Root mean square error (RMSE) of the training and test groups for each DFANN and RNN-LSTM deep learning models.
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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].
\nOgata [5] introduced epidemic-type aftershock sequence (ETAS) models for seismic hazard estimation; those models and their multiple extensions [6, 7, 8, 9, 10, 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 \n
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.
\nThe general purpose for this work is to use a deep learning (DL) approach with deep feedforward artificial neural networks (DFANNs) and a recurrent neural networks with long short-term memory (RNN-LSTM) for ground intensity function estimation. First, the data are preprocessed to estimate the daily ground intensity function; then the output is used as input for the DL networks (DFANN and RNN-LSTM). Finally, both DL approaches are compared to find the best model. A description of the proposed procedure is shown in Figure 1.
\nScheme for the two modular DL neural network framework: data preprocessing and estimation modules. In the data preprocessing module, all data are analyzed and prepared as inputs for the following modules; this considers estimating the daily ground intensity function. The estimation module will receive inputs from the previous model and use DFANN and RNN-LSTM DL to estimate and predict the ground intensity function.
The database consisted of 86,000 seismic event records occurred in Chile, from 2000 to 2017, obtained from the National Seismological Center (http://www.sismologia.cl); each record consists of a time location (year, month, day, hour, minute, and second), a spatial location (latitude and longitude), depth (in kilometers), and magnitude (on Richter scale). Figure 2 shows the spatial distribution of seismic events with magnitude superior to 6 (in Richter scale).
\nSpatial distribution of seismic events (magnitude >6 Richter) for the period 2000–2017 in Chile.
The data preprocessing module consists of estimating the conditional intensity function that represents a way of specifying how the present depends on the past in an evolutionary point process [17]. Point process models have become essential components in the assessment of seismic hazard. A particular class is given by the self-exciting temporal point process which models events whose rate at time t may depend on the history of events at times preceding t, allowing events to trigger new events (see [18, 19] and the references within). These models appeared for the first time in applications to population genetics, and for this they are also known as epidemic-type models. Ogata [5, 20] introduced the epidemic-type aftershock sequence (ETAS) models for modeling seismic events. These models are characterized by a parametric intensity function which represents the occurrence rate of an earthquake at time \n
ETAS models and its successive extensions have proven to be extremely useful in the description and modeling of earthquake occurrence times and locations. Self-exciting point process models [5, 19] were initially introduced in time and successively extended to the space [19]. The temporal self-exciting point processes can be defined in terms of the conditional ground intensity function (GIF):
\nwhere \n
where the component μ can be considered the base rate that prevents the process to die out, \n
Different parameterizations have been proposed for the functions \n
The ground intensity function estimation can be estimated using the PtProcess library available in R [21].
\nOnce the GIF databases are obtained for each magnitude (>3, >4, >5 and >6), they are structured for estimation with the DL models. The database is separated in two groups, training and test (67 and 33% of the data, respectively). A lookback of 3 is used, meaning that the output in time t will be estimated considering a window of \n
Deep feedforward artificial neural network (DFANN), also called feedforward neural networks or multilayer perceptron, is the most popular and widely known artificial neural network. In this network, the information is propagated in a forward direction, from the input nodes through the hidden nodes (if any) and to the output nodes. As stated by [22, 23], DFANNs are universal approximators, and the universal approximation theorem states that “every bounded continuous function with bounded support can be approximated arbitrarily closely by a multilayer perceptron by selecting enough but a finite number of hidden neurons with appropriate transfer function” [22, 24].
\nThe goal of a DFANN is to approximate some function \n
The DFANN model consists a set of elementary processing elements called neurons. These units are organized in an architecture with three types of layers: the input or sensory layer, the hidden, and the output layers. The neurons corresponding to one layer are linked to the neurons of the subsequent layer without any type of bridge, lateral, or feedback connections. The connections symbolize the flux of information between neurons. Figure 3 illustrates the architecture of this artificial neural network with \n
Deep feedforward artificial neural network (DFANN).
DFANN operates as follows. The input signal is received by the neurons of the input layer; these neurons are just in charge of propagating the signal to the first hidden layer, and they do not make any processing. The first hidden layer processes the signal (applying a nonlinear transformation or transfer function) and transfers it to the subsequent layer; the second hidden layer propagates the signal to the third and so on. The number of hidden layers gives the depth of the model, hence the term “deep.” When the signal is received and processed by the output layer, it generates the response.
