A method for magnetotelluric bayesian two-dimensional inversion based on neural operator

Abstract

The present application relates to the technical field of magnetotelluric inversion, in particular to a magnetotelluric Bayesian two-dimensional inversion method based on neural operator. The measured magnetotelluric data of the region to be inverted is obtained, the region to be inverted is discretized by finite difference and the resistivity spatial distribution model is defined; a Bayesian inversion model is established; a neural operator with the resistivity spatial distribution model as input and the apparent resistivity response as output is constructed and trained; the trained neural operator replaces the forward calculation in the Bayesian inversion model to perform inversion calculation on the region to be inverted; during the inversion process, the sampling samples are selected; the neural operator and the finite difference method are used to perform forward calculation on the sampling samples to obtain the first forward response and the second forward response; the relative error is calculated, and when the relative error exceeds the preset limit, the neural operator is corrected. The present application can efficiently and accurately realize two-dimensional magnetotelluric Bayesian inversion, and provide technical support for geophysical data inversion and uncertainty quantification.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of magnetotelluric inversion, and particularly relates to a magnetotelluric Bayesian two-dimensional inversion method based on a neural operator. BACKGROUND

[0002] Magnetotelluric (MT) is an important geophysical method for studying the electrical structure of the earth's interior by using natural electromagnetic fields as a source. It has been widely used in mineral exploration, geothermal exploration and deep structure research. Due to the noise contained in the magnetotelluric data and the finiteness of the measurement frequency, the magnetotelluric data inversion faces a serious multi-solution problem. The traditional deterministic inversion method based on regularization theory can only give a single optimal fitting data model under certain constraints, and lacks evaluation of the reliability of the model, which brings difficulties to the final evaluation of the model and geological interpretation.

[0003] The Bayesian method can not only better handle the nonlinearity of the inversion problem, but also accurately describe the uncertainty of the solution, providing a probability framework for quantifying the parameter uncertainty of the magnetotelluric inversion problem. In Bayesian inversion, the MCMC method is usually used to sample from the posterior probability density to approximate the target distribution. However, current research on MCMC methods still focuses on one-dimensional Bayesian problems. This is because MCMC methods require a large number of iterations to generate a sufficient number of samples. When searching in high-dimensional space, a large number of forward calculations are involved, which is very costly. This limits the application of this method in high-dimensional problems. A common way to reduce the computational cost is to replace the forward calculation in sampling with surrogate simulation.

[0004] As a new data-driven technology, the neural operator replaces the finite-dimensional linear layer in the neural network with a linear operator in the function space, thereby realizing the mapping of infinite-dimensional space. Such architecture also makes the neural operator have significantly better generalization ability than traditional neural networks, and is more suitable for solving high-dimensional problems. However, training a globally accurate neural operator requires a lot of computational resources, which is not practical. SUMMARY

[0005] In order to solve the problems in the prior art, the present application provides a magnetotelluric Bayesian two-dimensional inversion method based on a neural operator. The measured magnetotelluric data of the region to be inverted is obtained, the region to be inverted is discretized by finite difference and the resistivity spatial distribution model is defined; a Bayesian inversion model is established; a neural operator with the resistivity spatial distribution model as input and the apparent resistivity response as output is constructed and trained; the trained neural operator is used to replace the forward calculation in the Bayesian inversion model to perform inversion calculation on the region to be inverted; during the inversion process, a sampling sample is selected; the neural operator and the finite difference method are used to perform forward calculation on the sampling sample to obtain a first forward response and a second forward response; the relative error is calculated, and when the relative error exceeds the preset limit, the neural operator is corrected. The present application can efficiently and accurately realize two-dimensional magnetotelluric Bayesian inversion, and provides reliable technical support for geophysical data inversion and uncertainty quantification.

