Magnetotelluric Bayesian two-dimensional inversion method based on neural operator

Abstract

The invention relates to the technical field of magnetotelluric inversion, in particular to a magnetotelluric Bayesian two-dimensional inversion method based on a neural operator. Obtaining actually measured magnetotelluric data of a to-be-inverted region, performing finite difference discretization on the to-be-inverted region, and defining a resistivity spatial distribution model; establishing a Bayesian inversion model; a neural operator with the resistivity space distribution model as input and apparent resistivity response as output is constructed and trained; performing inversion calculation on the to-be-inverted region by using the trained neural operator instead of forward calculation in the Bayesian inversion model; selecting a sampling inspection sample in the inversion process; a neural operator and a finite difference method are adopted to carry out forward modeling calculation on the sampling inspection sample, and a first forward modeling response and a second forward modeling response are obtained; the relative error is calculated, and the neural operator is corrected when the relative error exceeds a preset limit. According to the method, the two-dimensional magnetotelluric Bayesian inversion can be efficiently and accurately realized, and technical support is provided 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 sample is selected for inspection; the neural operator and the finite difference method are used to perform forward calculation on the sample for inspection to obtain a first forward response and a second forward response; the relative error is calculated, and when the relative error exceeds a 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: Obtaining the measured magnetotelluric data of the region to be inverted, discretizing the region to be inverted by finite difference and establishing a resistivity spatial distribution model; 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 of the region to be inverted and the resistivity spatial distribution model; 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; Training data sets are obtained to train the neural operator, and a trained neural operator is obtained; The trained neural operator is used for forward calculation in the Bayesian inversion model, and inversion calculation on the region to be inverted is performed through the Bayesian inversion model.

[0007] Further, when the trained neural operator is used for forward calculation in the Bayesian inversion model, it further comprises: Selecting a sample for inspection at a set sampling interval in the inversion area; Respectively using the neural operator and the finite difference method to perform forward calculation on the sample for inspection 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 a preset limit, no correction operation is performed; When the relative error exceeds the preset limit, a correction operation is performed on the neural operator.

[0008] Further, the correction operation on the neural operator is specifically: With the resistivity parameter corresponding to the sampling sample as the center, a plurality of local samples are generated in a set radius range by using a Gaussian noise disturbance method; The local samples are forward calculated by using an alternating grid finite difference method; A supplementary training set is constructed according to the local samples and the forward calculation results of the local samples, and the neural operator is locally corrected by using the supplementary training set.

[0009] 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: The finite difference grid of the region to be inverted is obtained by finite difference discretization of the region to be inverted; The resistivity spatial distribution model is defined under the finite difference grid, and the forward operator of the region to be inverted is established; The likelihood function is established according to the forward operator, the parameter distribution in the resistivity spatial distribution model is taken as the prior distribution, and the posterior probability model is constructed by combining the likelihood function; The acceptance probability and the proposal distribution for 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.

[0010] Further, the parameter distribution in the resistivity spatial distribution model is taken as the prior distribution, including: the resistivity parameter vector of each node in the resistivity spatial distribution model is defined as the prior distribution by using a uniform distribution method.

[0011] Further, the acceptance probability and the proposal distribution for the Bayesian inversion of the region to be inverted are set, including: The proposal distribution adopts a multivariate Gaussian proposal distribution, and is expressed as: ; In the formula, is the parameter to be inverted, is a candidate parameter generated from the parameter to be inverted by the proposal distribution, represents the proposal distribution, which is used to judge the transition probability from the parameter to be inverted to the candidate parameter , is proportional to the sign, is an exponential function, is the i th parameter to be inverted, is the candidate parameter corresponding to the i th parameter to be inverted, represents the variance of the i th parameter to be inverted; Based on the posterior probability model, the acceptance probability for the Bayesian inversion of the region to be inverted is set according to the MH sampling algorithm, and is expressed as: ; In the formula, is a receiving probability, represents a minimum value function, is observation data, is a prior distribution of a to-be-inverted parameter, is a prior distribution of a candidate parameter, is a proposal distribution, represents a reverse proposal distribution for judging the transition of the candidate parameter to the to-be-inverted parameter , represents a conditional probability of the observation data under the candidate parameter, represents a conditional probability of the observation data under the to-be-inverted parameter.

