Highly efficient probabilistic inversion methods, media, and electronic equipment for electromagnetic resource exploration

Abstract

This invention relates to the field of electromagnetic exploration technology, and discloses an efficient probabilistic inversion method, medium, and electronic equipment for electromagnetic resource exploration. The method employs a Fourier neural network from machine learning, training it with a large number of conductivity models to obtain the electromagnetic forward response. This network, through a cascaded structure of multi-layer neurons, automatically extracts features from a large amount of magnetotelluric response data, constructing a mapping from conductivity models to magnetotelluric responses. This avoids traditional forward calculations for conductivity models obtained from each sampling, accelerating the forward calculation time during sampling. Prior constraints related to the structure are constructed in advance and added to the inversion prior distribution, reconstructing the Metropolis-Hasting acceptance criterion. The prior information is used to quickly search for the posterior probability density distribution of the model, reducing the search time in the inversion space during sampling, and quantitatively evaluating the obtained inversion results.

Description

Technical Field

[0001] This invention relates to the field of electromagnetic exploration technology, specifically to an efficient probabilistic inversion method, medium, and electronic equipment for electromagnetic exploration of resources. Background Technology

[0002] Electromagnetic sounding has significant applications in mineral exploration, geological exploration, deep structural research, and underground geothermal resource exploration. Through electromagnetic sounding, we can obtain electromagnetic response curves describing underground structures at each measurement point. Inversion based on these electromagnetic responses can reveal the underground conductivity structure, thereby inferring the distribution of underground structures. Therefore, electromagnetic inversion is of great importance in practical applications.

[0003] However, during electromagnetic inversion, the measurement is significantly affected by interference, and noise has a substantial impact on the stability of the inversion results. This can lead to multiple models fitting the measured data, resulting in non-uniqueness in the inversion. Therefore, it is necessary to quantitatively evaluate the inversion results. To address this nonlinear problem, a probabilistic inversion method based on a Bayesian framework can be employed. Within this framework, all possible solutions are contained in the posterior probability density distribution. By performing statistical analysis on this distribution, the inversion results can be effectively quantitatively evaluated. Currently, this method has made significant progress.

[0004] To obtain the unbiased posterior probability density distribution, existing algorithms require extensive sampling calculations, resulting in a very time-consuming process. This is especially true when inverting high-dimensional models, where the computational load increases dramatically, leading to the "curse of dimensionality." Therefore, improving sampling efficiency, reducing computation time, and quickly obtaining the posterior probability density distribution of the model's conductivity are of significant practical importance. Summary of the Invention

[0005] The purpose of this invention is to provide an efficient probabilistic inversion method, medium, and electronic device for electromagnetic resource exploration, to solve the problems of low sampling efficiency, long calculation time, and inability to quickly obtain the posterior probability density distribution of model conductivity in existing technologies. The specific technical solution is as follows:

[0006] An efficient probabilistic inversion method for electromagnetic exploration of resources includes the following steps:

[0007] S1. Obtain underground electromagnetic field response data of the study area using electromagnetic measuring instruments; construct different conductivity models; use Fourier neural networks to train the generated conductivity models according to different sampling frequencies; obtain the mapping output from conductivity model to electromagnetic response.

[0008] S2. Construct the tower-like structural model required for inversion; build the Markov chain starting from the first sampling, and in the... During the next sampling, corresponding candidate tower structure models are obtained according to different strategies based on the current tower structure model. The proposed model for the conductivity structure is obtained by performing inverse wavelet transform on the candidate tower structure model. At the same time, for the first Tower structure model during secondary sampling The corresponding resistivity model is obtained by performing inverse wavelet transform. ;

[0009] S3. The suggested model obtained in S2 and resistivity model The input is fed into a pre-trained network at each frequency point, and the forward modeling calculation is performed in parallel on the GPU to obtain the corresponding electromagnetic response;

[0010] S4. Apply zero-mean normal prior constraint distributions to the resistivity structures in the vertical and horizontal directions; construct the Metropolis-Hasting acceptance criterion based on the wavelet domain tower structure model with added prior constraints on the model structure, and calculate the acceptance rate of the proposed model.

[0011] S5. Perform a judgment: if the conditions are met, accept the tower structure candidate model, thus obtaining the first... Tower structure model at +1 sampling for: Otherwise, reject the candidate tower structure model, thus obtaining the first... Tower structure model at +1 sampling for: , This is the previous tower structure model; take = +1, perform a second check: if If the number of samples is less than or equal to the maximum number of samples designed, return to S2; otherwise, proceed to the next step.

[0012] S6. Perform statistical calculations on all suggested models to obtain the probability density distribution of underground electrical conductivity in the study area.

[0013] Preferably, in S2: constructing the required tower structure model for inversion includes designing the maximum depth of the tower structure model. The maximum number of nodes in the tower structure model was calculated. : ;

[0014] Before constructing the Markov chain from the first sampling, the number of permutations and combinations at different node depths is calculated. The formula for calculating permutations and combinations in S2 is as follows:

[0015] ;

[0016] in: Indicates in Depth and Number of arrangements of a four-node tower structure model under each node; Indicates in Depth and The number of permutations and combinations under each node; , , This represents the count during algorithm recursion; Indicates the number of nodes in the tower; This indicates the depth of the tower structure model.