[0006] The present application adopts the following technical scheme, a magnetotelluric Bayesian two-dimensional inversion method based on a neural operator, comprising:

[0007] The measured magnetotelluric data of the region to be inverted is obtained, the region to be inverted is discretized by finite difference and the resistivity spatial distribution model is defined;

[0008] Based on the finite difference discretization result of the region to be inverted, a Bayesian inversion model of the region to be inverted is established according to the measured magnetotelluric data and the resistivity spatial distribution model of the region to be inverted;

[0009] Based on the branch-main network architecture, a neural operator with the resistivity spatial distribution model as input and the apparent resistivity response as output is constructed;

[0010] The training data set is obtained to train the neural operator, and a trained neural operator is obtained;

[0011] The trained neural operator is used for forward calculation in the Bayesian inversion model, and the region to be inverted is calculated by the Bayesian inversion model.

[0012] Further, when the trained neural operator is used for forward calculation in the Bayesian inversion model, it further comprises:

[0013] Sampling samples are selected in the inversion area at a set sampling interval;

[0014] The neural operator and the finite difference method are used to perform forward calculation on the sampling samples respectively to obtain a first forward response corresponding to the neural operator and a second forward response corresponding to the finite difference method;

[0015] The relative error of the first forward response and the second forward response is calculated, and when the relative error does not exceed the preset limit, no correction operation is performed;

[0016] When the relative error exceeds a preset limit, a correction operation is performed on the neural operator.

[0017] Further, a correction operation is performed on the neural operator, in particular:

[0018] A plurality of local samples are generated within a set radius range using a Gaussian noise disturbance method with the resistivity parameter corresponding to the sampling sample as the center;

[0019] The local samples are forward calculated using the staggered grid finite difference method;

[0020] A supplementary training set is constructed according to the local samples and their forward calculation results, and the neural operator is locally corrected using the supplementary training set.

[0021] Further, based on the finite difference discrete results of the region to be inverted, a Bayesian inversion model of the region to be inverted is established according to the measured magnetotelluric data of the region to be inverted and the resistivity spatial distribution model, including:

[0022] The region to be inverted is discretized by finite difference to obtain a finite difference grid of the region to be inverted;

[0023] The resistivity spatial distribution model is defined under the finite difference grid, and a forward operator of the region to be inverted is established;

[0024] A likelihood function is established according to the forward operator, the parameter distribution in the resistivity spatial distribution model is taken as a prior distribution, and a posterior probability model is constructed by combining the likelihood function;

[0025] The receiving probability and the proposal distribution of the Bayesian inversion of the region to be inverted are set, and the Bayesian inversion model of the region to be inverted is obtained according to the posterior probability model.

[0026] Further, the parameter distribution in the resistivity spatial distribution model is taken as a prior distribution, including: the resistivity parameter vector of each node in the resistivity spatial distribution model is defined as a prior distribution in a uniform distribution manner.

[0027] Further, the receiving probability and the proposal distribution of the Bayesian inversion of the region to be inverted are set, including:

[0028] The proposal distribution adopts a multivariate Gaussian proposal distribution, which is expressed as:

[0029] ;

[0030] In the formula, is the parameter to be inverted, is a candidate parameter generated from the parameter to be inverted through the proposal distribution, represents a proposal distribution, used to determine the transition from the candidate parameter to the parameter to be inverted the transition probability, is proportional to the sign, is an exponential function, is the i-th parameter to be inverted, is the i-th candidate parameter corresponding to the parameter to be inverted, represents the variance of the i-th parameter to be inverted;

[0031] Based on the posterior probability model, the acceptance probability of Bayesian inversion of the region to be inverted is set according to the MH sampling algorithm, denoted as:

[0032] ;

[0033] In the formula, is the acceptance probability, represents the minimum value function, is the observation data, is the prior distribution of the parameter to be inverted, is the prior distribution of the candidate parameter, is the proposal distribution, represents the reverse proposal distribution used to determine the transition from the candidate parameter to the parameter to be inverted , represents the conditional probability of the observation data under the candidate parameter, represents the conditional probability of the observation data under the parameter to be inverted.

