Prediction of intensity and location of seismic events using deep learning

Abstract

The object of this work is to predict the seismic rate in Chile by using two Deep Neural Network (DNN) architectures, Long Short Term Memory (LSTM) and Convolutional Neural Networks (CNN). For this, we propose a methodology based on a three-module approach: a pre-processing module, a spatial and temporal estimation module, and a prediction module. The first module considers the Epidemic-Type Aftershock Sequences (ETAS) model for estimating the intensity function, which will be used for estimating the seismic rate on a 1 × 1 degree grid providing a sequence of daily images covering all the seismic area of Chile. The spatial and temporal estimation module uses the LSTM and CNN for predicting the intensity and the location of earthquakes. The last module integrates the information provided by the DNNs for predicting future values of the maximum seismic rate and their location. In particular, the LSTM will be trained using the maximum intensity of the last 30 days as input for predicting the maximum intensity of the next day, and the CNN will be trained on the last 30 images provided by the application of the ETAS model for predicting the probability that the next day the maximum event will be in certain area of Chile. Some performance indexes (such as $R^2$ and accuracy) will be used for validating the proposed models.

Introduction

Earthquakes represent one of the most destructive yet unpredictable natural disasters along the world, with a massive physical, psychological and economical impact in the population worldwide. Chile is considered one of most seismic-active country in the world, having the world’s largest instrumentally documented earthquake occurred in Valdivia (on May 22, 1960), as well as recently been affected by three major earthquakes with magnitudes $>$ 8.0 (on Richter scale). Thus, to have a better approximation or additional information on where and when an event of that magnitude could occur, it would represent an invaluable tool for managing and designing public policies regarding natural disasters. However, earthquake prediction is a very challenging task due to the high complexity associated to the process itself, and also due to the fact that their occurrences depend on a multitude of variables, that in most cases could be unidentified (Sobolev, 2015, Cimellaro and Marasco, 2018, Joffe et al., 2018). Most of the proposed prediction models are focused on some form of seismic hazard estimation (Budnitz et al., 1997, Woessner et al., 2015, Petersen et al., 2018). This term is defined as the probability that an earthquake will occur in a given geographic area, within a given window of time, and with a magnitude exceeding a given threshold. In fact, according to Allen (1976) and Joffe et al. (2018), a valid approach for earthquake prediction should consider a spatio-temporal window, a magnitude estimation, a scientific sound validation process, and an appropriate visualization procedure.

Self-exciting point process models have become essential components in the assessment of seismic hazard. A particular class is given by the Epidemic Time Aftershock Sequence (ETAS) models which have proven to be extremely useful in the description and modeling of earthquake occurrence times and locations. In that sense, Ogata, 1988, Ogata, 1998, introduced ETAS models for temporal and spatio-temporal seismic hazard estimation, respectively. Those models use a given parametrization of the conditional intensity function associated with the occurrence rate of an earthquake and its triggering function at time $t$ and within an $(x,y)$ location. Aftershocks are then estimated following the seismic aftershock propagation law, or Omori’s law (Utsu, 1961). Recently, many improvements and extensions have been proposed for incorporating local features of the seismic events (Lombardi et al., 2010, Ogata, 2011, Bansal and Ogata, 2013, Kumazawa and Ogata, 2014, Guo et al., 2015, Nicolis et al., 2015).

Although ETAS models have shown to be very useful for estimating the triggering earthquakes, they often fail when predicting future events. Nicolis et al. (2017) show that the ETAS normally underestimate the real number of seismic events, depending on the precise time that the main shock happened. For solving this problem, they introduced a correction factor that takes into account when the main earthquake happens just before the forecasting day. They also show the superiority of the temporal ETAS for predicting future values of the intensity respect the spatio-temporal ETAS model.

Joffe et al. (2018) stated that contemporary techniques are insufficiently sensitive to allow for precise modeling of future earthquake events. This raises the importance for new approaches that consider broader and bigger sources of information. In that sense, Deep Neural Networks (DNN) have state-of-art accuracy for most of the problems where statistical learning models are applied and where a precise mathematical formulation is hard to obtain. Moreover, DNN architectures, like Long Short Term Memory (LSTM) networks and Convolutional Neural Networks (CNN) have appeared in the last few years, with positive results in a variety of problems such as speech recognition, language modeling, translation, image classification and captioning, time series anomaly detection, stock market prediction, to name a few (Liu et al., 2017, Kumar et al., 2018).

