A ZTEM tilter response inversion method and system based on complex neural networks

Abstract

This invention discloses a method and system for ZTEM tilter response inversion based on complex neural networks. Addressing the problems of existing real neural network methods that sever the physical coupling between the real and imaginary parts of the tilter, lack physical prior constraints, and have low inversion accuracy for high-resistivity anomalies, this invention proposes: constructing a sample dataset containing the complex tilter response and corresponding electrical parameters, and performing complex standardization; building a complex neural network TInvNet, and inputting the modulo-derived complex feature map of the output into a physical constraint layer; obtaining the final resistivity profile map through embedded positive resistivity definiteness, spatial piecewise smoothing, and horizontal-vertical anisotropy constraints; and achieving real-time inversion of measured data after joint training. This invention preserves the physical coupling between the complex real and imaginary parts, improves inversion accuracy and boundary characterization, requires no initial model, has high inversion efficiency, and the physical constraint layer parameters are adaptive, making it suitable for airborne electromagnetic detection in complex and challenging mountainous areas.

Description

Technical Field

[0001] This invention relates to the field of geological inversion technology, and in particular to a ZTEM tilt response inversion method and system based on complex neural networks. Background Technology

[0002] In the exploration of long, deep-buried tunnels in complex and challenging mountainous areas, the need to ascertain the geological conditions of underground spaces necessitates the acquisition of high-quality, high-precision geophysical data with low risk and high efficiency. Traditional tunnel exploration methods, represented by magnetotelluric sounding, offer advantages such as large exploration depth, immunity to high-resistivity shielding, and sensitivity to low-resistivity layers. However, surface exploration in complex and challenging mountainous areas is inefficient and carries certain safety risks. Airborne electromagnetic methods, as a highly efficient and environmentally friendly detection method, can effectively fill the gaps in geophysical data in areas inaccessible to ground personnel. Among them, the airborne magnetotelluric tilter ZTEM (Z-Axis Tipper Electromagnetic) system has become an effective means of detecting concealed underground structures due to its high acquisition efficiency, minimal terrain limitations, sensitivity to low-resistivity layers, and high lateral resolution, providing geophysical basis for railway route selection. The core of ZTEM inversion lies in establishing the mapping relationship between tilter response and underground electrical structure.

[0003] Traditional tilt response inversion methods (such as OCCAM, fast relaxation inversion, and simplified OCCAM basis inversion) are based on the idea of ​​objective function optimization, and fit the observation data by iteratively correcting the initial model. These methods are mature, but they are heavily dependent on the selection of the initial model and have long inversion iteration times, making it difficult to meet the high efficiency and high accuracy requirements of exploration tasks.

[0004] In recent years, deep learning (DL) has been introduced into the field of geophysical inversion due to its powerful nonlinear mapping capabilities. In airborne magnetotelluric tilt inversion, Yao & Zhang (2025) first attempted to apply deep learning to ZTEM tilt data inversion, proposing the TipInv-net framework. However, this method employs a real-number neural network: the real and imaginary parts of the tilt data are separated into two independent real-number input networks, and all operations are performed using real numbers throughout the convolution, activation, and pooling processes. This approach essentially severs the physical coupling between the complex real and imaginary parts—the real and imaginary parts of the tilt are implicitly related through Maxwell's equations, and processing them independently will, to some extent, reduce the sensitivity of phase information to resistivity signs (high resistivity / low resistivity) and boundary directions. Experiments show that this real-number method has lower inversion accuracy for high-resistivity anomalies than for low-resistivity anomalies, and it also provides a blurred characterization of fault fracture zones.

[0005] Tilter data is inherently complex data, with its real and imaginary parts coupled through electromagnetic field propagation laws. Therefore, a complex neural network, capable of simultaneously processing both real and imaginary parts while preserving their correlation, is theoretically more suitable for inversion tasks. However, in current airborne magnetotelluric tilter response inversion technology, there is no precedent for using complex neural networks. Complex neural networks are commonly used in areas such as object classification. Therefore, this application provides a ZTEM tilter response inversion method and system based on a complex neural network. Summary of the Invention

[0006] Therefore, the purpose of this invention is to provide a ZTEM tilt response inversion method and system based on complex neural networks, which aims to invert airborne magnetotelluric tilts through complex neural networks to obtain accurate inversion results of anisotropic features such as horizontal layering of underground media.

[0007] To achieve the above objectives, this invention provides a ZTEM tilter response inversion method based on a complex neural network, comprising the following steps: S1. Obtain tilt response data from different geological models and construct a ZTEM response sample dataset. The tilt response data is complex data containing real and imaginary parts. S2. Standardize the tilt response data in the sample dataset; S3. Input the standardized tilt response data into the constructed complex neural network TInvNet. The complex neural network TInvNet includes an encoding stage and a decoding stage. In the encoding stage, complex convolution, complex activation function and complex pooling operations are used to downsample to extract deep complex features. In the decoding stage, complex transpose convolution, complex activation function and skip connection are used to upsample to restore spatial resolution. Finally, a complex feature map is output. S4. Take the modulus of each element of the complex feature map to obtain the initial resistivity distribution map. Input the initial resistivity distribution map into the physical constraint layer and use the physical constraint layer to perform resistivity positive definiteness constraint, spatial piecewise smoothing constraint and horizontal-vertical anisotropy constraint. Finally, output the final resistivity profile map that satisfies the physical layer constraints. S5. Using the sample dataset, the complex neural network TInvNet and the physical constraint layer are jointly trained. The measured tilt response data is processed by complex standardization and then input into the trained complex neural network TInvNet and the physical constraint layer to realize the distribution of electrical parameters in underground space in real time.