[0012] Further, based on the branch-main network architecture, a neural operator is constructed, taking the resistivity spatial distribution model as input and the apparent resistivity response as output, including: acquiring observation parameters under a polarization mode of a to-be-inverted region; the branch-main network architecture includes a branch network and a main network; the branch network is used for feature extraction on the resistivity spatial distribution model, to obtain a first feature vector; the main network is used for feature extraction on the observation parameters under each polarization mode, to obtain a second feature vector; inner product operation is performed on the first feature vector and the second feature vector, to obtain a fusion feature vector; after multi-layer Fourier transform is performed on the fusion feature vector, an apparent resistivity response is output through a projection layer.

[0013] Further, the training data set adopts a resistivity spatial distribution model generated based on a Gaussian random field, and the forward response thereof is calculated through a finite difference method.

[0014] The present application has the advantages that: the MCMC method is used to randomly sample the calculation space, and rich uncertainty information of model parameters can be given; meanwhile, two-dimensional inversion can better depict the change of physical property parameters in the horizontal direction, and provide more reliable guidance for actual exploration; the present application further adopts a neural operator which is computationally efficient and has strong generalization ability, significantly improves the calculation efficiency, and has stronger generalization ability for different data; by adaptively performing local correction on the neural operator, 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

[0015] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced. Obviously, the drawings in the following description only constitute some embodiments of the present application, and other drawings can be obtained by those skilled in the art without creative labor.

[0016] Figure 1 A flow chart of a two-dimensional Bayesian inversion method based on a neural operator for the embodiment of the present application; Figure 2 A schematic diagram of a chessboard model for the embodiment of the present application; Figure 3 A statistical result schematic diagram of a Bayesian inversion method based on a traditional Bayesian method and an adaptive surrogate simulation for the embodiment of the present application; Figure 3 The (a) part and the (c) part in the figure are adaptive surrogate simulation results, wherein the (a) part represents a statistical mean value of a Bayesian sampling model set, and the (c) part is a variance; Figure 3 The (b) part and the (d) part in the figure are numerical method results, wherein the (b) part represents a statistical mean value of a sampling model set, and the (d) part is a variance; Figure 4 A one-dimensional edge probability comparison chart of inversion results at a single point = 67.3 km based on a traditional Bayesian inversion method and a Bayesian inversion method based on an adaptive surrogate simulation proposed by the present application; Figure 4 The (a) part in the figure corresponds to adaptive surrogate simulation Bayesian inversion results, Figure 4 The (b) part in the figure corresponds to numerical Bayesian inversion results; Figure 5 A comparison histogram of edge probabilities at different depths based on a traditional Bayesian method and a Bayesian inversion method based on an adaptive surrogate simulation proposed by the present application at a single point x = 67.3 km; Figure 5 The (a) part and the (b) part in the figure are single-point posterior probability distributions at a depth of 1.8 km for a shallow high-resistance anomaly body, Figure 5 The (c) part and the (d) part in the figure are single-point posterior probability distributions at a depth of 9.5 km for a shallow high-resistance anomaly body. DETAILED DESCRIPTION

[0017] With reference to the accompanying drawings, the technical solutions in the embodiments of the present application will be clearly and completely described below, obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work are within the scope of protection of the present application.

[0018] A flowchart of a two-dimensional inversion method based on a neural operator for magnetotelluric data according to an embodiment of the present application is shown in FIG. 1, which comprises the following steps: Figure 1 Obtaining measured magnetotelluric data of the region to be inverted, discretizing the region to be inverted by finite difference method and establishing a resistivity spatial distribution model; In the embodiment of the present application, the magnetotelluric method is used to measure the measured magnetotelluric data in the region to be inverted, that is, the original electromagnetic field signal in the region to be inverted, which includes the electric field component and magnetic field component data at different observation points and different frequencies. After the measured data is collected, the measured data can be further preprocessed. The preprocessing operations that can be selected in the embodiment of the present application include noise suppression, data format conversion and coordinate normalization operations.

[0019] In the embodiment of the present application, 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. In the discretization process, the spatial coordinates, boundary conditions and refinement rules of the grid can be set by referring to the contents recorded in any one of the existing finite difference methods. In actual application, they can be set according to actual conditions.

[0020] In the embodiment of the present application, based on the geological information of the region to be inverted, an initial resistivity value is given to each node in the divided finite difference grid, that is, a resistivity spatial distribution model is obtained, which serves as a starting point for subsequent inversion calculation of the region to be inverted.

[0021] 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 of the region to be inverted and the resistivity spatial distribution model; In the embodiment of the present application, firstly, 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 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.