[0017] Preferably, in S2: the nodes of the tower structure model required for inversion are classified as existing nodes. Nodes can be generated and demiseable nodes , This is represented as an empty node; select any type of node to perform tower structure model transformations, forming a tower structure candidate model. ;

[0018] If the generation strategy (i.e., the generation of nodes) is selected, then the candidate model nodes for the tower structure are represented. The candidate model for the tower structure is: ;

[0019] If the elimination strategy (i.e., eliminating nodes) is selected, then the candidate nodes for the tower structure model are represented. The candidate model for the tower structure is: ;

[0020] If one of the existing nodes is selected, the perturbation strategy means that only the value of the selected node is changed. The candidate model for the tower structure is: ;

[0021] in: Indicates in Depth and The specific arrangement and combination of tower structure models under each node as candidate tower structure models; Indicates the number of nodes is Wavelet coefficient values ​​at time Indicates the selected first The values ​​of each node after the change;

[0022] In S4: the inverse transform uses wavelet basis functions.

[0023] Preferably, in S4: based on the first In the next sampling, a zero-mean normal prior distribution is applied to the resistivity structure in both the vertical and horizontal directions as follows:

[0024] ;

[0025] in: Representing two dimensions Prior structural constraints on orientation; Representing two dimensions Prior structural constraints on orientation; express The rank of the number of model parameters in the direction; express The rank of the number of model parameters in the direction; Indicates that it is ordered Different difference operator matrices; Indicates that it is ordered Different difference operator matrices; express The regularization factor given by the structural constraints in the direction; express The regularization factor given by the structural constraints in the direction; Indicates transpose;

[0026] Using wavelet inverse transform operator The wavelet domain model is inversely transformed into a conductivity model. For the first The prior distribution of the structure of the subsample needs to be calculated. Structural prior constraints as well as Structural prior constraints ;

[0027] It manifests as:

[0028] ;

[0029] Pick Then:

[0030] ;

[0031] in: ; ,

[0032] Regularization factor Treat it as a hyperparameter. .

[0033] Preferably, the Metropolis-Hasting acceptance criterion, based on a wavelet domain tower structure model with added model prior constraints, is constructed, and the acceptance rate of the proposed model is calculated. This process includes the following steps:

[0034] S4.1 Calculate the current number of elements under a given tower structure model. Prior distribution under the subsampled tower structure model and the prior distribution of candidate models for tower structures ;

[0035] S4.2. Calculate the likelihood function using the electromagnetic response obtained in S3. The calculation of the likelihood function involves predicting the electromagnetic response. Compare the data with electromagnetic data acquired using electromagnetic measuring instruments, and calculate the fitting difference between them. :

[0036] ;

[0037] ;

[0038] in: This represents the collected electromagnetic data; Indicates transpose; Represents the covariance matrix of the data;

[0039] Calculate the first in the same way Candidate models of tower structures obtained through subsampling Resistivity model obtained through inverse transformation likelihood function and fit difference Then, the existing conductivity model was calculated. With the new candidate conductivity model The ratio of the likelihood function values;

[0040] ;

[0041] S4.3 Calculation from the tower structure model Candidate models for tower structures Suggested distribution probability And from tower structure candidate models To tower structure model Suggested distribution ;

[0042] S4.4, in the During the second sampling, based on the obtained prior distribution, likelihood function, and proposal distribution, the following acceptance criterion is constructed to calculate the acceptance rate of the proposed model. :

[0043] ;

[0044] in: Let be a Jacobian matrix, take .

[0045] Preferably, the prior distribution in S6.1 is:

[0046] ;

[0047] in: Represented as the prior distribution of wavelet sparse values, ; Let be the prior distribution of the number of nodes. ; for Depth and Distribution of permutations under the condition of a number of nodes .

[0048] Preferred distribution Including the proposed distribution of perturbation strategies Recommended distribution of generation strategies And the suggested distribution of extinction strategies ,as follows:

[0049] Suggested distribution of perturbation strategy: ,in: Indicates from The change of any selected node value in the set, specifically the Gaussian perturbation of the current value; This indicates the distribution of the disturbance set, which is a uniform distribution. This indicates the change in wavelet coefficients.

[0050] Recommended distribution of generation strategies: ,in: Indicates from The changes in the value of any selected node in the set; the suggested distribution of the values ​​of newly created nodes. ; This indicates the distribution of the generated set, which is a uniform distribution.

[0051] Suggested distribution of extinction strategies: ,in: This represents the distribution of the extinction set, which is a uniform distribution.

[0052] Preferably, the recommended model acceptance rate for selecting existing nodes for perturbation steps is [not specified]. The expression is:

[0053] ;

[0054] Acceptance rate of recommended models that can generate nodes The expression is:

[0055] ;

[0056] in: Represented as a candidate model for a tower structure The number of candidate extinct nodes;

[0057] The acceptance rate of the suggested model that selects demiseable nodes The expression is:

[0058] ;

[0059] in: Represented as a candidate model for a tower structure The number of candidate generated nodes.

