A Magnetotelluric Missing Data Recovery Method and System Considering Spatiotemporal Characteristics

Abstract

The present invention belongs to the field of geophysical exploration research, and particularly relates to a magnetotelluric missing data recovery method and system considering spatio-temporal characteristics, including: combining the electromagnetic field time-domain data of adjacent magnetotelluric acquisition stations within a preset time period to form preset two-dimensional time-domain data, and constructing a magnetotelluric data set with spatio-temporal characteristics; designing a spatio-temporal depth neural network model; training the established spatio-temporal depth neural network model based on the constructed magnetotelluric data set, and selecting the optimal hyperparameters to obtain the optimal spatio-temporal depth neural network model; using the optimal spatio-temporal depth neural network model to recover the missing data from the processed real-time acquired electromagnetic field time-domain data, solving the problem that the existing processing methods lead to low precision in later data processing and unreliable interpretation results. The present invention realizes the recovery of missing data, improves the utilization rate of data, and improves the reliability of data interpretation.

Description

Technical Field

[0001] The present invention belongs to the field of geophysical exploration research, and specifically relates to a method and system for recovering missing magnetotelluric data considering spatio-temporal characteristics. Background Art

[0002] Magnetotelluric sounding (MT) is an important method in geophysical exploration. Magnetotelluric sounding has advantages such as large exploration depth and low exploration cost. Currently, magnetotelluric sounding has been widely used in fields such as mineral resource exploration, energy detection, and analysis of the deep structure of the earth.

[0003] Magnetotelluric sounding also has disadvantages such as unstable and irregular signals, being easily affected by human noise interference, and may also cause data loss due to instrument failures during long-term operation. The current common practice is to first observe the collected data. If the quality of a certain time period is relatively poor, it is directly discarded. This processing method will result in low precision in later data processing and unreliable interpretation results. Summary of the Invention

[0004] The purpose of the present invention is to provide a method for recovering missing magnetotelluric data considering spatio-temporal characteristics, which is used to solve the problem that the existing processing methods lead to low precision in later data processing and unreliable interpretation results. The present invention makes full use of the spatio-temporal relationship between adjacent acquisition stations of magnetotelluric sounding and data at different times of the same acquisition station to realize the recovery of missing data, improve the utilization rate of data, and improve the reliability of data interpretation.

[0005] On the other hand, the present invention provides a system for recovering missing magnetotelluric data considering spatio-temporal characteristics.

[0006] The present invention is implemented as follows

[0007] A method for recovering missing magnetotelluric data considering spatio-temporal characteristics includes the following steps

[0008] S1. Combine the electromagnetic field time-domain data of adjacent magnetotelluric acquisition stations within a preset time period to form preset two-dimensional time-domain data , and construct a magnetotelluric data set with spatio-temporal characteristics

[0009] S2. Design a spatio-temporal depth neural network model. The spatio-temporal depth neural network model includes: a time-frequency transformation layer, a spatial relationship learning layer, a time relationship learning layer, and an attention mechanism layer. The time-frequency transformation layer performs a Fourier transform on the input preset two-dimensional time-domain data to obtain the corresponding two-dimensional frequency-domain data , and splice the real part and the imaginary part of the two-dimensional frequency-domain data with the preset two-dimensional time-domain data to obtain time-frequency joint data , the spatial relationship learning layer and the temporal relationship learning layer utilize the time-frequency joint data to perform information fusion learning in the spatial dimension and the temporal dimension, and obtain the spatio-temporal relationship features between the acquisition station data; the self-attention mechanism layer processes the spatio-temporal relationship features between the acquisition station data to reduce the risk of gradient explosion in the spatio-temporal depth neural network model;

[0010] S3. Train the spatio-temporal depth neural network model established in step S2 based on the magnetotelluric data set constructed in step S1, and select the optimal hyperparameters to obtain the optimal spatio-temporal depth neural network model. The optimal hyperparameters are the hyperparameters of the optimal spatio-temporal depth neural network model selected by using the Bayesian optimization algorithm, and the hyperparameters include the number of kernel functions in the spatial relationship learning layer, the number of kernel functions in the temporal relationship learning layer, and the number of Transformer layers;

[0011] S4. Use the optimal spatio-temporal depth neural network model to recover the missing data in the real-time acquired electromagnetic field time-domain data processed in step S1.