[0034] Further, based on the branch-main network architecture, a neural operator is constructed with the resistivity spatial distribution model as input and the apparent resistivity response as output, including:

[0035] Obtaining observation parameters under polarization modes of a region to be inverted;

[0036] The branch-main network architecture includes a branch network and a main network;

[0037] The branch network is used for feature extraction of the resistivity spatial distribution model, and a first feature vector is obtained;

[0038] The main network is used for feature extraction of the observation parameters under each polarization mode, and a second feature vector is obtained;

[0039] The first feature vector and the second feature vector are subjected to inner product operation to obtain a fusion feature vector;

[0040] After the fusion feature vector is subjected to multi-layer Fourier transform, the apparent resistivity response is output through a projection layer.

[0041] Further, the training data set adopts a resistivity spatial distribution model generated based on a Gaussian random field, and a forward response thereof is calculated by a finite difference method.

[0042] The present application has the advantages that: the present application uses the MCMC method to randomly sample the calculation space, which can provide rich uncertainty information of the model parameters; at the same time, the two-dimensional inversion can better depict the variation of the physical property parameters in the horizontal direction, and provide more reliable guidance for actual exploration; the present application further uses the neural operator which is computationally efficient and has strong generalization ability, which significantly improves the calculation efficiency and has stronger generalization ability for different data; by adaptively correcting the neural operator locally, the approximation error is effectively controlled at a low level, while avoiding the construction of a huge offline training set, greatly reducing the calculation cost, so that the neural operator can replace the simulation technology and run under lower configuration of computing resources. BRIEF DESCRIPTION OF DRAWINGS

[0043] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiments or prior art description. Obviously, the drawings in the following description are only some embodiments of the present application, and for those skilled in the art, other drawings can also be obtained without creative labor.

[0044] Figure 1 A chessboard model schematic diagram for an embodiment of the present application;

[0045] Figure 2 A chessboard model schematic diagram for an embodiment of the present application;

[0046] Figure 3 A statistical result schematic diagram of a traditional Bayesian inversion method and a Bayesian inversion method based on adaptive substitute simulation for an embodiment of the present application; Figure 3 The (a) part and the (c) part in the figure are adaptive substitute simulation results, wherein the (a) part represents the statistical mean of the Bayesian sampling model set, and the (c) part is the variance; Figure 3 The (b) part and the (d) part in the figure are numerical method results, wherein the (b) part represents the statistical mean of the sampling model set, and the (d) part is the variance;

[0047] Figure 4 A one-dimensional edge probability comparison diagram of inversion results of a traditional Bayesian inversion method and a Bayesian inversion method based on adaptive substitute simulation for an embodiment of the present application at a single point; The (a) part in the figure corresponds to the adaptive substitute simulation Bayesian inversion result, Figure 4 The (a) part in the figure corresponds to the adaptive substitute simulation Bayesian inversion result,Figure 4 Part (b) in the table corresponds to the numerical Bayesian inversion result;

[0048] Figure 5 This invention provides an embodiment of a Bayesian inversion method based on traditional Bayesian methods and a Bayesian inversion method based on adaptive substitution simulation proposed in this invention, applicable to single-point... x Histograms comparing marginal probabilities at different depths at a depth of 67.3km. Figure 5 Parts (a) and (b) in the figure represent the single-point posterior probability distribution at a depth of 1.8 km for shallow high-resistivity anomalies. Figure 5 Parts (c) and (d) in the figure represent the single-point posterior probability distribution at a depth of 9.5 km for the shallow high-resistivity anomaly. 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] A schematic diagram of a magnetotelluric Bayesian two-dimensional inversion method based on neural operators according to an embodiment of the present invention is shown below. Figure 1 As shown, it includes:

[0051] Acquire measured magnetotelluric data of the area to be inverted, perform finite difference discretization on the area to be inverted, and establish a spatial distribution model of resistivity.

