Electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering

Abstract

The invention discloses an electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering, and belongs to the technical field of geophysical electromagnetic inversion, and the method comprises the steps: carrying out the time recursion of an initial sample set through the prediction step of ensemble Kalman filtering, and obtaining a prediction state variable; an observation variable of a prediction state variable is calculated through an updating step of ensemble Kalman filtering, a cross-covariance matrix is constructed based on the prediction state variable and the observation variable, and localization operation is performed on the cross-covariance matrix by using a localization weight matrix so as to correct estimation deviation of the cross-covariance matrix. A Kalman gain matrix is constructed based on the corrected cross covariance matrix, and prediction state variables are updated in combination with actual observation data; and performing electromagnetic inversion uncertainty evaluation based on the updated state variable. According to the method, the electromagnetic inversion precision and stability can be effectively improved, and uncertainty evaluation is provided for the magnetotelluric two-dimensional inversion result.

Description

Technical Field

[0001] The present invention belongs to the technical field of geophysical electromagnetic inversion, and in particular relates to an electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering. Background Art

[0002] Magnetotellurics (MT) is a passive exploration method that uses natural source excitation. By observing orthogonal electromagnetic fields at the surface and calculating impedance, various inversion techniques are then used to determine the subsurface electrical structure, enabling the detection of subsurface targets. MT boasts technical advantages such as simple field construction and great detection depth. It has played an important role in the detailed detection of underground structures, resource and energy exploration, tectonic activity monitoring, and the study of deep material migration and enrichment.

[0003] High-resolution imaging of subsurface structures is crucial and has become a hot topic in geophysical research. Inversion is currently the most widely used method for imaging surface data. Most mainstream inversion algorithms are based on gradient optimization methods, such as Gauss-Newton, nonlinear conjugate gradient, and quasi-Newton. These methods offer stable convergence and high computational efficiency, but they still suffer from the following drawbacks: they can only provide a single "optimal" inversion model under specific conditions, making it difficult to quantify the uncertainty of the inversion results; the inversion results are highly dependent on the initial model and are prone to falling into local minima; and the inversion results are severely affected by regularization terms.

[0004] Compared to conventional deterministic inversion methods, probabilistic inversion does not rely on an initial model and can provide key information, such as posterior probability density estimates of inversion parameters, from a statistical perspective. This is of great significance for evaluating the reliability of the results. Among these, the most widely used methods are those based on sampling, measurement invariance, and ergodicity, such as the Markov chain Monte Carlo (McC) method. This method generates a set of correlated samples in parameter space and constructs a Bayesian posterior probability distribution based on these samples, thereby obtaining the statistical properties of the probability density function (PDF), such as the mean, standard deviation, and marginal distribution. Green et al. improved the McMC method and proposed a cross-dimensional Bayesian inversion method based on reversible jump McMC. In this method, the number of model parameters is treated as inversion parameters and quantitatively calculated in the PDF. The perturbation, regeneration, and elimination of model parameters are achieved through a "birth-death" mechanism. Bayesian inversion methods based on reversible jump McMCs have rapidly attracted attention in geophysical research and have been widely applied in a variety of fields, including DC resistivity, electromagnetic data, gravity data, seismic traveltime data inversion, and seismic full waveform inversion, directly obtaining parameter uncertainty information. However, one of the main difficulties limiting the development of McMC methods is that each sample requires a forward modeling calculation, resulting in an extremely large amount of computation. For high-dimensional problems, the computational cost is unbearable, and McMC sampling methods have limitations. In classic sampling methods, the step size is inversely proportional to the problem dimension, resulting in the need for a large number of samples to obtain reliable results. Therefore, such methods are currently only suitable for problems with a small number of unknowns.