[0008] More preferably, in S1, the step of acquiring tilt response data from different geological models and constructing a ZTEM response sample dataset includes the following steps: S101. Determine the study area and use the finite element method to mesh the study area, dividing it into a geological body occurrence area and an extension area. The geological body occurrence area is meshed using a uniform mesh, and the extension area is meshed with a step size increasing by 1.5 times. S102. Construct multiple fault geological models, fix the background resistivity of the underground space, and make the position and shape of the resistivity anomaly change randomly to generate multiple anomaly geological models; at the same time, generate multiple fault geological models by changing the position of the fracture zone in space. S103. Using a two-dimensional forward modeling method based on the finite element method, for each fault geological model, complex tilt response data are obtained at P frequency points and Q measuring points. The electrical parameters of the underground space of the geological model and its corresponding geological model are used to generate a large amount of tilt response data for different geological models through tilt response forward modeling. S104. The calculated tilt response data is used as input features, and the underground spatial electrical parameters of the corresponding fault geological model are used as output labels to form input-output tilt and geoelectric parameter sample data pairs.

[0009] More preferably, in S2, the tilator response data in the sample dataset is standardized, including the following process: Input complex tilt data Calculate the mean μ of the complex oscillator data: ; in, and Let represent the mean of the real part of the tilt and the mean of the imaginary part of the tilt, respectively; Calculate the covariance matrix using the following formula. ; in, , , , ; The input skew data is standardized using the inverse square root of the covariance matrix: .

[0010] More preferably, the downsampling operation in the encoding stage described in S3 specifically includes: Complex convolution: using a complex convolution kernel For the input complex oscillator data Perform convolution; Complex bias is included in the convolution process to obtain the final convolution result. The real and imaginary parts are calculated separately in an alternating manner during the convolution process. Complex activation function: The modReLU function is used to activate the complex convolution output, keeping the complex phase unchanged and performing ReLU operation only on the modulus; Complex pooling: Max complex pooling is used, and the complex element with the largest modulus is selected as the output within the pooling window.

[0011] More preferably, the upsampling operation in the decoding stage of step S3 specifically includes: Complex transpose convolution: Perform complex transpose convolution on the current decoded feature map to double the spatial size. Both the transpose convolution kernel and the bias are complex numbers. Skip connection and feature concatenation: The complex feature map obtained by upsampling is concatenated with the complex feature map output by the corresponding layer in the encoding stage along the channel axis. After concatenation, the spatial size remains unchanged, but the number of channels increases. Complex convolution and activation: Complex convolution and modReLU activation functions are applied sequentially to the stitched complex feature map. The definitions of complex convolution and modReLU are the same as in the encoding stage, and they are used to extract fused features and restore details of underground electrical structure.

[0012] More preferably, in S4, the modulus of each element of the complex feature map is taken to obtain the initial resistivity distribution map, which is expressed by the following formula: ; in, and Let represent the real and imaginary parts of the feature map of a complex number, respectively. This is the output complex feature map.

[0013] More preferably, in S4, the physical constraint layer achieves resistivity positive definiteness constraint, spatial piecewise smoothing constraint, and horizontal-vertical anisotropy constraint by solving the following optimization objective function, thus obtaining the final resistivity profile: ; in, This is the final resistivity profile. Let be the resistivity vector to be solved; This is the initial resistivity vector after the two-dimensional resistivity map is vectorized into column vectors; This is the regularization intensity parameter in the horizontal direction; This is the regularization intensity parameter in the vertical direction; and These are the first-order difference matrices for the horizontal and vertical directions, respectively; This represents the square of the L2 norm of *. Let * denote the L1 norm of *.

[0014] More preferably, the objective function is solved using the Fast Iterative Shrinking Threshold Algorithm (FISTA), and the solution process is expanded into a differentiable computation graph with a fixed number of iterations, specifically including: Input initial resistivity plot Auxiliary variables Acceleration factor According to the maximum number of outer iterations gradient step size Repeat the following operations: Calculate the gradient step: ; Calculate the TV near-end operator: ; Calculate the orthogonal projection: ; Accelerate updates: , ; After the iteration is complete, output ,Will Remodeled into The two-dimensional matrix is ​​used as the final resistivity profile. in, This is the resistivity estimate after the k-th iteration. The initial resistivity plot is the input. Let be the auxiliary acceleration variable for the k-th step; Let k be the acceleration factor for step k. Let be the gradient vector at the k-th step; This is the intermediate variable after the TV near-end operator in the k-th step; Proximal operators; This is the positive lower bound of resistivity, with a value of 10. -3 .

