Three-dimensional inversion method and system based on convolutional neural network electromagnetic method

Abstract

The invention relates to the technical field of geophysics, in particular to an electromagnetic method three-dimensional inversion method and system based on a convolutional neural network, and the method comprises the following steps: firstly, achieving the end-to-end nonlinear mapping through a three-dimensional CNN processing module, and obtaining a corresponding three-dimensional resistivity model; the three-dimensional CNN processing module comprises an encoder used for extracting multi-scale features through a 3D convolution layer and down-sampling, a decoder used for recovering spatial resolution through a 3D deconvolution layer and jump connection, and a processor used for processing the multi-scale features through the decoder. And the output layer is used for restraining the resistivity range through a Sigmoid activation function. And then multi-frequency electromagnetic field data is used as joint input of a three-dimensional resistivity model, and TV regularization and physical property range constraint are introduced into a loss function to realize three-dimensional inversion. According to the method, efficient, high-precision and low-cost electromagnetic method three-dimensional inversion is realized through a three-dimensional CNN architecture, multi-frequency data fusion and physical constraint design, and the method is remarkably superior to a traditional iteration method.

Description

Technical Field

[0001] The present invention relates to the field of geophysical technologies, and specifically to a three-dimensional inversion method and system for electromagnetic methods based on a convolutional neural network (CNN). Background Art

[0002] Electromagnetic inversion infers the three-dimensional distribution of the electrical properties (such as resistivity) of underground media from the electromagnetic field data observed on the ground surface. The traditional inversion methods generally have the following defects:

[0003] 1) Dependence on iterative optimization, with low computational efficiency and sensitivity to the initial model;

[0004] 2) Usually adopting single-frequency successive processing, it is difficult to utilize the complementarity of multi-frequency data;

[0005] 3) Usually indirectly introducing physical property priors through mathematical regularization (such as smoothing constraints), which is prone to over-smoothing or false anomalies. Summary of the Invention

[0006] In order to overcome the deficiencies of the prior art, the present invention provides a three-dimensional inversion method and system for electromagnetic methods based on a convolutional neural network (CNN), aiming to solve the problems of low computational efficiency, dependence on the initial model, and easy to fall into local minima in traditional electromagnetic inversion methods.

[0007] In order to achieve the above object, the specific technical solutions adopted by the present invention are as follows:

[0008] A three-dimensional inversion method for electromagnetic methods based on a convolutional neural network includes the following steps:

[0009] S1. Implement an end-to-end non-linear mapping through a three-dimensional CNN processing module to obtain a corresponding three-dimensional resistivity model; wherein, the three-dimensional CNN processing module includes: an encoder for extracting multi-scale features through 3D convolutional layers and downsampling; a decoder for restoring the spatial resolution through 3D transposed convolutional layers and skip connections; and an output layer for constraining the resistivity range (such as 0.1 - 1000 Ω·m) through a Sigmoid activation function and outputting a three-dimensional resistivity model.

[0010] S2. Use multi-frequency electromagnetic field data as the combined input of the three-dimensional resistivity model, and at the same time introduce TV regularization and physical property range constraints into the loss function to achieve three-dimensional inversion. Specifically, the multi-frequency electromagnetic field data is input in a 4D tensor format: dimensions: `[Nx, Ny, Nz, Nf]`, where Nx is the number of grids in the east-west direction; Ny is the number of grids in the north-south direction; Nz is the number of grids in the vertical depth direction; and Nf is the number of frequencies. The loss function uses the MSE (mean square error) function.

