Prediction method of focal depth and epicenter distance based on physical information neural network

Abstract

The present invention is a method for predicting focal depth and epicentral distance based on physical information neural network, which is to solve the technical problems of low prediction accuracy of focal depth and epicentral distance and poor interpretability of data-driven network. Method for predicting focal depth and epicentral distance: 1. Select three-component seismic motion records in the data set as input parameters, and the corresponding focal depth and epicentral distance are label parameters; 2. Establish a deep neural network including convolutional layers and residual blocks, use linear rectification function as activation function, use Adam adaptive optimizer for back propagation, and combine mean square error function and seismic wave travel time difference equation as loss function; 3. Train the deep neural network model; 4. Predict focal depth and epicentral distance. The present invention adopts a deep neural network that incorporates physical information, which can not only improve the prediction accuracy, but also make the deep neural network model have a certain interpretability, thereby improving the prediction accuracy.

Description

Technical Field

[0001] The invention belongs to the field of seismology, and in particular relates to a method for predicting earthquake source depth and epicenter distance based on a physical information neural network. Background Art

[0002] Earthquakes are frequent and highly destructive disasters. The losses caused by each major earthquake are not to be underestimated. In order to reduce the losses caused by earthquakes, timely prediction of the location of the epicenter is the most important measure. The accurate location of the epicenter lays the foundation for assessing the degree of disaster in different regions and deploying earthquake relief work.

[0003] At present, the traditional prediction method is mainly to use the seismic wave travel time equation to invert the arrival time of the P wave and S wave picked up in the seismic motion record. Since the arrival time of the seismic phase and the soil velocity model in the equation are highly uncertain, and the inversion is nonlinear, this method has low prediction accuracy and large calculation amount.

[0004] In recent years, with the development of computer technology and artificial intelligence, neural networks have achieved good results in data regression and nonlinear inversion. However, data-driven neural networks generally have problems of poor interpretability and weak generalization ability. Therefore, a method for predicting focal depth and epicentral distance based on physical information neural network is proposed. Summary of the invention

[0005] The purpose of the present invention is to solve the technical problems of low prediction accuracy of focal depth and epicenter distance and poor interpretability of data-driven network, and to provide a method for predicting focal depth and epicenter distance based on physical information neural network.

[0006] The method for predicting focal depth and epicenter distance based on physical information neural network of the present invention is implemented according to the following steps:

[0007] Step 1: Collect earthquake records and build a data set:

[0008] The arrival time of P-wave and S-wave, focal depth and epicenter distance given in the database are used as label values ​​corresponding to the seismic motion data to obtain the focal position inversion data set;

[0009] Step 2: Build a deep neural network that incorporates physical information:

[0010] The deep neural network includes multiple inputs, N network blocks for predicting epicentral distances and N network blocks for predicting focal depths. The input data are N three-component earthquake motion records recorded by N stations. The network blocks for predicting epicentral distances and the network blocks for predicting focal depths have the same architecture, wherein the network blocks for predicting epicentral distances include multiple convolutional layers, multiple maximum pooling layers, multiple residual blocks, flattening layers and fully connected layers. The convolutional layers use 1D convolutions and use a linear rectifier function (ReLU) as an activation function. A batch normalization layer is added after each convolutional layer. The residual block includes two 1D convolutional layers and a batch normalization layer. A batch normalization layer is connected after each 1D convolutional layer and uses a ReLU activation function.

[0011] The mean square error function (MSE) and the seismic wave travel time difference equation are combined as the loss function to obtain a deep neural network that incorporates physical information.

[0012] Step 3: Deep neural network model training:

[0013] The deep neural network incorporating physical information is trained using the earthquake source location inversion dataset, and the training accuracy is ensured by using the loss function and the mean absolute error function (MAE), so that the loss function gradually decreases and the trained deep neural network model is obtained.

[0014] Step 4: Prediction of focal depth and epicenter distance:

[0015] Input the three-component earthquake motion records and the arrival times of P waves and S waves into the deep neural network model trained in step 3, and output the focal depth and epicenter distance, so as to realize the prediction of the focal depth and epicenter distance;

[0016] The loss function of the seismic wave travel time difference equation in step 2 is as follows:

[0017]

[0018] Where: MSE Loss,h : Mean square error loss function of focal depth;

[0019] MSE Loss,d : Mean square error loss function of epicenter distance;

[0020] Tps actual,i : The true value of the time difference between the P wave and the S wave picked up at the i-th station;

[0021] Tps predict,i : The arrival time difference of P wave and S wave calculated at the i-th station according to the predicted focal depth and epicenter distance;

[0022] n: the amount of data contained in a batch;

[0023] N: The number of stations required for network prediction.