[0012] Further, step S1 specifically includes: selecting adjacent acquisition stations in the array-type magnetotelluric exploration, 2 ≤ ≤ 100, and the distance between each acquisition station is ≤ 5000 m to ensure spatial correlation between the data;

[0013] For the electromagnetic field time-domain data collected by each acquisition station, select 10 ≤ ≤ 10000 consecutive time-point data in a preset time period, and select ≥ 1 consecutive time-point data in the target time period;

[0014] Synthesize the electromagnetic field time-domain data of all adjacent acquisition stations within a certain preset time period into a preset two-dimensional time-domain data with a dimension of , and synthesize the electromagnetic field time-domain data corresponding to the target time period into a target two-dimensional time-domain data with a dimension of , , ,

[0015] ,

[0016] ,

[0017] Use to represent one of the elements, and its meaning is the -th value of the electric field component of the -th acquisition station in the corresponding time period; where ​= 1 and 2 respectively represent the direction components of the electric field and the represents the matrix transpose operation;

[0018] Combining the preset two-dimensional time-domain data with the target two-dimensional time-domain data to form a sample , and different sample sets constitute the magnetotelluric data set , where represents the scale of the data set, i.e., the number of samples.

[0019] Furthermore, the time-frequency transformation layer performs a Fourier transform on the input preset two-dimensional time-domain data , which means performing a one-dimensional discrete Fourier transform on each column of the preset two-dimensional time-domain data to obtain the frequency-domain data :

[0020] ,

[0021] where represents the k-th value of the transformed frequency-domain data; represents the l-th value of the preset two-dimensional time-domain data; is the imaginary unit, is the rotation factor.

[0022] Furthermore, the step of splicing the real part and the imaginary part of the two-dimensional frequency-domain data with the preset two-dimensional time-domain data to obtain the time-frequency joint data means extracting the real part and the imaginary part of the two-dimensional frequency-domain data , and then splicing the real part and the imaginary part of the two-dimensional frequency-domain data with the two-dimensional time-domain data in a new dimension to obtain the time-frequency joint data The spatial dimension of is

[0023] Furthermore, the spatial relationship learning layer adopts a two-layer graph convolutional neural network. In the graph convolutional neural network, information fusion learning in the spatial dimension is performed on the time-frequency joint data to obtain the feature data of each acquisition station in the preset time period, specifically including:

[0024] Inputting the time-frequency joint data into the spatial relationship learning layer, and the spatial relationship learning layer learns the spatial relationship between the data of adjacent acquisition stations in each layer of the graph convolutional neural network. The output data performs max pooling in the last dimension to obtain a dimension of New data, transpose the new data to obtain the feature data of all acquisition stations in the preset time period, with the dimension of , and input it into the time relationship learning layer.

[0025] Further, the time relationship learning layer adopts a two-layer bidirectional long short-term memory network to perform information fusion learning on the time dimension of the feature data of all acquisition stations in the preset time period, that is, the feature data of each acquisition station is processed by the same bidirectional long short-term memory network to obtain the corresponding spatio-temporal relationship features.