[0011] The present invention also provides an electromagnetic method three-dimensional inversion system based on a convolutional neural network. The convolutional neural network includes: a multi-frequency electromagnetic data input module, a three-dimensional CNN processing module, and a physical constraint module; wherein:

[0012] The multi-frequency electromagnetic data input module is used to receive and format multi-frequency electromagnetic field data into a 4D tensor: dimension: `[Nx, Ny, Nz, Nf]`, where Nx is the number of grids in the east-west direction; Ny is the number of grids in the north-south direction; Nz is the number of grids in the vertical depth direction; Nf is the number of frequencies;

[0013] The three-dimensional CNN processing module includes:

[0014] An encoder, which is used to extract multi-scale features through 3D convolutional layers and downsampling;

[0015] A decoder, which is used to restore the spatial resolution through 3D deconvolutional layers and skip connections;

[0016] An output layer, which is used to constrain the resistivity range (such as 0.1 - 1000 Ω·m) through a Sigmoid activation function and output a three-dimensional resistivity model: dimension: `[Nx, Ny, Nz]`;

[0017] The physical constraint module adopts a loss function that integrates TV regularization and physical property range constraints:

[0018]

[0019] where ρ pred is input for training, ρ true is actual data, the MSE (mean square error) function is used to quantify the error of the model, and the parameters of the model are adjusted through an optimization algorithm. TV regularization is used to force the model to be smooth and avoid false anomalies; the weight coefficients α and β are determined through cross-validation.

[0020] In the electromagnetic method three-dimensional inversion system based on a convolutional neural network according to the present invention, the convolutional neural network is constructed by the following method:

[0021] S1. Generate a large number of three-dimensional resistivity models and their corresponding electromagnetic response data sets through forward simulation;

[0022] S2. Construct a three-dimensional CNN architecture, with the input being multi-frequency electromagnetic field data and the output being the resistivity distribution;

[0023] S3. Training and validation: Use the synthesized three-dimensional resistivity models and their corresponding electromagnetic response data sets to train the network, and verify the generalization ability through measured data;

[0024] S4. Introduce physical constraints: Introduce a regularization term (such as a smoothing constraint) into the loss function.

[0025] Furthermore, in step S1, the finite element method (FEM) or the finite volume method (FVM) is used to generate a three-dimensional resistivity model and its corresponding electromagnetic response dataset. By rotating, scaling, and adding noise to expand the dataset, the robustness of the dataset is improved.

[0026] The present invention has the following characteristics and beneficial effects:

[0027] 1) A non-linear mapping from electromagnetic field data to resistivity model is directly established through a three-dimensional CNN without iteration, and the inversion speed is increased by more than a hundred times (for example, shortened from several hours to the second level), and it does not depend on the initial model.

[0028] 2) The input data is a multi-frequency electromagnetic field joint tensor (dimension: `[Nx, Ny, Nz, Nf]`). Cross-frequency features are automatically extracted through 3D convolutional layers, and the complementarity of multi-frequency data can be fully utilized to improve the resolution ability for complex geological bodies.

[0029] 3) Total variation (TV) regularization and resistivity range constraints (such as a Sigmoid output layer) are introduced into the loss function to force the inversion result to conform to geological laws (such as continuous physical properties and reasonable resistivity range), and reduce false anomalies.

[0030] 4) An encoder-decoder architecture with 3D convolutional layers + skip connections is adopted to retain three-dimensional spatial details and avoid information loss. BRIEF DESCRIPTION OF THE DRAWINGS

[0031] By reading the detailed description of the non-limiting embodiments with reference to the following drawings, other features, purposes, and advantages of the present invention will become more obvious:

[0032] Figure 1 It is a working principle diagram of a three-dimensional inversion method of electromagnetic method based on a convolutional neural network according to an embodiment of the present invention.

[0033] Figure 2 It is a three-dimensional CNN encoder-decoder architecture in an embodiment of the present invention.

[0034] Figure 3 It is a comparison of inversion results (horizontal slice) in an embodiment of the present invention;

[0035] In the figure: (a) True model: Clearly shows layered media and anomalies; (b) Inversion result of the traditional method Occam: The boundary of the anomaly is blurred; (c) Inversion result of the present invention: The shape of the anomaly highly coincides with the true model.