[0024] The present invention selected 7316 three-component earthquake records from the Southern California region (STEAD database) and proposed a deep neural network that incorporates physical information to predict epicenter distance and focal depth. The network uses multi-layer convolutional layers to extract features from earthquake records and adds multiple residual block structures to improve network depth while avoiding network degradation and gradient disappearance. The present invention also adds the travel time difference equation of P waves and S waves to the loss function of network training, and uses physical information to constrain the network, which avoids the problem of insufficient interpretability of traditional data-driven networks to a certain extent and improves the generalization performance of the network.

[0025] Compared with the traditional inversion method, the prediction method of focal depth and epicenter distance based on physical information neural network of the present invention has high calculation efficiency and high degree of automation. Compared with the current data-driven neural network method, the present invention has higher accuracy and certain interpretability. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 This is the distribution map of the selected earthquake epicenters and stations, where the yellow circle represents the epicenter of the earthquake and the red triangle represents the station;

[0027] Figure 2 The distribution diagram of focal depth and epicenter distance in the dataset;

[0028] Figure 3 : is a residual block structure diagram of the network in the embodiment, in which A represents a 1D convolutional layer, B represents a ReLU activation function, and C represents a batch normalization layer;

[0029] Figure 4 A schematic diagram of the derivation of the travel time equation of a seismic wave in the embodiment;

[0030] Figure 5 This is a diagram of the overall architecture of the deep neural network in the embodiment, where 1 represents a network block for predicting focal depth, and 2 represents a network block for predicting epicenter distance;

[0031] Figure 6 Schematic diagram of network blocks and various network layers in a deep neural network in an embodiment, where ● represents a ReLU activation function and ★ represents a batch normalization layer;

[0032] Figure 7 This is a comparison chart of the loss reduction of the validation set under different Dropout ratios in the embodiment;

[0033] Figure 8 It is a distribution diagram of focal depth and prediction error of the deep neural network model in the embodiment on the test set;

[0034] Fig. 9 This is a distribution diagram of epicenter distance and prediction error of the deep neural network model in the embodiment on the test set. DETAILED DESCRIPTION

[0035] Specific implementation method 1: The method for predicting focal depth and epicenter distance based on physical information neural network in this implementation method is implemented according to the following steps:

[0036] Step 1: Collect earthquake records and build a data set:

[0037] The arrival time of P-wave and S-wave, focal depth and epicenter distance given in the database are used as label values ​​corresponding to the seismic motion data to obtain the focal position inversion data set;

[0038] Step 2: Build a deep neural network that incorporates physical information:

[0039] The deep neural network includes multiple inputs, N network blocks for predicting epicentral distances and N network blocks for predicting focal depths. The input data are N three-component earthquake motion records recorded by N stations. The network blocks for predicting epicentral distances and the network blocks for predicting focal depths have the same architecture, wherein the network blocks for predicting epicentral distances include multiple convolutional layers, multiple maximum pooling layers, multiple residual blocks, flattening layers and fully connected layers. The convolutional layers use 1D convolutions and use a linear rectifier function (ReLU) as an activation function. A batch normalization layer is added after each convolutional layer. The residual block includes two 1D convolutional layers and a batch normalization layer. A batch normalization layer is connected after each 1D convolutional layer and uses a ReLU activation function.

[0040] The mean square error function and the seismic wave travel time difference equation are combined as the loss function to obtain a deep neural network that incorporates physical information.

[0041] Step 3: Deep neural network model training:

[0042] The deep neural network incorporating physical information is trained using the earthquake source location inversion dataset, and the training accuracy is ensured by using the loss function and the mean absolute error function (MAE), so that the loss function gradually decreases and the trained deep neural network model is obtained.

[0043] Step 4: Prediction of focal depth and epicenter distance:

[0044] Input the three-component earthquake motion records and the arrival times of P waves and S waves into the deep neural network model trained in step 3, and output the focal depth and epicenter distance, so as to realize the prediction of the focal depth and epicenter distance;

[0045] The loss function of the seismic wave travel time difference equation in step 2 is as follows:

[0046]

[0047] Where: MSE Loss,h : Mean square error loss function of focal depth;

[0048] MSE Loss,d : Mean square error loss function of epicenter distance;

[0049] Tps actual,i : The true value of the time difference between the P wave and the S wave picked up at the i-th station;

[0050] Tps predict,i : The arrival time difference of P wave and S wave calculated at the i-th station according to the predicted focal depth and epicenter distance;

[0051] n: the amount of data contained in a batch;

[0052] N: The number of stations required for network prediction.