[0026] Further, the self-attention mechanism layer includes M layers of Transformer networks, uses a multi-head attention mechanism encoder to perform position encoding on the spatio-temporal relationship features, uses the neuron dropout technique to reduce the connection between the front and back levels, and finally passes through a fully connected layer to obtain the feature data of all acquisition stations in the preset time period;

[0027] Position encoding and position encoding are respectively:

[0028] ,

[0029] ,

[0030] Among them, is the position index, is the dimension index, is the total dimension of the position encoding;

[0031] The formula for each attention head in the self-attention mechanism layer is:

[0032] ,

[0033] ,

[0034] ,

[0035] ,

[0036] Among them represents the input matrix, and each row represents an input, represents the query matrix, represents the key matrix, represents the value matrix; is to linear transformation matrix, is to linear transformation matrix, is to linear transformation matrix represents the number of columns of the query matrix and the key matrix represents matrix transpose operation is a non-linear activation function is the score output of the attention head

[0037] Furthermore, the training process in S3 is specifically as follows:

[0038] Initialize the connection weight parameters of the spatio-temporal depth neural network model;

[0039] Input the magnetotelluric data set of adjacent acquisition stations into the spatio-temporal depth neural network model;

[0040] The spatio-temporal depth neural network model processes the input data to obtain the feature data of all acquisition stations within a preset time period as the prediction output;

[0041] Compare the measured values of the acquisition stations in the target time period in the magnetotelluric data set with the corresponding feature data within the preset time period, calculate the loss function value, if the termination condition is met, the training is completed, and the trained spatio-temporal depth network model is obtained; otherwise, use the gradient descent method to repeat the training process; among them, the loss function uses the Huber Loss function:

[0042] ,

[0043] where y represents the measured value represents the predicted value is a hyperparameter

[0044] Furthermore, the Bayesian optimization algorithm is used to select the optimal hyperparameters of the spatio-temporal depth neural network model, including: for the hyperparameter combinations of the spatio-temporal depth neural network model, randomly initialize multiple groups, use the hyperparameter combinations to initialize the spatio-temporal depth neural network model respectively, conduct training and verification, set a checkpoint every time training for a period of time, and each hyperparameter combination adjusts itself according to the quality of the spatio-temporal depth neural network model obtained by the training of other hyperparameter combinations; if it is not good itself, replace it with a better hyperparameter combination and add random perturbations; continue training until the optimal hyperparameter combination is obtained; for the spatio-temporal depth neural network model corresponding to the optimal hyperparameter combination, prune according to the connection weights between neurons to obtain the optimal spatio-temporal depth neural network model.

[0045] On the other hand, the present invention provides a magnetotelluric missing data recovery system considering spatio-temporal characteristics, including:

[0046] A data preprocessing module combines the electromagnetic field time-domain data of adjacent magnetotelluric acquisition stations within a preset time period to form preset two-dimensional time-domain data and constructs a magnetotelluric data set with spatio-temporal characteristics;

[0047] A network design module is used to design a spatio-temporal depth neural network model. The spatio-temporal depth neural network model includes: a time-frequency transformation layer, a spatial relationship learning layer, a time relationship learning layer, and an attention mechanism layer. The time-frequency transformation layer performs a Fourier transform on the input preset two-dimensional time-domain data to obtain the corresponding two-dimensional frequency-domain data and splices the real part and the imaginary part of the two-dimensional frequency-domain data with the preset two-dimensional time-domain data to obtain time-frequency joint data . The spatial relationship learning layer and the time relationship learning layer use the time-frequency joint data to perform information fusion learning in the spatial dimension and the time dimension to obtain the spatio-temporal relationship characteristics between the acquisition station data; the self-attention mechanism layer processes the spatio-temporal relationship characteristics between the acquisition station data to reduce the risk of gradient explosion in the spatio-temporal depth neural network model;

[0048] A training module trains the spatio-temporal depth neural network model based on the constructed magnetotelluric data set and selects the optimal hyperparameters to obtain the optimal spatio-temporal depth neural network model;

[0049] A prediction module is used to receive the output of the data preprocessing module and perform magnetotelluric sounding missing data recovery based on the optimal spatio-temporal depth neural network model.