\nThe knowledge of the DFANN is registered, by the learning algorithms, in the connections between the neurons of each layer \n
As firstly proposed by Rumelhart [26], recurrent neural networks have a primitive type of memory, in the form of recurrent layers that can operate in time [27]. Each recurrent layer takes both the output of the previous layer and an internal output of the current layer as inputs. Thus, RNNs are ideal for dealing with time series data [27]. RNNs can solve the purpose of sequence handling to a great extent but not entirely; they are great when it comes to short contexts, but to be able to build a story and remember it, the models need to be able to understand and remember the context behind longer sequences, just like a human brain. This is not possible with a simple RNN. Long short-term memory (LSTM) networks [28] are a type of RNN precisely designed to escape the long-term dependency issue of recurrent networks. LSTM recurrent networks (RNN-LSTM) have memory cells that have an internal recurrence (a self-loop), in addition to the outer recurrence of the RNN. The latter adds a nonlinear transformation to the inputs [28]. These memory cells, A, are controlled mainly by the memory door, the forgetting door (\n
LSTM cells structure, based on the work by [
In addition, they classify and predict based on time series data, since there may be delays of unknown duration between important events in a series of time. It allows clearly remembering events selected from far away in the past, which contrasts with basic NRs, for which the memory of an event decays over time [27]. A 1-layer RNN-LSTM with 12 cells was implemented for this work. Both DL models were implemented using Keras, with TensorFlow as backend, in Python.
\nFigure 5 shows GIF estimation for the data preprocessing module, estimated for magnitudes >3, >4, >5, and >6, respectively. Note that with higher magnitudes, the GIF time series become thinner, due to the decrease of seismic events that fit in the category.
\nGround intensity function (GIF) estimation.
The structure implemented for both DFANN and RNN-LSTM models is shown in Figure 6.
\nStructure for the DL models, for both DFANN (on the left) and RNN-LSTM (on the right).
The DFANN model performs slightly better than the RNN-LSTM models, in particular for lesser magnitudes (>3). Table 1 shows the training and test performance measures (root mean square error, RMSE) for each magnitude group and DL model. Both models show better performances with magnitude >3, that is, when more information are available.
\nRMSE training/test | \n||
---|---|---|
Mag | \nDFANN | \nRNN-LSTM | \n
>3 | \n0.5651/0.5167 | \n|
>4 | \n0.4624/0.3440 | \n0.6698/0.4732 | \n
>5 | \n0.5894/0.4457 | \n0.7572/0.4449 | \n
>6 | \n0.4226/0.4654 | \n0.7941/0.4741 | \n
Root mean square error (RMSE) of the training and test groups for each DFANN and RNN-LSTM deep learning models.
In bold the best model.
Also, a representation of the training and test results for the best model are shown in Figure 7. The model captures the trend very well; however, it does not perform accordingly in terms of the magnitude of the intensity function.
\nTraining and test groups for the best model (DFANN, Mag > 3).
This work introduces a novel approach to predict the temporal ETAS-GIF alternative to the statistical approach proposed by [14]. The deep learning method has recently been used for predicting locations of aftershock events [31] especially based on ground motion data. The first use of a feedforward neural network for the prediction of seismic hazard was introduced by [32] in the spatial domain.
\nPossible extensions of the deep learning approach could be to include the ground motion together to other variables [30, 31] as inputs of the model and to incorporate the spatial dimension for a spatiotemporal prediction [33, 34, 35]. Some statistical techniques could be used for identifying possible patterns and inputs [36, 37].
\nAlso, since seismic events could be characterized by different features depending of the different locations of the principal events, we think that DL neural network models could be used for characterizing earthquakes in some specific seismic areas such as the local ETAS models [7, 11].
\nDifferent neural networks models could be used for comparing earthquake predictions [38]. For example, Bayesian DL neural networks could be used for a new prediction scenario considering the uncertainty of major earthquake occurrences and the probability of recurrence in a similar way to the Bayesian approach proposed by [32]. Additionally, other DL and machine learning approaches as convolutional neural networks (CNN), generative networks (GN), and random forest regression (RFR) could be implemented by incorporating the spatial component and allowing to “generate” new prediction seismic risk maps.
