Magnetotelluric inversion method fusing deep learning and jacobian matrix optimization

Abstract

The invention belongs to the technical field of geophysics and statistics, and particularly discloses a magnetotelluric inversion method fusing deep learning and Jacobian matrix optimization, which has the beneficial effects that compared with a deep learning method of an end-to-end direct mapping inversion result, a mathematical physical process is reserved, and inversion iteration still follows an optimal mathematical law; generalization is improved, the adaptive capacity of the algorithm to unknown data is higher, the overfitting risk of a pure data driving method is avoided, and compared with a traditional inversion method, calculation time consumption is greatly reduced; forward modeling repeated calling is skipped, and the problem that forward modeling simulation needs to be scheduled for multiple times in traditional Jacobian matrix calculation is avoided; and the inversion result is consistent with the reduction degree of the electrical structure in the traditional method.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of geophysics and statistics, and particularly relates to a magnetotelluric inversion method fusing deep learning and Jacobian matrix optimization. BACKGROUND

[0002] Resource and energy development and utilization hold the economic lifeline of a country. With the implementation of a new round of national prospecting strategy, resource and energy exploration has ushered in a new wave of technological boom. Usually, geophysical, geochemical and geological modeling methods are used before mining. Among them, the geophysical method plays an important role in deep mineral exploration and reserve estimation. The traditional geophysical method of direct current or electromagnetic method has a more sensitive advantage than other methods in detecting the electrical structure difference of minerals. Generally speaking, the range of mineral deposits can be circled by the resistivity distribution map of the inversion result of the direct current or electromagnetic method (hereinafter referred to as electromagnetic method), and the mineral reserves can be comprehensively analyzed and evaluated in combination with other geological data.

[0003] In the existing geophysical method, the magnetotelluric method has become one of the important methods for deep resource exploration due to its advantages of large detection depth and low cost. However, in the traditional magnetotelluric method, the calculation of the Jacobian matrix in the objective function is very time-consuming, and the forward calculation is called multiple times to finally find the optimization gradient direction. In recent years, with the rise of artificial intelligence algorithms, deep learning algorithms have been introduced into the forward and inversion of the magnetotelluric method. However, most of the methods only use end-to-end direct mapping method and do not analyze the inversion iteration process, ignoring the mathematical and physical process in the inversion process, which has a deficiency in the generalization of the model.

[0004] The magnetotelluric inversion method fusing deep learning and Jacobian matrix optimization proposed in the present application optimizes the model generalization problem to a certain extent. In the objective function, the gradient of the Jacobian matrix, i.e. the operator of the forward calculation, is a very important calculation process, which determines the optimization gradient of the inversion iteration. The traditional calculation method needs to solve the partial differential equation and do difference numerical simulation calculation, which is complex and time-consuming. The present application uses the ability of the deep learning network to map and solve the partial differential equation to directly map the data input and the Jacobian matrix. In the actual inversion iteration, the Jacobian matrix is obtained through the deep learning network, and then substituted into the objective function to obtain the iteration gradient direction. The method not only has fast solving speed, but also can obtain a better gradient direction, which improves the inversion efficiency and enhances the generalization to a certain extent, thereby enhancing the practical value. SUMMARY

[0005] To solve the above problems, the application provides a magnetotelluric inversion method combining deep learning and Jacobian matrix optimization, which is based on a traditional geophysical inversion method, uses a deep learning network to map data and a Jacobian matrix in a target function, avoids solving complex and time-consuming partial differential equations, and finally forms an iterative solution of a fusion inversion algorithm.

[0006] A magnetotelluric inversion method combining deep learning and Jacobian matrix optimization, characterized in that it comprises the following steps:

[0007] S01, constructing a classic model sample set containing a resistivity model, simulated data and a Jacobian matrix of an iterative process by using a traditional forward and inversion technology;

[0008] S02, constructing a deep convolutional neural network, taking iterative data, model parameters, regularization parameters and other data as multi-channel input, training the Jacobian matrix as a label, and establishing a mapping relationship from multi-channel data such as model parameters to the Jacobian matrix;

[0009] S03, embedding the trained Jacobian matrix prediction model into a traditional magnetotelluric inversion target function, replacing the original Jacobian calculation, forming a new iterative formula for inversion solution;

[0010] S04, based on the new iterative formula, establishing a complete inversion algorithm process, inputting the preprocessed and normalized actual collected data into the pre-trained model to predict the Jacobian matrix, and obtaining the electrical structure distribution through iteration;

[0011] S05, analyzing the potential distribution and range of resources and energy in the target area according to the electrical structure distribution obtained by inversion, and evaluating the exploitation value.