[0050] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0051] In the process of recovering magnetotelluric missing data, the present invention not only considers the time correlation between the data before and after of the same acquisition station, but also fully considers the spatial relationship between the data of different acquisition stations, and improves the influence of important features through the attention mechanism of the Transformer layer. This combination of spatio-temporal relationship and attention mechanism can make more full use of the data, help reduce the influence of noise, bring higher accuracy than only using the time relationship for recovery, reduce the error caused by long-term prediction, and more accurately recover the missing data. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] Figure 1 is a flowchart of the recovery method provided by an embodiment of the present invention;

[0053] Figure 2 is a schematic structural diagram of the spatio-temporal depth neural network model provided by an embodiment of the present invention. DETAILED DESCRIPTION

[0054] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without creative efforts shall fall within the protection scope of the present invention.

[0055] The objective of the present invention is to provide a method for restoring missing magnetotelluric data considering spatio-temporal characteristics, so as to make full use of the spatio-temporal relationship between adjacent acquisition stations in magnetotelluric sounding and data at different times of the same acquisition station, realize the restoration of missing data, improve the data utilization rate, and improve the reliability of data interpretation.

[0056] As Figure 1 shown, it includes:

[0057] S1. Combine the electromagnetic field time-domain data of adjacent magnetotelluric acquisition stations within a preset time period to form preset two-dimensional time-domain data , and construct a magnetotelluric data set with spatio-temporal characteristics; assume there are acquisition stations, and use the data of preset time periods in history to predict the data of the target time period. If ≥1, then the dimension of each sample constituting the magnetotelluric data set is , where the first columns are inputs, and the last

[0058] columns are label outputs; Specifically, it includes: select adjacent acquisition stations in array-type magnetotelluric exploration, 2 ≤ ≤ 100, and the distance between each acquisition station is

[0059] ≤ 5000m to ensure spatial correlation between data; For the electromagnetic field time-domain data collected by each acquisition station, select the data of 10 ≤ ≤ 10000 consecutive time points in the preset time period, and select the

[0060] data of ≥ 1 consecutive time points in the target time period; Combine the electromagnetic field time-domain data of all adjacent acquisition stations within a certain preset time period into preset two-dimensional time-domain data , and combine the electromagnetic field time-domain data corresponding to the target time period into

[0061] ,

[0062] ,

[0063] Using to represent one of the elements, its meaning is the th electric field component of the th value of the th acquisition station in the corresponding time period; where = 1, 2 respectively represent the direction component and direction component of the electric field; represents matrix transpose operation;

[0064] Combining the preset two-dimensional time-domain data with the target two-dimensional time-domain data to form a sample , and different sample sets constitute the magnetotelluric data set , where represents the scale of the data set, that is, the number of samples.

[0065] S2. Design a spatio-temporal depth neural network model;

[0066] S3. Train the spatio-temporal depth neural network model established in step S2 based on the magnetotelluric data set constructed in step S1, and select the optimal hyperparameters to obtain the optimal spatio-temporal depth neural network model. The optimal hyperparameters are the hyperparameters of the optimal spatio-temporal depth neural network model selected by the Bayesian optimization algorithm. The hyperparameters include the number of kernel functions in the spatial relationship learning layer, the number of kernel functions in the time relationship learning layer, and the number of Transformer layers. Here, Transformer refers to a deep learning model architecture used for natural language processing (NLP) and other sequence-to-sequence tasks;

[0067] S4. Use the optimal spatio-temporal depth neural network model to recover the missing data in the real-time collected electromagnetic field time-domain data processed in step S1.

[0068] The preset time period in the present invention is a long time period before the target time period, also called history.

[0069] Figure 2 is a schematic diagram of the architecture of the spatio-temporal depth neural network model, including: The spatio-temporal depth neural network model includes: a time-frequency transformation layer, a spatial relationship learning layer, a time relationship learning layer, and an attention mechanism layer. The time-frequency transformation layer performs Fourier transform on the input preset two-dimensional time-domain data to obtain the corresponding two-dimensional frequency-domain data , and splice the real part and the imaginary part of the two-dimensional frequency-domain data with the preset two-dimensional time-domain data to obtain the time-frequency joint data . The spatial relationship learning layer and the temporal relationship learning layer use the time-frequency joint data to perform information fusion learning in the spatial dimension and the temporal dimension, obtain the spatio-temporal relationship characteristics between the acquisition station data, and the characteristic data of the target acquisition station in the target time period can be obtained according to the spatio-temporal relationship characteristics; the self-attention mechanism layer processes the spatio-temporal relationship characteristics between the acquisition station data to reduce the risk of gradient explosion in the spatio-temporal depth neural network model.