[0053] Compared with the traditional inversion method, the prediction method of focal depth and epicenter distance based on physical information neural network in this embodiment has high calculation efficiency and high degree of automation. Compared with the current data-driven neural network method, the present invention has higher accuracy and certain interpretability.

[0054] Specific implementation method 2: The difference between this implementation method and specific implementation method 1 is that the earthquake record in step 1 is selected from the STEAD database.

[0055] Specific implementation method three: This implementation method is different from specific implementation methods one or two in that in step one, seismic data are selected according to the criteria that the epicenter distance does not exceed 100 km and the signal-to-noise ratio is greater than 25.

[0056] Specific implementation method four: The difference between this implementation method and any one of specific implementation methods one to three is that the network block for predicting the epicenter distance in step two includes 7 convolutional layers, 4 maximum pooling layers, 3 residual blocks, a flattening layer and 1 fully connected layer, and the first convolutional layer, the second convolutional layer, the first maximum pooling layer, the third convolutional layer, the first residual block, the second maximum pooling layer, the fourth convolutional layer, the second residual block, the third maximum pooling layer, the fifth convolutional layer, the third residual block, the fourth maximum pooling layer, the sixth convolutional layer, the seventh convolutional layer, the flattening layer and the fully connected layer are connected in sequence.

[0057] Specific implementation mode five: This implementation mode is different from specific implementation mode four in that the fully connected layer contains 512 neurons.

[0058] Specific implementation method six: The difference between this implementation method and any one of specific implementation methods one to five is that in step two, the output data of the N network blocks for predicting focal depths are connected into a group using the concatenate function and then input into a fully connected layer, and then connected to an output layer.

[0059] Specific implementation method seven: The difference between this implementation method and any one of specific implementation methods one to six is ​​that the output data of each network block for predicting epicenter distance in step two is respectively input into a fully connected layer containing 512 neurons.

[0060] The output data of this embodiment are respectively input into a fully connected layer containing 512 neurons, and then input into N output layers to obtain the predicted epicenter distances corresponding to N stations.

[0061] Specific implementation eight: This implementation is different from specific implementations one to seven in that the expression of the seismic wave travel time equation described in step two is as follows:

[0062]

[0063]

[0064] Where: Δ—distance from the epicenter; T—wave propagation time from the earthquake source to the station; d z —The distance from the earthquake source to the top of the earthquake source layer; θ j —The exit angle of the jth layer where the earthquake source is located; V j —wave velocity of the jth layer; d l —thickness of the first layer; V l —wave velocity of the lth layer; l—the lth layer of the soil layer velocity model, j—the jth layer of the soil layer velocity model.

[0065] Specific implementation method 9: The difference between this implementation method and any one of specific implementation methods 1 to 8 is that the Dropout layer ratio in the training process in step 3 is 30% to 50%.

[0066] In this embodiment, the 30% ratio with the highest test accuracy is used as the ratio of the Dropout layer in the final network model.

[0067] Specific implementation ten: The difference between this implementation and any one of specific implementations one to nine is that the batch size (Batchsize) of the deep neural network model after training in step three is 16, the training round (Epoch) is 60, the initial learning rate is 0.001, and every 20 epochs, the learning rate is reduced to one tenth of the original.

[0068] Embodiment: The method for predicting focal depth and epicenter distance based on physical information neural network in this embodiment is implemented according to the following steps:

[0069] Step 1: Collect earthquake records and build a data set:

[0070] In the STEAD database, 7316 three-component seismic data recorded by four seismic stations were selected according to the selection criteria of epicentral distance less than 100km and signal-to-noise ratio greater than 25. The P-wave and S-wave picking time, focal depth and epicentral distance given in the database were used as the label values ​​corresponding to the seismic data to obtain the source position inversion data set. Each seismic data was subjected to 1-40Hz bandpass filtering using an eighth-order Butterworth bandpass filter to remove the influence of abnormal noise. The filtered data was intercepted from 2s before to 28s after the P wave, and then the intercepted data was normalized as the final network input data;

[0071] The formula of the normalization method is as follows:

[0072]

[0073] Where: x * : Normalized data; x max : Maximum value of data; x min : minimum value of data; x: data before normalization;

[0074] Step 2: Divide the data set;

[0075] The earthquake motion dataset is randomly divided into training set, validation set and test set, and the ratio of training set, validation set and test set is 7:1.5:1.5;

[0076] Step 3: Build a deep neural network that incorporates physical information:

[0077] The deep neural network includes four input networks, four network blocks for predicting epicentral distances and four network blocks for predicting focal depths. The input data are four three-component earthquake motion records recorded by four stations. The network block for predicting epicentral distances has the same architecture as the network block for predicting focal depths. The network block for predicting epicentral distances includes 7 convolutional layers, 4 maximum pooling layers, 3 residual blocks, a flattening layer and 1 fully connected layer. The first convolutional layer, the second convolutional layer, the first maximum pooling layer, the third convolutional layer, the first residual block, the second maximum pooling layer, the fourth convolutional layer, the second residual block, the third maximum pooling layer, the fifth convolutional layer , the third residual block, the fourth maximum pooling layer, the sixth convolutional layer, the seventh convolutional layer, the flattening layer and the fully connected layer are connected in sequence, a batch normalization layer is added after each convolutional layer, the number of convolution kernels of the 7 convolutional layers gradually increases, and the number of convolution kernels from the first convolutional layer to the seventh convolutional layer is 3, 4, 8, 16, 32, 32, 32 respectively; the linear rectification function (ReLU) is used as the activation function, and a batch normalization layer is added after each convolutional layer; the residual block contains two 1D convolutional layers and a batch normalization layer, and a batch normalization layer is connected after each 1D convolutional layer, using the ReLU activation function;

[0078] Four three-component earthquake motion data recorded by four stations were used as the input of the main network, and the focal depth and four epicentral distances corresponding to the four stations were output. The network used the Adam adaptive optimization function for back propagation, and the mean square error function (MSE) and the seismic wave travel time difference equation were combined with a weight of 50:1 as the loss function. The mean absolute error function (MAE), error standard deviation (SD) and determination coefficient (R 2 ) is used as the evaluation index to obtain a deep neural network that incorporates physical information;

[0079] Step 4: Deep neural network model training:

[0080] The deep neural network model is trained, mainly using the loss function and mean absolute error function (MAE) to ensure training accuracy. The batch size (Batchsize) of the network model is 16, the training round (Epoch) is 60, the initial learning rate is 0.001, and every 20 epochs, the learning rate is reduced to one tenth of the original, and a trained physical information neural network model is obtained;

[0081] Step 5: Prediction of focal depth and epicenter distance:

[0082] The three-component seismic motion records and the arrival times of P waves and S waves are input into the deep neural network model trained in step 4, and the focal depth and epicenter distance are output, thereby realizing the prediction of the focal depth and epicenter distance.

[0083] The loss function selected in this embodiment is a combination of MSE loss and seismic wave travel time equation, and the specific form is as follows:

[0084]

[0085] Where: MSE Loss,h : Mean square error loss function of focal depth;

[0086] MSE Loss,d : Mean square error loss function of epicenter distance;

[0087] Tps actual,i : The true value of the time difference between the P wave and the S wave picked up at the i-th station;

[0088] Tps predict,i : The arrival time difference of P wave and S wave calculated at the i-th station according to the predicted focal depth and epicenter distance;

[0089] n: The amount of data contained in a batch.

[0090] In step three of this embodiment, the output data of the four network blocks for predicting focal depth are connected into a group using the concatenate function and then input into a fully connected layer containing 2048 neurons, and then connected to an output layer, which is the predicted focal depth.

[0091] The equation for calculating the travel time of seismic waves uses the tomographic velocity model of the Southern California region constructed by Kamer. The soil stratification and the wave velocity of each layer are shown in Table 1:

[0092] Table 1 Velocity model for Southern California

[0093]

[0094] With the development of computer technology and deep learning, earthquake data has gradually increased, the number of neural network layers has gradually increased, and the nonlinear fitting ability has become stronger and stronger. Various network models have been used for the inversion of earthquake source locations. However, the network is based on data-driven and ignores the inherent physical mechanism, making the network lack of interpretability. The present invention compares the current deep learning model. The comparison results are shown in Table 2. The deep neural network model trained in this embodiment performs better. The MAE in the table dep and MAE dis are the mean absolute errors of focal depth prediction and epicenter distance prediction, SD dep and SD dis Represents the standard deviation of the residuals of focal depth prediction and epicenter distance prediction, m dis Represents the mean of the residual errors of the epicentral distance predictions.

[0095] Table 2 Comparison of prediction results between the present invention and the current deep learning model

[0096]

[0097] *Ristea in the table represents the deep learning model mentioned in the paper published by Ristea in 2021 titled Complex neural networks forestimating epicentral distance, depth, and magnitude of seismic waves.

