**Abstract**

Earthquakes represent one of the most destructive yet unpredictable natural disasters around the world, with a massive physical, psychological, and economical impact in the population. Earthquake events are, in some cases, explained by some empirical laws such as Omori's law, Bath's law, and Gutenberg-Richter's law. However, there is much to be studied yet; due to the high complexity associated with the process, nonlinear correlations among earthquake occurrences and also their occurrence depend on a multitude of variables that in most cases are yet unidentified. Therefore, having a better understanding on occurrence of each seismic event, and estimating the seismic hazard risk, would represent an invaluable tool for improving earthquake prediction. In that sense, this work consists in the implementation of a machine learning approach for assessing the earthquake risk in Chile, using information from 2012 to 2018. The results show a good performance of the deep neural network models for predicting future earthquake events.

**Keywords:** deep neural networks, conditional intensity function, DFANN, RNN-LSTM, seismic hazard prediction

## **1. Introduction**

Chile is a one of the most seismic countries in the world, with an average of a major earthquake (> 8 in Richter scale) every 10 years. The last major earthquake in Chile was registered on February 27, 2010, that affected almost 80% of the Chilean population, registering 525 deaths and several wounded. Therefore, having a better approximation or additional information on where, when an event of that magnitude could occur would represent an invaluable tool for managing and designing public policies regarding natural disasters [1, 2]. However, earthquake prediction is a very challenging task, due to its highly complex, chaotic, or nonlinear nature, and also, their occurrence depend on a multitude of variables that in most cases are yet unidentified [3, 4].

Ogata [5] introduced epidemic-type aftershock sequence (ETAS) models for seismic hazard estimation; those models and their multiple extensions [6–11] are statistical models that use a given parametrization of the expected number of events in a given region conditional on the past events, also known as the conditional ground intensity function (GIF). The GIF is 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 [12]. Also, it is widely used for earthquake forecast applications [11, 13, 14]. Although the ETAS models are very good for estimating the intensity function and forecasting triggering events, they normally fail to predict the risk of main events

due to their limitations in identifying foreshock events. Then, their performance could also be affected by the use of very large datasets.

Joffe et al. [15] stated that current techniques are insufficiently sensitive to allow for precise modeling of future earthquake occurrences. The above raises the importance for new approaches that consider broader and bigger sources of information. In that sense, deep learning (DL) models 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, DL methods, like deep feedforward artificial neural networks (DFANNs) and recurrent neural networks with long short-term memory (RNN-LSTM), have appeared in the last few years, with incredible success to a variety of problems: speech recognition, language modeling, translation, time series anomaly detection, and stock market prediction, to name a few [16]. This paper presents a temporal deep learning approach for ground intensity function estimation in Chile, using historical information from seismic event catalogs.