[0005] The Kalman filter method is a method based on the Bayesian theorem. It takes the posterior distribution of the previous state parameter as the prior distribution of the current state parameter and obtains the posterior state of the inversion parameter by solving the recursive Bayesian formula. The probability transfer of the parameter distribution of the Kalman filter inversion model is as follows: Figure 1 Compared with the conventional gradient-based deterministic inversion method, the Kalman filter inversion method starts from multiple initial models at the same time, reducing the degree of dependence on the initial model. The convergence paths of the conventional gradient-based inversion method and the Kalman filter inversion method are shown in Figure 2. Figure 2 As shown in the figure, Kalman filter inversion eliminates the need to solve the sensitivity matrix; the updated values for each model can be obtained through forward modeling. Furthermore, when performing Kalman filtering, random noise perturbations are applied to the initial set to update the model parameter set from different perspectives, resulting in statistically significant inversion results. Compared to other probabilistic inversion methods, Kalman filter inversion requires fewer forward modeling runs, and multiple model forward models can be run in parallel, resulting in higher efficiency.

[0006] While the Kalman filter itself is suitable for linear problems, for nonlinear problems, state estimation is equivalent to the calculation of a multidimensional vector integral, expressed as the product of a nonlinear function and a Gaussian probability density function. However, the closed-form solution to this integral is difficult to obtain, requiring an approximation of the integral of a Gaussian-weighted multidimensional nonlinear function. This led to the development of the extended Kalman filter, which approximates nonlinear functions, and the ensemble Kalman filter, which approximates Gaussian probability density functions. The extended Kalman method uses Taylor decomposition to convert nonlinear functions into linear functions for solution, but this method is computationally intensive and introduces linear errors. The ensemble Kalman filter approximates the statistical properties of random quantities using a finite number of parameters, namely, an approximation of the Gaussian probability density function.

[0007] As a method based on coupling, Ensemble Kalman Filter (EnKF) is a method for sequential data assimilation that mainly couples prior and posterior. In contrast, McMC sampling methods usually require О (10 4 ) or more iterations to reach statistical convergence, while the EnKF method usually only requires О (10) Iterations can converge, and the number of forward modeling calculations per iteration depends on the number of inversion unknowns, which has better computational efficiency. However, when applying the EnKF method to high-dimensional geophysical inversion problems, the limited number of samples can introduce false correlations, resulting in unstable or even divergent inversion updates. Therefore, it is necessary to further introduce improved strategies to improve the inversion accuracy and stability. Summary of the Invention

[0008] In view of the above, the purpose of the present invention is to provide an electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering, realize magnetotelluric two-dimensional inversion based on ensemble Kalman filtering, and provide uncertainty evaluation for the magnetotelluric two-dimensional inversion results. At the same time, a covariance localization method is introduced to effectively suppress unreliable correlation estimates between long-distance variables by performing distance weight correction on the cross-covariance matrix, thereby improving the robustness of the inversion.

[0009] To achieve the above-mentioned purpose, the present invention provides the following technical solutions: In a first aspect, an embodiment of the present invention provides an electromagnetic inversion uncertainty assessment method based on ensemble Kalman filtering, comprising the following steps: The initial sample set is recursively extended through the prediction step of the ensemble Kalman filter to obtain the predicted state variables; The observed variables of the predicted state variables are calculated through the update step of the ensemble Kalman filter. A cross-covariance matrix is constructed based on the predicted state variables and the observed variables. The cross-covariance matrix is localized using a localization weight matrix to correct its estimation bias. The Kalman gain matrix is constructed based on the corrected cross-covariance matrix and the predicted state variables are updated in combination with the actual observation data. The uncertainty evaluation of electromagnetic inversion is performed based on the updated state variables.

[0010] Preferably, the step of performing time recursion on the initial sample set through the prediction step of the ensemble Kalman filter to obtain the predicted state variable includes: Generating the initial sample set of geoelectric model based on Gaussian random field , superscript j Indicates the index of the collection member, Indicates the total number of set members, subscript Indicates the initial step. In the prediction step, the set members Perform time recursion to obtain the predicted state at the new moment, expressed as: , in, Indicates the j The predicted status of the ensemble members, represents the predicted random noise, represents the weight factor, Denotes prior, subscript Indicates the index of the prediction step; The mean of the predicted state of the set is expressed as: , in, Represents the mean of the predicted states of all ensemble members, As the optimal estimate of the current state variables.