Claims

1. A method for predicting focal depth and epicenter distance based on physical information neural network, Features The prediction method is implemented according to the following steps: Step 1: Collect earthquake records and build a data set: The arrival time of P-wave and S-wave, focal depth and epicenter distance given in the database are used as label values ​​corresponding to the seismic motion data to obtain the focal position inversion data set; Step 2: Build a deep neural network that incorporates physical information: The deep neural network includes multiple inputs, N network blocks for predicting epicentral distances and N network blocks for predicting focal depths. The input data is N three-component earthquake motion records recorded by N stations. The network block for predicting epicentral distances and the network block for predicting focal depths have the same architecture, wherein the network block for predicting epicentral distances includes multiple convolutional layers, multiple maximum pooling layers, multiple residual blocks, flattening layers and fully connected layers. The convolutional layer uses 1D convolution, uses a linear rectification function as an activation function, and adds a batch normalization layer after each convolutional layer; wherein the residual block contains two 1D convolutional layers and a batch normalization layer, and a batch normalization layer is connected after each 1D convolutional layer, and a ReLU activation function is used; The mean square error function and the seismic wave travel time difference equation are combined as the loss function to obtain a deep neural network that incorporates physical information. Step 3: Deep neural network model training: The deep neural network incorporating physical information is trained using the earthquake source location inversion data set, and the training accuracy is ensured by using the loss function and the mean absolute error function, so that the loss function gradually decreases and the trained deep neural network model is obtained. Step 4: Prediction of focal depth and epicenter distance: Input the three-component earthquake motion records and the arrival times of P waves and S waves into the deep neural network model trained in step 3, and output the focal depth and epicenter distance, so as to realize the prediction of focal depth and epicenter distance; The loss function of the seismic wave travel time difference equation in step 2 is as follows: Where: MSE Loss,h : Mean square error loss function of focal depth; MSE Loss,d : Mean square error loss function of epicenter distance; Tps actual,i : The true value of the time difference between the P wave and the S wave picked up at the i-th station; Tps predict,i : The arrival time difference of P wave and S wave calculated at the i-th station according to the predicted focal depth and epicenter distance; n: the amount of data contained in a batch; N: The number of stations required for network prediction.

2. The method for predicting focal depth and epicenter distance based on physical information neural network according to claim 1, Features The ground motion records in step 1 are selected from the STEAD database.

3. The method for predicting focal depth and epicenter distance based on physical information neural network according to claim 2, Features In step 1, seismic data are selected according to the criteria that the epicenter distance does not exceed 100 km and the signal-to-noise ratio is greater than 25.

4. The method for predicting focal depth and epicenter distance based on physical information neural network according to claim 1, Features The network block for predicting the epicenter distance in step 2 includes 7 convolutional layers, 4 maximum pooling layers, 3 residual blocks, a flattening layer and 1 fully connected layer. The first convolutional layer, the second convolutional layer, the first maximum pooling layer, the third convolutional layer, the first residual block, the second maximum pooling layer, the fourth convolutional layer, the second residual block, the third maximum pooling layer, the fifth convolutional layer, the third residual block, the fourth maximum pooling layer, the sixth convolutional layer, the seventh convolutional layer, the flattening layer and the fully connected layer are connected in sequence.

5. The method for predicting focal depth and epicenter distance based on physical information neural network according to claim 4, Features The fully connected layer contains 512 neurons.

6. The method for predicting focal depth and epicenter distance based on physical information neural network according to claim 1, Features In step 2, the output data of the N network blocks for predicting focal depths are connected into a group using the concatenate function and then input into the fully connected layer, and then connected to an output layer.

7. The method for predicting focal depth and epicenter distance based on physical information neural network according to claim 1, Features The output data of each network block for predicting epicenter distance in step 2 is input into a fully connected layer containing 512 neurons.

8. The method for predicting focal depth and epicenter distance based on physical information neural network according to claim 1, Features The expression of the seismic wave travel time equation described in step 2 is as follows: Where: Δ—distance from the epicenter; T—wave propagation time from the earthquake source to the station; d z —The distance from the earthquake source to the top of the earthquake source layer; θ j —The exit angle of the jth layer where the earthquake source is located; V j —wave velocity of the jth layer; d l —thickness of the first layer; V l —wave velocity of the lth layer; l—the lth layer of the soil layer velocity model, j—the jth layer of the soil layer velocity model.

9. The method for predicting focal depth and epicenter distance based on physical information neural network according to claim 1, Features The Dropout layer ratio during the training process in step 3 is 30% to 50%.

10. The method for predicting focal depth and epicenter distance based on physical information neural network according to claim 1, Features The batch size of the deep neural network model after training in step 3 is 16, the training rounds are 60, the initial learning rate is 0.001, and the learning rate is reduced to one tenth of the original every 20 epochs.

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