A method for estimating earthquake source parameters from multiple stations based on graph theory

Abstract

The present invention discloses a multi-station earthquake source parameter estimation method based on graph theory, which takes each earthquake detection station as a node of a graph, intercepts the earthquake three-component waveform data of a certain time length, uses a convolutional neural network to extract waveform features, and takes them as the attributes of the nodes; encodes the position of the earthquake detection station and fuses it with the extracted waveform features; uses the seismic phase picking method to detect the P wave first arrival information, and takes it as the attribute of the edge in the graph, and constructs the edge in the graph based on it; fuses the nodes and edges using the graph convolution operation, and interacts the information of each station node in the graph; uses the transformer structure to perform feature convergence of the overall graph attributes on all station nodes; and uses a mixed Gaussian density network to obtain a fitting estimate of the magnitude, epicenter position, focal depth, etc. of the earthquake source. The present invention can quickly and accurately estimate and predict earthquake source parameters based on a multi-station model.

Description

Technical Field

[0001] The invention belongs to the field of earthquake early warning, and in particular relates to a multi-station earthquake source parameter estimation method based on graph theory. Background Art

[0002] As the requirements of earthquake early warning systems increase, more and more earthquake stations are established, and a large amount of earthquake waveform data is detected. It is difficult for traditional methods to make full use of the information therein. Therefore, the present invention hopes to apply the method of deep learning to solve the problem of source parameter estimation. Source parameter estimation includes early warning estimation of the magnitude, focal depth and epicenter position of the earthquake. At present, most traditional source parameter estimation methods are based on single-station models, and the application of multiple stations can theoretically bring further improvement in accuracy. In the multi-station model, the arrangement of platforms has always been a difficulty, and its sparse structure is difficult to process using traditional Euclidean object methods. Therefore, this data structure has a large application space here, and can explore the potential of source parameter estimation of the multi-station model in one step. Summary of the invention

[0003] In view of the above problems existing in the prior art, the present invention aims to provide a multi-station earthquake source parameter estimation method based on graph theory, which extracts waveform features using convolutional neural networks by treating stations as graph nodes, generates edge attributes using seismic phase information, uses graph convolution to interact with station information, and uses transformer self-attention structure to aggregate features, and finally uses a mixed Gaussian model to output the estimation results of the source parameters. The present invention can accurately estimate the source parameters based on multiple stations, explores the potential of the graph theory method of constructing edges with seismic phase information in the multi-station source parameter estimation model, and has great application space in earthquake early warning.

[0004] To achieve the purpose of the present invention, the technical solution adopted by the present invention is as follows:

[0005] A multi-station earthquake source parameter estimation method based on graph theory, the method comprising the following steps:

[0006] Step 1: Apply convolutional neural network to extract waveform features on seismic station nodes;

[0007] Step 2: Encode the longitude and latitude of the station;

[0008] Step 3: Use the phase picking method to detect the first arrival time of the P wave at the station and convert it into the attributes of the edge in the graph;

[0009] Step 4: Use graph convolution to interact with nodes and edges in the graph;

[0010] Step 5: Use the transformer structure to aggregate graph nodes;

[0011] Step 6: Use the mixed Gaussian model to fit and estimate the source parameters.

[0012] As an improvement of the present invention, in step 1, the method for extracting waveform features from seismic station nodes by applying a convolutional neural network is:

[0013] Assuming that the number of stations is N, the length of the intercepted waveform is T, and the sampling frequency is f, the input of each sample is (N, T*f, 3). Then, the convolution, pooling, and multi-layer perceptron operations in the convolutional neural network are used to extract the features of the station node as (N, M), thereby obtaining a deeper expression of the seismic waveform data. The structure of the convolutional layer is shown in the following table:

[0014]

[0015] As an improvement of the present invention, in step 2, the method for encoding the latitude, longitude, altitude, etc. of the platform node is sinusoidal position encoding. Assuming that k is one of the N platforms, the method for generating the position vector is:

[0016]

[0017] Where lat, lon, and depth are the latitude, longitude, and altitude values ​​of each station, respectively. lat , d lon , d depth are the vector dimensions for encoding assigned to the three position elements, i is the sequence number of the element in the position vector, and PE is the value of the position element encoded for each position component;

[0018] The generated position matrix is ​​merged with the node feature matrix to add the position information to the node platform waveform information.

