A novel method for constructing earthquake prediction models

Abstract

This invention discloses a novel method for constructing an earthquake prediction model, named the CL-ETAS model, belonging to the fields of mathematics and computer science. By studying the respective advantages of the ETAS model, which relies on empirical earthquake patterns, and the Convolutional Long Short-Term Memory (ConvLSTM) deep learning model applied to spatiotemporal sequence prediction, this invention proposes a novel composite model, called the CL-ETAS model. This model outperforms both the ETAS model and ConvLSTM in predicting the number, magnitude, and spatial distribution of earthquake events. This invention provides a novel, effective, and universal solution to the earthquake prediction problem, possessing significant theoretical research value and high potential for widespread application.

Description

TECHNICAL FIELD

[0001] The application discloses a new method for constructing a seismic prediction model, and belongs to the fields of mathematics and computer science. BACKGROUND

[0002] Earthquakes are one of the most destructive natural disasters on Earth, posing a significant threat to people's lives and property. The scientific community has been actively researching earthquake prediction, but there is still limited understanding in this field. Unlike natural phenomena such as rainfall or hurricanes, which can be accurately predicted to some extent, there is currently no unified mechanism to predict when and where the next major earthquake will occur. The scientific community has different views on earthquake prediction. Some studies show that earthquakes cannot be reliably predicted, while other studies propose various methods to predict future seismic events.

[0003] Some people have tried to predict earthquakes using diagnostic precursors through some observable signals, but so far there has been no successful and reliable prediction scheme. Currently, earthquake prediction is mainly based on established laws of earthquakes. Among them, the ETAS model is the most commonly used, which incorporates Gutenberg-Richter law, Utsu law and Omori law into the Hawkes process. In this model, earthquakes above a certain magnitude that have occurred in the past trigger subsequent earthquakes according to the same law. Through proof, the ETAS model is superior to other models in terms of prediction accuracy, but still has limitations in explaining some basic characteristics of earthquakes. In addition, the statistical physical characteristics related to seismic activity still need to be explored.

[0004] The development of artificial intelligence and big data has attracted widespread attention in various industries, among which machine learning is one of the fastest growing technologies worldwide; in geological and earth science research, earthquake prediction has been one of the most challenging problems; since the 1990s, machine learning has been used for earthquake prediction. In recent years, many successful deep learning models have made significant breakthroughs in earthquake prediction, mainly using convolutional neural networks (CNN) and long short-term memory networks (LSTM); based on CNN and LSTM, a ConvLSTM framework combining the two models is proposed; ConvLSTM is more accurate than other deep learning models for earthquake prediction, but there is still room for improvement.

[0005] Currently, most earthquake prediction models rely solely on statistical models or deep learning models. Some studies consider deep learning models trained by the intensity function of the ETAS model; however, they ignore real earthquake catalogs to train the model; therefore, the present application proposes a new type of earthquake prediction model called CL-ETAS, which has important theoretical research significance and high application value. SUMMARY

[0006] The object of the present application is to provide a new method for constructing a seismic prediction model, which combines an epidemic-type aftershock sequence (ETAS) model and a deep learning model to obtain a new seismic prediction model, named CL-ETAS model, and specifically comprises the following steps:

[0007] (1) Using the ETAS model to generate combined data as a training set: using the first day of historical data to predict the second day of data using the ETAS model, repeating several times to obtain multiple ETAS model prediction results, and using the first day of real data plus the second day of data predicted by ETAS, the resulting combined data is a training prediction model required for the third day, and new combined data is continuously produced in sequence as time goes on.

[0008] (2) Data preprocessing: renumbering and combining these new combined data into a matrix as a training set; specifically, the rows of the matrix represent spatial data, i.e. longitude and latitude, and the columns of the matrix represent magnitude data, and then the matrix is arranged in chronological order to produce processed spatio-temporal matrix data.

[0009] (3) Training model: repeat the above data generation and data preprocessing process, input and start training ConvLSTM, and finally obtain the trained model, which is the CL-ETAS model.