[0015] More preferably, in S5, the complex neural network TInvNet and the physical constraint layer are jointly trained using the sample dataset, including the following steps: S501. Divide the sample dataset into a training set, a test set, and a validation set in a ratio of 18:1:1; S502. Using root mean square error as the loss function, the Adam optimization algorithm is used to jointly update all trainable parameters of the complex neural network TInvNet and the physical constraint layer. The trainable parameters include complex convolution kernel, complex bias, learnable bias in the modReLU activation function, and regularization strength parameter in the physical constraint layer. S503, Set the initial learning rate to 0.001, and follow... The learning rate decreases by 50% every 10 rounds of training. This represents the initial learning rate; E is the number of training epochs, which is a multiple of 10. After the number of training rounds reaches the set value, the TInvNet network completes training.

[0016] The present invention also provides a ZTEM tilter response inversion system based on a complex neural network, comprising: Sample dataset construction module: used to acquire electromagnetic tilter response data of different geological models, construct ZTEM response sample datasets, each set of sample data includes the tilter response in complex form and its corresponding underground space electrical parameters; Complex normalization module: used to perform complex normalization processing on the complex oscillator response data in the sample dataset; The complex neural network TInvNet module is used to receive the normalized complex tilson response data. The complex neural network TInvNet includes an encoding unit and a decoding unit. The encoding unit is used to downsample through complex convolution, complex activation function and complex pooling operations to extract deep complex features. The decoding unit is used to upsample through complex transpose convolution, complex activation function and skip connection to restore spatial resolution and finally output complex feature map. The physical constraint layer module is used to take the modulus of the complex feature map element by element to obtain the initial resistivity distribution map. Then, it applies resistivity positive definiteness constraint, spatial piecewise smoothing constraint, and horizontal-vertical anisotropy constraint to the initial resistivity distribution map and outputs the final resistivity profile map that satisfies the physical laws. The physical constraint layer module includes a trainable regularization strength parameter that participates in backpropagation along with the network parameters. Joint training module: used to jointly train the complex neural network TInvNet module and the physical constraint layer module using the sample dataset; Real-time inversion module: This module processes the measured electromagnetic tilter response data in the same way as the complex normalization module and then inputs it into the trained complex neural network TInvNet module and physical constraint layer module to invert the distribution of electrical parameters in underground space in real time.

[0017] The ZTEM tilter response inversion method and system based on complex neural networks disclosed in this application have at least the following advantages compared with the prior art: Higher inversion accuracy: The complete complex neural network is used to process the tilt data, preserving the physical coupling relationship between the real and imaginary parts. The inversion accuracy of high-resistivity anomalies, low-resistivity anomalies and fault boundaries is better than that of the real neural network method.

[0018] Enhanced physical consistency: An embedded differentially differentiable anisotropic total variational physical constraint layer forces positive resistivity, piecewise smoothness, and horizontal-vertical anisotropy, effectively suppressing spurious structures and non-physical negative values.

[0019] No initial model required: A direct mapping from tilter response to electrical parameters is established through end-to-end offline training, and the inversion of measured data takes only milliseconds to seconds, significantly improving inversion efficiency. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the network structure of the ZTEM tilter response inversion method based on complex neural networks according to the present invention.

[0021] Figure 2 A flowchart for establishing the dataset used for deep learning training in this method.

[0022] Figure 3 The TInvNet network structure built for this method.

[0023] Figure 4 The loss curve is shown when training the TInvNet network using tilt responses from a large number of geological models (including anomaly models and fault structure models).

[0024] Figure 5 It is a comparison chart of the real-time inversion results of the observed data, the prediction results of different address models, and the resistivity change curves.

[0025] Figure 6 It is a geological model diagram of the fault line based on observation data.

[0026] Figure 7 This is a fault inversion prediction map. Detailed Implementation

[0027] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0028] like Figure 1 As shown, one embodiment of the present invention provides a ZTEM tilter response inversion method based on complex neural networks. This method is based on exploration data of long, deep-buried tunnels in complex and challenging mountainous areas, and forms a ZTEM tilter response inversion based on complex neural networks, mainly including: Data preparation phase: geoelectric model parameters, tilter response forward modeling, tilter data, complex normalization; Network training phase: training set, TinvNet network, output predictions, loss function; Practical application stage: Measured tilt data, completed training of the network model, geoelectric model parameters, and interpretation output.

[0029] Specifically, the following steps are included: S1. Obtain tilt response data from different geological models and construct a ZTEM response sample dataset. The tilt response data is complex data containing real and imaginary parts. In the geological body occurrence area, the background resistivity of the fixed underground space remains unchanged, and the resistivity anomalies are randomly distributed in the underground space. Their positions and shapes change, but their resistivity values ​​remain unchanged. For fault-type geological models, various geological anomaly models are obtained by changing the spatial position of the fracture zone in the above manner, and then forward modeling is performed to obtain their tilt response, forming a sample dataset.

[0030] like Figure 2 In S1, the acquisition of tilt response data from different geological models and the construction of a ZTEM response sample dataset includes the following steps: S101. Determine the study area; use the finite element method to mesh the study area, dividing it into a geological body occurrence area and an extension area. The geological body occurrence area is meshed using a uniform mesh, and the extension area is meshed with a step size increasing by 1.5 times. S102. Construct various fault geological models, fix the background resistivity of the underground space, and randomly vary the location and morphology of resistivity anomalies to generate various anomaly geological models; for complex geological conditions, construct two main datasets: Irregular Blocky Dataset: By changing the shape, location, and resistivity of the anomalous body, we can simulate blocky anomalous bodies of different sizes, shapes, and electrical characteristics.