[0019] As an improvement of the present invention, in step 3, the method for seismic phase picking adopts the existing EQTransformer method which has a relatively good effect. The model designs a deep encoder structure, which combines the residual convolutional network, the long short-term memory network and the attention mechanism to detect the first arrival time of the P wave. Its detection accuracy of seconds can meet the requirements for seismic phase picking in the present invention.

[0020] As an improvement of the present invention, in step 4, the edges in the graph are constructed according to the seismic phase information, the absolute value of the difference in the first arrival time of the P wave between the two stations is calculated, and a threshold is set at the same time. The threshold is set to 3 seconds (combined with the sampling frequency of 300 sampling points). When the difference between the two stations exceeds the threshold, no connection is made. Otherwise, an undirected edge is used to connect, and the difference is used as the element value of the corresponding position in the adjacency matrix. Then, the adjacency matrix is ​​normalized according to each row, and the creation of the adjacency matrix is ​​completed. The calculated adjacency matrix is ​​used for graph convolution with the platform node features, and the formula is as follows:

[0021]

[0022] In the formula is the node feature matrix in the graph of the lth and l+1th layers in the graph convolution layer, is the adjacency matrix, plus the identity matrix I N Avoid having zero elements at the diagonal of the adjacency matrix. is the degree matrix of the adjacency matrix, which is used to normalize it, W (l) is a learnable parameter, σ(·) is an activation function;

[0023] According to the above formula, the graph convolution operation is performed, and the activation function uses ReLU(·)=max(0,·). At the same time, the learnable parameter matrix is ​​set to a square matrix, so that the dimension of the feature matrix will not be changed after the graph convolution. After the graph convolution, the interaction of the station node information is completed.

[0024] As an improvement of the present invention, in step 5, the transformer structure is used to aggregate the station node information, which mainly consists of three parts, namely self-attention, feedforward neural network and layer normalization. The formula of the self-attention mechanism is as follows:

[0025] Q=W Q *X,K=W K *X,V=W V *X

[0026]

[0027] Where d k is the vector dimension, X is the node feature matrix, W Q , W K , W V is a learnable parameter matrix, Q, K, V are the query, key and value in the attention mechanism, and softmax is the activation function; the query Q, key K and value V are calculated according to all station features, and then the attention score and output value are calculated;

[0028] The feedforward neural network provides nonlinear transformation, which is performed separately on the attention value sequence obtained in the previous step. The nonlinearization formula is as follows:

[0029] FFN(x)=GELU(xW1+b1)W2+b2

[0030]

[0031] Where W1, W2, b1, b2 are learnable weights and bias parameters, respectively, and x is the feature vector of each position element in the input sequence;

[0032] Layer normalization is used to process sequence data and normalize individual sample sequences in a batch according to their sequence order. The process is shown in the following formula.

[0033]

[0034] In the formula, z (l) is the input of the lth layer of neurons, with dimension n (l) , μ (l) , σ (l) are its mean and variance, γ, β are learnable parameter vectors for scaling and translation, and ∈ is a small amount set to prevent the denominator from being zero.

[0035] Treat the station node as a sequence, use the encoder part of the transformer structure, add a blank token at the beginning of the input sequence, and use it as the feature vector representing all the information in the output sequence. Figure 4 The steps in the figure go through a multi-head self-attention layer, a feed-forward network layer, and layer normalization to complete the aggregation of information in the figure.