[0012] As a further scheme of the application, the specific steps of step S01 are as follows: using traditional geophysical forward and inversion technology, establishing N classic resource and energy model sample sets, including a resistivity random distribution data set P(n), an electrical anomaly model set M(n) and a corresponding simulated data set N(n) under each random model, in addition, saving the Jacobian matrix data set J k and the corresponding iteration data set m k of each iteration in the inversion iteration process, wherein k is the iteration round of the current data set, is a cycle from 1 to i*n, n is the total number of data sets, and i is the iteration round.

[0013] As a further scheme of the application, the specific steps of step S02 are as follows:

[0014] constructing a deep convolutional neural network framework, m k as an input data set, J k as a label value for supervised learning, let symbol ΘL To represent the mapping relationship, we have:

[0015] Θ L (m k ) = J k

[0016] During the training process, m k It also includes multi-channel data, such as key parameters in the objective function like Lagrange multipliers, to improve the generalization of the mapping. The training process is established using this mapping relationship:

[0017]

[0018] Where, Θ L * represents the trained neural network, inputted by m. k Predict the optimal Jacobian matrix J k This minimizes the objective function.

[0019] As a further aspect of the present invention, the specific steps of step S03 are as follows:

[0020] The pre-trained model Θ L *Integrated into the objective function of traditional magnetotelluric inversion, and the iterative formula adjusted to:

[0021]

[0022] The k+1 round iterative model m can then be calculated. k+1 In practical applications, the calculations for other parts remain consistent with traditional magnetotelluric inversion. Only the calling function needs to be redirected to the calling function of the deep learning pre-trained model when calculating the Jacobian matrix. The formula for calculating the L2 norm fitting difference during the iteration process is:

[0023] X k+1 (μ)=||Wd-WF[m k+1 (μ)]|| 2

[0024] Where d is the original data and W is the data weight matrix. The iteration ends when the fitting difference meets the requirements or the number of iterations k reaches the set upper limit.

[0025] As a further aspect of the present invention, the efficiency and quality of the inversion in step S03 can be improved through the following steps:

[0026] S31. Input neural network data is set to be processed simultaneously through multiple channels. Multiple data in the objective function are flexibly selected according to the dimension and data characteristics of the actual inversion task to extract more robust feature information.

[0027] S32. Select a more suitable deep learning network based on the input data in S31. For example, when the input is only the model parameters, a basic convolutional neural network can be used, while when adding Lagrange multiplier inputs, a composite framework with a recurrent neural network can be selected to increase the prediction function.

[0028] S04. Based on the iterative process obtained in step S03, establish a magnetotelluric inversion algorithm based on Jacobian matrix deep learning. Preprocess the magnetotelluric field data, normalize the input dataset, use the pre-trained model to predict the Jacobian matrix, and iterate successively to obtain the inverted electrical structure distribution.

[0029] S05. Based on the electrical structure distribution obtained in step S04, infer and analyze the potential distribution and range of resources and energy in the target area, assess the mining value, and achieve the purpose of advanced detection.

[0030] The beneficial effects of this invention are as follows:

[0031] 1. Enhance the generalization ability of the inversion algorithm.

[0032] Technical approach: Construct a deep learning network mapping framework in the objective function, use a deep neural network to solve the Jacobian matrix (i.e., the gradient of the forward operator) in the iteration, and then return it to the objective function for iterative optimization;

[0033] Technical effects:

[0034] Compared to deep learning methods that directly map inversion results end-to-end:

[0035] The mathematical and physical processes are preserved: the inversion iteration still follows the mathematical laws of optimization (such as gradient descent);

[0036] Improved generalization ability: The algorithm is more adaptable to unknown data, avoiding the risk of overfitting in purely data-driven methods.