[0031] Fault dataset: By varying the thickness of the hanging wall and footwall, the dip angle and location of the breccia zone, we can simulate fault structures with different attitudes and structures.

[0032] At the same time, by changing the spatial location of the fracture zone, various fault geological models are generated.

[0033] S103. Tilter Response Forward Modeling: For each fault geological model, acquire complex tilter response data at P frequency points and Q measuring points. Electrical parameters of the underground space and its corresponding geological model Through tilt response forward modeling, a large amount of tilt response data for different geological models are generated.

[0034] S104. The calculated tilt response data is used as input features, and the underground spatial electrical parameters of the corresponding fault geological model are used as output labels to form input-output tilt and geoelectric parameter sample data pairs.

[0035] S2. Standardize the tumbler response data in the sample dataset; specifically, this includes the following process: Input complex tilt data Calculate the mean μ of the complex oscillator data: ; in, and Let represent the mean of the real part of the tilt and the mean of the imaginary part of the tilt, respectively; Calculate the covariance matrix using the following formula. ; in, , , , ; The input skew data is standardized using the inverse square root of the covariance matrix: .

[0036] S3. Input the standardized tilt response data into the constructed complex neural network TInvNet. The complex neural network TInvNet includes an encoding stage and a decoding stage. In the encoding stage, the data is downsampled sequentially through complex convolution, complex activation function and complex pooling operations to extract deep complex features of the tilt response data. In the decoding stage, the data is upsampled through complex transpose convolution, complex activation function and skip connection to restore spatial resolution. Finally, a complex feature map is output. The core idea behind implementing the ZTEM response based on complex neural networks lies in establishing a nonlinear mapping relationship between the tilt response and the geological model by training a large number of tilt response models using TInvNet. ; Where R represents the electrical parameter value of the underground space, TInvNet represents the complex neural network structure proposed in this application, and Tipper represents the tilter response data.

[0037] like Figure 3 The TinvNet network architecture is a complex neural network model based on an improved U-Net network structure. Its architecture consists of three downsampling layers, three upsampling layers, a feature extraction layer, and a prediction output layer. Each downsampling layer includes complex convolution, complex activation, and complex pooling techniques; each upsampling layer includes complex transposed convolution, complex activation, and upsampling techniques; the feature extraction layer uses concatenation to achieve multi-feature fusion, and the prediction output is implemented using a 1*1 convolutional layer. After completing the progressive upsampling and feature fusion of the complex decoding network, the final complex feature map output by the decoding network is obtained, where each element in the feature map is a complex number.

[0038] To obtain the initial resistivity distribution, the complex characteristic map is first moduloed element by element. This parameter initially reflects the underground electrical structure, but may contain spurious oscillations caused by noise or local non-physical negative values. Therefore, this invention adds a differentiable complex-domain resistivity reconstruction layer (CRRL) after the modulo operation to correct the initial resistivity map with geophysical prior constraints. The predicted resistivity profile is finally obtained after passing through the CRRL layer.

[0039] The downsampling operation in the encoding stage described in S3 specifically includes: For the input complex oscillator ; in, Indicates the real part of the tilted piece. Indicate the imaginary part of the tilt; First, the encoding stage is entered, where downsampling is performed. This step includes: complex convolution, complex activation (modReLU), and complex max pooling. Complex convolution: employing a complex convolution kernel For the input complex oscillator data Perform convolution; ; Complex bias is included in the convolution process to obtain the final convolution result. The real and imaginary parts are calculated separately in an alternating manner during the convolution process. : ; The above formula can be expressed in matrix form as follows: 1. Complex convolution part: ; 2. Bias addition part: ; Therefore, the final convolution result is: ; In the TinvNet network, there exists a multi-channel complex convolution. For the p-th channel, the output of the q-th layer can be expressed as: ; in, It is the output of the p-th channel and the q-th layer. It is the c-th channel, the p-th convolutional kernel, and the convolutional kernel of the q-th layer. It is the c-th channel, the input of the n-th layer. It is the bias of the p-th channel and the q-th layer.

[0040] Complex activation function: The modReLU function is used to activate the complex convolution output, keeping the complex phase unchanged and performing ReLU operation only on the modulus; After completing the convolution operation, the modReLU function is used to perform multi-channel complex activation to obtain... To illustrate this better, here is... , a is The real part, b is The imaginary part of is then: ; in, , This is a learnable bias (usually initialized to 0). The function maintains the phase invariant and performs a ReLU operation only on the magnitude. This applies to the convolution output. Activate element by element: ; Complex pooling: Max complex pooling is used, and the complex element with the largest modulus is selected as the output within the pooling window.

[0041] After completing the multi-channel complex activation operation, a maximum complex pooling operation is performed. The complex matrix obtained after the multi-channel complex activation operation is then processed. , ; A and B represent the real and imaginary parts, respectively. Assume the pooling window size is... For a step size of s, the coordinates (m, n) of the output feature map correspond to the top-left corner position of the pooling window on the input feature map, which is (x, y). The result of the max pooling operation is then output. : ; u and v are indices that vary in the range [0, f-1], and they are used for traversal. Each element within the pooling window has (x, y) coordinates of the input feature map.