[0036] As an improvement of the present invention, in step 6, a mixed Gaussian density network is used as the result output of the source parameter estimation, the input is passed through the hidden layer DNN, and then the relevant parameters of the mixed Gaussian distribution are obtained through the fully connected layer. After mixing, a probability output model is obtained. The process is shown in the following formula:

[0037]

[0038] Where X is the input feature, H(x) is the hidden layer element, W, b are learnable weights and bias parameters, α(x) is the weight of different components in the mixed distribution, RELU, softmax are the corresponding activation functions, μ(x), σ(x) are the mean and variance of the Gaussian distribution;

[0039] The magnitude and location of the earthquake source are estimated respectively. For the magnitude estimation, the number of mixed Gaussian distribution components is set to 5, and the output is a mixed distribution parameter with a dimension of (5, 3). For the location estimation (three components of depth, longitude, and latitude), the number of mixed Gaussian distribution components is set to 15. At the same time, since the location has three elements, the output dimension is a mixed distribution parameter with a dimension of (15, 7);

[0040] The output of the model is the related parameters of the mixed Gaussian probability distribution. To obtain the results of the earthquake source parameters from a single data sample, the conditional mean must be derived from the probability density and calculated according to the following formula to obtain the results of the earthquake source parameter estimation;

[0041]

[0042] Where x is the input feature, α(x) is the weight of different components in the mixed distribution, μ(x) is the mean of the Gaussian distribution, is the conditional mean, p(y|x) is the conditional probability density distribution, and y is the predicted value of the output source parameter variable.

[0043] Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects: for the problem of earthquake source parameter estimation, the present invention proposes a new multi-station model based on graph theory, which adopts a graph convolutional neural network, can extract waveform information of multiple earthquake detection stations, and use the picked P wave first arrival time phase as the attribute of the edge to better explore and interact with the source information contained in the multiple stations, effectively improving the real-time and accuracy of the estimation of the source position parameters; the transformer self-attention mechanism used in the model effectively gathers information related to the source height, and learns the relationship between stations with longer distances in the multi-station sequence; the mixed Gaussian model represents the earthquake source parameter estimation results by checking the probability distribution, which is convenient for analyzing the uncertainty of the model and improving the fitting efficiency of the model; the use of graph theory methods to solve the information interaction of the multi-station model provides a reference, improves the accuracy and real-time of the earthquake source parameter estimation based on multiple stations, and shows huge potential for exploration for the application of the multi-station source parameter estimation model. BRIEF DESCRIPTION OF THE DRAWINGS

[0044] Figure 1 It is a flow chart of a multi-station earthquake source parameter estimation method based on graph theory of the present invention;

[0045] Figure 2 It is a structural diagram of a multi-station source parameter estimation model used in the present invention;

[0046] Figure 3It is a structural diagram of the key parts of the seismic phase picking method used in step 3 of the present invention; wherein (a) is a ResCNN structural diagram, (b) is a LSTM structural diagram, and (c) is an Attention structural diagram;

[0047] Figure 4 is a structural diagram of the Transformer encoder used in step 5 of the present invention;

[0048] Figure 5 This is the mixed Gaussian distribution network result diagram used in step six of the present invention. DETAILED DESCRIPTION

[0049] The technical solution of the present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0050] Example: Figure 1 As shown, the present invention proposes a multi-station earthquake source parameter estimation method based on graph theory, and the detailed steps of the method are:

[0051] (1) Apply convolutional neural network to extract waveform features from seismic station nodes;

[0052] The amount of original waveform data of the platform is very large. In order to better process it, the neural network method is first used to extract features to obtain a deeper feature expression of the platform waveform information.

[0053] Assume that the number of stations is N, the length of the intercepted waveform is T, and the sampling frequency is f. Therefore, the input of each sample is (N, T*f, 3). Then, the convolution, pooling, and multi-layer perceptron operations in the convolutional neural network are used to extract the features of the station nodes as (N, M). The convolution layer parameter settings are shown in the following table:

[0054]

[0055] Since the length of the earthquake waveform is 30s, according to the propagation speed of the earthquake P wave, its approximate coverage range is calculated, and the number of earthquake detection stations contained in the range is selected. Finally, the number of stations used in the present invention is determined to be 25. For the case where the number of stations in the earthquake case is greater than or equal to 25, the nearest 25 stations are selected according to the seismic phase information; for the case where the number of stations is less than 25, the insufficient station data is supplemented with 0. The time length is set to 30s, the sampling frequency is 100hz, and the feature dimension after extraction is set to 500.