[0037] 2. Significantly improves inversion efficiency

[0038] Technical means: Use the feature extraction and fast mapping capabilities of deep learning to directly predict the Jacobian matrix, replacing the complex calculation process based on numerical solutions of partial differential equations (such as the finite difference method) in traditional methods;

[0039] Technical effects:

[0040] Compared to traditional inversion methods (such as regularized numerical optimization):

[0041] The computation time has been significantly reduced;

[0042] Skip repeated forward modeling calls: Avoid the problem of needing to schedule forward simulations multiple times for traditional Jacobian matrix calculations;

[0043] Non-destructive accuracy: The inversion results are consistent with the electrical structure reduction of traditional methods. Attached Figure Description

[0044] To more clearly illustrate the technical solution of the present invention, the accompanying drawings used in the description of the specific embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0045] Figure 1 This is a flowchart of the method described in this invention;

[0046] Figure 2 This is a schematic diagram of the algorithm fusion process in the geothermal resource exploration example described in this invention;

[0047] Figure 3 This is a comparison of the effects of the inversion method described in this invention with traditional inversion methods;

[0048] Figure 4 This is a comparison of the accuracy of the inversion method described in this invention with that of traditional inversion methods. Detailed Implementation

[0049] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0050] like Figures 1-4 As shown, the present invention has the following two specific embodiments.

[0051] Example 1

[0052] A magnetotelluric inversion method integrating deep learning and Jacobian matrix optimization includes the following steps:

[0053] S1. Using traditional geophysical forward and inverse retrieval techniques, establish N classic resource and energy model sample sets, including a resistivity random distribution dataset P(n), an electrical anomaly model set M(n), and the corresponding simulation dataset N(n) under each random model. Furthermore, during the inversion iteration process, save the Jacobian matrix dataset J for each iteration. k and the corresponding dataset m for each iteration k , where k is the iteration round of the current dataset, which is a loop from 1 to i*n, n is the total number of datasets, and i is the iteration round;

[0054] S2. Construct a deep convolutional neural network framework, m k As the input dataset, J k Let the symbol Θ be the label value for supervised learning. L To represent the mapping relationship, we have:

[0055] Θ L (m k ) = J k

[0056] During the training process, m k It also includes multi-channel data, such as key parameters in the objective function like Lagrange multipliers, to improve the generalization of the mapping. The training process is established using this mapping relationship:

[0057]

[0058] Where, Θ L * represents the trained neural network, inputted by m. k Predict the optimal Jacobian matrix J k Minimize the objective function;

[0059] S3, The pre-trained model Θ L *Integrated into the objective function of traditional magnetotelluric inversion, and the iterative formula adjusted to:

[0060]

[0061] The k+1 round iterative model m can then be calculated. k+1 In practical applications, the calculations for other parts remain consistent with traditional magnetotelluric inversion. Only the calling function needs to be redirected to the calling function of the deep learning pre-trained model when calculating the Jacobian matrix. The formula for calculating the L2 norm fitting difference during the iteration process is:

[0062] X k+1 (μ)=||Wd-WF[m k+1 (μ)]|| 2

[0063] Where d is the original data, W is the data weight matrix, and the iteration ends when the fitting difference meets the requirements or the number of iterations k reaches the set upper limit.

[0064] The efficiency and quality of the inversion in step S03 can be improved through the following steps:

[0065] S31. Input neural network data is set to be processed simultaneously through multiple channels. Multiple data in the objective function are flexibly selected according to the dimension and data characteristics of the actual inversion task to extract more robust feature information.

[0066] S32. Select a more suitable deep learning network based on the input data in S31. For example, when the input is only the model parameters, a basic convolutional neural network can be used, while when adding Lagrange multiplier inputs, a composite framework with a recurrent neural network can be selected to increase the prediction function.

[0067] Example 2

[0068] A deep learning network mapping framework was constructed from the objective function of the core module of magnetotelluric inversion. Compared with the end-to-end magnetotelluric deep learning inversion method that directly maps data with inversion results, it is obviously more mathematical and physical. With the objective function subject unchanged, the Jacobian matrix in the iteration is solved by deep neural network and then returned to the objective function. The inversion iteration still conforms to the mathematical and physical laws of optimization, making the overall inversion algorithm more generalizable.

[0069] Traditional magnetotelluric inversion methods define the objective function using regularization principles, perform rigorous mathematical and physical derivations, and finally conduct numerical simulations. Each iteration requires enormous computational resources and time, especially when calculating the Jacobian matrix, which often involves multiple scheduling of forward modeling calculations to determine the optimal value. In contrast, this scheme utilizes the feature extraction and fast mapping capabilities of deep learning to directly solve for the Jacobian matrix, skipping the complex and time-consuming Jacobian matrix solution process in the iterations to achieve rapid iteration. Figure 3 To compare the performance of the proposed new inversion method with traditional inversion methods under a simple model, the results show that the new algorithm and the two traditional algorithms are very close and can accurately restore the electrical structure of the model. However, in terms of time, the proposed method ( Figure 3 -b) Total time: 8.76 seconds, traditional method A ( Figure 3 -c) Total time was 25.72 seconds, traditional method B ( Figure 3 -d) The total time was 32.12 seconds, which shows that the proposed application has a significant advantage in inversion efficiency.