[0036] Figure 4 This is an example of multi - frequency electromagnetic field data input in the embodiments of the present invention.

[0037] Figure 5 This is a schematic diagram of three - dimensional space grid division in the embodiments of the present invention. Detailed implementation manners

[0038] The present invention will be described in detail below with reference to specific embodiments. The following embodiments will help those skilled in the art to further understand the present invention, but do not limit the present invention in any form. It should be noted that, without conflict, the embodiments in the present invention and the features in the embodiments can be combined with each other.

[0039] To solve the problems of low computational efficiency, dependence on the initial model, and easy entrapment in local minima in traditional electromagnetic inversion methods, the present invention provides an electromagnetic three - dimensional inversion method based on a convolutional neural network through a three - dimensional CNN architecture, multi - frequency data fusion, and physical constraint design, including the following steps:

[0040] S1. Implement an end - to - end non - linear mapping through a three - dimensional CNN processing module to obtain a corresponding three - dimensional resistivity model; wherein, the three - dimensional CNN processing module includes: an encoder for extracting multi - scale features through 3D convolutional layers and downsampling; a decoder for restoring the spatial resolution through 3D transposed convolutional layers and skip connections; and an output layer for constraining the resistivity range (such as 0.1 - 1000 Ω·m) through a Sigmoid activation function and outputting a three - dimensional resistivity model.

[0041] S2. Take multi - frequency electromagnetic field data in a 4D tensor format (dimensions: `[Nx, Ny, Nz, Nf]`, where Nx is the number of grids in the east - west direction; Ny is the number of grids in the north - south direction; Nz is the number of grids in the vertical depth direction; Nf is the number of frequencies) as the joint input of the three - dimensional resistivity model, extract multi - scale features through 3D convolutional layers and downsampling, and restore the spatial resolution through 3D transposed convolutional layers and skip connections; at the same time, introduce TV regularization and physical property range constraints in the loss function (using the MSE (mean square error) function) to achieve three - dimensional inversion.

[0042] The second aspect of the present invention provides an electromagnetic three - dimensional inversion system based on a convolutional neural network. The convolutional neural network includes: a multi - frequency electromagnetic data input module, a three - dimensional CNN processing module, and a physical constraint module; wherein:

[0043] The multi - frequency electromagnetic data input module is used to receive and format multi - frequency electromagnetic field data into a 4D tensor: Dimensions: `[Nx, Ny, Nz, Nf]`, where Nx is the number of grids in the east - west direction; Ny is the number of grids in the north - south direction; Nz is the number of grids in the vertical depth direction; Nf is the number of frequencies;

[0044] The 3D CNN processing module includes:

[0045] An encoder, which is used to extract multi - scale features through 3D convolutional layers and downsampling;

[0046] A decoder, which is used to restore the spatial resolution through 3D transposed convolutional layers and skip connections;

[0047] An output layer, which is used to constrain the resistivity range (such as 0.1 - 1000 Ω·m) through the Sigmoid activation function and output a 3D resistivity model: Dimensions: `[Nx, Ny, Nz]`;

[0048] The physical constraint module adopts a loss function that integrates TV regularization and physical property range constraints:

[0049]

[0050] Among them, the MSE (mean square error) function is used to quantify the error of the model, and the parameters of the model are adjusted through an optimization algorithm. TV regularization is used to enforce the smoothness of the model and avoid false anomalies; the weight coefficients α and β are determined through cross - validation.

[0051] The third aspect of the present invention provides a construction method of a convolutional neural network in the three - dimensional inversion system of electromagnetic method based on convolutional neural network, including the following steps:

[0052] S1. Generate a large number of 3D resistivity models and their corresponding electromagnetic response datasets through forward simulation; specifically, use the finite element method (FEM) or the finite volume method (FVM) to generate 3D resistivity models and their corresponding electromagnetic response datasets, and improve the robustness of the dataset by means of rotating, scaling, and adding noise to expand the dataset.