[0010] The ETAS model described in the present application combines Gutenberg-Richter, Usoskin and Omori laws into the Hawkes (point) process, so that each earthquake (above a certain magnitude) in the past will trigger other earthquakes according to the same law.

[0011] The ETAS model in step (1) of the present application is a conventional model, which assumes that the earthquake event is a spatio-temporal random point process, in which each aftershock can trigger further aftershocks; each event above a certain magnitude is independently selected from the Gutenberg-Richter distribution; the conditional probability λ at location x, y and time t is given by the following formula, which can be represented by the following formula:

[0012]

[0013] In the formula: λ is the conditional probability; x and y are spatial positions; t is the time; H t is the historical process; μ is the background intensity; t i is the time of past events; k(M i ) is the dependence of triggering ability on magnitude; M i is the magnitude of past events; g(t-t i ) follows the Omori law; f(x-x i ,y-y i ,M i) for spatial kernel function.

[0014] The dependence of triggering capability on magnitude is given by the Utsu law:

[0015] k(M i ) = A exp(a(M i -M w )) (2)

[0016] where: A - the seismicity rate at zero lag; M w - the magnitude threshold of the earthquake; a - the productivity parameter.

[0017] g(t-t i ) follows the Omori law:

[0018]

[0019] where: c, p - the parameters of the Omori law;

[0020] The spatial clustering of aftershocks is achieved by introducing a spatial kernel function f(x-x i ,y-y i ,M i ):

[0021]

[0022] ζ = D exp[γ m (M i -M w )] (4)

[0023] where: ζ - represents the distance between the triggering event and the triggered event depends on the size of the triggering event; q, D, γ m - the estimated parameters.

[0024] Preferably, the ConvLSTM in step (3) of the present application can be expressed as follows:

[0025]

[0026]

[0027]

[0028]

[0029] H t = o t tanh(C t )

[0030] where: t - time; t-1 - the last time; i t— is the input gate at time t; f t — is the forget gate at time t; o t — is the output gate at time t; C t — is the cell state at time t; C t-1 — is the cell state at time t-1; H t — is the hidden state at time t; H t-1 — is the hidden state at time t-1; b i ,b f ,b c ,b o — are respectively the input gate bias, the forget gate bias, the cell state bias, the output gate bias; W xi ,W hi ,W ci — are respectively the feature number weight of the input gate, the hidden state weight, the cell state weight; W xf ,W hf ,W cf — are respectively the feature number weight of the forget gate, the hidden state weight, the cell state weight; W xc ,W hc — are respectively the feature number weight of the cell state, the hidden state weight; W xo ,W ho ,W co — are respectively the feature number weight of the output gate, the hidden state weight, the cell state weight; X t — is the number of input features at time t; σ— sigmoid activation function; tanh— is the activation function; *— is the convolution operation; — is the Hadamard product.

[0031] Advantages of the present application:

[0032] (1) The method of the present application combines a statistical model and a deep learning model to propose a novel model, which greatly improves and enhances the prediction of the number of earthquakes, magnitude and spatial distribution.

[0033] (2) The method of the present application provides a novel, effective and general solution to the problem of earthquake prediction, which has important theoretical research significance and high application value. BRIEF DESCRIPTION OF DRAWINGS

[0034] Figure 1 is the process flowchart of the present application;

[0035] Figure 2 Cumulative function prediction comparison chart of the number of earthquakes;

[0036] Figure 3 Comparison chart of predicting the magnitude and spatial distribution of earthquakes within one day;

[0037] Figure 4 Comparison chart of predicted earthquake magnitude and spatial distribution within fifteen days;

[0038] Figure 5 Comparison chart of predicted earthquake magnitude and spatial distribution within thirty days;

[0039] Figure 6 Comparison chart of three models for predicting earthquake situation within one day using pycsep;

[0040] Figure 7 Comparison chart of three models for predicting earthquake situation within fifteen days using pycsep;

[0041] Figure 8 Comparison chart of three models for predicting earthquake situation within thirty days using pycsep. DETAILED DESCRIPTION

[0042] The present application will be further described in conjunction with specific embodiments, but the scope of protection of the present application is not limited to the described content.

