Hz and exhibiting a logarithmic uniform distribution, were used to acquire the corresponding apparent resistivity response data. Then, traditional Occam smoothing constraint inversion was performed on the response data. In AMT inversion, the objective function typically includes a data fitting term and a model constraint term. The data fitting term measures the difference between the observed data and the model prediction, while the model constraint term ensures the physical plausibility of the model. The general expression of the objective function is as follows: （9） Where m is the resistivity model parameter; d is the observation data of the AMT method, which is the apparent resistivity in the TM mode; Forward response of AMT; W d W is the diagonal inverse matrix of data noise error; m m is the model smoothing matrix; ref This is the reference model; α is the regularization factor. In the AMT inversion process, by finding the extreme value of the objective function formula (9), we can derive the expression for the model update quantity of the k-th iteration using the Gauss-Newton method: （10） in, Let A be the model parameter update amount in the k-th iteration; k-1 It is a Jacobian matrix; This is the transpose of the Jacobian matrix; W is the regularization factor. d T This is the transpose of the diagonal inverse matrix of the data noise error; The corresponding traditional Occam inversion physical prior benchmark results are obtained through the above inversion method, and then 1000 training set samples containing "simulation model-response data-physical prior benchmark" are formed.

4. The two-dimensional deep learning inversion method for audio-magnetic resonance based on physical priors as described in claim 1, characterized in that: In step three, the response data from step two is input into the observed response feature branch to extract the nonlinear response features contained in the data. Input the physical prior benchmark from step two into the physical prior feature branch to extract the construction boundary features that contain physical law constraints; A heterogeneous dual-path parallel encoder architecture is adopted. The observation response feature branch inputs AMT observation data, which extracts the nonlinear response features contained in the observation data. The physical prior feature branch inputs the traditional Occam smoothing constraint inversion results, which extracts the construction boundary features containing physical law constraints. The symmetric encoder realizes independent feature extraction and cross-modal association learning of multi-source heterogeneous data. Each branch adopts a four-level hierarchical coding structure. Each level consists of two 3×3 convolutional layers, BatchNorm and ReLU activation, followed by a 2×2 max pooling with a stride of 2 to form a feature compression unit. Through progressive downsampling operations, the heterogeneous dual paths respectively construct feature pyramids containing shallow high-resolution details and deep high-dimensional semantics, effectively capturing the geoelectric structure response characteristics at different scales. Each branch outputs a four-level feature map, with the resolution progressively reduced to 1 / 8 of the original image and the number of channels increasing to 8 times the original.

5. The two-dimensional deep learning inversion method for audio-magnetic resonance based on physical priors as described in claim 1, characterized in that: In step four, a spatially adaptive dynamic gating aggregation module is proposed. The feature maps of the two branches are concatenated along the channel dimension, and weights are calculated using a multilayer perceptron. This MLP consists of two 1×1 convolutional layers, a batch normalization layer, a ReLU activation function, and a Sigmoid activation function. The weights are then separated, and finally, these two weights are used to perform a weighted summation of the original features to obtain the fused features. This module dynamically generates a weight matrix with spatial attention characteristics using 1×1 convolutional kernels, and its mathematical description is as follows: （11） in, F 1 and F 2 represents the feature vectors extracted from the two branches. It is a three-dimensional vector. C For the number of channels, H For height, W Width; F cat That is F 1 and F 2. Concatenate the two feature vectors. Concat Indicates a splicing operation; This represents the Sigmoid activation function. Represents the ReLU activation function; ω 1 and ω The weights are divided into two independent channels; F fusion Ä represents the feature result after fusion, and Ä represents element-wise multiplication.

6. The two-dimensional deep learning inversion method for audio-visual magnetotelluric resonance based on physical priors as described in claim 1, characterized in that: In step five, a loss function that coordinates data and physical mechanisms is constructed. This function introduces the data error of the two-dimensional forward response as a physical constraint. The newly constructed loss function expression is as follows: （12） （13） （14） in, L The loss function is the collaboration between data and physical mechanisms. L m The model parameter inversion error is calculated based on the mean square error. L d The forward response matching error is calculated based on the mean square error. N For model parameters, T The number of samples used in training. For network-predicted resistivity models, m i,j For the true resistivity model, d i,j These are actual measured data. F ( m i,j ) is the forward operator, and λ1 and λ2 are the weighting coefficients; This represents a double summation, i.e., traversing all... T There are N training samples, and the N model parameters in each sample are summed; physics-driven terms L d By forced prediction model The forward modeling response approximates the observation data, ensuring that the network output satisfies the physical equations.

7. The two-dimensional deep learning inversion method for audio-magnetic resonance based on physical priors as described in claim 1, characterized in that: In step six, the network is optimized and trained using a loss function that combines data and physical mechanisms. The parameters cover information such as the weights and biases of each layer of the network. After training, new AMT response data for testing and physical prior benchmarks are used as inputs. The saved optimal model parameters are loaded, and the model is output as a high-resolution two-dimensional resistivity prediction model through multi-scale feature splicing and restoration by the decoder according to the established network structure and parameter settings, so as to achieve accurate evaluation of the location attributes of underground anomalies.

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