[0052] In this embodiment of the invention, magnetotelluric method is used to measure and collect measured magnetotelluric data in the area to be inverted. The measured magnetotelluric data is the original electromagnetic field signal in the area to be inverted, which includes electric field and magnetic field components at different observation points and frequencies. After the measured magnetotelluric data is collected, it can be further preprocessed. The preprocessing operations that can be selected in this embodiment of the invention include noise suppression, data format conversion, and coordinate normalization.

[0053] In this embodiment of the invention, based on the geological structure of the region to be inverted, the two-dimensional space of the region to be inverted is discretized into a finite difference grid by using the finite difference method. During the discretization process, the spatial coordinates, boundary conditions and refinement rules of the grid can be set with reference to any finite difference method recorded in the prior art. In practical applications, the settings can be made according to the actual situation.

[0054] In the embodiment of the present application, initial resistivity values are given to each node in the divided finite difference grid based on the geological information of the region to be inverted, so that a resistivity spatial distribution model is obtained, which serves as the starting point for subsequent inversion calculation of the region to be inverted.

[0055] Based on the finite difference grid of the region to be inverted, a Bayesian inversion model of the region to be inverted is established according to the measured magnetotelluric data and the resistivity spatial distribution model of the region to be inverted.

[0056] In the embodiment of the present application, first, a forward operator of the region to be inverted is established based on the finite difference grid; the measured magnetotelluric data of the region to be inverted is taken as observation data, and the resistivity spatial distribution model is taken as the parameter to be inverted, and a likelihood function is established in combination with the forward operator; the parameter distribution in the resistivity spatial distribution model is taken as a prior distribution, and a posterior probability model is constructed in combination with the likelihood function; the acceptance probability and the proposal distribution for Bayesian inversion of the region to be inverted are set, and the Bayesian inversion model of the region to be inverted is obtained according to the posterior probability model.

[0057] In one specific embodiment of the present application, a boundary value problem of the magnetotelluric field is established in the finite difference grid based on the Maxwell equations, and the finite difference method is used to discretize the control equation into a linear equation group to form a forward operator, and by solving the linear equation group, the electromagnetic response under different frequencies is obtained, so as to realize the mapping from the resistivity spatial distribution model to the magnetotelluric response. In the embodiment of the present application, the error between the measured magnetotelluric data and the model prediction data obtained through the forward operator is subjected to a multivariate Gaussian distribution, so that the likelihood function can be defined according to the Gaussian distribution probability density function.

[0058] In one specific embodiment of the present application, the parameter distribution in the resistivity spatial distribution model is obtained based on the geological information of the inversion region, so that the parameter distribution corresponding to each node in the resistivity spatial distribution model can be set as the prior distribution; and then according to the Bayes theorem, the prior distribution is combined with the likelihood function, so that the posterior probability model is obtained.

[0059] In the embodiment of the present application, the multivariate Gaussian distribution is used as the proposal distribution for the resistivity spatial distribution model, so that the candidate parameter of the parameter to be inverted can be generated, which can be expressed as:

[0060] ;

[0061] In the formula, is the parameter to be inverted, is the candidate parameter generated from the parameter to be inverted through the proposal distribution, represents the proposal distribution, which is used to judge the probability of generating the candidate parameter from the parameter to be inverted, ​is proportional to the symbol, is an exponential function, is the i-th parameter to be inverted, is the i-th candidate parameter corresponding to the i-th parameter to be inverted, represents the variance of the i-th parameter to be inverted;