[0056] (2) Position coding of the longitude and latitude of the station;

[0057] The method for encoding the latitude, longitude, altitude, etc. of the platform node is sinusoidal position encoding. Assuming k is one of the N platforms, the method for generating its position vector is:

[0058]

[0059] Where lat, lon, and depth are the latitude, longitude, and altitude values ​​of each station, respectively. lat , d lon , d depth They are the vector dimensions for encoding assigned to the three position elements respectively, i is the sequence number of the element in the position vector, and PE is the encoded value of the corresponding position element of each position component.

[0060] First, generate a position matrix (25, 500), and assign the dimension of 500 to the longitude, latitude and altitude of the station location according to 200, 200, and 100. There is a cycle for every five positions in the feature vector. For example, positions 0 and 1 are given to longitude, positions 2 and 3 are given to latitude, and position 4 is given to altitude. This is repeated in sequence. Each element is set to an arithmetic sequence of the corresponding dimension in the relative position, and then sine and cosine operations are performed. Then, it is multiplied by the position element of the station as a coefficient and encoded according to the above formula.

[0061] The generated position matrix is ​​integrated with the node features to add the position information to the node platform waveform information.

[0062] (3) Use the phase picking method to detect the first arrival time of the P wave at the station and convert it into the attributes of the edge in the graph;

[0063] The method of seismic phase picking adopts the existing EQTransformer method which has a relatively good effect now. The model designs a deep encoder structure, which combines the residual convolution network, the long short-term memory network and the attention mechanism to detect the first arrival time of the P wave. Its detection accuracy of seconds can fully meet the requirements of the present invention. The main structure is as follows:

[0064] The convolutional layer in the encoder is used to extract local features of the waveform, using local structures and providing the model with better time invariance, resulting in better generalization. Since the deeper the network, the stronger the expression ability, in order to expand the network depth without causing model degradation, the encoder in this method adds a convolutional layer block with residual connection (ResCNN, as shown in the attached manual) Figure 3 At the same time, an extended bidirectional long short-term memory (LSTM) block is added to the encoder (see Appendix Figure 3 (b) is used to model waveform sequences, where the memory unit receives input at each time step, outputs a hidden state, and updates the memory unit based on a gate mechanism to help increase the network depth without increasing the number of learnable parameters. After the LSTM block, this method passes its output sequence through an attention mechanism (as shown in the attached manual). Figure 3 (c) in order to learn the relatively important parts of the sequence and ignore the less relevant parts. The attention mechanism formula is as follows:

[0065]

[0066] Where h t ,h t′ are the hidden states of the LSTM blocks at time steps t and t′, respectively. W and b are the weight matrix and bias vector, respectively. σ is the sigmoid activation function. α t，t′ is the attention score that characterizes the degree of correlation between sequence elements, c t is a sequence of context-aware encodings relative to surrounding elements, defining the attention that should be given to a feature at each time step based on the neighborhood context.

[0067] In the decoder of this method, the probability distribution of picking up the first arrival time of the P wave is also obtained through LSTM blocks, attention mechanisms and convolutional layers, and the point with the maximum probability is regarded as the picking time of the P wave.

[0068] (4) Use graph convolution to interact with nodes and edges in the graph;

[0069] According to the seismic phase information, the edges in the graph are constructed, and the absolute value of the difference in the first arrival time of the P wave between the two stations is calculated. At the same time, a threshold is set, which is set to 3 seconds (combined with the sampling frequency of 300 sampling points). When the difference between the two stations exceeds the threshold, no connection is made. Otherwise, an undirected edge is used to connect them, and the difference is used as the element value of the corresponding position in the adjacency matrix. Then, the adjacency matrix is ​​normalized for each row to complete the creation of the adjacency matrix. The calculated adjacency matrix is ​​used for graph convolution with the station node features. The formula is as follows:

[0070]

[0071] In the formula is the node feature matrix in the graph of the lth and l+1th layers in the graph convolution layer, is the adjacency matrix, plus the identity matrix I N Avoid having zero elements at the diagonal of the adjacency matrix. is the degree matrix of the adjacency matrix, which is used to normalize it, W (l) is a learnable parameter and σ(·) is an activation function.