[0011] Preferably, the updating step of the ensemble Kalman filter to calculate the observed variable of the predicted state variable comprises: In the update step, the predicted value of the observation data is calculated, that is, the current state is projected into the observation space through forward operation, which is expressed as: , in, Indicates the j The predicted value of the observed data of the set members, Indicates the j The predicted status of the ensemble members, represents the total number of set members, represents the forward operation; The mean of the predicted observations of the set is expressed as: , in, Represents the mean of the predicted observation data of all ensemble members, As the optimal estimate of the current observed variable.

[0012] Preferably, the cross covariance matrix constructed is expressed as: , in, represents the cross-covariance matrix, the superscript Indicates transpose.

[0013] Preferably, the using a localized weight matrix to perform a localized operation on the cross-covariance matrix to correct its estimation bias includes: Introducing localization operation in the ensemble covariance estimation, the cross covariance matrix Perform element-wise fine-tuning, expressed as: , in, represents the Hadamard product, represents the localization weight matrix, whose elements are constructed based on the physical or geometric distance between the state variables and the observation variables and calculated using the Gaspari-Cohn localization kernel function. represents the corrected cross-covariance matrix.

[0014] Preferably, the constructed Kalman gain matrix is expressed as: , in, represents the Kalman gain matrix, Represents the autocovariance matrix of the observed variables.

[0015] Preferably, the update of the state variables is expressed as: , , in, and Represents the first j The state variables of the set members, represents the Kalman gain matrix, represents the actual observation data, Indicates the j The predicted value of the observed data of the set members, Indicates the j The observation noise of the ensemble members, represents the mean of the state variables of the updated set, Indicates the total number of set members.

[0016] Preferably, performing electromagnetic inversion uncertainty assessment based on the updated state variables includes: The uncertainty evaluation of electromagnetic inversion is performed by calculating the posterior standard deviation, which is characterized by calculating the degree of dispersion of the ensemble members, expressed as: , in, Representative geoelectric model i The posterior standard deviation of the model parameters at the grid points, Indicates the j The geoelectric model is i The state variable values at the grid points, The sample set representing the geoelectric model is in i The average value of the state variables at each grid point directly reflects the uncertainty intensity of the electromagnetic inversion parameter estimation through the size of the posterior standard deviation.

[0017] In a second aspect, an embodiment of the present invention further provides an electromagnetic inversion uncertainty evaluation device based on an ensemble Kalman filter, which is implemented using the above-mentioned electromagnetic inversion uncertainty evaluation method based on an ensemble Kalman filter, and includes: an ensemble Kalman filter calculation module and an electromagnetic inversion uncertainty evaluation module; The ensemble Kalman filter calculation module is used to perform time recursion on the initial sample set through the prediction step of the ensemble Kalman filter to obtain the predicted state variables; it is also used to calculate the observed variables of the predicted state variables through the update step of the ensemble Kalman filter, construct a cross-covariance matrix based on the predicted state variables and the observed variables, and use a localization weight matrix to perform a localization operation on the cross-covariance matrix to correct its estimation bias, construct a Kalman gain matrix based on the corrected cross-covariance matrix, and update the predicted state variables in combination with actual observation data; The electromagnetic inversion uncertainty evaluation module is used to perform electromagnetic inversion uncertainty evaluation based on the updated state variables.

[0018] In a third aspect, an embodiment of the present invention further provides an electronic device comprising a memory and one or more processors, wherein the memory is used to store a computer program, and the processor is used to implement the above-mentioned electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering when executing the computer program.