[0062] The embodiment of the present application further sets the acceptance probability of the Bayesian inversion of the region to be inverted according to the MH sampling algorithm based on the constructed posterior probability model, the MH sampling algorithm is an important algorithm in the Markov Chain Monte Carlo (MCMC) method, and the full name is the Metropolis-Hastings algorithm. In the embodiment of the present application, the parameters of the MH sampling adopt an adaptive adjustment strategy to balance the sampling efficiency and the calculation accuracy, that is, in the early stage of sampling, a larger step size is adopted, and a proposal distribution with a larger standard deviation is set to quickly obtain the approximate outline of the inverted model. With the progress of sampling, the sampling step size is gradually reduced, and the standard deviation of the proposal distribution is reduced, so as to more accurately depict the local details of the anomaly body. The basis for parameter adjustment is the acceptance probability of the last round, and in actual operation, the neural operator test can be carried out first. According to the acceptance probability under different sampling numbers, a specific adjustment strategy is formulated, and the acceptance probability is represented as:

[0063] ;

[0064] In the formula, is the acceptance probability, represents the minimum value function, is the observation data, is the prior distribution of the parameter to be inverted, is the prior distribution of the candidate parameter, is the proposal distribution, represents the reverse proposal distribution used to judge the transition from the candidate parameter to the parameter to be inverted , represents the conditional probability of the observation data under the candidate parameter, represents the conditional probability of the observation data under the parameter to be inverted.

[0065] Based on the branch-main network architecture, a neural operator is constructed with the resistivity spatial distribution model as input and the apparent resistivity response as output;

[0066] In the embodiment of the present application, the neural operator adopts the branch-trunk network architecture of the deep neural operator network, wherein the branch network processes the resistivity spatial distribution model input, and the trunk network (Trunk net) processes the observation parameters of the region to be inverted, and the two networks elevate the resistivity and the observation parameters to a higher dimension, and after fusion by inner product operation, input multiple Fourier layers and U-Fourier layers combined with U-shaped networks for parameterization processing; finally, the data is transformed back to the output space of the target through the projection layer and position mapping, and the mapping relationship learned by the neural operator is represented as follows:

[0067] ;

[0068] wherein, represents the neural operator, represents the component of the electric field in the direction of at different positions and different frequencies, represents the component of the electric field in the direction of at different positions and different frequencies, represents the position parameter, represents the frequency parameter; represents the component of the magnetic field in the direction of at different positions and different frequencies, represents the component of the magnetic field in the direction of at different positions and different frequencies, is the resistivity.

[0069] The data processing process is as follows:

[0070] First, the observation parameters under the polarization mode of the region to be inverted are obtained, and in the embodiment of the present application, the observation parameters can be the observation frequency, the current intensity and the observation point coordinates of the region to be inverted; then the branch network is used to extract features from the resistivity spatial distribution model to obtain a first feature vector; the trunk network is used to extract features from the observation parameters under the polarization mode to obtain a second feature vector; the first feature vector and the second feature vector are subjected to inner product operation to obtain a fusion feature vector; after the fusion feature vector is subjected to multi-layer Fourier transform, the apparent resistivity response is output through the projection layer.

[0071] The training data set is obtained to train the neural operator, and the trained neural operator is obtained.

[0072] In the embodiment of the present application, the training data set is obtained based on the resistivity spatial distribution model generated by the Gaussian random field method, and the magnetotelluric response is calculated by using the staggered grid finite difference method, so as to construct the training data set to train the neural operator.

[0073] The trained neural operator is used for forward calculation in the Bayesian inversion model, and inversion calculation is performed on the region to be inverted by the Bayesian inversion model.

[0074] In the embodiment of the present application, the trained neural operator replaces the forward calculation and is embedded in the Bayesian inversion framework to perform inversion on the calculation region. When the trained neural operator is used for forward calculation in the Bayesian inversion model, it further comprises: selecting a sampling sample at a set sampling interval during the inversion process; using the neural operator and the finite difference method to perform forward calculation on the sampling sample respectively to obtain a first forward response corresponding to the neural operator and a second forward response corresponding to the finite difference method; calculating the relative error of the first forward response and the second forward response, and when the relative error does not exceed the preset limit, not performing a correction operation; when the relative error exceeds the preset limit, performing a correction operation on the neural operator.

[0075] In one specific embodiment of the present application, the last parameter in the medium parameters of the inversion region can also be used as a sampling sample to test the accuracy of the neural operator.