[0072] According to the above formula, the graph convolution operation is performed, and the activation function uses ReLU(·)=max(0,·). At the same time, the learnable parameter matrix is ​​set to a square matrix, so that the dimension of the feature matrix will not be changed after the graph convolution. After the graph convolution, the interaction of the station node information is completed.

[0073] (5) Use transformer structure to aggregate graph nodes;

[0074] The transformer structure is used to aggregate the information of the platform nodes. It mainly consists of three parts: self-attention, feedforward neural network and layer normalization. The formula of the self-attention mechanism is as follows:

[0075] Q=W Q *X,K=W K *X,V=W V *X

[0076]

[0077] Where d k is the vector dimension, X is the node feature matrix, W Q , W K , W V is a learnable parameter matrix, Q, K, V are the query, key, and value in the attention mechanism, and softmax is the activation function.

[0078] First, the query Q, key value K and value V are calculated according to all station features, and then the attention score and output value are calculated. The feedforward neural network provides nonlinear transformation, and this operation is performed separately on the attention value sequence obtained in the previous step. The nonlinearization formula is shown in the following formula.

[0079] FFN(x)=GELU(xW1+b1)W2+b2

[0080]

[0081] Layer normalization is used to process sequence data and normalize individual sample sequences in a batch according to their sequence order. The process is shown in the following formula.

[0082]

[0083] In the formula, z (l) is the input of the lth layer of neurons, with dimension n (l) , μ (l) , σ (l) are its mean and variance, γ, β are learnable parameter vectors for scaling and translation, and ∈ is a small amount set to prevent the denominator from being zero.

[0084] In order to complete the aggregation, we refer to the method in the NLP field, treat the station node as a sequence, use the encoder part of the transformer structure, add a blank flag (Token) at the beginning of the input sequence, and use it as the feature vector representing all the information in the output sequence. Figure 4The steps in the figure go through a multi-head self-attention layer, a feed-forward network layer, and layer normalization to complete the aggregation of information in the figure.

[0085] (6) Use the mixed Gaussian model to fit and estimate the source parameters.

[0086] Gaussian mixture can theoretically simulate any probability density function, and its conditional probability is shown in the following formula.

[0087]

[0088] Where C is the number of mixed components, α c is the weight coefficient of each component, is the Gaussian distribution model of the component, μ c (x),σ c (x) is the mean and variance of the Gaussian distribution.

[0089] A mixed Gaussian density network is used as the output of the source parameter estimation result. The mixed density network (MDN) is a mixture of a deep neural network (DNN) and a distribution. The deep neural network provides parameters for multiple distributions, which are then mixed through some weights, which are also provided by it. The resulting conditional probability distribution helps model complex models in real-world data and helps better predict the possibility of certain values. Its structure is shown in the attached manual. Figure 5 shown.

[0090] The input is passed through the hidden layer DNN, and then through the fully connected layer to obtain the relevant parameters of the mixed Gaussian distribution. After mixing, the probability output model is obtained. The process is shown in the following formula:

[0091]

[0092] Where x is the input feature, H(x) is the hidden layer element, W, b are learnable weights and bias parameters, α(x) is the weight of different components in the mixture distribution, RELU, softmax are the corresponding activation functions, μ(x), σ(x) are the mean and variance of the Gaussian distribution.

[0093] The magnitude and position of the earthquake source are estimated respectively. For the estimation of the magnitude, the number of mixed Gaussian distribution components is set to 5, and the output is a mixed distribution parameter with a dimension of (5, 3). For the estimation of the position (three components of depth, longitude and latitude), the number of mixed Gaussian distribution components is set to 15. At the same time, since the position has three elements, the output dimension is a mixed distribution parameter with a dimension of (15, 7).