\nHowever, the main limitation of neural networks is that they are considered “black boxes” since it is difficult to quantify the correlation between the involved variables and their uncertainty.
\nThis chapter deals with the estimation of seismic risk given by the temporal ETAS conditional intensity function. To achieve this goal, two deep learning models were implemented: a deep feedforward artificial neural network and a recurrent long short-term memory network. The results show a good estimation, in particular with the DFANN model. However, it should be pointed out that both implemented models could be improved by adding more hidden layers or stacking more LSTM layers in the DFANN and RNN-LSTM models, respectively. Also, exogenous variables (such as ground motion among others) could be considered for improving the predictions. Since the proposed model only considers a temporal model, extensions to the prediction of earthquake locations will be considered in future works. We think that deep learning algorithms could be useful tools for many earthquake prediction approaches.
\nThe authors thank the National Research Center for Integrated National Disaster Management (CIGIDEN), CONICYT/FONDAP/15110017 (Chile) and CONICYT PFCHA/DOCTORADO BECAS CHILE/2018 – 21182037 for financing this work.
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\\n\\nCopyright on the individual Works belongs to the specific Author, subject to an agreement with IntechOpen. The Creative Common license is granted to all others to:
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The CC BY 3.0 and CC BY 4.0 license permits Works to be freely shared in any medium or format, as well as the reuse and adaptation of the original contents of Works (e.g. figures and tables created by the Authors), as long as the source Work is cited and its Authors are acknowledged in the following manner:
\\n\\nContent reuse:
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\\n\\nRepublishing – More about Attribution Policy can be found here.
\\n\\nThe same principles apply to Works published under the CC BY-NC-SA 3.0 license, with the caveats that (1) the content may not be used for commercial purposes, and (2) derivative works building on this content must be distributed under the same license. The restrictions contained in these license terms may, however, be waived by the copyright holder(s). Users wishing to circumvent any of the license terms are required to obtain explicit permission to do so from the copyright holder(s).
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\\n\\nAll rights to Books and Journals and all other compilations published on the IntechOpen platform and in print are reserved by IntechOpen.
\\n\\nThe copyright to Books, Journals and other compilations is subject to separate copyright from those that exist in the included Works.
\\n\\nAll Long Form Monographs/Compacts are licensed under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license granted to all others.
\\n\\nCopyright to the individual Works (Chapters) belongs to their specific Authors, subject to an agreement with IntechOpen and the Creative Common license granted to all others to:
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\\n\\nShare — copy and redistribute the material in any medium or format
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\\n\\nUsers wishing to repost and share the Video Lectures are welcome to do so as long as they acknowledge the source in the following manner:
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\\n\\nPolicy last updated: 2016-06-08
\\n"}]'},components:[{type:"htmlEditorComponent",content:'Copyright is the term used to describe the rights related to the publication and distribution of original Works. Most importantly from a publisher's perspective, copyright governs how Authors, publishers and the general public can use, publish, and distribute publications.
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\n\nHOW COPYRIGHT WORKS WITH OPEN ACCESS LICENSES?
\n\nAgreement samples are listed here for the convenience of prospective Authors:
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\n\nAuthor - in order to be identified as an Author, three criteria must be met: (i) Substantial contribution to the conception or design of the Work, or the acquisition, analysis, or interpretation of data for the Work; (ii) Participation in drafting or revising the Work; (iii) Approval of the final version of the Work to be published.
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\n\nIntechOpen - Registered publisher with office at 5 Princes Gate Court, London, SW7 2QJ - UNITED KINGDOM
\n\nIntechOpen platform - IntechOpen website www.intechopen.com whose main purpose is to host Monographs in the format of Book Chapters, Long Form Monographs, Compacts, Conference Proceedings, Scientific Journals and Videos.
\n\nVideo Lecture – an audiovisual recording of a lecture or a speech given by a Lecturer, recorded, edited, owned and published by IntechOpen.
\n\nTERMS
\n\nAll Works published on the IntechOpen platform and in print are licensed under a Creative Commons Attribution 3.0 Unported and Creative Commons 4.0 International License, a license which allows for the broadest possible reuse of published material.