[0070] It should be noted that normalization needs to be performed first before data input, and its input dimension is , and the corresponding two-dimensional frequency-domain data is obtained through Fourier transform including the real part and the imaginary part, which are spliced with the preset two-dimensional time-domain data to obtain the time-frequency joint data . First, the real part and the imaginary part of the two-dimensional frequency-domain data are extracted, and then the real part and the imaginary part of the two-dimensional frequency-domain data are spliced with the two-dimensional time-domain data in a new dimension to obtain the time-frequency joint data . The spatial dimension of is

[0071] Among them, the spatial relationship learning layer adopts a two-layer graph convolutional neural network (GCN). In the graph convolutional neural network, the time-frequency joint data is input into the graph convolutional neural network, so that the graph convolutional neural network learns the spatial relationship between adjacent acquisition station data in each layer according to its own transfer function. For the output data of the graph convolutional neural network, after passing through the activation function, it is input into the next layer, and finally the characteristic data of each acquisition station in the preset time period is obtained;

[0072] Specifically, it includes:

[0073] Input the time-frequency joint data into the spatial relationship learning layer. The spatial relationship learning layer learns the spatial relationship between adjacent acquisition station data in each layer, and the output data performs max pooling in the last dimension to obtain new data with a dimension of . The new data is transposed to obtain the characteristic data of all acquisition stations in the preset time period, with a dimension of , and input it into the temporal relationship learning layer.

[0074] The time relationship learning layer adopts a two-layer bidirectional long short-term memory network to perform information fusion learning on the feature data of all acquisition stations in a preset time period in the time dimension, that is, the feature data of each acquisition station is processed by the same bidirectional long short-term memory network to obtain the corresponding spatio-temporal relationship features.

[0075] The self-attention mechanism layer is used to process the spatio-temporal relationship features between the acquisition station data, reduce the risk of model gradient explosion, and improve the generalization ability and accuracy of the model;

[0076] The self-attention mechanism layer adopts an N-layer Transformer network. Specifically: the multi-head attention mechanism encoder is used to perform position encoding on the spatio-temporal relationship features, and the neuron dropout technique is used to reduce the connections between the front and back levels. Finally, through the fully connected layer, the feature data of all acquisition stations in the preset time period is obtained;

[0077] Position encoding and position encoding are respectively:

[0078] ,

[0079] ,

[0080] where is the position index, is the dimension index, is the total dimension of the position encoding;

[0081] The formula for each attention head in the self-attention mechanism layer is:

[0082] ,

[0083] ,

[0084] ,

[0085] ,

[0086] where represents the input matrix, and each row represents an input, represents the query matrix, represents the key matrix, represents the value matrix; is to linear transformation matrix, is to linear transformation matrix, is to The linear transformation matrix, represents the number of columns of the generation query matrix and the key matrix, represents the matrix transpose operation, is a non-linear activation function, is the score output of the attention head.

[0087] Control the attention time series encoder, perform long-distance dependence modeling and feature fusion on the feature time series corresponding to all acquisition stations according to the multi-head self-attention mechanism to capture the complex temporal relationships between data; and use the neuron dropout technique to reduce the connections between the front and back stages, reduce the complexity of the network, reduce the risk of gradient explosion, and improve the generalization performance of the model; through the fully connected layer, obtain the feature data of all acquisition stations within the preset time period, that is, the data predicted in the target time period.