[0019] Compared with the prior art, the present invention has the following beneficial effects: This paper uses an ensemble Kalman filter (EnKF) method to efficiently invert two-dimensional magnetotelluric (MT) data and quantitatively evaluate model uncertainty. This method dynamically updates the geoelectrical model, enabling real-time data assimilation and improving the stability and convergence efficiency of the inversion results. Compared to traditional gradient optimization methods, the proposed method effectively avoids initial model dependency and reduces the risk of falling into local extremes. It eliminates the need for explicit gradient construction during the inversion process, naturally adapts to multi-parameter and multi-scale geoelectrical analysis, and provides uncertainty estimates for model parameters, thereby enhancing the reliability of geological interpretation. Numerical experiments on typical geoelectric anomalies demonstrate that the proposed method can more accurately recover the subsurface electrical structure and provide a reasonable uncertainty distribution. Compared with existing methods, it improves the robustness of the inversion and reduces the influence of artificial a priori assumptions on the results, providing a new, efficient and reliable method for magnetotelluric inversion. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0021] Figure 1 It is a schematic diagram of the probability transfer of parameter distribution of the Kalman filter inversion model; Figure 2 This is a comparison of the convergence paths of the conventional gradient inversion method and the Kalman filter inversion method; Figure 3 1 is a flow chart of an electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering provided by an embodiment of the present invention; Figure 4 1 is a schematic diagram of a framework of an electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering provided by an embodiment of the present invention; Figure 5 is a comparison diagram of the SEG model inversion results provided by an embodiment of the present invention; Figure 6 This is a graph of the posterior standard deviation results of the SEG model provided by an embodiment of the present invention; Figure 7 It is a structural diagram of an electromagnetic inversion uncertainty evaluation device based on ensemble Kalman filtering provided in an embodiment of the present invention. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and do not limit the scope of protection of the present invention.

[0023] The inventive concept of the present invention is: in response to the problems in the inversion method in the prior art, such as large amount of calculation, high calculation cost and slow convergence speed, and easy to cause unstable or even divergent inversion updates, the embodiment of the present invention provides an electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering, which updates the state variables through the ensemble Kalman filtering method, and uses the localized weight matrix to perform localized operations on the cross-covariance matrix to correct the cross-covariance matrix estimation deviation constructed in the ensemble Kalman filtering. It can not only optimize the model without relying on gradient information, but also improve calculation efficiency, accelerate convergence, and provide uncertainty evaluation for the inversion results.

[0024] like Figure 3 and Figure 4 As shown, the embodiment provides an electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering, comprising the following steps: S1, through the prediction step of the ensemble Kalman filter, the initial sample set is time-recursed to obtain the predicted state variables.

[0025] The Kalman filter considers the following stochastic dynamical system: , , Where, Indicates the parameters to be inverted, such as resistivity parameters, etc. 、 represent prediction noise and observation noise respectively, represents the weight, represents the forward response of the geoelectric model, which satisfies the independent zero-mean Gaussian distribution. Since the noise is Gaussian distributed rather than a fixed value, we can finally get The posterior distribution of represents the forward function, and denote the covariance matrices of prediction noise and observation noise, respectively.

[0026] The ensemble Kalman filter Parameter set is used for prediction, and the empirical approximation of covariance is calculated for the subsequent update step to establish and 's mapping.

[0027] In the embodiment, in the prediction step of the ensemble Kalman filter, an initial sample set of the geoelectric model is generated based on the Gaussian random field. , superscript j Indicates the index of the collection member, Indicates the total number of set members, subscript Indicates the initial step. In the prediction step, the set members Perform time recursion to obtain the predicted state at the new moment, expressed as: , in, Indicates the j The predicted status of the ensemble members, represents the predicted random noise, represents the weight factor, Denotes prior, subscript Indicates the index of the prediction step.

[0028] Then calculate the mean of the predicted state of the set, which is expressed as: , in, Represents the mean of the predicted states of all ensemble members, As the optimal estimate of the current state variables.

[0029] S2, calculates the observed variables of the predicted state variables through the update step of the ensemble Kalman filter, constructs a cross-covariance matrix based on the predicted state variables and the observed variables, and uses the localization weight matrix to localize the cross-covariance matrix to correct its estimation bias, constructs the Kalman gain matrix based on the corrected cross-covariance matrix and updates the predicted state variables in combination with the actual observation data.

[0030] In the embodiment, in the update step of the ensemble Kalman filter, the predicted value of the observation data is calculated, that is, the current state is projected into the observation space through forward operation, which is expressed as: , in, Indicates the j The predicted value of the observed data of the set members, Indicates the j The predicted status of the ensemble members, represents the total number of set members, Represents forward operation.