\n\nCopyright on the individual Works belongs to the specific Author, subject to an agreement with IntechOpen. The Creative Common license is granted to all others to:
\n\nAnd for any purpose, provided the following conditions are met:
\n\nAll Works are published under the CC BY 3.0 and CC BY 4.0 license. However, please note that book Chapters may fall under a different CC license, depending on their publication date as indicated in the table below:
\n\n\n\n
LICENSE | \n\t\t\tUSED FROM - | \n\t\t\tUP TO - | \n\t\t
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The CC BY 3.0 and CC BY 4.0 license permits Works to be freely shared in any medium or format, as well as the reuse and adaptation of the original contents of Works (e.g. figures and tables created by the Authors), as long as the source Work is cited and its Authors are acknowledged in the following manner:
\n\nContent reuse:
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\n\nRepublishing – More about Attribution Policy can be found here.
\n\nThe same principles apply to Works published under the CC BY-NC-SA 3.0 license, with the caveats that (1) the content may not be used for commercial purposes, and (2) derivative works building on this content must be distributed under the same license. The restrictions contained in these license terms may, however, be waived by the copyright holder(s). Users wishing to circumvent any of the license terms are required to obtain explicit permission to do so from the copyright holder(s).
\n\nDISCLAIMER: Neither the CC BY 3.0 license, CC BY 4.0, nor any other license IntechOpen currently uses or has used before, applies to figures and tables reproduced from other works, as they may be subject to different terms of reuse. In such cases, if the copyright holder is not noted in the source of a figure or table, it is the responsibility of the User to investigate and determine the exact copyright status of any information utilised. Users requiring assistance in that regard are welcome to send an inquiry to permissions@intechopen.com.
\n\nAll rights to Books and Journals and all other compilations published on the IntechOpen platform and in print are reserved by IntechOpen.
\n\nThe copyright to Books, Journals and other compilations is subject to separate copyright from those that exist in the included Works.
\n\nAll Long Form Monographs/Compacts are licensed under the Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license granted to all others.
\n\nCopyright to the individual Works (Chapters) belongs to their specific Authors, subject to an agreement with IntechOpen and the Creative Common license granted to all others to:
\n\nUnder the following terms:
\n\nThere must be an Attribution, giving appropriate credit, provision of a link to the license, and indication if any changes were made.
\n\nNonCommercial - The use of the material for commercial purposes is prohibited. Commercial rights are reserved to IntechOpen or its licensees.
\n\nNo additional restrictions that apply legal terms or technological measures that restrict others from doing anything the license permits are allowed.
\n\nThe CC BY-NC 4.0 license permits Works to be freely shared in any medium or format, as well as reuse and adaptation of the original contents of Works (e.g. figures and tables created by the Authors), as long as it is not used for commercial purposes. The source Work must be cited and its Authors acknowledged in the following manner:
\n\nContent reuse:
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\n\nAll Book cover design elements, as well as Video image graphics are subject to copyright by IntechOpen.
\n\nEvery reproduction of a front cover image must be accompanied by an appropriate Copyright Notice displayed adjacent to the image. The exact Copyright Notice depends on who the Author of a particular cover image is. Users wishing to reproduce cover images should contact permissions@intechopen.com.
\n\nAll Video Lectures under IntechOpen's production are subject to copyright and are property of IntechOpen, unless defined otherwise, and are licensed under the Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) license. This grants all others the right to:
\n\nShare — copy and redistribute the material in any medium or format
\n\nUnder the following terms:
\n\nUsers wishing to repost and share the Video Lectures are welcome to do so as long as they acknowledge the source in the following manner:
\n\n© {year} IntechOpen. Published under CC BY-NC-ND 4.0 license. Available from: {DOI}
\n\nUsers wishing to reuse, modify, or adapt the Video Lectures in a way not permitted by the license are welcome to contact us at permissions@intechopen.com to discuss waiving particular license terms.
\n\nAll software used on the IntechOpen platform, any used during the publishing process, and the copyright in the code constituting such software, is the property of IntechOpen or its software suppliers. As such, it may not be downloaded or copied without permission.
\n\nUnless otherwise indicated, all IntechOpen websites are the property of IntechOpen.
\n\nAll content included on IntechOpen Websites not forming part of contributed materials (such as text, images, logos, graphics, design elements, videos, sounds, pictures, trademarks, etc.), are subject to copyright and are property of, or licensed to, IntechOpen. Any other use, including the reproduction, modification, distribution, transmission, republication, display, or performance of the content on this site is strictly prohibited.
\n\nPolicy last updated: 2016-06-08
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