[0060] The present invention also discloses a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the resource electromagnetic exploration efficient probabilistic inversion method described above.

[0061] The present invention also discloses an electronic device, comprising: a processor and a memory communicatively connected to the processor;

[0062] The memory stores computer-executed instructions;

[0063] The processor executes computer execution instructions stored in the memory to implement the efficient probabilistic inversion method for electromagnetic resource exploration as described above.

[0064] The effect of applying the technical solution of this invention is:

[0065] This invention provides an efficient probabilistic inversion method for electromagnetic resource exploration. This method employs a Fourier neural network from machine learning, training it with a large number of conductivity models to obtain the electromagnetic forward response. Through a cascaded structure of multiple neurons, this network can automatically extract features from a large amount of magnetotelluric response data, constructing a mapping from the conductivity model to the magnetotelluric response. This avoids the need for traditional forward calculations of the conductivity model obtained from each sampling, significantly accelerating the forward calculation time during sampling. Prior constraints related to the structure are constructed in advance and added to the inversion prior distribution, reconstructing the Metropolis-Hasting acceptance criterion. Using prior information, the posterior probability density distribution of the model is quickly searched, effectively reducing the search time in the inversion space during sampling. Furthermore, the obtained inversion results are quantitatively evaluated, quantifying the uncertainty of the inversion results.

[0066] In addition to the objectives, features, and advantages described above, the present invention has other objectives, features, and advantages. The invention will now be described in further detail with reference to the figures. Attached Figure Description

[0067] To more clearly illustrate the technical solutions of the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0068] Figure 1 This is the algorithm flow in the embodiment;

[0069] Figure 2 This is a schematic diagram of the tower structure model when the maximum depth is 3 in the embodiment (1-16 in the figure are serial numbers).

[0070] Figure 3 This is a schematic diagram of the perturbable, generated, and destroyed nodes of the tower structure model in the embodiment (1-16 in the figure are serial numbers).

[0071] Figure 4 This is a frame diagram of the electronic device in the embodiment;

[0072] Figure 5 This is a schematic diagram of the theoretical model designed in the embodiment;

[0073] Figure 6 The comparison shows the mean models obtained by inversion under and without model constraints, where: (a) is the posterior mean model obtained by sampling one chain of the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; (b) is the posterior mean model obtained by parallel tempering sampling of five chains of the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; and (c) is the posterior mean model obtained by sampling one chain in the embodiment of the present invention.

[0074] Figure 7 The comparison shows the uncertainty of the inversion results obtained with and without model constraints, where: (a) is the posterior probability density distribution of the conductivity of the central location profile obtained by sampling one chain of the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; (b) is the posterior probability density distribution of the conductivity of the central location profile obtained by parallel tempering sampling of five chains of the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; (c) is the posterior probability density distribution of the conductivity of the central location profile obtained by sampling one chain in the embodiment of the present invention.

[0075] Figure 8 This is a comparison of the fitting difference between the implementation examples with and without model constraints;

[0076] Figure 9 The results show the comparison of the number of nodes with and without model constraints, where: (a) is the number of nodes calculated by one chain of the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; (b) is the number of nodes calculated by parallel tempering of 5 chains of the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; and (c) is the number of nodes calculated by one chain in the embodiment of the present invention.

[0077] Figure 10 The regularization coefficient in the embodiment Distribution map;

[0078] Figure 11 This is a comparison chart showing the time taken to run 10,000 times using the present invention (represented as 1) and the time taken to run 10,000 times using the image compression-based high-efficiency probabilistic inversion method for electromagnetic exploration of geodetic resources (represented as 2).

[0079] Figure 12 This is a schematic diagram of parallel computation of the Fourier neural network in the embodiment;

[0080] Figure 13 The image shows the prediction result of a certain input model during training in the embodiment, where: (a) represents the conductivity model of a certain input; (b) represents the error between the predicted electromagnetic response and the actual electromagnetic response; (c) represents the actual electromagnetic response; and (d) represents the predicted electromagnetic response. Detailed Implementation

[0081] To enable those skilled in the art to better understand the present invention, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. Obviously, the described embodiments are merely 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.

[0082] Example:

[0083] A highly efficient probabilistic inversion method for electromagnetic exploration of resources, the flowchart of which is detailed below. Figure 1 Specifically, it includes the following steps:

[0084] Step 1: Obtain underground electromagnetic field response data of the study area using electromagnetic measuring instruments, and calculate the measured underground depth (i.e., electromagnetic attraction depth) by analyzing the frequency range of the sampled data; construct different conductivity models based on different geological data; use Fourier neural networks to train the generated conductivity models according to different sampling frequencies, thereby constructing forward modeling networks at different frequencies and obtaining the mapping output from conductivity models to electromagnetic responses.