[0042] Features from each layer of the encoder's output are passed to the corresponding layer of the decoder via skip connections. The patent employs concatenation fusion. For example, the output of the encoder's k-th layer... The decoder output after upsampling of the corresponding layer splicing: ; in, This indicates that the feature map is spliced ​​along the channel axis. The spatial size of the spliced ​​feature map remains unchanged, but the number of channels increases. The spliced ​​features then pass through complex convolutional layers.

[0043] The upsampling operation in the decoding stage described in step S3 specifically includes: complex transpose convolution (upsampling), complex activation (modReLU), and finally 1×1 complex convolution; The decoder's role is to upsample the deep complex features extracted by the encoder step by step to restore the spatial resolution, and at the same time combine the detailed information of the corresponding layer of the encoder to finally output a complex feature map of the same size as the underground electrical model.

[0044] Let the tilt feature output by the encoder at layer l (l=1, 2, 3) be... ,in For the number of channels, This refers to the spatial dimension. The decoder's processing steps are the reverse of the encoder's steps, and consist of three steps: Complex transpose convolution: Perform complex transpose convolution on the current decoded feature map to double the spatial size. Both the transpose convolution kernel and the bias are complex numbers. Current decoding tilt response features Perform a complex transpose convolution to double its spatial size. The operational rules for the complex transpose convolution are the same as for the ordinary complex convolution: Let the transpose convolution kernel be... Bias convolution Then output : ; in, This indicates a transpose convolution operation, where the real and imaginary parts are computed in an alternating manner: ; Skip connection and feature concatenation: The complex feature map obtained by upsampling is concatenated with the complex feature map output by the corresponding layer in the encoding stage along the channel axis. After concatenation, the spatial size remains unchanged, but the number of channels increases. The complex features obtained by upsampling Features output by the layer corresponding to the encoder Concatenate along the channel dimension. The concatenation operation maintains the connection between the real and imaginary parts respectively: ; The spatial size of the feature map remains unchanged after stitching, but the number of channels increases.

[0045] Complex convolution and activation: Complex convolution and modReLU activation functions are applied sequentially to the stitched complex feature map. The definitions of complex convolution and modReLU are the same as in the encoding stage, and they are used to extract fused features and restore details of underground electrical structure.

[0046] Features of the concatenated complex number Two complex convolution operations are applied, followed by activation using the modReLU function after each operation. Complex convolution and the modReLU function have already been introduced in the coding section above and will not be repeated here. This activation function maintains the complex phase unchanged, performing only a nonlinear mapping on the modulus, which is beneficial for preserving the phase information of the subsurface electrical interface.

[0047] Repeat the above downsampling-decoding correspondence three times (l=1, 2, 3) to finally obtain the decoder output features. ,in The same mesh size as the subsurface resistivity model, Regarding the number of output channels, this patent uses single-channel output, therefore .

[0048] Complex feature map output by the decoder Each element in is denoted as It carries electrical information from the corresponding underground location.

[0049] S4. Take the modulus of each element of the complex feature map to obtain the initial resistivity distribution map. Input the initial resistivity distribution map into the physical constraint layer and use the physical constraint layer to perform resistivity positive definiteness constraint, spatial piecewise smoothing constraint and horizontal-vertical anisotropy constraint. Finally, output the final resistivity profile map that satisfies the physical layer constraints. In S4, the initial resistivity distribution map is obtained by taking the modulus of each element of the complex characteristic map, which is expressed by the following formula: ; in, and Let represent the real and imaginary parts of the feature map of a complex number, respectively. This is the output complex feature map.

[0050] While the initial resistivity map provides a preliminary reflection of the underground electrical structure, it may contain spurious oscillations or local non-physical negatives due to noise in the tilt data or instability in the network's nonlinear mapping. Therefore, this invention adds a complex domain resistivity reconstruction layer (CRLL) after the modulus operation to further refine the resistivity map. By imposing geophysical prior constraints, the final resistivity profile that satisfies physical laws is output. .

[0051] In S4, the physical constraint layer achieves resistivity positive definiteness constraint, spatial piecewise smoothness constraint, and horizontal-vertical anisotropy constraint by solving the following optimization objective function. The three constraints of the physical constraint layer can be understood as follows: (1) The resistivity value is positive; (2) The underground electrical structure is spatially piecewise continuous, that is, the resistivity in areas without geological boundaries should change smoothly, while a step change is allowed at the boundaries of faults or anomalies; (3) The underground medium is usually mainly horizontally layered, so the resistivity change in the vertical direction should be gentler than that in the horizontal direction; the final resistivity profile is obtained: ; in, This is the final resistivity profile. Let be the resistivity vector to be solved; This is the initial resistivity vector after the two-dimensional resistivity map is vectorized into column vectors; This is the regularization intensity parameter in the horizontal direction; This is the regularization intensity parameter in the vertical direction; and These are the first-order difference matrices for the horizontal and vertical directions, respectively; This represents the square of the L2 norm of *. Let * denote the L1 norm of *.

