**2. Methods**

The 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**.

#### **2.1 Data**

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).

#### **Figure 1.**

*Scheme 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.*

**5**

**Figure 2.**

**2.2 Data preprocessing module**

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

*Spatial distribution of seismic events (magnitude >6 Richter) for the period 2000–2017 in Chile.*

*Assessing Seismic Hazard in Chile Using Deep Neural Networks*

*DOI: http://dx.doi.org/10.5772/intechopen.83403*

*Assessing Seismic Hazard in Chile Using Deep Neural Networks DOI: http://dx.doi.org/10.5772/intechopen.83403*

*Natural Hazards - Risk, Exposure, Response, and Resilience*

could also be affected by the use of very large datasets.

due to their limitations in identifying foreshock events. Then, their performance

estimation in Chile, using historical information from seismic event catalogs.

A description of the proposed procedure is shown in **Figure 1**.

events with magnitude superior to 6 (in Richter scale).

The 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.

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

*Scheme 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.*

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

**4**

**Figure 1.**

**2. Methods**

**2.1 Data**

**Figure 2.**

*Spatial distribution of seismic events (magnitude >6 Richter) for the period 2000–2017 in Chile.*

#### **2.2 Data preprocessing module**

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 *t* conditional on the past history of the occurrence.

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):

$$\text{defined in terms of the conditional ground intensity function (GIF):}$$

$$\lambda\_{\text{g}}(t|\mathcal{H}\_t) = \lim\_{\Delta t \downarrow 0} \frac{E[N\{(t, t + \Delta t)\}|\mathcal{H}\_t]}{\Delta t} \tag{1}$$

where *N*(*A*) is the number of events occurring at time *t* ∈ *A* and {ℋ*t*:*t* ≥ 0} is the history of all events up to time t. By denoting *ti* ∈ [0,*T*), a simple point process with *ti* < *ti*+1,the GIF can be written as

$$
\lambda\_{\mathbf{g}}\{t|\mathcal{H}\_t\} = \mu + \sum\_{i:t\_i < t} c\_i(m\_i)\mathbf{g}\{t - t\_i\} \tag{2}
$$

where the component μ can be considered the base rate that prevents the process to die out, *mi* is the magnitude at the time *ti,* and *g* is the triggering function which determines the form of the self-excitation [5]. This process with intensity function λ*g*(*t*|ℋ*t*) is also known as marked self-exciting point process, where the mark is given by the magnitude associated to each event. For example, the magnitude of an earthquake also influences how many aftershocks there will be.

Different parameterizations have been proposed for the functions *m* and *f*. Ogata [5] proposed the use of *c*(*m*) <sup>=</sup> *<sup>e</sup>* <sup>β</sup>(*m*−*<sup>M</sup> <sup>t</sup>*) and *f*(*t*) <sup>=</sup> *<sup>K</sup>* \_\_\_\_\_ (*<sup>t</sup>* <sup>+</sup> *<sup>c</sup>*) *<sup>p</sup>* , where the parameter <sup>β</sup> measures the effect of magnitude in the production of aftershocks and f is the modified Omori formula [12], with *t* representing the time of occurrence of the shock, *K* a normalizing constant depending on the lower bound of the aftershocks, and *c* and *p* are characteristic parameters of the seismic activity of a given region.

The ground intensity function estimation can be estimated using the PtProcess library available in R [21].