[0022] ​In one specific embodiment of the present application, a boundary value problem of a magnetotelluric field is established in a finite difference grid based on Maxwell equations, and a finite difference method is used to discretize the control equation into a linear equation set to form a forward operator, and by solving the linear equation set, electromagnetic responses at different frequencies are obtained to realize mapping of a resistivity spatial distribution model to magnetotelluric responses. In the embodiment of the present application, errors between measured magnetotelluric data and model predicted data obtained through the forward operator are subject to a multivariate Gaussian distribution, and then a likelihood function can be defined according to a Gaussian distribution probability density function.

[0023] In one specific embodiment of the present application, parameter distributions in the resistivity spatial distribution model are obtained based on geological information of an inversion area, so that the parameter distributions corresponding to each node in the resistivity spatial distribution model can be set as prior distributions; and then according to the Bayes theorem, the prior distributions and the likelihood function are combined to obtain a posterior probability model.

[0024] For the resistivity spatial distribution model, a multivariate Gaussian distribution is used as a proposal distribution in the embodiment of the present application to generate candidate parameters of the parameters to be inverted, which can be expressed as: ; 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 the proposal distribution, and is used to judge a probability of generating the candidate parameter from the parameter to be inverted, is proportional to a symbol, is an exponential function, is the i th parameter to be inverted, is a candidate parameter corresponding to the i th parameter to be inverted, represents a variance of the i th parameter to be inverted; ​The embodiment of the application is further based on the constructed posterior probability model, and sets the receiving probability of the Bayesian inversion of the to-be-inverted region according to the MH sampling algorithm, that 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 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 length is adopted, and a proposal distribution with a larger standard deviation is set to quickly obtain the general outline of the to-be-inverted model. With the sampling, the sampling step length 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 receiving probability of the last round, and in actual operation, the neural operator test can be performed first. According to the receiving probability under different sampling numbers, a specific adjustment strategy is formulated. The receiving probability is represented as: ; In the formula, is the receiving probability, represents the minimum value function, is the observation data, is the prior distribution of the to-be-inverted parameter, is the prior distribution of the candidate parameter, is the proposal distribution, represents the reverse proposal distribution for judging the transition from the candidate parameter to the to-be-inverted parameter , represents the conditional probability of the observation data under the candidate parameter, represents the conditional probability of the observation data under the to-be-inverted parameter.

[0025] Based on the branch-trunk network architecture, a neural operator is constructed, taking the resistivity spatial distribution model as the input and the apparent resistivity response as the output. In the embodiment of the application, the neural operator adopts the branch-trunk network architecture of the deep neural operator network, in which the branch network processes the resistivity spatial distribution model input, and the trunk network (Trunk net) processes the observation parameters of the to-be-inverted region. The two networks promote the resistivity and the observation parameters to a higher dimension, and after fusion through 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 the position mapping. The mapping relationship learned by the neural operator is represented as follows: ; In the formula, represents the neural operator, represents the component of the electric field in the direction under different positions and different frequencies, This indicates the electric field at different locations and frequencies. directional components, Indicates position parameters, Indicates frequency parameters; This indicates the magnetic field at different locations and frequencies. directional components, This indicates the magnetic field at different locations and frequencies. directional components, is the resistivity.

[0026] The data processing procedure is as follows: First, the observation parameters of the polarization mode of the region to be inverted are obtained. In this embodiment of the invention, the observation parameters may be the observation frequency, current intensity, and coordinates of the observation points of the region to be inverted. Then, the branch network is used to extract features from the resistivity spatial distribution model to obtain the first feature vector. The backbone network is used to extract features from the observation parameters of the polarization mode to obtain the second feature vector. The inner product operation of the first feature vector and the second feature vector is performed to obtain the fused feature vector. After performing a multi-level Fourier transform on the fused feature vector, the apparent resistivity response is output through the projection layer.

[0027] The neural operator is trained using a training dataset to obtain a well-trained neural operator. In this embodiment of the invention, the training dataset is obtained based on the resistivity spatial distribution model generated by the Gaussian random field method, and the magnetotelluric response is calculated using the staggered grid finite difference method, thereby constructing a training dataset to train the neural operator.

[0028] The trained neural operators are used for forward modeling in the Bayesian inversion model, which then performs inversion calculations on the region to be inverted. In other words, the neural operators replace the forward modeling calculations and are embedded in the Bayesian inversion framework to perform inversion on the computational region.

[0029] In this embodiment of the invention, a trained neural operator is used to replace forward modeling and embedded into a Bayesian inversion framework to invert the computational region. When the trained neural operator is used for forward modeling in the Bayesian inversion model, the method further includes: selecting sampled data at a set sampling interval during the inversion process; performing forward modeling on the sampled data using the neural operator and the finite difference method 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 between the first and second forward responses; not performing a correction operation when the relative error does not exceed a preset limit; and performing a correction operation on the neural operator when the relative error exceeds the preset limit.