[0076] The expression for calculating the relative error of the first forward response and the second forward response is:

[0077] ;

[0078] wherein, the relative error is represented by, the first forward response is represented by, the second forward response is represented by, the Euclidean norm is represented by, the sampling sample is represented by.

[0079] In one specific embodiment of the present application, when the relative error exceeds the preset limit, it means that the neural operator has not learned the features well under the current parameter distribution, and therefore a supplementary training set needs to be constructed locally and the neural operator needs to be corrected. The method for performing an update operation on the neural operator is as follows: using the resistivity parameter corresponding to the sampling sample as the center, a plurality of local samples are generated within a set radius range by using a Gaussian noise disturbance method; the local samples are calculated by using the staggered grid finite difference method; a supplementary training set is constructed according to the local samples and their forward calculation results, and the neural operator is locally corrected using the supplementary training set. During the local correction, different hyperparameters are used for transfer learning in the original operator neural network to adapt to the features of the current region, and a high-precision neural operator is obtained.

[0080] In another specific embodiment of the present application, the inversion adopts a core calculation region of 100*200 km, which is discretized into 64*64 grids by finite difference, wherein, in the horizontal direction, the model is distributed from-100 km to 100 km and is evenly discretized into 64 grids, and in the vertical direction, the model is discretized into three groups: the first group is from 0-1 km, the model is divided into 20 grids with increasing size; the second group is from 1 to 20 km, the model is divided into 20 grids with logarithmic increase; and the third group is from 20 to 100 km, the model is divided into 24 grids with logarithmic increase. Considering the boundary effect, the resistivity spatial distribution model is expanded in the horizontal direction and the vertical direction: in the horizontal direction, 10 grids with logarithmic increase are set on the left and right of the core region, respectively, with the range of 100 km to 500 km and-100 km to-500 km, respectively; in the vertical direction, 10 grids with logarithmic increase are set for the air layer, distributed from-400 km to 0 km, and 10 grids with logarithmic increase are set for the expanded layer underground, distributed from 100 km to 500 km; the above expansion ensures that the boundary conditions of the electromagnetic field are met, and the present application example sets 64 measurement points at equal intervals on the ground surface and calculates the response data corresponding to 16 logarithmically equidistant frequencies from 10 Hz to 0.07 Hz.

[0081] For the training of the neural operator, the present application embodiment adopts 6000 resistivity spatial distribution models generated by a Gaussian random field and the forward response calculated by the finite difference method as the training set, trains for 100 rounds with a learning rate of 0.0003, wherein the data amount processed by each batch is 5, the learning rate is halved after every 35 rounds of training, the sampling number of each small cycle in the correction process is 3000 samples, and an inspection is performed after each small cycle is completed; the correction error limit is 0.02, the local sampling radius Q is 15, and the number of local sampling samples m is 1500; for local correction, the learning rate is 0.00008, and the training is performed for 30 rounds, wherein the data amount processed by each batch is 4, and the learning rate is halved every 10 rounds.

[0082] The present application embodiment further designs a neural operator as Figure 2As shown in the chessboard model, the chessboard model contains 6 abnormal bodies, the upper three abnormal bodies have the same size of 3km*16km, the lower three abnormal bodies have the same size of 7km*16km, the high resistance abnormal body is 300Ω*m, the low resistance abnormal body is 5Ω*m, and the background resistivity is 100Ω*m. The embodiment of the application selects a uniform half-space model with a resistivity of 100Ω*m as a resistivity spatial distribution model, carries out 60000 times of sampling, selects a Gaussian distribution as a proposal distribution, sets the mean value of the distribution as a two-dimensional random array, samples from the two-dimensional random array to obtain new samples to ensure randomness of the samples, sets the sub-diagonal elements of the covariance matrix corresponding to the proposal distribution to 1, and sets the initial values of the main diagonal elements to 20, and then attenuates to 0.6 times of the previous value every 1 / 3 of the sampling; the initial sampling step is 2.5, and then attenuates to 0.6 times of the previous value every 1 / 3 of the sampling.