[0085] In this preferred embodiment, to obtain the conductivity model for training, the geometry of the grid is defined based on electromagnetic properties, uniformly subdivided horizontally, and using an incremental grid in the vertical direction to better simulate the longitudinal variations of the underground electrical structure. A conductivity generation function is used to simulate randomly generated resistivity values ​​from underground blocky anomalies. For example, within the range of 10–1000 Ω·m, the values ​​are arbitrarily changed in the 20–25 layers vertically and the 9–16 and 17–24 columns horizontally to simulate layered or blocky geological structures, thereby representing the non-uniformity of the geological background and the anomalies.

[0086] The Fourier neural network used in this invention is a 5-layer Fourier neural network architecture. Each layer contains a dual-branch structure: a frequency domain processing branch, which performs a Fast Fourier Transform (FFT) on the input data, filters out high-frequency components (retaining the first 20% of low-frequency components), and then performs an Inverse Fourier Transform (IFFT) to extract global frequency domain features; and a spatial feature branch, which captures local electrical structure details through 2×2 convolutional kernels. The outputs of the two branches are weighted and fused, then passed to the next layer via a linear connection, and finally output a 2×2 dimensional result through a fully connected layer. The network input contains three channels of data: a two-dimensional resistivity model, and the real and imaginary parts of the electromagnetic response. The generated model is divided into training, validation, and test sets in a 6:2:2 ratio, and trained separately according to the sampling frequency, thus achieving a Fourier neural network with one training frequency per frequency.

[0087] Step 2: Construct the required tower structure model for inversion and obtain the tower structure model; calculate the number of tower permutations and combinations at different depth nodes, and construct the Markov chain starting from the first sampling.

[0088] In this embodiment, the preferred embodiment is detailed in [reference]. Figure 2 The construction of the required tower structure model for inversion includes designing the maximum depth of the tower structure model. ( Figure 2 The diagram illustrates a maximum depth of 3); the maximum number of nodes in the tower structure model is calculated. : ;

[0089] The formulas for calculating permutations and combinations in S2 are as follows:

[0090] ;

[0091] in: Indicates in Depth and Number of arrangements of a four-node tower structure model under each node; Indicates in Depth and The number of permutations and combinations under each node; , , This represents the count during algorithm recursion; Indicates the number of nodes in the tower; This indicates the depth of the tower structure model.

[0092] Step 3: Based on the tower structure model, obtain the first... Candidate tower structure models under the tower structure model at the second sampling time .

[0093] In this preferred embodiment, the nodes of the tower structure model are classified as existing nodes. Nodes can be generated and demiseable nodes , This is represented as an empty node; see details. Figure 3 Choose any type of node to modify the tower structure model, thus forming a candidate tower structure model. ;

[0094] If the generation strategy (i.e., the generation of nodes) is selected, then the candidate model nodes for the tower structure are represented. The candidate model for the tower structure is: ;

[0095] If the elimination strategy (i.e., eliminating nodes) is selected, then the candidate nodes for the tower structure model are represented. The candidate model for the tower structure is: ;

[0096] If one of the existing nodes is selected, the perturbation strategy means that only the value of the selected node is changed. The candidate model for the tower structure is: ;

[0097] in: Indicates in Depth and The specific arrangement and combination of tower structure models under each node as candidate tower structure models; Indicates the number of nodes is Wavelet coefficient values ​​at time Indicates the selected first The value after the node changes.

[0098] Step 4: Take the result from Step 3... Candidate tower structure models under the tower structure model at the second sampling time The proposed model for obtaining the conductivity structure is obtained by performing inverse wavelet transform. ; will the first Tower structure model during secondary sampling Resistivity model obtained by inverse transformation In this embodiment, the preferred inverse transform uses wavelet basis functions.

[0099] Step 5: Develop the proposed model of the conductivity structure obtained in Step 4. and resistivity model Forward modeling is performed using the trained networks at different frequencies. In this step, the CUDA computing library is used to call the GPU to distribute the model in parallel to the trained Fourier neural networks at different frequencies, and output the corresponding electromagnetic responses.

[0100] Step Six: Apply zero-mean normal prior constraint distributions to the resistivity structures in the vertical and horizontal directions; construct the Metropolis-Hasting acceptance criterion based on the wavelet domain tower structure model with added prior constraints on the model structure, and calculate the acceptance rate of the proposed model. .

[0101] In this preferred embodiment, based on the first... In the next sampling, a zero-mean normal prior distribution is applied to the resistivity structure in both the vertical and horizontal directions as follows:

[0102] ;

[0103] in: Representing two dimensions Prior structural constraints on orientation; Representing two dimensions Prior structural constraints on orientation; express The rank of the number of model parameters in the direction; express The rank of the number of model parameters in the direction; Indicates that it is ordered Different difference operator matrices; Indicates that it is ordered Different difference operator matrices; express The regularization factor given by the structural constraints in the direction; express The regularization factor given by the structural constraints in the direction; Indicates transpose;

[0104] Using wavelet inverse transform operator The wavelet domain model is inversely transformed into a conductivity model. For the first The prior distribution of the structure of the subsample needs to be calculated. Structural prior constraints as well as Structural prior constraints ;

[0105] It manifests as:

[0106] ;

[0107] Here, since we assume that the influence of structural constraint terms in the y-direction should be the same as that in the z-direction, the choice of regularization should be consistent, i.e., take... Then:

[0108] ;

[0109] in: ; .

