Rapid Bayesian inversion method based on machine learning

Abstract

The invention relates to the technical field of geophysical electromagnetic data exploration, in particular to a fast Bayesian inversion method based on machine learning. Acquiring aviation electromagnetic model data for electromagnetic forward modeling; establishing a candidate forward modeling model for training according to the aviation electromagnetic model information, and obtaining electromagnetic response data obtained by forward modeling; preprocessing the aviation electromagnetic model data and the electromagnetic response data; constructing an optimized neural network, taking the preprocessed aviation electromagnetic model data as input, taking the electromagnetic response data as output, and training the neural network; according to the trained neural network, obtaining a weight and a bias coefficient used for fitting forward modeling calculation, and obtaining an optimized forward modeling fitting matrix; and obtaining forward modeling data according to the optimized forward modeling fitting matrix, establishing a Bayesian inversion model, and performing Bayesian inversion according to the forward modeling data. According to the method, the fitting matrix after machine learning is used for replacing a forward modeling calculation process, and the efficiency of variable-dimension Bayesian inversion can be effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical field of geophysical electromagnetic data exploration, and in particular to a fast Bayesian inversion method based on machine learning. Background Art

[0002] In recent years, in order to carry out geophysical exploration in areas that are difficult for humans to measure directly, such as mountains, lakes, and deserts, airborne electromagnetics has greatly reduced the difficulty of exploration in complex areas due to its mobile platform characteristics; for airborne electromagnetics, time domain electromagnetic methods have higher detection depth and lower cost deep conductor detection capabilities compared to frequency domain electromagnetic methods, so they are widely used in mineral and groundwater exploration, geothermal and environment, and engineering.

[0003] With the rapid development of AEM systems, Bayesian inversion occupies a very important position in time-domain airborne electromagnetic inversion because of its low dependence on the initial model and the advantages of not only providing a single inversion result but also providing parameter distribution and uncertainty information of the inverse model. However, since the model samples required for calculating the probability distribution require a large number of forward calculations, the traditional variable-dimensional Bayesian method is inefficient and can only invert simple models, and cannot perform calculations for a large number of measurement points, which means that there are certain difficulties in the inversion of actual geophysical data. Summary of the invention

[0004] In order to solve the problems existing in the prior art, the present invention provides a fast Bayesian inversion method based on machine learning. The scheme includes: obtaining airborne electromagnetic model data for electromagnetic forward modeling; establishing a candidate forward model according to the airborne electromagnetic model data, and obtaining electromagnetic response data obtained by forward modeling; preprocessing the airborne electromagnetic model data and the electromagnetic response data; constructing an optimized neural network, taking the preprocessed airborne electromagnetic model data as input and the electromagnetic response data as output, and training the optimized neural network; obtaining weights and bias coefficients for optimizing the candidate forward model according to the trained optimized neural network, and obtaining an optimized candidate forward model; obtaining forward simulation data according to the optimized forward model, establishing a Bayesian inversion model, and performing Bayesian inversion according to the forward simulation data. The present invention replaces the forward calculation process with a fitting matrix after machine learning, which can effectively improve the efficiency of variable-dimensional Bayesian inversion.

[0005] The present invention adopts the following technical solution, a fast Bayesian inversion method based on machine learning, comprising: Acquire airborne electromagnetic model data for electromagnetic forward modeling; establish a candidate forward model for training based on the airborne electromagnetic model data, and acquire electromagnetic response data obtained by forward modeling; Preprocessing the aero-electromagnetic model data and the electromagnetic response data; Constructing a neural network, taking the preprocessed airborne electromagnetic model data as input and the preprocessed electromagnetic response data as output, and training the neural network; Obtain weights and bias coefficients for fitting the candidate forward model according to the trained neural network, and obtain an optimized forward fitting matrix; Forward modeling data are obtained according to the optimized forward modeling fitting matrix, a Bayesian inversion model is established, and Bayesian inversion is performed according to the forward modeling data.

[0006] Furthermore, the optimized neural network is a fully connected neural network consisting of two fully connected hidden layers.

[0007] Furthermore, the airborne electromagnetic model data and the electromagnetic response data are preprocessed in the following manner: The aero-electromagnetic model data and the electromagnetic response data are pre-processed by using a logarithmic normalization method.

[0008] Further, the weights and bias coefficients for fitting the candidate forward model are obtained according to the trained neural network, including: According to the weights and bias coefficients obtained from the candidate forward model, the candidate forward model is converted into a product addition process of the weight and bias matrices.