[0088] Train the spatio-temporal deep neural network model based on the constructed dataset and select the optimal hyperparameters. The process of training the spatio-temporal deep neural network is specifically as follows:

[0089] Initialize the connection weight parameters of the spatio-temporal deep neural network model;

[0090] Input the magnetotelluric dataset of adjacent acquisition stations into the spatio-temporal deep neural network model;

[0091] The spatio-temporal deep neural network model processes the input data to obtain the feature data of all acquisition stations within the preset time period as the predicted output;

[0092] Compare the measured values of the acquisition stations in the target time period in the magnetotelluric dataset with their corresponding feature data within the preset time period, calculate the loss function value. If the termination condition is met, the training is completed to obtain the trained spatio-temporal deep network model; otherwise, use the gradient descent method to repeat the training process; among them, the loss function uses the Huber Loss function:

[0093] ,

[0094] where y represents the measured value, represents the predicted value, is a hyperparameter.

[0095] The Bayesian optimization algorithm is used to select the optimal hyperparameters of the spatio-temporal deep neural network model, including: for the hyperparameter combinations of the spatio-temporal deep neural network model, multiple groups are randomly initialized. The spatio-temporal deep neural network model is initialized using the hyperparameter combinations respectively, trained and verified. A checkpoint is set every time training is carried out for a period of time. Each hyperparameter combination adjusts itself according to the quality of the spatio-temporal deep neural network model obtained by the training of other hyperparameter combinations. If itself is not good, it is replaced by a better hyperparameter combination and a random perturbation is added. Training continues until the optimal hyperparameter combination is obtained. For the spatio-temporal deep neural network model corresponding to the optimal hyperparameter combination, pruning is performed according to the connection weights between neurons to obtain the optimal spatio-temporal deep neural network model.

[0096] In another embodiment, the present invention provides a magnetotelluric missing data recovery system considering spatio-temporal characteristics, including:

[0097] A data preprocessing module combines the electromagnetic field time-domain data of adjacent magnetotelluric acquisition stations within a preset time period to form preset two-dimensional time-domain data and constructs a magnetotelluric data set with spatio-temporal characteristics;

[0098] A network design module designs a spatio-temporal deep neural network model for magnetotelluric sounding work;

[0099] A training module trains the established spatio-temporal deep neural network model based on the constructed magnetotelluric data set and selects the optimal hyperparameters to obtain the optimal spatio-temporal deep neural network model;

[0100] A prediction module is used to receive the output of the data preprocessing module and perform magnetotelluric sounding missing data recovery based on the optimal spatio-temporal deep neural network model.

[0101] The above are only the preferred embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent replacements, and improvements made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

Claims

1. A magnetotelluric missing data recovery method considering spatio-temporal characteristics, characterized in that, It includes the following steps: S1. Combine the electromagnetic field time-domain data of adjacent magnetotelluric acquisition stations within a preset time period to form preset two-dimensional time-domain data , and construct a magnetotelluric data set with spatio-temporal characteristics; S2. Design a spatio-temporal deep neural network model, where the spatio-temporal deep neural network model includes: a time-frequency transformation layer, a spatial relationship learning layer, a time relationship learning layer, and a self-attention mechanism layer. The time-frequency transformation layer performs a Fourier transform on the input preset two-dimensional time-domain data to obtain the corresponding two-dimensional frequency-domain data , and splices the real part and the imaginary part of the two-dimensional frequency-domain data with the preset two-dimensional time-domain data to obtain time-frequency joint data . The spatial relationship learning layer and the time relationship learning layer use the time-frequency joint data to perform information fusion learning in the spatial dimension and the time dimension, and obtain the spatio-temporal relationship characteristics between the acquisition station data; The self-attention mechanism layer processes the spatio-temporal relationship features among the data of the acquisition stations, which is used to reduce the risk of gradient explosion in the spatio-temporal depth neural network model; S3. Train the spatio-temporal depth neural network model established in step S2 based on the magnetotelluric data set constructed in step S1, and select the optimal hyperparameters to obtain the optimal spatio-temporal depth neural network model. The optimal hyperparameters are the hyperparameters of the optimal spatio-temporal depth neural network model selected by the Bayesian optimization algorithm. The hyperparameters include the number of kernel functions in the spatial relationship learning layer, the number of kernel functions in the time relationship learning layer, and the number of Transformer layers; S4. Use the optimal spatio-temporal depth neural network model to recover the missing data in the real-time acquired electromagnetic field time-domain data processed in step S1.