[0110] In this embodiment, to avoid affecting the regularization factor Human selection introduces uncertainties into the inversion results; this invention addresses this by incorporating a regularization factor. Treating it as a hyperparameter, given a relatively wide uniform prior range, we take... This allows it to adaptively constrain itself to a relatively small range during the inversion process.

[0111] In this embodiment, a Metropolis-Hasting acceptance criterion with added model prior constraints is constructed based on a wavelet domain tower structure model, and the acceptance rate of the proposed model is calculated. Specifically, it includes the following steps:

[0112] Step 6.1: Calculate the current number of steps under the given tower structure model. Prior distribution under the subsampled tower structure model and the prior distribution of candidate models for tower structures ;

[0113] Step 6.2: Calculate the likelihood function using the electromagnetic response obtained in S5. The calculation of the likelihood function involves predicting the electromagnetic response. Compare the data with electromagnetic data acquired using electromagnetic measuring instruments, and calculate the fitting difference between them. :

[0114] ;

[0115] ;

[0116] in: This represents the collected electromagnetic data; Indicates transpose; Represents the covariance matrix of the data;

[0117] Calculate the first in the same way Candidate models of tower structures obtained through subsampling Resistivity model obtained through inverse transformation likelihood function and fit difference Then, the existing conductivity model was calculated. With the new candidate conductivity model The ratio of the likelihood function values;

[0118] ;

[0119] Step 6.3: Calculate from the tower structure model Candidate models for tower structures Suggested distribution probability And from tower structure candidate models To tower structure model Suggested distribution ;

[0120] Step 6.4, in the... During the second sampling, based on the obtained prior distribution, likelihood function, and proposal distribution, the following acceptance criterion is constructed to calculate the acceptance rate of the proposed model. :

[0121] ;

[0122] in: Let be a Jacobian matrix, take .

[0123] In this embodiment, the prior distribution is further preferably:

[0124] ;

[0125] in: This is represented as the prior distribution of wavelet sparse values. In this invention, we restrict the prior distribution of wavelet coefficients to a uniform distribution in the range [-1.5, 1.5]. ; Let be the prior distribution of the number of nodes. ; for Depth and Distribution of permutations under the condition of a number of nodes .

[0126] In this embodiment, a further preferred distribution is recommended. Including the proposed distribution of perturbation strategies Recommended distribution of generation strategies And the suggested distribution of extinction strategies ,as follows:

[0127] Suggested distribution of perturbation strategy: ,in: Indicates from The change of any selected node value in the set, specifically the Gaussian perturbation of the current value; This indicates the distribution of the disturbance set, which is a uniform distribution. This indicates the change in wavelet coefficients.

[0128] Recommended distribution of generation strategies: ,in: Indicates from The changes in the value of any selected node in the set; the suggested distribution of the values ​​of newly created nodes. ; This indicates the distribution of the generated set, which is a uniform distribution.

[0129] Suggested distribution of extinction strategies: ,in: This represents the distribution of the extinction set, which is a uniform distribution.

[0130] In this embodiment, the acceptance rate of the suggested model for selecting existing nodes for perturbation steps The expression is:

[0131] ;

[0132] Acceptance rate of recommended models that can generate nodes The expression is:

[0133] ;

[0134] in: Represented as a candidate model for a tower structure The number of candidate extinct nodes;

[0135] The acceptance rate of the suggested model that selects demiseable nodes The expression is:

[0136] ;

[0137] in: Represented as a candidate model for a tower structure The number of candidate generated nodes.

[0138] Step 7: Make a judgment, specifically: if the acceptance rate of the suggested model is... If the condition is greater than 0 and less than 1, then the candidate tower structure model is accepted, thus obtaining the first... Tower structure model at +1 sampling for: Otherwise, reject the candidate tower structure model, thus obtaining the first... Tower structure model at +1 sampling for: , This is the previous tower structure model; take = +1, perform a second check: if If the number of samples is less than or equal to the maximum design sampling number, return to step three; otherwise, proceed to the next step.

[0139] Step 8: Perform statistical calculations on all proposed models to obtain the probability density distribution of underground electrical conductivity within the study area. Having obtained the probability density distribution of underground electrical conductivity within the study area, the uncertainty of the inversion results can be derived from the probability distribution of conductivity.

[0140] A schematic diagram of the theoretical model designed in this embodiment can be found in [reference needed]. Figure 5 The detection range is 20km × 20km, and the background conductivity is The conductivity of the abnormal body is The eight frequencies used are: 0.05, 0.20, 0.5, 1.0, 5.0, 20, 50.0, and 100 Hz, and the station is identified by a red triangle.