[0009] Furthermore, after obtaining the forward modeling simulation data according to the optimized forward modeling fitting matrix, the method further includes: performing inverse normalization processing on the forward modeling simulation data.

[0010] Further, performing Bayesian inversion based on the forward simulation data includes: The posterior probability density function of the model parameters established according to the Bayesian method is: ; Among them, d is the observation data set, and m represents the number of layers: k , layer interface depth y, each layer resistivity ρ, and flight height h The model parameters, is the posterior probability density function of the model parameter m, is the prior probability density function of the model parameter m, expressed as: ; is the likelihood function of the observed data d given the model parameter m, represents the marginal likelihood, which is a constant that depends on the observed data, Is the number of layers k The prior probability density function of is the flight altitude h The prior probability density function of is the prior probability density function of resistivity under the premise of given number of layers and flight height, is the prior probability density function of the interface depth y, and its expression is: ; in , represents the minimum thickness of the layer given in the prior information. The prior probability density function of resistivity is defined as a multidimensional normal distribution, expressed as: ; in, is the best matching uniform half-space resistivity obtained by Marquette inversion given the initial model, is the weight coefficient; To best match the uniform half-space resistivity data matrix; The data noise in the Bayesian inversion model obeys Gaussian noise, and the likelihood function is defined as a multidimensional normal distribution, which is expressed as: ; in, is the number of data, which is expressed as the number of time channels in time domain electromagnetic inversion. is the prior data variance matrix, is the observed data, Forward modeling data.

[0011] The beneficial effects of the present invention are as follows: the present invention proposes a fast variable-dimensional Bayesian inversion based on an artificial neural network, and replaces the forward calculation process with a fitting matrix after machine learning. This method can effectively improve the efficiency of the variable-dimensional Bayesian inversion without affecting the accuracy of the results, so that the profile of the underground structure can be formed by inverting the measurement points of multiple measured data, which provides the possibility of applying this method to situations in the future where the underground structure is more complex and the model quantity demand is greater. BRIEF DESCRIPTION OF THE DRAWINGS

[0012] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. 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 paying creative labor.

[0013] Figure 1 A schematic diagram of a process flow of a fast Bayesian inversion method based on machine learning according to an embodiment of the present invention; Figure 2 A schematic diagram of an optimized neural network structure according to an embodiment of the present invention; Figure 3 A schematic diagram of forward calculation process optimization according to an embodiment of the present invention; Figure 4 A schematic diagram of inversion result comparison and model response comparison according to an embodiment of the present invention. DETAILED DESCRIPTION

[0014] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0015] A flow chart of a fast Bayesian inversion method based on machine learning according to an embodiment of the present invention is as follows: Figure 1 As shown, including: Acquire airborne electromagnetic model data for electromagnetic forward modeling; establish a candidate forward model for training based on the airborne electromagnetic model data, and acquire electromagnetic response data obtained by forward modeling; Preprocessing the aero-electromagnetic model data and the electromagnetic response data; Constructing a neural network, taking the preprocessed airborne electromagnetic model data as input and the preprocessed electromagnetic response data as output, and training the neural network; Obtain weights and bias coefficients for fitting the candidate forward model according to the trained neural network, and obtain an optimized forward fitting matrix; Forward modeling data are obtained according to the optimized forward modeling fitting matrix, a Bayesian inversion model is established, and Bayesian inversion is performed according to the forward modeling data.

[0016] In another specific embodiment of the present invention: The airborne electromagnetic model data is used as the independent variable, and the electromagnetic response data obtained by the candidate forward model is used as the dependent variable. At the same time, both the independent variable and the dependent variable are converted into matrix form, which is expressed as follows: ; ; ; Where M represents the resistivity , layer thickness , flight altitude The aero-electromagnetic model data matrix, including Y It represents the electromagnetic response data of each model after forward calculation, y represents the layer interface information, Expressed as the difference between the interfaces of two adjacent layers.

[0017] The method of preprocessing the aero-electromagnetic model data and the electromagnetic response data is: preprocessing the aero-electromagnetic model data and the electromagnetic response data by using a logarithmic normalization method, which is expressed as: ; ; in, Respectively represent the maximum and minimum values ​​of all electromagnetic response data, Respectively represent the maximum and minimum values ​​of all electromagnetic model data, represents the electromagnetic response data of the i-th layer, Represents the electromagnetic model data of the i-th layer.