[0043] According to the data of the United States Geological Survey (USGS), based on the geological characteristics of southern California, a major earthquake with a magnitude of 7 or more occurs about once every ten years; therefore, this embodiment selects 3 main earthquakes occurring from 1999 to 2019 as experimental objects; which includes the Hector Mine earthquake in 1999, the Lower California earthquake in 2010 and the Ridgecrest earthquake in 2019.

[0044] The data set used in this embodiment is the earthquake catalog of the southern California region, covering the period from 1981 to 2022, which can be downloaded from SCEDC (Southern California Earthquake Data Center, https: / / scedc.caltech.edu / data / alt-2011-dd-hauksson-yang-shearer.html); it is worth noting that this data set only contains earthquake events, quarry explosions and other irrelevant events have been deleted; in this study, only 15,534 earthquakes with a magnitude of 3 or more are considered as valid data, because the detection capability of the seismic network is weak, earthquakes below 3 may be missed.

[0045] Preprocessing of data

[0046] Before starting training the model, the 15,534 earthquake catalog data downloaded from SCEDC need to be reprocessed, because the ConvLSTM model is suitable for the prediction of spatio-temporal sequences, so the input data need to be processed into a series of matrix data. As part of the training set, the earthquake catalog data from 1981 to 1999 is selected. From the original earthquake catalog data, relevant attributes such as magnitude, longitude, latitude, and time are extracted, and these data are combined to form each individual matrix; specifically, the rows of the processed matrix represent the spatial distribution, i.e. the longitude and latitude, starting from 30°N and -122°W, with a degree interval of 2 degrees; the columns of the matrix represent the magnitude distribution, with the first four starting from 3 degrees and a magnitude interval of 0.5 degrees; the last one represents the magnitude greater than or equal to 5 degrees (this is done because the number of earthquakes above 5 degrees is small); therefore, each matrix represents the number of earthquakes occurring in a certain region within a day and within a certain magnitude range, i.e. each element in the matrix represents the number of earthquakes occurring in a certain spatial region and within a certain magnitude range; then the matrix is arranged in chronological order to generate the processed spatio-temporal matrix data; finally, the training set used in this experiment consists of 3263 matrices, each with a size of 5x20.

[0047] Parameter selection for ETAS model:

[0048] Based on the R language package "ETAS" model, Zhuang, Ogata and Vere-Jones introduced the random declustering method to fit the parameters of the ETAS model, and the following parameters were selected: A = 10.73047, a = 1.124465, M w = 3, mu = 0.2554078, P = 1.065735, c = 0.003961263, q = 1.378174, D = 0.001658387, gamma m = 0.8093304.

[0049] Selection of ConvLSTM structure:

[0050] The network selected by the present application is a ConvLSTM architecture composed of four ConvLSTM2D layers, which can be used for prediction and classification tasks; each ConvLSTM2D layer contains 40 filters with a size of 3x3; the first layer has a specified input shape, and the last layer adds a Conv3D layer to ensure that the output shape corresponds to the input shape; the present application deliberately selects a relatively simple network structure for this experiment to prove that the model trained using the training process described in this paper exhibits excellent generalization performance.

[0051] Prediction using ETAS model:

[0052] The ETAS model can directly use the real earthquake catalog for prediction, and in this application, the parameters are adjusted for prediction, and the prediction results include the three major earthquakes mentioned above, the Hector Mine earthquake in 1999, the Baja California earthquake in 2010 and the Ridgecrest earthquake in 2019, each of which is predicted for thirty days after the main shock.

[0053] Train ConvLSTM and use it for prediction:

[0054] The processed real earthquake catalog matrix data described above is input into ConvLSTM for training, and then the trained model is obtained and used for prediction, and the prediction results include the three major earthquakes mentioned above, the Hector Mine earthquake in 1999, the Baja California earthquake in 2010 and the Ridgecrest earthquake in 2019, each of which is predicted for thirty days after the main shock.

[0055] Generate combined data for training CL-ETAS:

[0056] Here, the application is all using the model to predict the future one day, therefore, the combined data needs to use the above-mentioned ETAS model to predict the earthquake catalog of the future one day, and use the prediction results to replace the real data of that day, so as to obtain new combined data, and process it into a matrix data according to the above data preprocessing method. In this way, a new model training set is obtained.