[0052] satisfy: , ; |, L1 norm constraints (anisotropic total variational regularization) are applied to the gradients in the horizontal and vertical directions, respectively. and As a regularization strength parameter, this patent sets it as a trainable variable, with initial values ​​taken as follows: , . This represents the resistivity in the i-th row and j-th column of the two-dimensional resistivity plot; these resistivities participate in backpropagation training along with the parameters of the network encoder and decoder, thereby automatically adapting to the noise level and geological features of the dataset. This is used to set a lower bound for resistivity, which is then used to enforce a positive constraint.

[0053] The first term in the objective function of CRRL for solving the optimization problem forces the corrected resistivity map to remain within the initial estimate; the second and third terms utilize the properties of the L1 norm—allowing a finite number of gradient components to take large values ​​(corresponding to geological boundaries) while suppressing small oscillations at other locations (corresponding to noise).

[0054] The objective function is solved using the Fast Iterative Shrinking Threshold Algorithm (FISTA), and the solution process is expanded into a differentiable computation graph with a fixed number of iterations, specifically including: Input initial resistivity plot Auxiliary variables Acceleration factor According to the maximum number of outer iterations gradient step size Repeat the following operations: Calculate the gradient step: ; Calculate the TV near-end operator: ; The proximal operator is iterated within the Chambolle-Pock dual algorithm. The implementation is achieved step by step, and all internal iteration operations (difference, soft thresholding, projection) are differentiable operators; Calculate the orthogonal projection: ; Accelerate updates: , ; After the iteration is complete, output ,Will Remodeled into The two-dimensional matrix is ​​used as the final resistivity profile. During training, and Updated along with other network weights via the Adam optimizer; in, This is the resistivity estimate after the k-th iteration. The initial resistivity plot is the input. Let be the auxiliary acceleration variable for the k-th step; Let k be the acceleration factor for step k. Let be the gradient vector at the k-th step; This is the intermediate variable after the TV near-end operator in the k-th step; Proximal operators; This is the positive lower bound of resistivity, with a value of 10. -3 .

[0055] S5. Using the sample dataset, the complex neural network TInvNet and the physical constraint layer are jointly trained. The measured tilt response data is processed by complex standardization and then input into the trained complex neural network TInvNet and the physical constraint layer to realize the distribution of electrical parameters in underground space in real time.

[0056] In S5, the complex neural network TInvNet and the physical constraint layer are jointly trained using the sample dataset, including the following steps: S501. Divide the sample dataset into a training set, a test set, and a validation set in a ratio of 18:1:1. Specifically, the sample dataset contains 20,000 pairs, of which 18,000 pairs are in the training set, 1,000 pairs are in the test set, and 1,000 pairs are in the validation set.

[0057] S502, Use root mean square error as the loss function, i.e. ; in, This represents the predicted resistivity value obtained through the TInvNet output. This indicates that the sample data represents the true resistivity value. Figure 4 This is a schematic diagram of the loss function curve.

[0058] The Adam optimization algorithm is used to jointly update all trainable parameters in the complex neural network TInvNet and the physical constraint layer. The trainable parameters include complex convolution kernels, complex biases, learnable biases in the modReLU activation function, and regularization strength parameters in the physical constraint layer. S503, Set the initial learning rate to 0.001, and follow... The learning rate decreases by 50% every 10 rounds of training. This represents the initial learning rate; E is the number of training epochs, which is a multiple of 10. After the number of training rounds reaches the set value, the TInvNet network completes training.

[0059] After setting the relevant hyperparameters for TInvNet, it is trained. The TInvNet network completes training after the set number of training epochs. ZTEM tilter response inversion based on complex neural networks is a nonlinear regression task, and the performance of the trained TInvNet network needs to be determined through the loss function curve.

[0060] After completing the training and optimization of TInvNet, it was determined that the network did not exhibit overfitting or insufficient generalization ability, and it could be applied to the inversion of observed data.

[0061] After the observation data is processed by complex standardization and then input into the trained TInvNet, the electrical parameters of underground space can be obtained in a very short time.

[0062] Example like Figure 5-7 In order to verify the validity of this invention patent, such as Figure 5Three geological models were designed for inversion using TInvNet: an isolated high-resistivity step-shaped anomaly model, an isolated low-resistivity step-shaped anomaly model, and a combined high- and low-resistivity anomaly model. In the high-resistivity step-shaped anomaly model, the high-resistivity anomaly resistance is 2000 Ω·m, and the background resistivity is 200 Ω·m. In the low-resistivity step-shaped anomaly model, the low-resistivity anomaly resistance is 20 Ω·m, and the background resistivity is 200 Ω·m. In the combined high- and low-resistivity anomaly model, the anomaly resistances from left to right are 2000 Ω·m, 20 Ω·m, and 500 Ω·m, respectively, and the background resistivity is 200 Ω·m. Figure 5 The comparison chart of various geological models and their inversion results shows that, regardless of whether it is a high-resistivity or low-resistivity anomaly, accurate inversion results can be obtained for its resistivity value, shape, and location. Figure 6 and Figure 7 The comparison chart showing the change in resistivity at a certain depth also illustrates the effectiveness of TInvNet for tilt response inversion.

[0063] For the fault model, a geological model was also designed for inversion. The inversion results show that the resistivity and thickness of the overburden and bedrock were well inverted, and the location, dip and extent of the fractured layer were also accurately inverted, indicating that TInvNet also has a good inversion effect on the fault model.