[0018] The present invention further designs a fully connected neural network composed of two fully connected hidden layers. The network structure is as follows: Figure 2 As shown in the figure, the preprocessed airborne electromagnetic model data is input into the input end of the network, and the electromagnetic response data given by different time channels is used as the output end to train the neural network. The model parameter of the input layer is 2 k , its representative k In the layer model, k Different resistivity and k -1 layer thickness, the last layer is a uniform half-space, numerically defined as the flight height; n Representatives have n A fully connected layer of neurons, nt The time channel corresponding to the transient electromagnetic response result is represented by the activation function of the fully connected hidden layer being set to relu, and the activation function of the output layer being set to sigmoid; The embodiment of the present invention outputs the weights and bias coefficients that meet the set requirements in the trained neural network to convert the forward model into a product addition process of the weight and bias matrix, such as Figure 3 As shown, it is expressed as: ; ; ; Finally, the obtained results are denormalized to obtain the forward simulation data obtained through machine learning training simulation.

[0019] The embodiment of the present invention performs Bayesian inversion based on forward simulation data, specifically including: First, according to the Bayesian method, the posterior probability density function of the model is established given the observed data set and prior information: ; Among them, d is the observation data set, and m represents the number of layers: k , layer interface depth y, each layer resistivity ρ, and flight height h The model parameters, is the posterior probability density function of the model parameter m, represents the marginal likelihood, which is a constant that depends on the observed data, is the likelihood function of the observed data d given the model parameter m, is the prior probability density function of m, expressed as: ; in, Is the number of layers k The prior probability density function of is the flight altitude h The prior probability density function of is the prior probability density function of resistivity under the premise of given number of layers and flight height, is the prior probability density function of the interface depth y, and its expression is: ; in , represents the minimum thickness of the layer given in the prior information, represents factorial, i represents the i-th layer, Indicates the maximum number of layers, Represents the minimum number of layers. The prior probability density function of resistivity is defined as a multidimensional normal distribution, expressed as: ; in, is the best matching uniform half-space resistivity obtained by Marquette inversion given the initial model, is the weight coefficient; To best match the uniform half-space resistivity data matrix, the subscript T indicates the transpose of the matrix.

[0020] The data noise in the Bayesian inversion model obeys Gaussian noise, and the likelihood function is defined as a multidimensional normal distribution, which is expressed as: ; in, is the number of data, which is expressed as the number of time channels in time domain electromagnetic inversion. is the prior data variance matrix, is the observed data, It is the forward simulation data, that is, the part obtained by replacing the forward calculation through machine learning.

[0021] Further, in another embodiment of the present invention, since the number of layers of variable-dimensional Bayesian inversion is also variable as a parameter, this embodiment adopts a method of training different numbers of layers separately, setting the maximum number of layers to 10 and the minimum number of layers to 1, generating ten sets of training sets for training respectively, and taking the average relative error of the validation set part of the training set generated by each number of layers to detect the overall fitting condition, it is found that the average relative error of each layer is less than 2%, and it can be considered that the training is effective, so the traditional Bayesian inversion and the forward calculation method replaced by machine learning are respectively performed and the forward calculation is performed simultaneously, and the calculation results are compared as shown in Table 1; Table 1 Comparison of forward modeling results of traditional Bayesian method and machine learning replacement forward modeling method with different numbers of layers ; By comparing the time of calculating 10,000 forward modelings with the traditional Bayesian method and the machine learning method, it can be seen that the time consumed by the traditional forward modeling method is more than ten times that of the machine learning method. The smaller the number of layers, the greater the time difference. Since the variable-dimensional Bayesian inversion tends to accept a smaller number of layers, it is more beneficial to improve the efficiency of the variable-dimensional Bayesian inversion.