[0141] For a detailed comparison of the mean models obtained by inversion with and without model constraints, please refer to [link / reference]. Figure 6 Wherein: (a) is the posterior mean model obtained by sampling one chain in the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; (b) is the posterior mean model obtained by parallel tempering sampling of five chains in the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; and (c) is the posterior mean model obtained by sampling one chain in the embodiment of the present invention. The results show that when using image compression-based electromagnetic probabilistic inversion, multiple Markov chains need to be tempered in parallel to avoid the model getting trapped in local extrema. However, after adding model constraint terms in this invention, the location and size of underground anomalies can be inverted using only one Markov chain.

[0142] For a detailed comparison of the uncertainties obtained from the inversion results with and without model constraints, please refer to [link / reference]. Figure 7 Among them: (a) is the posterior probability density distribution of conductivity of the central location profile obtained by sampling one chain of the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; (b) is the posterior probability density distribution of conductivity of the central location profile obtained by parallel tempering sampling of five chains of the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; (c) is the posterior probability density distribution of conductivity of the central location profile obtained by sampling one chain in the embodiment of the present invention. The results show that after adding model constraint terms, its ability to constrain model uncertainty is strengthened, especially the conductivity uncertainty in deep regions is small.

[0143] For details of the comparison results of the fitting difference with and without model constraints in the embodiments of the present invention, please refer to [link / reference]. Figure 8 The figures show the following: the orange line represents the fitting error of 5 parallel tempering chains under no model constraints as a function of iteration number; the yellow line represents the fitting error of 1 chain under model constraints as a function of iteration number; and the blue line represents the fitting error of 1 chain under no model constraints as a function of iteration number. The results show that the yellow line converges to a static sampling process after 6,000 samplings, while the blue line requires more than 10,000 samplings, and the orange line requires 5 chains for parallel tempering sampling.

[0144] For details on the comparison of the number of nodes with and without model constraints, please see [link / reference]. Figure 9 Where: (a) is the number of nodes calculated by one chain in the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; (b) is the number of nodes calculated by parallel tempering of five chains in the efficient probabilistic inversion method for electromagnetic exploration of geodetic resources based on image compression; and (c) is the number of nodes calculated by one chain in the embodiment of the present invention. From the perspective of the number of nodes, after adding the model constraint term, the number of nodes will decrease rapidly, reducing the burden of parameter dimensions during inversion.

[0145] Regularization coefficients in the embodiments of the present invention For distribution map details, please see Figure 10 By giving the regularization coefficient The statistical distribution plot shows that the regularization factor of this invention... The inversion step can be adaptively constrained to a certain range, and this range is relative to a given... The very narrow prior range indicates a significant effect, avoiding biases caused by human intervention and redundant debugging. The value of is used to obtain better results in time.

[0146] For details, see the comparison chart in this embodiment of the invention, which compares the time taken to run 10,000 times (denoted as 1) with the time taken to run 10,000 times using the image compression-based high-efficiency probabilistic inversion method for electromagnetic exploration of geodetic resources (denoted as 2). Figure 11 The comparison between the two clearly shows that the computation time of the present invention is greatly reduced, requiring only 3.18 minutes to run 10,000 times, which greatly improves the efficiency of the inversion.

[0147] For a detailed schematic diagram of parallel computation of Fourier neural networks in this embodiment of the invention, please refer to [link / reference]. Figure 12 In this invention, we use Fourier neural networks for model response prediction. In the model loading part, we load the neural networks with different frequencies that we have trained into the inversion algorithm, and call the neural networks with different frequencies in parallel during the forward calculation so that they can calculate the electromagnetic response at all the required frequencies at once, thereby efficiently calculating the electromagnetic response of the model.

[0148] For details of the prediction results of a certain input model during network training in this invention, please refer to the following diagram. Figure 13 Where: (a) represents the conductivity model of a certain input; (b) represents the absolute error between the predicted electromagnetic response and the actual electromagnetic response; (c) represents the actual electromagnetic response; and (d) represents the predicted electromagnetic response. By comparing (c) and (d), only the deep shape prediction effect is poor while the other shapes are basically consistent. Moreover, judging from the error value of (b), its maximum absolute error value is only 0.00088, indicating that the network trained by this invention is accurate.

[0149] In addition, such as Figure 4 As shown, this embodiment also provides an electronic device 200, including: a processor 201 and a memory 202 communicatively connected to the processor 201;

[0150] The memory 202 stores computer-executed instructions;

[0151] The processor 201 executes computer execution instructions stored in the memory 202 to implement the electromagnetic probability inversion method described above.

[0152] In addition, this embodiment also provides a computer-readable storage medium storing computer-executable instructions, which, when executed by a processor, are used to implement the file generation method described above.

[0153] It should be noted that the division of the various modules in the above system is merely a logical functional division. In actual implementation, they can be fully or partially integrated into a single physical entity, or they can be physically separated. These modules can be implemented entirely in software via processing element calls; they can be fully implemented in hardware; or some modules can be implemented by processing element calls to software, while others are implemented in hardware. Each module can be a separate processing element, or it can be integrated into a chip in the aforementioned device. Alternatively, it can be stored as program code in the memory of the aforementioned device, and its functions can be called and executed by a processing element of the device. Furthermore, these modules can be fully or partially integrated together, or they can be implemented independently. The processing element here can be an integrated circuit with signal processing capabilities. In the implementation process, each step of the above method or each of the above modules can be completed through the integrated logic circuits in the hardware of the processor element or through software instructions.

