Despite the occurrence of several large earthquakes during the last decade, Chile continues to have a great tsunamigenic potential. This arises as a consequence of the large amount of strain accumulated along a subduction zone that runs parallel to its long coast, and a distance from the trench to the coast of no more than 100 km. These conditions make it difficult to implement real-time tsunami forecasting. Chile issues local tsunami warnings based on preliminary estimations of the hypocenter location and magnitude of the seismic sources, combined with a database of pre-computed tsunami scenarios. Finite fault modeling, however, does not provide an estimation of the slip distribution before the first tsunami wave arrival, so all pre-computed tsunami scenarios assume a uniform slip distribution. We implemented a processing scheme that minimizes this time gap by assuming an elliptical slip distribution, thereby not having to wait for the more time-consuming finite fault model computations.We then solve the linear shallow water equations to obtain a rapid estimation of the run-up distribution in the near field. Our results show that, at a certain water depth, our linear method captures most of the complexity of the run-up heights in terms of shape and amplitude when compared with a fully nonlinear tsunami model. In addition, we can estimate the run-up distribution in quasi-real-time as soon as the results of seismic finite fault modeling become available.

For decades, countries exposed to coastal
inundation have done a lot of work to develop their tsunami warning systems

We can separate this problem into three main parts: (1) the estimation of a
seismic source model, (2) the generation of initial conditions, and (3) the
corresponding tsunami simulation. We define a computation domain around the
earthquake source and the coastal areas in the near field. We use the SRTM15
bathymetric data with a 15 arcsec resolution, based on the SRTM30

The core idea consists in trading off some accuracy to gain speed. Within the context of tectonic tsunamis generated in the near field we want to know the places with the maximum inundation, the extension of the inundation until it decreases to 0.5–1 m, and the average run-up. Our model does not aim at computing a detailed inundation map with the best possible accuracy, but rather to provide a fast estimate of the main area prone to inundation relying on the W-phase CMT, currently considered one of the fastest and more accurate methods to characterize the source of large earthquakes

Once a W-phase solution provides a characterization of an earthquake, we use
an elliptical slip distribution

Schematic showing the discretization of the calculation domain for parallel computation.

Despite evidence of influence of the source time components in the tsunami
generation process, for speed purposes we model a static seafloor deformation
induced by a nonuniform slip distribution that includes the horizontal
components, as suggested by

Near-field simulation of the 2015 Illapel earthquake with an
elliptical source

Regional field simulation of the 2015 Illapel earthquake for an
elliptical source

The last part of this methodology is the estimation of the tsunami heights
along the coast. Usually, tsunami modeling involves complex codes to solve
the fully coupled nonlinear shallow water equations. Depending on the domain
size and resolution, a full tsunami simulation run can take several hours,
which makes real-time forecast nearly impossible. To overcome this
limitation, we solve the linear shallow water equations with a forward finite
difference scheme. The propagation inside the domain is governed by the
second-order partial differential equation (PDE) with initial conditions:

Normalized run-up energy rate during the first 2 h of tsunami
simulation. Panel

Tsunami travel times across the Pacific basin for the 2015 Illapel
earthquake. Panel

To evaluate the performance of our approach, we modeled nearly all the largest
tsunamis of the last 2 decades. Most of them were already tested with an
analytical approach in

Correlation of the run-up distribution obtained from our linear model solution and the JAGURS code. Correlation is computed with the standard Pearson coefficient. Details can be found in the Supplement.

All the earthquakes presented here have produced tsunamis. The range of
magnitude varies from 7.7 to 9.1. They occurred in different subduction zones
around the world. The largest ones are Tohoku in Japan and Maule in Chile.
All of them show a thrust mechanism except for the Samoa event in 2009, which
is a normal event. There are a few tsunami earthquakes in this section such
as the 1992

the 1992

the 2001

the 2003

the 2006

the 2007

the 2007

the 2009

the 2010

the 2011

the 2012

the 2014

the 2015

For each event we apply the methodology previously described, and use the
W-phase centroid moment tensor, a scaling law, and an elliptic slip
distribution to define the first source. Then, the linear and nonlinear
tsunami simulations are performed. The resulting run-up distributions are
decomposed along latitude and longitude in order to compare both models. The
same procedure is repeated, this time considering an FFM solution instead.
Table 1 shows the correlation between the run-up distributions obtained with
the JAGURS code (nonlinear method) and the method presented in this paper
(linear method). Table 2 summarizes the CPU times in seconds for different
stages of the process for each simulation. There is a high degree of
agreement within a short time. Detailed figures showing the results for the
24 simulations are provided in the Supplement, where maximum amplitudes,
run-up distribution, and field measurements are listed. For comparison
purposes, for the event in 2014 in Chile, the DART station 32 401 registered 0.25 m
of amplitude

Summary of the CPU time in seconds for the 12 events.

Flow chart of the methodology proposed in this study.

On 16 September 2017 an 8.3

In this study we propose a method that disregards the fine complexity of the
seismic source while using fine bathymetric data and a set of simplified
equations. Implementation of this method allows us to model more than 80 %
of the tsunami run-ups with enough accuracy for tsunami warning purposes up to
20 times faster. Our method also aims at rapidly predicting the spatial
distribution of the tsunami run-ups using some simplifications in the tsunami
equations. Despite lacking the mathematical rigor that we would
otherwise prefer, the method we propose is not inexact within the context of
an emergency response system that needs to trigger actions that can
potentially save lives and reduce economic losses after the occurrence of a
large earthquake. We summarized our approach in the flowchart shown in
Fig.

Although other tsunami warning centers use linear theory as part of their operations, for instance at the Pacific Tsunami Warning Center (PTWC) (

The non-complexity of the adopted source does not seem to significantly affect the results of a fast tsunami run-up estimation for emergency response purposes. By computing different levels of tsunami hazard in near-real time we can estimate more accurately the extent of the area potentially affected by the tsunami, the maximum level of inundation, and how many people will be exposed to this hazard along the Chilean coast.

Using the methodology of

When compared to other tsunami modeling codes such as JAGURS, results obtained from our method match more than 80 % of the predicted run-up for 15 arcsec bathymetry while obtaining the results at least 20 times faster.

The simple method proposed in this study provides a fast, reliable, and intuitive characterization of the tsunami threat, which in turn allows disaster mitigation agencies to take appropriate action.

No data sets were used in this article.

The supplement related to this article is available online at:

MF developed the idea and primary codes and tests. SA wrote all codes in C language with parallel computing and ran the simulations. SR compiled the catalogs of earthquakes used in this study and BD provided some FFMs to test the numerical tsunami model. The manuscript was prepared by MF and SR with supervision and contribution from all authors.

The authors declare that they have no conflict of interest.

This study was enterally supported by the Programa de Riesgo Sśmico.

This paper was edited by Maria Ana Baptista and reviewed by Victor Sardina and three anonymous referees.