[0022] The embodiment of the present invention further designs a theoretical model to verify the efficiency and inversion effect improved by replacing the forward modeling part with the machine learning method in the inversion. The model is a six-layer model with deep low resistance. The first layer has a resistivity of 420Ω·m and a layer thickness of 54m; the second layer has a resistivity of 360Ω·m and a layer thickness of 54m; the third layer has a resistivity of 160Ω·m and a layer thickness of 54m; the fourth layer has a resistivity of 10Ω·m and a layer thickness of 54m; the fifth layer has a resistivity of 180Ω·m and a layer thickness of 36m; the sixth layer is a uniform half-space with a resistivity of 100Ω·m. The schematic diagram for comparing the inversion results is shown in FIG. Figure 4 As shown in Figure 4, the inversion results of the inversion method proposed in the present invention and the traditional Bayesian method are compared with the real model response of the model, where the inversion model is obtained from the maximum probability. It can be seen that both methods can effectively restore the underground resistivity distribution, but the inversion method proposed in the present invention shows better performance than the traditional method. In terms of time consumption, the traditional Bayesian method requires 16665.7 seconds for inversion, while the network method of the present invention only requires 1361 seconds, which means that the proposed method is more than 12 times faster than the traditional method.

[0023] In summary, through the verification of the theoretical model and inversion method provided by the embodiment of the present invention, the use of machine learning methods to replace the traditional forward modeling part can not only significantly improve the efficiency of the inversion process, but also perform well in recovering the accuracy of underground resistivity distribution. The high efficiency of this method is of great significance in practical applications, especially in situations where a large amount of data needs to be processed quickly, which can greatly save time and resources and improve work efficiency.

[0024] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A fast Bayesian inversion method based on machine learning, characterized in that: include: Acquire airborne electromagnetic model data for electromagnetic forward modeling; establish a candidate forward model for training based on the airborne electromagnetic model data, and acquire electromagnetic response data obtained by forward modeling; Preprocessing the aero-electromagnetic model data and the electromagnetic response data; Constructing a neural network, taking the preprocessed airborne electromagnetic model data as input and the preprocessed electromagnetic response data as output, and training the neural network; Obtain weights and bias coefficients for fitting the candidate forward model according to the trained neural network, and obtain an optimized forward fitting matrix; Forward modeling data are obtained according to the optimized forward modeling fitting matrix, a Bayesian inversion model is established, and Bayesian inversion is performed according to the forward modeling data.

2. The fast Bayesian inversion method based on machine learning according to claim 1, characterized in that: The neural network is a fully connected neural network consisting of two fully connected hidden layers.

3. The fast Bayesian inversion method based on machine learning according to claim 1, characterized in that: The method of preprocessing the aero-electromagnetic model data and the electromagnetic response data is as follows: The aero-electromagnetic model data and the electromagnetic response data are pre-processed by using a logarithmic normalization method.

4. The fast Bayesian inversion method based on machine learning according to claim 1, characterized in that: Obtaining weights and bias coefficients for fitting the candidate forward model according to the trained neural network, including: According to the weights and bias coefficients obtained from the candidate forward model, the candidate forward model is converted into a product addition process of the weight and bias matrices.

5. The fast Bayesian inversion method based on machine learning according to claim 1, characterized in that: After obtaining the forward modeling simulation data according to the optimized forward modeling fitting matrix, the method further includes: performing inverse normalization processing on the forward modeling simulation data.

6. The fast Bayesian inversion method based on machine learning according to claim 1, characterized in that: A Bayesian inversion is performed based on the forward modeling data, including: The posterior probability density function of the model parameters established according to the Bayesian method is: ； Among them, d is the observation data set, and m represents the number of layers: k , layer interface depth y, resistivity of each layer ρ, and flight height h The model parameters, is the posterior probability density function of the model parameter m, is the prior probability density function of the model parameter m, expressed as: ； is the likelihood function of the observed data d given the model parameter m, represents the marginal likelihood, which is a constant that depends on the observed data, Is the number of layers k The prior probability density function of is the flight altitude h The prior probability density function of is the prior probability density function of resistivity under the premise of given number of layers and flight height, is the prior probability density function of the interface depth y, and its expression is: ； in , represents the minimum thickness of the layer given in the prior information, represents factorial, i represents the i-th layer, Indicates the maximum number of layers, Represents the minimum number of layers. The prior probability density function of resistivity is defined as a multidimensional normal distribution, expressed as: ； in, is the best matching uniform half-space resistivity obtained by Marquette inversion given the initial model, is the weight coefficient; is the best matching uniform half-space resistivity data matrix; the subscript T indicates the transpose of the matrix; The data noise in the Bayesian inversion model obeys Gaussian noise, and the likelihood function is defined as a multidimensional normal distribution, which is expressed as: ； in, is the number of data, which is expressed as the number of time channels in time domain electromagnetic inversion. is the prior data variance matrix, is the observed data, Forward modeling data.

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