[0070] The preferred embodiments of the present invention disclosed above are merely illustrative of the invention. These preferred embodiments do not exhaustively describe all details, nor do they limit the invention to any specific implementation. Clearly, many modifications and variations can be made based on the content of this specification. This specification selects and specifically describes these embodiments to better explain the principles and practical applications of the invention, thereby enabling those skilled in the art to better understand and utilize the invention.

Claims

1. A magnetotelluric inversion method integrating deep learning and Jacobian matrix optimization, characterized in that, Includes the following steps: S01. Construct a classic model sample set containing resistivity model, simulation data and Jacobian matrix of iterative process using traditional forward and inverse modeling techniques; S02. Construct a deep convolutional neural network, using iterative data, model parameters, regularization parameters, and other data as multi-channel inputs and the Jacobian matrix as labels for training, and establish a mapping relationship between multi-channel iterative data and the Jacobian matrix. S03. Embed the trained Jacobian matrix prediction model into the traditional magnetotelluric inversion objective function, replace the original Jacobian calculation, and form a new iterative formula for inversion solution. S04. Based on the new iterative formula, establish a complete inversion algorithm process, preprocess and normalize the actual collected data, input it into the pre-trained model to predict the Jacobian matrix, and obtain the electrical structure distribution through iteration. S05. Analyze the potential distribution and range of resources and energy in the target area based on the electrical structure distribution obtained from the inversion, and assess the mining value.

2. The magnetotelluric inversion method integrating deep learning and Jacobian matrix optimization according to claim 1, characterized in that, The specific steps of step S01 are as follows: Using traditional geophysical forward and inverse retrieval techniques, establish N classic resource and energy model sample sets, including a resistivity random distribution dataset P(n), an electrical anomaly model set M(n), and the corresponding simulation dataset N(n) under each random model. Furthermore, during the inversion iteration process, save the Jacobian matrix dataset J for each iteration. k and the corresponding dataset m for each iteration k , where k is the iteration round of the current dataset, which is a loop from 1 to i*n, n is the total number of datasets, and i is the iteration round.

3. The magnetotelluric inversion method integrating deep learning and Jacobian matrix optimization according to claim 1, characterized in that, The specific steps of step S02 are as follows: Building a deep convolutional neural network framework, m k As the input dataset, J k Let the symbol Θ be the label value for supervised learning. L To represent the mapping relationship, we have: I L (m k )=J k During the training process, m k It also includes multi-channel data, such as key parameters in the objective function like Lagrange multipliers, to improve the generalization of the mapping. The training process is established using this mapping relationship: Where, Θ L * represents the trained neural network, inputting multi-channel data item m. k Predict the optimal Jacobian matrix J k This minimizes the objective function.

4. The magnetotelluric inversion method integrating deep learning and Jacobian matrix optimization according to claim 1, characterized in that: The specific steps of step S03 are as follows: The pre-trained model Θ L *Integrated into the objective function of traditional magnetotelluric inversion, and the iterative formula adjusted to: The k+1 round iterative model m can then be calculated. k+1 In practical applications, the calculations for other parts remain consistent with traditional magnetotelluric inversion. Only the calling function needs to be redirected to the calling function of the deep learning pre-trained model when calculating the Jacobian matrix. The formula for calculating the L2 norm fitting difference during the iteration process is: X k+1 (μ)=||Wd-WF[m k+1 (m)]|| 2 Where d is the original data and W is the data weight matrix. The iteration ends when the fitting difference meets the requirements or the number of iterations k reaches the set upper limit.

5. The magnetotelluric inversion method integrating deep learning and Jacobian matrix optimization according to claim 1, characterized in that: The efficiency and quality of the inversion in step S03 can be improved through the following steps: S31. Input neural network data is set to be processed simultaneously through multiple channels. Multiple data in the objective function are flexibly selected according to the dimension and data characteristics of the actual inversion task to extract more robust feature information. S32. Select a more suitable deep learning network based on the input data in S31. For example, when the input is only the model parameters, a basic convolutional neural network can be used, while when the input of Lagrange multipliers is added, a composite framework with a recurrent neural network can be selected to increase the prediction function.

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