[0064] The technical steps included in the method proposed in this invention patent can be implemented by hardware related to program instructions. This invention also provides a ZTEM tilter response inversion system based on a complex neural network for implementing the above method, comprising: Sample dataset construction module: used to acquire electromagnetic tilter response data of different geological models, construct ZTEM response sample datasets, each set of sample data includes the tilter response in complex form and its corresponding underground space electrical parameters; Complex normalization module: used to perform complex normalization processing on the complex oscillator response data in the sample dataset; The complex neural network TInvNet module is used to receive the normalized complex tilson response data. The complex neural network TInvNet includes an encoding unit and a decoding unit. The encoding unit is used to downsample through complex convolution, complex activation function and complex pooling operations to extract deep complex features. The decoding unit is used to upsample through complex transpose convolution, complex activation function and skip connection to restore spatial resolution and finally output complex feature map. The physical constraint layer module is used to take the modulus of the complex feature map element by element to obtain the initial resistivity distribution map. Then, it applies resistivity positive definiteness constraint, spatial piecewise smoothing constraint, and horizontal-vertical anisotropy constraint to the initial resistivity distribution map and outputs the final resistivity profile map that satisfies the physical laws. The physical constraint layer module includes a trainable regularization strength parameter that participates in backpropagation along with the network parameters. Joint training module: used to jointly train the complex neural network TInvNet module and the physical constraint layer module using the sample dataset; Real-time inversion module: This module processes the measured electromagnetic tilter response data in the same way as the complex normalization module and then inputs it into the trained complex neural network TInvNet module and physical constraint layer module to invert the distribution of electrical parameters in underground space in real time.

[0065] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A ZTEM tilter response inversion method based on complex neural networks, characterized in that, Includes the following steps: S1. Obtain tilt response data from different geological models and construct a ZTEM response sample dataset. The tilt response data is complex data containing real and imaginary parts. S2. Standardize the tilt response data in the sample dataset; S3. Input the standardized tilt response data into the constructed complex neural network TInvNet. The complex neural network TInvNet includes an encoding stage and a decoding stage. In the encoding stage, the data is downsampled sequentially through complex convolution, complex activation function and complex pooling operations to extract deep complex features of the tilt response data. In the decoding stage, the data is upsampled through complex transpose convolution, complex activation function and skip connection to restore spatial resolution. Finally, a complex feature map is output. S4. Take the modulus of each element of the complex feature map to obtain the initial resistivity distribution map. Input the initial resistivity distribution map into the physical constraint layer and use the physical constraint layer to perform resistivity positive definiteness constraint, spatial piecewise smoothing constraint and horizontal-vertical anisotropy constraint. Finally, output the final resistivity profile map that satisfies the physical layer constraints. S5. Using the sample dataset, the complex neural network TInvNet and the physical constraint layer are jointly trained. The measured tilt response data is processed by complex standardization and then input into the trained complex neural network TInvNet and the physical constraint layer to realize the distribution of electrical parameters in underground space in real time.

2. The ZTEM tilter response inversion method based on complex neural networks according to claim 1, characterized in that, In S1, the process of acquiring tilt response data from different geological models and constructing a ZTEM response sample dataset includes the following steps: S101. Determine the study area and use the finite element method to mesh the study area, dividing it into a geological body occurrence area and an extension area. The geological body occurrence area is meshed using a uniform mesh, and the extension area is meshed with a step size increasing by 1.5 times. S102. Construct multiple fault geological models, fix the background resistivity of the underground space, and make the position and shape of the resistivity anomaly body change randomly to generate multiple anomaly geological models; at the same time, generate multiple fault geological models by changing the position of the fracture zone in space. S103. Using a two-dimensional forward modeling method based on the finite element method, for each fault geological model, complex tilt response data are obtained at P frequency points and Q measuring points. The electrical parameters of the underground space of the geological model and its corresponding geological model are used to generate a large amount of tilt response data for different geological models through tilt response forward modeling. S104. The calculated tilt response data is used as input features, and the underground spatial electrical parameters of the corresponding fault geological model are used as output labels to form input-output tilt and geoelectric parameter sample data pairs.

3. The ZTEM tilter response inversion method based on complex neural networks according to claim 1, characterized in that, In S2, the tilator response data in the sample dataset are standardized. Includes the following processes: Input complex tilt data Calculate the mean μ of the complex oscillator data: ； in, and Let represent the mean of the real part of the tilt and the mean of the imaginary part of the tilt, respectively; Calculate the covariance matrix using the following formula. ; in, , , , ; The input skew data is standardized using the inverse square root of the covariance matrix: 。 4. The ZTEM tilter response inversion method based on complex neural networks according to claim 1, characterized in that, The downsampling operation in the encoding stage described in S3 specifically includes: Complex convolution: using a complex convolution kernel For the input complex oscillator data Perform convolution; Complex bias is included in the convolution process to obtain the final convolution result. The real and imaginary parts are calculated separately in an alternating manner during the convolution process. Complex activation function: The modReLU function is used to activate the complex convolution output, keeping the complex phase unchanged and performing ReLU operation only on the modulus; Complex pooling: Max complex pooling is used, and the complex element with the largest modulus is selected as the output within the pooling window.