2. The magnetotelluric missing data recovery method considering spatio-temporal characteristics according to claim 1, characterized in that, Step S1 specifically includes: Selecting adjacent acquisition stations in the array magnetotelluric sounding, where 2 ≤ ≤ 100, and the distance between each acquisition station is ≤ 5000 m to ensure spatial correlation between data; For the electromagnetic field time-domain data collected by each acquisition station, select the data of 10 ≤ ≤ 10,000 consecutive time points in the preset time period, and select the ≥ 1 consecutive time point data in the target time period; Synthesize the electromagnetic field time-domain data of all adjacent acquisition stations within a preset time period into preset two-dimensional time-domain data with a dimension of and synthesize the electromagnetic field time-domain data corresponding to the target time period into target two-dimensional time-domain data with a dimension of , ,​ ， ， Use to represent one of the elements, which means the electric field component of the th acquisition station at the th value during the corresponding time period; where = 1, 2 respectively represent the direction component and direction component of the electric field; represents the matrix transpose operation; Combine the preset two-dimensional time-domain data with the target two-dimensional time-domain data to form a sample . Different sample sets constitute the magnetotelluric data set , where represents the scale of the data set, i.e., the number of samples.

3. The magnetotelluric missing data recovery method considering spatio-temporal characteristics according to claim 2, characterized in that The time-frequency transformation layer performs a Fourier transform on the input preset two-dimensional time-domain data which means performing a one-dimensional discrete Fourier transform on each column of the preset two-dimensional time-domain data to obtain frequency-domain data : ， wherein represents the k-th value of the frequency-domain data after transformation; represents the l-th value of the preset two-dimensional time-domain data; is the imaginary unit, is the rotation factor.

4. The magnetotelluric missing data recovery method considering spatio-temporal characteristics according to claim 2, characterized in that The real part and the imaginary part of the two-dimensional frequency-domain data are concatenated with the preset two-dimensional time-domain data to obtain the time-frequency joint data , which means extracting the real part and the imaginary part of the two-dimensional frequency-domain data , and then concatenating the real part and the imaginary part of the two-dimensional frequency-domain data with the two-dimensional time-domain data in a new dimension to obtain the time-frequency joint data whose spatial dimension is .

5. The magnetotelluric missing data recovery method considering spatio-temporal characteristics according to claim 2, characterized in that The spatial relationship learning layer adopts a two-layer graph convolutional neural network. In the graph convolutional neural network, information fusion learning in the spatial dimension is performed on the time-frequency joint data to obtain the feature data of each acquisition station in the preset time period, specifically including: Input the time-frequency joint data into the spatial relationship learning layer. The spatial relationship learning layer learns the spatial relationship between adjacent acquisition station data in each layer of the graph convolutional neural network, and performs max pooling on the output data in the last dimension to obtain new data with a dimension of . Transpose the new data to obtain the feature data of all acquisition stations in the preset time period, with a dimension of , and input it into the time relationship learning layer.

6. The magnetotelluric missing data recovery method considering spatio-temporal characteristics according to claim 1, characterized in that The time relationship learning layer uses 2 layers of bidirectional long short-term memory networks to perform information fusion learning in the time dimension on the feature data of all acquisition stations in a preset time period, that is, the feature data of each acquisition station is processed by the same bidirectional long short-term memory network to obtain the corresponding spatio-temporal relationship features.