[0031] Then calculate the mean of the predicted observation data of the set, which is expressed as: , in, Represents the mean of the predicted observation data of all ensemble members, As the optimal estimate of the current observed variable.

[0032] In order to effectively combine observation information during the update process, it is necessary to calculate the covariance matrix between the state variables and the observation variables. The cross covariance matrix of the state variables and the observation variables is The calculation is as follows: , in, represents the cross-covariance matrix, the superscript Indicates transpose.

[0033] Introducing localization operation in the ensemble covariance estimation, the cross covariance matrix Perform element-wise fine-tuning, expressed as: , in, represents the Hadamard product, Represents a localized weight matrix whose elements are constructed based on the physical or geometric distance between the state variable and the observation variable and calculated using the Gaspari-Cohn localized kernel function. This process can effectively alleviate the covariance matrix estimation bias caused by insufficient sample size. represents the corrected cross-covariance matrix.

[0034] Then, the Kalman gain matrix is calculated and expressed as: , in, represents the Kalman gain matrix, represents the autocovariance matrix of the observed variables, where Describes the correlation between state variables and observation variables, Incorporating the effects of observation noise. Kalman gain matrix It is used to feed back the information of the observed data into the update of the state variables, to measure the impact of the observed data on the state variables, and to adjust the predicted state during the state update process to make it more consistent with the observed data.

[0035] The autocovariance matrix of the observed variables is expressed as: , in, represents the covariance matrix of the observation noise.

[0036] Finally, the Kalman gain matrix is used to update the state variables in combination with the observed data, which can be expressed as: , , in, and Represents the first j The state variables of the set members, represents the Kalman gain matrix, represents the actual observation data, Indicates the j The predicted value of the observed data of the set members, Indicates the j The observation noise of the ensemble members, represents the mean of the state variables of the updated set, Indicates the total number of set members.

[0037] S3, perform electromagnetic inversion uncertainty evaluation based on the updated state variables.

[0038] The ensemble Kalman inversion method uses a set of samples (ensemble) to represent the posterior probability distribution of model parameters (such as resistivity). By analyzing the statistical characteristics of the sample ensemble, uncertainty information about the inversion results can be obtained. The first-order statistics in the ensemble Kalman inversion include two key indicators: mean and standard deviation. The ensemble mean field is obtained by arithmetic averaging and reflects the best quality of parameter estimation. Its mathematical expression is the simple average of all ensemble members at each spatial point, as shown in Equations (11) and (12).

[0039] In the embodiment, the uncertainty evaluation of electromagnetic inversion is performed by calculating the posterior standard deviation, which is characterized by calculating the degree of dispersion of the set members, expressed as: , in, Representative geoelectric model i The posterior standard deviation of the model parameters (such as resistivity) at each grid point, Indicates the j The geoelectric model is i The state variable values at the grid points, The sample set representing the geoelectric model is in i The value of the experimental standard deviation directly reflects the uncertainty of the parameter estimation. The larger the value, the lower the credibility of the location.

[0040] Furthermore, the present invention verifies the effectiveness of the method by designing a two-dimensional magnetotelluric inversion example. The theoretical example uses the SEG salt dome model, such as Figure 5 As shown in (a), the model resistivity is 10 , the background resistivity is 100 The theoretical data uses the apparent resistivity and phase data of 30 logarithmically equally spaced frequencies from -0.5 to 3 of the SEG model. The measurement points are evenly distributed along the surface, totaling 40 measurement points. The number of initial sample sets is 1000. The ensemble Kalman filter inversion is performed, and the average logarithmic conductivity model of the 1000 initial sample sets is obtained statistically, as shown in Figure 2. Figure 5 As shown in (b), it can be seen that the inversion method of the present invention can basically restore the contour characteristics of the SEG model. Moreover, by further introducing the covariance localization technology, the stability of the ensemble covariance estimation can be significantly improved, effectively suppressing the false correlation between long distances.