Some of the first machine learning applications on earthquake analysis appeared in the 1990s, and used multilayer perceptrons or artificial neural networks for event detection and phase picking (Wang and Teng, 1995, Tiira, 1999, Zhao and Takano, 1999). In the next decades, along with the further development of new techniques, several new machine learning methods have been successfully applied, for instance, Asim et al. (2018a) used Support Vector Machine Regression and Hybrid Neural Networks to predict earthquake occurrences based on a combination of relevant seismic features such as Gutenberg–Richter law, seismic rate changes, foreshock frequency, seismic energy release and total recurrence time, and Reyes et al. (2013) showed a Neural Network approach for earthquake prediction in Chile from 1960 to 2011, taking into account seismic areas of Talca, Pichilemu, Santiago and Valparaíso.

Furthermore, the application of DNN to seismological problems is at its dawn (Kriegerowski et al., 2019). In that sense, recent works proposed the application of DNNs for seismic analysis, most of these works used CNN or LSTM networks. Kislov and Gravirov (2018) analyzed the potential of using Deep Neural Networks for the analysis of seismic data, where DNN has a higher level of abstraction which, consequently, improves the generalization ability of the model. Zhou et al. (2019) introduced a hybrid CNN-RNN to detect earthquake events from seismograms signals. Linville et al. (2019) applied CNN and RNN to discriminate between quarry blasts and tectonic sources from event catalogs and the spectrograms of the sensors, with a performance higher than 99%. Kriegerowski et al. (2019) have applied CNN to accurately predict de hypocenter locations from full-waveform records of multiple stations. Perol et al. (2018) proposed the ConvNetQuake model, a CNN for earthquake detection and location from waveforms. Vijayasankari and Indhuja (2018) used LSTM networks for spatio-temporal earthquake forecast. Geng et al. (2019) proposed a dilated causal temporal convolution network and a CNN-LSTM network to forecast seismic events. Huang et al. (2018) proposed to project the seismic events into a topographic map and generated a dataset of images where the earthquake with magnitude $>$ 6 is marked with a label “1”. The authors used a CNN to detect and predict if these large earthquake events will occur in the next 30 days. Li et al. (2019) proposed a method for seismic fault detection using a CNN, moreover, to augment the dataset they developed an encoder–decoder CNN to enrich very small training set. Wang et al. (2018) trained the ResNets for seismic data antialiasing interpolation, where the model is used to reconstruct dense data with halved trace intervals. The generated data can be used to improve the accuracy of subsequent algorithms. On the other hand, Oliveira et al. (2018) assessed the performance of a conditional generative adversarial network to interpolate and generate seismic data. Recently, Plaza et al. (2019) used a LSTM for predicting the intensity function of a temporal ETAS in Chile. LSTM were also applied by Reyes et al., 2013, Wang et al., 2017, Asim et al., 2018b and Vardaan et al. (2019) for the temporal and spatial prediction of earthquakes.

In this work we explore a new approach based on a Long Short Term Memory (LSTM) network (Hochreiter and Schmidhuber, 1997) and a Convolutional Neural Network (CNN) (LeCun et al., 1989)) for predicting the intensity function and the probability that a seismic event with a given magnitude occurs in a certain area. In particular, first we use the seismic catalogue of Chile for estimating the ETAS model on a grid of 1 × 1 degree for the period 2000–2017 using three different threshold magnitudes ($\ge 4.0$, $\ge 5.0$ and $\ge 6.0$). Then, we take the spatial maximum value of the intensity and we use a LSTM for predicting the maximum rate of seismic event occurrence on the next day. A CNN is also applied to the same data for predicting the probability that the maximum value of intensity is in a certain area. For this goal we divide the data in 6 areas and a classification of the areas are provided. By crossing the outputs of the two neural networks we can predict the maximum intensity and the location of the next seismic event.

This work is structured as follows. In Section 2 we briefly show the methodological modular approach with a brief description of the ETAS model, and the LSTM and CNN neural networks. In Section 3 we apply the latter models for data preprocessing and intensity and location prediction of future seismic events. Some results are shown in Section 4. Conclusions and further developments are provided in Section 5.