7. The magnetotelluric missing data recovery method considering spatio-temporal characteristics according to claim 1, characterized in that The self-attention mechanism layer includes M layers of Transformer networks, uses the multi-head attention mechanism encoder to perform position encoding on the spatio-temporal relationship features, and uses the neuron dropout technique to reduce the connections between the front and back levels. Finally, through the fully connected layer, the feature data of all acquisition stations in a preset time period is obtained; Position encoding and the position encoding are respectively as follows: ， ， Among them, is the position index, is the dimension index, is the total dimension of the position encoding; The formula for each attention head in the self-attention mechanism layer is: ， ， ， ， Among them represents the input matrix, where each row represents an input, represents the query matrix, represents the key matrix, represents the value matrix; is to 's linear transformation matrix, is to 's linear transformation matrix, is to 's linear transformation matrix, represents the number of columns of the query matrix and the key matrix, represents the matrix transpose operation, is a non-linear activation function, is the score output of the attention head.

8. The magnetotelluric missing data recovery method considering spatio-temporal characteristics according to claim 1, characterized in that, The specific training process in S3 is as follows: Initialize the connection weight parameters of the spatio-temporal depth neural network model; Input the magnetotelluric data set of adjacent acquisition stations into the spatio-temporal depth neural network model; The spatio-temporal depth neural network model processes the input data to obtain the feature data of all acquisition stations in a preset time period as the prediction output; Compare the measured values of the acquisition stations in the target time period in the magnetotelluric data set with the corresponding feature data in the preset time period, calculate the loss function value. If the termination condition is met, the training is completed to obtain the trained spatio-temporal depth network model; otherwise, use the gradient descent method to repeat the training process; among them, the loss function uses the Huber Loss function: ， Among them, y represents the measured value, represents the predicted value, is a hyperparameter.

9. The magnetotelluric missing data recovery method considering spatio-temporal characteristics according to claim 8, characterized in that, Use the Bayesian optimization algorithm to select the hyperparameters of the optimal spatio-temporal depth neural network model, including: for the hyperparameter combinations of the spatio-temporal depth neural network model, randomly initialize multiple groups, use the hyperparameter combinations to initialize the spatio-temporal depth neural network model respectively, perform training and verification, set a checkpoint every time training for a period of time, and each hyperparameter combination adjusts itself according to the quality of the spatio-temporal depth neural network model obtained by the training of other hyperparameter combinations; if itself is not good, replace it with a better hyperparameter combination and add random perturbations; continue training until the optimal hyperparameter combination is obtained; for the spatio-temporal depth neural network model corresponding to the optimal hyperparameter combination, prune it according to the connection weights between neurons to obtain the optimal spatio-temporal depth neural network model.

10. A magnetotelluric missing data recovery system considering spatio-temporal characteristics, characterized in that, The system includes: A data preprocessing module combines the electromagnetic field time-domain data of adjacent magnetotelluric acquisition stations within a preset time period to form preset two-dimensional time-domain data and constructs a magnetotelluric data set with spatio-temporal characteristics; A network design module for designing a spatio-temporal deep neural network model, the spatio-temporal deep neural network model including: a time-frequency transformation layer, a spatial relationship learning layer, a temporal relationship learning layer, and a self-attention mechanism layer, the time-frequency transformation layer performing Fourier transform on the input preset two-dimensional time-domain data to obtain corresponding two-dimensional frequency-domain data , and concatenating the real part and the imaginary part of the two-dimensional frequency-domain data with the preset two-dimensional time-domain data to obtain time-frequency joint data . The spatial relationship learning layer and the temporal relationship learning layer use the time-frequency joint data to perform information fusion learning in the spatial dimension and the temporal dimension to obtain spatio-temporal relationship features between acquisition station data; the self-attention mechanism layer processes the spatio-temporal relationship features between acquisition station data to reduce the risk of gradient explosion in the spatio-temporal deep neural network model; A training module that trains a spatio-temporal deep neural network model based on the constructed magnetotelluric dataset and selects the optimal hyperparameters to obtain the optimal spatio-temporal deep neural network model; A prediction module that receives the output of the data preprocessing module and performs magnetotelluric sounding missing data recovery based on the optimal spatio-temporal deep neural network model.

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