[0053] S2. Construct a 3D CNN architecture, with the input being multi - frequency electromagnetic field data and the output being the resistivity distribution;

[0054] S3. Training and verification: Use the synthesized 3D resistivity models and their corresponding electromagnetic response datasets to train the network, and verify the generalization ability through measured data;

[0055] S4. Introduce physical constraints: Introduce a regularization term (such as smoothness constraint) into the loss function.

[0056] The performance of the present invention will be described in detail below using a traditional method as a comparative example.

[0057] 1.1 Synthetic data experiment

[0058] Test model: containing multiple complex anomalies (such as layered media, faults, cavities);

[0059] Evaluation metrics: mean squared error (MSE), structural similarity (SSIM), comparison of inversion time.

[0060] 1.2 Verification with measured data

[0061] Data source: electromagnetic exploration data (CSAMT or MT method) of a certain mining area;

[0062] Result analysis: The CNN inversion result is compared with the traditional Occam inversion method to verify the coincidence degree of the anomaly position and depth.

[0063] Results:

[0064] Table 1 Comparison of quantitative indicators

[0065]

[0066] Table 2 Comparison of SSIM under different noises

[0067]

[0068] 1. The inversion efficiency is significantly improved

[0069] As can be seen from Table 1 and Figure 3 It can be known that the result of the traditional Occam inversion method: it takes 4.2 hours and the boundary of the anomaly is blurred; while the time of the 3D CNN inversion of the present invention is 0.1 second, and the shape of the anomaly is highly consistent with the real model. It can be seen that the present invention can realize end-to-end direct mapping through 3D CNN, and can shorten the inversion time to the second level, and the efficiency is improved by more than a hundred times.

[0070] 2. The inversion accuracy and resolution are improved

[0071] As can be seen from Table 1, the SSIM (structural similarity) between the results of the present invention and the true model is 0.92, while the SSIM (structural similarity) between the traditional method and the true model is 0.76. It can be seen that the SSIM (structural similarity) index of the present invention is superior to the traditional method. The main reason is that on the one hand, the input data of the present invention is designed as a multi-frequency point electromagnetic field joint tensor (dimension: `[Nx, Ny, Nz, Nf]`), and the cross-frequency features can be automatically extracted through the 3D convolutional layer, which can make full use of the complementarity of multi-frequency data and improve the resolution ability for complex geological bodies. On the other hand, TV regularization and resistivity range limitation are introduced into the loss function, making the inversion result more in line with geological laws and reducing false anomalies.

[0072] 3. Robustness enhancement

[0073] As can be seen from Table 2, false anomalies appear in the background of the Occam inversion result under 30dB noise, while the CNN inversion result effectively suppresses the noise and the abnormal body is complete. In the verification of measured data, compared with the traditional inversion, the CNN three-dimensional inversion result has a high degree of coincidence (for example, the depth error of the abnormal body in a certain mining area is <5%). It can be seen that the multi-frequency joint input method of the present invention can compensate for the information loss of single-frequency data and adapt to complex exploration environments (such as strongly disturbed mining areas).

[0074] 4. Interpretability and scalability

[0075] The network output result (three-dimensional resistivity model) of the present invention is consistent with the true geological model, which can intuitively display the underground structure and facilitate geological interpretation.

[0076] In addition, the modular design of the present invention supports multi-source data input, supports the joint inversion of multiple types of electromagnetic data (such as CSAMT, MT, TEM), can be adapted to embedded hardware (such as GPU acceleration devices), and realizes real-time processing and on-site decision-making (such as mineral exploration, geological disaster warning). The present invention does not require manual setting of the initial model or adjustment of regularization parameters, reduces the dependence on professionals, and can be deployed on FPGA or edge computing devices.

[0077] In summary, the present invention realizes efficient, high-precision, and low-cost three-dimensional electromagnetic inversion, which is significantly superior to traditional iterative methods, is applicable to fields such as mineral exploration, engineering geology, and environmental monitoring, and has clear practical value and market prospects.