[0057] Train CL-ETAS model and use it for prediction:

[0058] A large amount of combined data is input into ConvLSTM for training, so as to obtain the CL-ETAS model, and then the trained model is obtained and used for prediction, and the prediction results include the three major earthquakes mentioned above, the Hector Mine earthquake in 1999, the Baja California earthquake in 2010 and the Ridgecrest earthquake in 2019, each of which is predicted for thirty days after the main shock.

[0059] Visualize and compare the prediction results of the three models:

[0060] The application draws comparison charts of 1 day, 15 days and 30 days, in which the Hector Mine earthquake in 1999 is abbreviated as E1, the Baja California earthquake in 2010 is abbreviated as E2, and the Ridgecrest earthquake in 2019 is abbreviated as E3. The comparison of the number of earthquakes is shown in Figure 2 , and the magnitude and spatial distribution of the earthquake is shown in Figure 3 , 4, 5. The application finds that the CL-ETAS model is more accurate than the ETAS model and ConvLSTM in predicting the number of earthquakes, the magnitude of the earthquake and the spatial distribution of the earthquake.

[0061] The model is evaluated using pycsep:

[0062] To evaluate the proposed model, the present invention employs pycsep, a Python package developed by Collaboratory for the Study of Earthquake Predictability (CSEP) for earthquake prediction and data analysis; the package includes four catalog-based prediction evaluations: Number test, Magnitude test, Spatial test, and Pseudo-likelihood test; the test results are shown in Figure 6 , 7, 8; the present invention finds that the CL-ETAS performs better than the ETAS model and ConvLSTM in each test.

Claims

1. A method for constructing a new earthquake prediction model, characterized in that, Specifically comprising the following steps: (1) Generate combined data as a training set using the ETAS model: use the ETAS model to predict the data of the second day with the historical data of the first day, repeat several times to obtain different prediction results of the ETAS model, and add the real data of the first day to the data of the second day predicted by the ETAS to obtain the combined data required for the model to predict the third day, and continuously produce new combined data in sequence over time; (2) Data preprocessing: renumber and combine these new combined data into matrices as a training set; Specifically, the rows of the matrix represent spatial data, i.e. longitude and latitude, and the columns of the matrix represent magnitude data, and then arrange the matrix in time sequence to generate processed spatio-temporal matrix data; (3) Train the model: repeat the above data generation and data preprocessing process, input and start training ConvLSTM, and finally obtain the trained model, i.e. the CL-ETAS model.

2. The method for constructing the new earthquake prediction model according to claim 1, characterized in that: The ETAS model in step (1) can be represented by the following formula: where: λ— is conditional probability; x, y— are spatial locations; t— is time; H t — is historical progression; μ— is background intensity; t i — is time of past event; k(M i )— is dependence of triggering ability on amplitude; M i — magnitude of past event; g(t - t i )— follows Omori's law; f(x - x i ,y-y i ,M i )— spatial kernel function.

3. The method of claim 1, wherein the new earthquake prediction model is constructed by: In step (3), ConvLSTM can be represented by the following formula: H t = o t tanh(C t ), where: t - time; t-1 - previous time; i t - input gate at t; f t - forget gate at t; o t - output gate at t; C t - cell state at t; C t-1 - cell state at t-1; H t - hidden state at t; H t-1 - hidden state at t-1; b i ,b f ,b c ,b o - input gate bias, forget gate bias, cell state bias, output gate bias, respectively; W xi ,W hi ,W ci - input gate feature number weight, hidden state weight, cell state weight, respectively; W xf ,W hf ,W cf - forget gate feature number weight, hidden state weight, cell state weight, respectively; W xc ,W hc - cell state feature number weight, hidden state weight, respectively; W xo ,W ho ,W co - output gate feature number weight, hidden state weight, cell state weight, respectively; X t - number of input features at t; σ - sigmoid activation function; tanh - activation function; * - convolution operation; - Hadamard product.

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