[0041] like Figure 6 As shown in the figure, information from a set of 1000 samples is statistically analyzed to obtain the posterior standard deviation of the model inversion results. It can be seen that the posterior uncertainty is small in low-resistance regions, while it is larger in high-resistance regions. This is because the induced current is concentrated in low-resistance regions, resulting in a strong signal response and low uncertainty. However, the signal response in high-resistance regions is weaker, resulting in large uncertainty. The uncertainty information provided by this method is consistent with the physical truth, demonstrating its effectiveness. Furthermore, the introduction of localization techniques allows for more stable uncertainty estimates even with limited set size, making it particularly suitable for high-dimensional geophysical inversion problems.

[0042] In this example, the inversion results converged quickly after four iterations, and the uncertainty information for the inversion results was obtained after 4000 forward modeling calls. This significantly reduces computational costs compared to conventional methods such as McMC sampling.

[0043] In summary, the method proposed in this embodiment of the present invention is less susceptible to the influence of the initial model than conventional gradient-based methods, while also providing uncertainty information about the inversion results. Furthermore, compared to traditional probabilistic methods such as McMC, it significantly reduces computational costs and improves the efficiency of probabilistic inversion methods. Therefore, it is well-suited for 2D magnetotelluric inversion and uncertainty assessment.

[0044] Based on the same inventive concept, Figure 7 As shown, an embodiment of the present invention further provides an electromagnetic inversion uncertainty evaluation device 700 based on ensemble Kalman filtering, which is implemented using the above-mentioned electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering, and includes: an ensemble Kalman filtering calculation module 710 and an electromagnetic inversion uncertainty evaluation module 720.

[0045] The ensemble Kalman filter calculation module 710 is used to perform time recursion on the initial sample set through the prediction step of the ensemble Kalman filter to obtain the predicted state variables; it is also used to calculate the observed variables of the predicted state variables through the update step of the ensemble Kalman filter, construct a cross-covariance matrix based on the predicted state variables and the observed variables, and use the localization weight matrix to localize the cross-covariance matrix to correct its estimation bias, construct a Kalman gain matrix based on the corrected cross-covariance matrix, and update the predicted state variables in combination with the actual observation data.

[0046] The electromagnetic inversion uncertainty evaluation module 720 is used to perform electromagnetic inversion uncertainty evaluation based on the updated state variables.

[0047] Based on the same inventive concept, an embodiment of the present invention also provides an electronic device, including a memory and one or more processors, the memory is used to store computer programs, and the processor is used to implement the above-mentioned electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering when executing the computer program.

[0048] It should be noted that the electromagnetic inversion uncertainty evaluation device and electronic device based on ensemble Kalman filtering provided in the above embodiments belong to the same inventive concept as the electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering. The specific implementation process is detailed in the embodiment of the electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering, which will not be repeated here.

[0049] The specific implementation methods described above provide a detailed description of the technical solutions and beneficial effects of the present invention. It should be understood that the above is only the most preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, supplements and equivalent substitutions made within the scope of the principles of the present invention should be included in the scope of protection of the present invention.

Claims

1. A method for evaluating uncertainty in electromagnetic inversion based on ensemble Kalman filtering, characterized in that: The following steps are involved: The initial sample set is recursively extended through the prediction step of the ensemble Kalman filter to obtain the predicted state variables; The observed variables of the predicted state variables are calculated through the update step of the ensemble Kalman filter. A cross-covariance matrix is constructed based on the predicted state variables and the observed variables. The cross-covariance matrix is localized using a localization weight matrix to correct its estimation bias. The Kalman gain matrix is constructed based on the corrected cross-covariance matrix and the predicted state variables are updated in combination with the actual observation data. The uncertainty evaluation of electromagnetic inversion is performed based on the updated state variables.

2. The electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering according to claim 1 is characterized in that: The prediction step of the ensemble Kalman filter is used to perform time recursion on the initial sample set to obtain the predicted state variable, including: Generating the initial sample set of geoelectric model based on Gaussian random field , superscript j Indicates the index of the collection member, Indicates the total number of set members, subscript Indicates the initial step. In the prediction step, the set members Perform time recursion to obtain the predicted state at the new moment, expressed as: ， in, Indicates the j The predicted status of the ensemble members, represents the predicted random noise, represents the weight factor, Denotes prior, subscript Indicates the index of the prediction step; The mean of the predicted state of the set is expressed as: ， in, Represents the mean of the predicted states of all ensemble members, As the optimal estimate of the current state variables.