[0094] The model outputs the relevant parameters of the mixed Gaussian probability distribution. To obtain the results of the source parameters from a single data sample, the conditional mean must be derived from the probability density and calculated according to the following formula to obtain the results of the source parameter estimation.

[0095]

[0096] Where x is the input feature, α(x) is the weight of different components in the mixed distribution, μ(x) is the mean of the Gaussian distribution, is the conditional mean, p(y|x) is the conditional probability density distribution, and y is the distribution value of the earthquake source parameter variable predicted by the model.

[0097] The loss function of the model uses the average negative log-likelihood function to indirectly optimize the parameters of the mixed Gaussian probability distribution, as shown in the following formula:

[0098]

[0099] Where p(y|x) is the conditional probability density value, is the distribution range of the input variable x and the output predicted value y, and Θ is all the parameters that need to be estimated in the model.

[0100] The loss function is defined as follows when training the model. There are four components (magnitude, longitude, latitude, and focal depth) that need to be estimated. The number of Gaussian distributions in the magnitude mixed density network is 5, and the loss weight is 1. The number of Gaussian distributions in the position mixed density network is 15, and the loss weight is 0.3. Because the position has three components, they share the distribution weight, but the mean and variance of their Gaussian distributions are not the same.

[0101]

[0102] In the formula are the weight parameters for magnitude and location, y mag ,y lat ,y lon ,y depth are the true values ​​of earthquake source magnitude, latitude, longitude and depth, μ mag (x), μ lat (x), μ lon (x), μ depth (x) are the estimated mean values ​​of the Gaussian distributions of earthquake source magnitude, latitude, longitude and depth, respectively, and σ mag (x)σ lat (x),σ lon (x)σ depth (x) are the estimated values ​​of the variance of the Gaussian distribution of earthquake source magnitude, latitude, longitude and depth, respectively, and loss is the value of the loss function.

[0103] It should be noted that the above embodiments are merely preferred embodiments of the present invention and are not intended to limit the protection scope of the present invention. Equivalent replacements or substitutions made on the basis of the above technical solutions all fall within the protection scope of the present invention.