[0030] In one specific embodiment of the present application, the last parameter in the medium parameters inverted in the inversion area can be used as the spot check sample to perform precision inspection on the neural operator.

[0031] The expression for calculating the relative error of the first forward response and the second forward response is: ; wherein, represents the relative error, represents the first forward response, represents the second forward response, represents the Euclidean norm, represents the spot check sample.

[0032] In one specific embodiment of the present application, when the relative error exceeds the preset limit, it indicates that the neural operator has not learned the features under the current parameter distribution well, and therefore it is necessary to construct a supplementary training set locally and correct the neural operator. The method for performing the updating operation on the neural operator is specifically as follows: taking the resistivity parameter corresponding to the spot check 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 the calculation results thereof, and the neural operator is locally corrected by using the supplementary training set. In the local correction, different hyperparameters are used for transfer learning in the original operator neural network to adapt to the features of the current area, so as to obtain a high-precision neural operator.

[0033] In another specific embodiment of the present application, the inversion adopts a core calculation region of 100x200 km, which is discretized into 64x64 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, which is discretized into 20 grids with increasing size; the second group is from 1 to 20 km, which is discretized into 20 grids with logarithmic increase; and the third group is from 20 to 100 km, which is discretized 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, with the range of-400 km to 0 km, and 10 grids with logarithmic increase are set for the expanded layer underground, with the range of 100 km to 500 km; the above expansion ensures that the boundary conditions of the electromagnetic field are satisfied, 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.

[0034] 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, and the learning rate is halved after every 35 rounds of training, in the correction process, the sampling number of each small cycle 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.

[0035] The present application embodiment further designs a neural operator as Figure 2The chessboard model shown contains six anomalies. The top three anomalies have the same size of 3km × 16km, and the bottom three anomalies have the same size of 7km × 16km. The high-resistivity anomaly is 300Ω·m, the low-resistivity anomaly is 5Ω·m, and the background resistivity is 100Ω·m. In this embodiment, a uniform half-space model with a resistivity of 100Ω·m is selected as the resistivity spatial distribution model. 60,000 samples are taken, and a Gaussian distribution is chosen as the proposed distribution. The mean of this distribution is set to a two-dimensional random array, from which new samples are obtained to ensure randomness. The second diagonal element of the covariance matrix corresponding to the proposed distribution is set to 1, and the initial value of the main diagonal element is set to 20. After each 1 / 3 of sampling is completed, the value decreases by 0.6 times. The initial sampling step size is 2.5, and after each 1 / 3 of sampling is completed, the value decreases by 0.6 times.

[0036] Figure 3 The statistical results provided for embodiments of the present invention are based on traditional Bayesian methods and Bayesian inversion methods based on adaptive substitution simulation, wherein... Figure 3 Parts (a) and (c) in the figure are adaptive substitution simulation results, where part (a) represents the statistical mean of the Bayesian sampling model set and part (c) represents the variance; Figure 3 Parts (b) and (d) in the table represent the results of the numerical method, where part (b) represents the statistical mean of the sampled model set, and part (d) represents the variance. Figure 3 As can be seen from the mean results of parts (a) and (c) in the present invention, both methods can basically recover the shape and value of the anomaly. The present invention further provides a comparison of the computational efficiency of the two methods as shown in Table 1. It can be seen that, under the condition of obtaining similar inversion statistical results, the computational speed of the alternative simulation Bayesian method in this embodiment is 13 times that of the traditional Bayesian method, which greatly improves the computational efficiency. This makes it possible to sample more and quantify uncertainty more accurately.

[0037] Table 1. Comparison of computational efficiency ; like Figure 4 As shown, the embodiments of the present invention provide single-point Bayesian inversion methods based on traditional Bayesian inversion methods and the Bayesian inversion method based on adaptive substitution simulation proposed in this invention. A comparison chart of one-dimensional marginal probabilities of the inversion results. Figure 4 Part (a) in the diagram corresponds to the Bayesian inversion result of the adaptive substitution simulation. Figure 4 Part (b) in the figure corresponds to the numerical Bayesian inversion result, which shows that both methods can basically invert the location and physical property parameters of the anomaly.

[0038] like Figure 5As 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.

[0039] 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 method for magnetotelluric Bayesian two-dimensional inversion based on neural operators, characterized in that, The method comprises the following steps: Obtaining the measured magnetotelluric data of the region to be inverted, discretizing the region to be inverted by finite difference, and establishing a resistivity spatial distribution model; Based on the finite difference discretization result of the region to be inverted, according to the measured magnetotelluric data of the region to be inverted and the resistivity spatial distribution model, a Bayesian inversion model of the region to be inverted is established; 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; Obtain the training data set to train the neural operator, and obtain the trained neural operator; 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.