[0078] The basic principles, main features and advantages of the present invention have been shown and described above. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and the descriptions in the specification are only preferred examples of the present invention and are not used to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. A three-dimensional inversion method of electromagnetic method based on convolutional neural network, characterized in that: Including the following steps: S1. Implement end-to-end non-linear mapping through a 3D CNN processing module to obtain a corresponding 3D resistivity model; S2. Use multi-frequency electromagnetic field data as the combined input of the 3D resistivity model, and introduce TV regularization and physical property range constraints into the loss function to achieve 3D inversion.

2. The electromagnetic three-dimensional inversion method based on a convolutional neural network according to claim 1, characterized in that: The 3D CNN processing module includes: An encoder for extracting multi-scale features through 3D convolutional layers and downsampling; A decoder for restoring the spatial resolution through 3D transposed convolutional layers and skip connections; An output layer for constraining the resistivity range through a Sigmoid activation function and outputting a 3D resistivity model.

3. The three-dimensional inversion method of electromagnetic method based on convolutional neural network according to claim 1, characterized in that: The multi-frequency electromagnetic field data is input in a 4D tensor format: Dimensions: `[Nx, Ny, Nz, Nf]`, where Nx is the number of grids in the east-west direction; Ny is the number of grids in the north-south direction; Nz is the number of grids in the vertical depth direction; Nf is the number of frequencies.

4. A three-dimensional inversion system for electromagnetic method based on convolutional neural network, characterized in that: The convolutional neural network includes: a multi-frequency electromagnetic data input module, a 3D CNN processing module, and a physical constraint module; where: The multi-frequency electromagnetic data input module is used to receive and format the multi-frequency electromagnetic field data into a 4D tensor; The 3D CNN processing module includes: An encoder for extracting multi-scale features through 3D convolutional layers and downsampling; A decoder for restoring the spatial resolution through 3D transposed convolutional layers and skip connections; An output layer for constraining the resistivity range through a Sigmoid activation function and outputting a 3D resistivity model; The physical constraint module uses a loss function that integrates TV regularization and physical property range constraints.

5. The electromagnetic three-dimensional inversion system based on a convolutional neural network according to claim 4, characterized in that: The format of the multi-frequency electromagnetic data input module is: Dimensions: `[Nx, Ny, Nz, Nf]`, where Nx is the number of grids in the east-west direction; Ny is the number of grids in the north-south direction; Nz is the number of grids in the vertical depth direction; Nf is the number of frequencies; the output format of the output layer is Dimensions: `[Nx, Ny, Nz]`.

6. The three-dimensional inversion system of electromagnetic method based on convolutional neural network according to claim 4, characterized in that: The loss function is: Among them, the MSE function is used to quantify the error of the model, and the parameters of the model are adjusted through an optimization algorithm. TV regularization is used to enforce the smoothness of the model; the weight coefficients α and β are determined through cross-validation.

7. The three-dimensional inversion system of electromagnetic method based on convolutional neural network according to claim 4, characterized in that: The convolutional neural network is constructed by the following method: S1. Generate a large number of 3D resistivity models and their corresponding electromagnetic response datasets through forward simulation; S2. Construct a 3D CNN architecture with multi-frequency electromagnetic field data as the input and resistivity distribution as the output; S3. Training and validation: Use the synthesized 3D resistivity models and their corresponding electromagnetic response datasets to train the network, and verify the generalization ability through measured data; S4. Introduce physical constraints: Introduce a regularization term into the loss function.

8. The three-dimensional inversion system of electromagnetic method based on convolutional neural network according to claim 7, characterized in that: In step S1, the finite element method (FEM) or the finite volume method (FVM) is used to generate 3D resistivity models and their corresponding electromagnetic response datasets. The robustness of the dataset is improved by rotating, scaling, and adding noise to expand the dataset.

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