Claims

1. A multi-station earthquake source parameter estimation method based on graph theory, characterized by: The method comprises the following steps: Step 1: Apply convolutional neural network to extract waveform features on seismic station nodes; Step 2: Encode the longitude and latitude of the station; Step 3: Use the phase picking method to detect the first arrival time of the P wave at the station and convert it into the attributes of the edge in the graph; Step 4: Use graph convolution to interact with nodes and edges in the graph; Step 5: Use the transformer structure to aggregate graph nodes; Step 6: Use the mixed Gaussian density network to fit and estimate the source parameters; In step 1, the waveform features extracted by applying convolutional neural network to the seismic station nodes are: Assuming that the number of stations is N, the length of the intercepted waveform is T, and the sampling frequency is f, the input of each sample is (N, T*f, 3). Then, the convolution, pooling and multi-layer perceptron operations in the convolutional neural network are used to extract the features of the station node as (N, M), thereby obtaining a deeper expression of the seismic waveform data. The structure of the convolutional layer is shown in the following table: In step 2, the method for encoding the latitude, longitude and altitude of the platform node is sinusoidal position encoding. Assuming that k is one of the N platforms, the method for generating its position vector is: Where lat, lon, and depth are the latitude, longitude, and altitude values ​​of each station, respectively. lat , d lon , d depth are the vector dimensions for encoding assigned to the three position elements, i is the sequence number of the element in the position vector, and PE is the value of the position element encoded for each position component; The generated position matrix is ​​merged with the node feature matrix to add the position information to the node platform waveform information; In step 3, the phase picking method adopts the EQTransformer method; In step 4, the edges in the graph are constructed according to the seismic phase information, and the absolute value of the difference in the first arrival time of the P wave between the two stations is calculated. At the same time, a threshold is set, and the threshold is set to 3 seconds (combined with the sampling frequency of 300 sampling points). When the difference between the two stations exceeds the threshold, no connection is made. Otherwise, an undirected edge is used to connect them, and the difference is used as the element value of the corresponding position in the adjacency matrix. Then, the adjacency matrix is ​​normalized per row to complete the creation of the adjacency matrix. The adjacency matrix is ​​calculated and used for graph convolution with the station node features. The formula is as follows: In the formula It is the first convolutional layer in the graph l，l+1 The node feature matrix of the layer graph, is the adjacency matrix, plus the identity matrix I N Avoid having zero elements at the diagonal of the adjacency matrix. is the degree matrix of the adjacency matrix, which is used to normalize it, W (l) is the learnable parameter of the lth layer of graph convolution, σ(·) is the activation function; According to the above formula, the graph convolution operation is performed, and the activation function uses ReLU(·)=max(0,·). At the same time, the learnable parameter matrix is ​​set to a square matrix. The dimension of the feature matrix will not be changed after the graph convolution. After the graph convolution, the interaction of the station node information is completed; In step 5, the transformer structure is used to aggregate the platform node information, which mainly consists of three parts: self-attention, feedforward neural network and layer normalization; the formula of the self-attention mechanism is as follows: Q=W Q *X,K=W K *X,V=W V *X Where d k is the vector dimension, X is the node feature matrix, W Q , W K , W V is a learnable parameter matrix, Q, K, V are the query, key and value in the attention mechanism, and softmax is the activation function; the query Q, key K and value V are calculated according to all station features, and then the attention score and output value are calculated; The feedforward neural network provides nonlinear transformation, which is performed separately on the attention value sequence obtained in the previous step. The nonlinearization formula is as follows: FFN(x)=GELU(xW1+b1)W2+b2 Where W1, W2, b1, n2 are learnable weights and bias parameters, respectively, and x is the feature vector of each position element in the input sequence; Layer normalization is used to process sequence data and normalize the individual sample sequences in the batch according to their sequence order. The process is shown in the following formula: In the formula, z (l) is the input of the lth layer of neurons, with dimension n (l) , μ (l) , σ (l) is its mean and variance, γ, β are the learnable parameter vectors of scaling and translation, ∈ is a small amount set to prevent the denominator from being zero; Treat the station node as a sequence, use the encoder part of the transformer structure, add a blank flag (Token) at the beginning of the input sequence, and use it as the feature vector representing all the information in the output sequence; the input sequence with token added is passed through the multi-head self-attention layer, feedforward network layer and layer normalization in sequence to complete the information aggregation; In step 6, a mixed Gaussian density network is used as the result output of the source parameter estimation, the input is passed through the hidden layer DNN, and then the relevant parameters of the mixed Gaussian distribution are obtained through the fully connected layer. After mixing, a probability output model is obtained. The process is shown in the following formula: H(x)=RELU(W T x+b,0) Where x is the input feature, H(x) is the hidden layer element, W, b are learnable weights and bias parameters, α(x) is the weight of different components in the mixed distribution, RELU, softmax are the corresponding activation functions, μ(x), σ(x) are the mean and variance of the Gaussian distribution; The magnitude and position of the earthquake source are estimated respectively. For the magnitude estimation, the number of mixed Gaussian distribution components is set to 5, and the output is a mixed distribution parameter with a dimension of (5, 3). For the estimation of the three components of depth, longitude, and latitude, the number of mixed Gaussian distribution components is set to 15. At the same time, since the position has three elements, the output dimension is a mixed distribution parameter with a dimension of (15, 7); The output of the model is the related parameters of the mixed Gaussian probability distribution. To obtain the results of the earthquake source parameters from a single data sample, the conditional mean must be derived from the probability density and calculated according to the following formula to obtain the results of the earthquake source parameter estimation; Where x is the input feature, α(x) is the weight of different components in the mixed distribution, μ(x) is the mean of the Gaussian distribution, is the conditional mean, p(y|x) is the conditional probability density distribution, and y is the distribution value of the earthquake source parameter variable predicted by the model.

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