2. The method of claim 1, wherein the method is a two-dimensional magnetotelluric Bayesian inversion method based on neural operators. When the trained neural operator is used for forward calculation in the Bayesian inversion model, it further comprises the following steps: In the inversion process, select the sampling samples at a set sampling interval; Respectively using the neural operator and the finite difference method to carry out forward calculation on the sampling samples, and obtaining the first forward response corresponding to the neural operator and the second forward response corresponding to the finite difference method; Calculate the relative error of the first forward response and the second forward response, and when the relative error does not exceed the preset limit, do not perform correction operation; When the relative error exceeds the preset limit, perform correction operation on the neural operator.

3. The magnetotelluric Bayesian two-dimensional inversion method based on neural operators of claim 2, wherein: The correction operation on the neural operator is specifically: Using the Gaussian noise disturbance method to generate a plurality of local samples within a set radius range with the resistivity parameter corresponding to the sampling sample as the center; Using the staggered grid finite difference method to carry out forward calculation on the local samples; According to the local samples and their forward calculation results, a supplementary training set is constructed, and the neural operator is locally corrected by using the supplementary training set.

4. The method of claim 1, wherein the method is a two-dimensional magnetotelluric Bayesian inversion method based on neural operators. Based on the finite difference discretization result of the region to be inverted, according to the measured magnetotelluric data of the region to be inverted and the resistivity spatial distribution model, a Bayesian inversion model of the region to be inverted is established, comprising: Discretizing the region to be inverted by finite difference to obtain the finite difference grid of the region to be inverted; Defining the resistivity spatial distribution model under the finite difference grid, and establishing the forward neural operator of the region to be inverted; According to the forward neural operator, a likelihood function is established, the parameter distribution in the resistivity spatial distribution model is taken as the prior distribution, and the posterior probability model is constructed by combining the likelihood function; Set the acceptance probability and proposal distribution of the Bayesian inversion of the region to be inverted, and obtain the Bayesian inversion model of the region to be inverted according to the posterior probability model.

5. The magnetotelluric Bayesian two-dimensional inversion method based on neural operators of claim 4, wherein: Taking the parameter distribution in the resistivity spatial distribution model as the prior distribution comprises: defining the resistivity parameter vector of each node in the resistivity spatial distribution model as the prior distribution in a uniform distribution manner.

6. The magnetotelluric Bayesian two-dimensional inversion method based on neural operators of claim 4, wherein: Setting the acceptance probability and proposal distribution of the Bayesian inversion of the region to be inverted comprises: The proposal distribution adopts a multivariate Gaussian proposal distribution, which is expressed as: ； wherein, is the parameter to be inverted, is a candidate parameter generated from the parameter to be inverted by a proposal distribution, denotes the proposal distribution used to judge whether to transfer the parameter to be inverted to the candidate parameter , and is proportional to the sign, exp() is an exponential function, is the i-th parameter to be inverted, is the candidate parameter corresponding to the i-th parameter to be inverted, denotes the variance of the i-th parameter to be inverted; Based on the posterior probability model, the acceptance probability of the Bayesian inversion of the region to be inverted is set according to the MH sampling algorithm, which is expressed as: ； where, is the receiving probability, denotes the min 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, denotes the function for judging whether the candidate parameter is transferred to the parameter to be inverted, is the reverse proposal distribution, denotes the conditional probability of the observation data under the candidate parameter, denotes the conditional probability of the observation data under the parameter to be inverted.

7. The method of claim 1, wherein the method is a two-dimensional magnetotelluric Bayesian inversion method based on neural operators. 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, comprising: Obtaining observation parameters of a to-be-inverted region under different polarization modes; The branch-main network architecture comprises a branch network and a main network; Feature extraction is performed on the resistivity spatial distribution model by using the branch network to obtain a first feature vector; Feature extraction is performed on the observation parameters under each polarization mode by using the main network to obtain a second feature vector; Inner product operation is performed on the first feature vector and the second feature vector to obtain a fusion feature vector; After multi-layer Fourier transform is performed on the fusion feature vector, a resistivity response is output by a projection layer.

8. The method of claim 1, wherein the method is a two-dimensional magnetotelluric Bayesian inversion method based on neural operators. The training data set adopts a resistivity spatial distribution model generated based on a Gaussian random field, and the forward response thereof is calculated by using a finite difference forward method.

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