5. The ZTEM tilter response inversion method based on complex neural networks according to claim 1, characterized in that, The upsampling operation in the decoding stage described in step S3 specifically includes: Complex transpose convolution: Perform complex transpose convolution on the current decoded feature map to double the spatial size. Both the transpose convolution kernel and the bias are complex numbers. Skip connection and feature concatenation: The complex feature map obtained by upsampling is concatenated with the complex feature map output by the corresponding layer in the encoding stage along the channel axis. After concatenation, the spatial size remains unchanged, but the number of channels increases. Complex convolution and activation: Complex convolution and modReLU activation functions are applied sequentially to the stitched complex feature map. The definitions of complex convolution and modReLU are the same as in the encoding stage, and they are used to extract fused features and restore details of underground electrical structure.

6. The ZTEM tilter response inversion method based on complex neural networks according to claim 1, characterized in that, In S4, the initial resistivity distribution map is obtained by taking the modulus of each element of the complex characteristic map, which is expressed by the following formula: ； in, and Let represent the real and imaginary parts of the feature map of a complex number, respectively. This is the output complex feature map.

7. The ZTEM tilter response inversion method based on complex neural networks according to claim 5, characterized in that, In S4, the physical constraint layer achieves resistivity positive definiteness constraint, spatial piecewise smoothing constraint, and horizontal-vertical anisotropy constraint by solving the following optimization objective function, resulting in the final resistivity profile: ； in, This is the final resistivity profile. Let be the resistivity vector to be solved; This is the initial resistivity vector after the two-dimensional resistivity map is vectorized into column vectors; This is the regularization intensity parameter in the horizontal direction; This is the regularization intensity parameter in the vertical direction; and These are the first-order difference matrices for the horizontal and vertical directions, respectively; This represents the square of the L2 norm of *. Let * denote the L1 norm of *.

8. The ZTEM tilter response inversion method based on complex neural networks according to claim 7, characterized in that, The objective function is solved using the Fast Iterative Shrinking Threshold Algorithm (FISTA), and the solution process is expanded into a differentiable computation graph with a fixed number of iterations, specifically including: Input initial resistivity diagram Auxiliary variables Acceleration factor According to the maximum number of outer iterations gradient step size Repeat the following operations: Calculate the gradient step: ; Calculate the TV near-end operator: ; Calculate the orthogonal projection: ; Accelerate updates: , ; After the iteration is complete, output ,Will Remodeled into The two-dimensional matrix is ​​used as the final resistivity profile. in, This is the resistivity estimate after the k-th iteration. The initial resistivity plot is the input. Let be the auxiliary acceleration variable for the k-th step; Let k be the acceleration factor for step k. Let be the gradient vector at the k-th step; This is the intermediate variable after the TV near-end operator in the k-th step; Represents the proximal operator; This is the positive lower bound of resistivity, with a value of 10. -3 .

9. The ZTEM tilter response inversion method based on complex neural networks according to claim 1, characterized in that, In S5, the complex neural network TInvNet and the physical constraint layer are jointly trained using the sample dataset, including the following steps: S501. Divide the sample dataset into a training set, a test set, and a validation set in a ratio of 18:1:1; S502. Using root mean square error as the loss function, the Adam optimization algorithm is used to jointly update all trainable parameters of the complex neural network TInvNet and the physical constraint layer. The trainable parameters include complex convolution kernel, complex bias, learnable bias in the modReLU activation function, and regularization strength parameter in the physical constraint layer. S503, Set the initial learning rate to 0.001, and follow... The learning rate decreases by 50% every 10 rounds of training. This represents the initial learning rate; E is the number of training epochs, which is a multiple of 10. After the number of training rounds reaches the set value, the TInvNet network completes training.

10. A ZTEM tilter response inversion system based on complex neural networks, characterized in that, include: Sample dataset construction module: used to acquire electromagnetic tilter response data of different geological models, construct ZTEM response sample datasets, each set of sample data includes the tilter response in complex form and its corresponding underground space electrical parameters; Complex normalization module: used to perform complex normalization processing on the complex oscillator response data in the sample dataset; The complex neural network TInvNet module is used to receive the normalized complex tilson response data. The complex neural network TInvNet includes an encoding unit and a decoding unit. The encoding unit is used to downsample through complex convolution, complex activation function and complex pooling operations to extract deep complex features. The decoding unit is used to upsample through complex transpose convolution, complex activation function and skip connection to restore spatial resolution and finally output complex feature map. The physical constraint layer module is used to take the modulus of the complex feature map element by element to obtain the initial resistivity distribution map. Then, it applies resistivity positive definiteness constraint, spatial piecewise smoothing constraint, and horizontal-vertical anisotropy constraint to the initial resistivity distribution map and outputs the final resistivity profile map that satisfies the physical laws. The physical constraint layer module includes a trainable regularization strength parameter that participates in backpropagation along with the network parameters. Joint training module: used to jointly train the complex neural network TInvNet module and the physical constraint layer module using the sample dataset; Real-time inversion module: This module processes the measured electromagnetic tilter response data in the same way as the complex normalization module and then inputs it into the trained complex neural network TInvNet module and physical constraint layer module to invert the distribution of electrical parameters in underground space in real time.

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