[0083] Figure 3 The statistical results of the Bayesian inversion method based on the traditional Bayesian method and the Bayesian inversion method based on adaptive surrogate simulation provided for the embodiment of the application are as follows, Figure 3 The (a) part and the (c) part in the table are adaptive surrogate simulation results, wherein the (a) part represents statistical mean values of the Bayesian sampling model set, and the (c) part is variance; Figure 3 The (b) part and the (d) part in the table are numerical method results, wherein the (b) part represents statistical mean values of the sampling model set, and the (d) part is variance. From the (a) part and the (c) part in the table, Figure 3 It can be seen from the mean values of the (a) part and the (c) part in the table that both the methods can basically recover the shapes and values of the abnormal bodies, the calculation efficiency comparison of the two methods is shown in Table 1, and it can be seen that, in the case of obtaining similar inversion statistical results, the calculation speed of the surrogate simulation Bayesian method in the embodiment of the application is 13 times that of the traditional Bayesian method, which greatly improves the calculation efficiency, and this makes more sampling and more accurate uncertainty quantification possible.

[0084] Table 1: Calculation efficiency comparison table

[0085] ;

[0086] As shown in the table, Figure 4 The embodiment of the application provides a one-dimensional edge probability comparison diagram of inversion results at a single point in the table, Figure 4 The (a) part in the table corresponds to the adaptive surrogate simulation Bayesian inversion result, Figure 4 The (b) part in the table corresponds to the numerical Bayesian inversion result, and it can be seen that both the methods can basically invert the positions and physical property parameters of the abnormal bodies.

[0087] As Figure 5 shown, the embodiment of the present application provides a comparison histogram of edge probability at different depths under the single point x = 67.3km based on the traditional Bayesian method and the Bayesian inversion method based on the adaptive surrogate simulation method proposed in the present application; for the shallow high-resistivity anomaly body, it can be seen that, Figure 5 the (a) part and the (b) part in the figure are the single-point posterior probability distribution at the depth of 1.8km for the shallow high-resistivity anomaly body, Figure 5 the (c) part and the (d) part in the figure are the single-point posterior probability distribution at the depth of 9.5km for the shallow high-resistivity anomaly body, it can be seen that the numerical recovery of the traditional Bayesian method is slightly better than that of the adaptive surrogate simulation method; for the deep low-resistivity anomaly body, the two methods are more similar, and the adaptive surrogate simulation method can be used as a high-efficiency and reliable reference.

[0088] The above merely describes preferred embodiments of the present application but should not be used to limit the present application, and any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A two-dimensional magnetotelluric Bayesian inversion method based on neural operators, characterized in that, include: Acquire measured magnetotelluric data of the area to be inverted, perform finite difference discretization on the area to be inverted, and establish a spatial distribution model of resistivity. Based on the finite difference discretization results of the region to be inverted, a Bayesian inversion model of the region to be inverted is established according to the measured magnetotelluric data and resistivity spatial distribution model of the region to be inverted. Based on a branch-backbone network architecture, a neural operator is constructed that takes a resistivity spatial distribution model as input and considers the resistivity response as output; including: Obtain observation parameters of the region to be inverted under different polarization modes; The branch-backbone network architecture includes a branch network and a backbone network; The first feature vector is obtained by extracting features from the resistivity spatial distribution model using the branch network. The backbone network is used to extract features from the observation parameters under each polarization mode to obtain a second feature vector; Perform an inner product operation on the first feature vector and the second feature vector to obtain a fused feature vector; After performing a multi-level Fourier transform on the fused feature vector, the apparent resistivity response is output through a projection layer. The neural operator is trained using a training dataset to obtain a trained neural operator. The trained neural operators are used for forward calculations in the Bayesian inversion model, and the Bayesian inversion model is used to perform inversion calculations on the region to be inverted.