[0154] It should be understood that the above-described device embodiments are merely illustrative, and the device of this application can also be implemented in other ways. For example, the division of units / modules in the above embodiments is only a logical functional division, and there may be other division methods in actual implementation. For example, multiple units, modules, or components may be combined, or integrated into another system, or some features may be ignored or not executed.

[0155] Furthermore, unless otherwise specified, the functional units / modules in the various embodiments of this application can be integrated into one unit / module, or each unit / module can exist physically separately, or two or more units / modules can be integrated together. The integrated units / modules described above can be implemented in hardware or as software program modules.

[0156] When an integrated unit / module is implemented in hardware, the hardware can be digital circuits, analog circuits, etc. The physical implementation of the hardware structure includes, but is not limited to, transistors, memristors, etc. Unless otherwise specified, the processor can be any suitable hardware processor, such as a Central Processing Unit (CPU), Graphics Processing Unit (GPU), Application Specific Integrated Circuit (ASIC), Digital Signal Processor (DSP), Programmable Logic Device (PLD), Field Programmable Gate Array (FPGA), controller, microcontroller, microprocessor, or other electronic component. Unless otherwise specified, memory can be implemented from any type of volatile or non-volatile storage device or a combination thereof, such as a USB flash drive, Random-Access Memory (RAM), Static Random-Access Memory (SRAM), Dynamic Random-Access Memory (DRAM), Enhanced Dynamic Random-Access Memory (EDRAM), Electrically Erasable Programmable Read-Only Memory (EEPROM), Erasable Programmable Read-Only Memory (EPROM), Programmable Read-Only Memory (PROM), Read-Only Memory (ROM), Resistive Random Access Memory (RRAM), High-Bandwidth Memory (HBM), and Hybrid Memory Cube (HMC). Cube, magnetic storage, flash memory, disk, optical disk, portable hard drive or magnetic disk, and other media that can store program code.

[0157] If the integrated unit / module is implemented as a software program module and sold or used as an independent product, it can be stored in a computer-readable storage device. Based on this understanding, the technical solution of this application, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a memory and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of this application.

[0158] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention. Various modifications and variations can be made to the present invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for efficient probabilistic inversion of resource electromagnetic exploration, characterized in that, The method comprises the following steps: S1, obtaining underground electromagnetic field response data of a study area by using an electromagnetic measuring instrument; constructing different conductivity models; training the generated conductivity models according to different sampling frequencies by using a Fourier neural network; obtaining mapping output from the conductivity model to the electromagnetic response; S2, constructing the tower structure model required by inversion; constructing the Markov chain from the first sampling, and according to the current tower structure model, obtaining the corresponding tower structure candidate model according to different strategies at the second sampling . ​ Wavelet inverse transform is performed on the tower structure candidate model to obtain a suggested model of the conductivity structure , and the tower structure model at the second sampling time is wavelet inverse transformed to obtain a corresponding resistivity model ;​​ S3, the suggestion model obtained in S2 and the resistivity model The trained network at each frequency point is input, forward calculation is completed in parallel on the GPU, and the corresponding electromagnetic response is obtained; S4, imposing a zero-mean normal prior constraint distribution on the vertical and horizontal resistivity structures; constructing a Metropolis-Hasting acceptance criterion based on the wavelet domain tower structure model with added model structure prior constraints, and calculating the acceptance rate of the proposed model; S5, make a decision, specifically: if the acceptance rate of the proposed model is greater than 0 and less than 1, then accept the tower structure candidate model, that is, get the tower structure model at the first sampling Satisfy greater than 0 and less than 1, then accept the tower structure candidate model, that is, get the tower structure model at the first sampling +1 sampling Tower structure model is: ; Otherwise, reject the tower structure candidate model, i.e., get the first Tower structure model at +1 sampling is: , is the previous tower structure model; take = +1, and make a second judgment: if is less than or equal to the designed maximum sampling number, return to S2, otherwise go to the next step; ​ S6, statistically calculating all proposed models to obtain the underground conductivity probability density distribution in the study area.

2. The resource electromagnetic survey efficient probabilistic inversion method of claim 1, wherein, In S2: The required tower structure model for the inversion includes designing the maximum depth of the tower structure model ; The maximum number of nodes of the tower structure model is calculated : ; The arrangement combination number under the node at different depths is calculated before the Markov chain is constructed from the first sampling, and the arrangement combination calculation formula is as follows: ； wherein: represents the number of permutations at depth and nodes under a four-node tower structure model; represents the number of permutations at depth and nodes under a four-node tower structure model; , , represents the count when the algorithm recurses; represents the number of tower nodes; represents the depth of the tower structure model.