3. The electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering according to claim 1 or 2, characterized in that: The update step of the ensemble Kalman filter is used to calculate the observed variables of the predicted state variables, including: In the update step, the predicted value of the observation data is calculated, that is, the current state is projected into the observation space through forward operation, which is expressed as: ， in, Indicates the j The predicted value of the observed data of the set members, Indicates the j The predicted status of the ensemble members, represents the total number of set members, represents the forward operation; The mean of the predicted observations of the set is expressed as: ， in, Represents the mean of the predicted observation data of all ensemble members, As the optimal estimate of the current observed variable.

4. The electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering according to claim 3 is characterized in that: The constructed cross covariance matrix is expressed as: ， in, represents the cross-covariance matrix, the superscript Indicates transpose.

5. The electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering according to claim 1 or 4, characterized in that: The method of using the localized weight matrix to perform a localized operation on the cross-covariance matrix to correct its estimation bias includes: Introducing localization operation in the ensemble covariance estimation, the cross covariance matrix Perform element-wise fine-tuning, expressed as: ， in, represents the Hadamard product, represents the localization weight matrix, whose elements are constructed based on the physical or geometric distance between the state variables and the observation variables and calculated using the Gaspari-Cohn localization kernel function. represents the corrected cross-covariance matrix.

6. The electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering according to claim 5, characterized in that: The constructed Kalman gain matrix is expressed as: ， in, represents the Kalman gain matrix, Represents the autocovariance matrix of the observed variables.

7. The electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering according to claim 1 or 6, characterized in that: The update of state variables is expressed as: ， ， in, and Represents the first j The state variables of the set members, represents the Kalman gain matrix, represents the actual observation data, Indicates the j The predicted value of the observed data of the set members, Indicates the j The observation noise of the ensemble members, represents the mean of the state variables of the updated set, Indicates the total number of set members.

8. The electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering according to claim 7 is characterized in that: The uncertainty assessment of electromagnetic inversion is performed based on the updated state variables, including: The uncertainty evaluation of electromagnetic inversion is performed by calculating the posterior standard deviation, which is characterized by calculating the degree of dispersion of the ensemble members, expressed as: ， in, Representative geoelectric model i The posterior standard deviation of the model parameters at the grid points, Indicates the j The geoelectric model is i The state variable values at the grid points, The sample set representing the geoelectric model is in i The average value of the state variables at each grid point directly reflects the uncertainty intensity of the electromagnetic inversion parameter estimation through the size of the posterior standard deviation.

9. An electromagnetic inversion uncertainty assessment device based on ensemble Kalman filtering, implemented using the electromagnetic inversion uncertainty assessment method based on ensemble Kalman filtering according to any one of claims 1 to 8, characterized in that: include: Ensemble Kalman filter calculation module and electromagnetic inversion uncertainty evaluation module; The ensemble Kalman filter calculation module is used to perform time recursion on the initial sample set through the prediction step of the ensemble Kalman filter to obtain the predicted state variables; it is also used to calculate the observed variables of the predicted state variables through the update step of the ensemble Kalman filter, construct a cross-covariance matrix based on the predicted state variables and the observed variables, and use a localization weight matrix to perform a localization operation on the cross-covariance matrix to correct its estimation bias, construct a Kalman gain matrix based on the corrected cross-covariance matrix, and update the predicted state variables in combination with actual observation data; The electromagnetic inversion uncertainty evaluation module is used to perform electromagnetic inversion uncertainty evaluation based on the updated state variables.

10. An electronic device comprising a memory and one or more processors, wherein the memory is used to store a computer program, characterized in that: The processor is used to implement the electromagnetic inversion uncertainty evaluation method based on ensemble Kalman filtering as described in any one of claims 1 to 8 when executing the computer program.

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