2. The magnetotelluric Bayesian two-dimensional inversion method based on neural operators according to claim 1, characterized in that: When using trained neural operators for forward modeling in Bayesian inversion models, the following is also included: During the inversion process, samples are selected for random inspection at set sampling intervals; The sampled data were subjected to forward modeling using both neural operators and the finite difference method to obtain the first forward modeling response corresponding to the neural operators and the second forward modeling response corresponding to the finite difference method. Calculate the relative error between the first forward response and the second forward response. If the relative error does not exceed a preset limit, no correction operation is performed. When the relative error exceeds a preset limit, a correction operation is performed on the neural operator.

3. The magnetotelluric Bayesian two-dimensional inversion method based on neural operators according to claim 2, characterized in that: Perform a correction operation on the neural operator, specifically: Using the resistivity parameter corresponding to the sampled sample as the center, a Gaussian noise perturbation method is used to generate multiple local samples within a set radius. The local samples were forward modeled using the staggered grid finite difference method. A supplementary training set is constructed based on the local samples and their forward modeling results, and the neural operator is locally corrected using the supplementary training set.

4. The magnetotelluric Bayesian two-dimensional inversion method based on neural operators according to claim 1, characterized in that: Based on the finite difference discretization results of the region to be inverted, and according to the measured magnetotelluric data and resistivity spatial distribution model of the region, a Bayesian inversion model for the region to be inverted is established, including: Finite difference discretization is performed on the region to be inverted to obtain a finite difference grid of the region to be inverted. A resistivity spatial distribution model is defined under the finite difference grid, and a forward modeling neural operator is established for the region to be inverted; A likelihood function is established based on the forward neural operator, and the parameter distribution in the resistivity spatial distribution model is used as the prior distribution. A posterior probability model is constructed by combining the likelihood function. The acceptance probability and suggestion distribution for Bayesian inversion of the region to be inverted are set, and the Bayesian inversion model of the region to be inverted is obtained according to the posterior probability model.

5. The magnetotelluric Bayesian two-dimensional inversion method based on neural operators according to claim 4, characterized in that: Using the parameter distribution in the resistivity spatial distribution model as the prior distribution includes: defining the resistivity parameter vector of each node in the resistivity spatial distribution model as the prior distribution using a uniform distribution method.

6. The magnetotelluric Bayesian two-dimensional inversion method based on neural operators according to claim 4, characterized in that: Define the acceptance probability and proposal distribution for performing Bayesian inversion on the region to be inverted, including: The proposed distribution adopts a multivariate Gaussian proposed distribution, denoted as: ； In the formula, The parameters to be inverted, Candidate parameters are generated from the parameters to be inverted using the proposed distribution. This represents the suggested distribution, used to determine the parameters to be inverted. Transition to candidate parameters The transition probability, Proportional to the sign, exp ( ) is an exponential function. For the first i One parameter to be inverted, For the first i Candidate parameters corresponding to the parameters to be inverted Indicates the first i The variance of the parameters to be inverted; Based on the aforementioned posterior probability model, the receiving probability for performing Bayesian inversion on the region to be inverted is set according to the MH sampling algorithm, and is expressed as: ； In the formula, For the probability of receiving, This represents the function that takes the minimum value. For observation data, Let be the prior distribution of the parameters to be inverted. Let be the prior distribution of the candidate parameters. For the proposed distribution, This indicates the parameter used to determine the candidate parameters. Transfer to the parameters to be inverted The reverse proposal distribution, This represents the conditional probability of observed data occurring under candidate parameters. This represents the conditional probability of the observed data occurring under the parameters to be inverted.

7. The magnetotelluric Bayesian two-dimensional inversion method based on neural operators according to claim 1, characterized in that: The training dataset is obtained by using a resistivity spatial distribution model based on Gaussian random fields and calculating its forward response using the finite difference forward modeling method.

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