3. The resource electromagnetic survey efficient probabilistic inversion method of claim 2, wherein, In S2: the nodes of the tower model required for the inversion are classified as existing nodes , nodes that can be generated , and nodes that can be annihilated , are represented as empty nodes; Optionally, the nodes of one class are changed to form a tower structure candidate model ; If the node generation strategy is selected, it means that the tower structure candidate model node is generated , and the tower structure candidate model is ; If the vanishing node is selected, i.e. the vanishing strategy, it means that the tower structure candidate model node , and the tower structure candidate model is: ; If one of the existing nodes is selected, i.e. the perturbation strategy, it means that only the value of the selected node is changed, , the tower structure candidate model is: ; wherein: represents in depth and specific tower structure model arrangement of the tower structure candidate model under represents the wavelet coefficient value when the number of nodes is represents the value after the change of the selected node.​ 4. The resource electromagnetic survey efficient probabilistic inversion method of claim 3, wherein, In S4: Based on the first Sub-sampling, a zero-mean normal prior is imposed on the vertical and horizontal resistivity structures as follows: ； wherein: represents the structure prior constraint in the direction of ; represents the structure prior constraint in the direction of ; represents the rank of the number of model parameters in the direction of ; represents the rank of the number of model parameters in the direction of ; represents the difference operator matrix with rank ; represents the difference operator matrix with rank ; represents the regularization factor given by the structure constraint in the direction of ; represents the regularization factor given by the structure constraint in the direction of ; represents the transpose; by a wavelet inverse transform operator inverse transforming the wavelet domain model to the conductivity model for the first structure prior distribution needs to be calculated structure prior constraint and structure prior constraint ; The performance is shown as: ； The structure constraint term in the y direction has the same effect as the structure constraint term in the z direction, i.e. take then we have: ； where: ; , the regularization factor is considered as a hyperparameter, .

5. The resource electromagnetic survey high efficiency probabilistic inversion method of claim 4, wherein, constructing a Metropolis-Hasting acceptance criterion based on the wavelet domain tower structure model with added model prior constraints, and calculating the acceptance rate of the proposed model, which specifically comprises the following steps: S4.1, compute the current first prior distribution of the tower structure model under the second sampling and the prior distribution of the tower structure candidate model ; S4.

2. Calculate the likelihood function using the electromagnetic response obtained in S3. The calculation of the likelihood function involves predicting the electromagnetic response. Compare the data with electromagnetic data acquired using electromagnetic measuring instruments, and calculate the fitting difference between them. : ； ； wherein: represents the acquired electromagnetic data; represents the transpose; represents the covariance matrix of the data; Calculate the first in the same way Candidate models of tower structures obtained through subsampling Resistivity model obtained through inverse transformation likelihood function and fit difference Then, the existing conductivity model was calculated. With the new candidate conductivity model The ratio of the likelihood function values; ； S4.3, computing a proposal distribution probability from a tower structure model to a tower structure candidate model and a proposal distribution from a tower structure candidate model to a tower structure model ;​​ S4.4、in the fourth step At the sub-sampling stage, the acceptance rate of the proposal model is calculated based on the obtained prior distribution, likelihood function and proposal distribution as follows : ； where: is the Jacobian matrix, taken as .

6. The resource electromagnetic survey efficient probabilistic inversion method of claim 5, wherein, The prior distribution is: ； where is the wavelet sparsity prior distribution, which is chosen to be a uniform distribution on , i.e. , is set to 1.5, is set to -1.5, thus obtaining ; is the prior distribution of the number of nodes, ; is the depth and number of nodes under the condition, .

7. The resource electromagnetic survey efficient probabilistic inversion method of claim 5, wherein, suggested distribution suggested distribution including perturbation strategies suggested distribution of generation strategies suggested distribution of extinction strategies as follows: The suggestion distribution of the perturbation strategy is: Wherein: represents the change of an arbitrary node value selected from the set The specific operation is Gaussian perturbation of the current value; represents the perturbation set distribution, which is a uniform distribution, represents the change of the wavelet coefficient; Generating a proposal distribution for a strategy: where: represents the change in value of an arbitrary node selected from the set ; the proposal distribution for a new node value ; represents generating a set distribution, which is a uniform distribution; The proposed distribution of extinction strategies is: where: represents the extinction set distribution, which is a uniform distribution.

8. The resource electromagnetic survey efficient probabilistic inversion method of claim 5, wherein, Suggested model acceptance rate of selecting existing nodes for perturbation step The expression is: ； Selecting a suggested model acceptance rate for a generatable node The expression is: ； wherein: candidate model represented as a tower structure candidate dead nodes; Selecting a suggested model acceptance rate for evolvable nodes The expression is: ； wherein: candidate model represented as a tower structure candidate generation nodes.

9. A computer-readable storage medium, characterized in that, The computer readable storage medium stores computer execution instructions, and the computer execution instructions are executed by the processor to implement the resource electromagnetic exploration efficient probability inversion method in any one of claims 1-8.

10. An electronic device, comprising: It comprises: a processor and a memory connected in communication with the processor; the memory stores computer execution instructions; the processor executes the computer execution instructions stored in the memory to implement the resource electromagnetic exploration efficient probability inversion method in any one of claims 1-8.

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