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.
Introduction
For decades, countries exposed to coastal
inundation have done a lot of work to develop their tsunami warning systems
. Most tsunamis are generated by large subduction
earthquakes and landslides, which, owing to the characteristics of the tsunami
source process, places a real-time tsunami forecast out of reach. Regular
earthquakes follow a scaling law that links their energy release (seismic
moment) to their duration . For instance, a regular 8.5
Mw earthquake can last for about 2 min, whereas we can consider
tsunami generation nearly instantaneously after the source origin time. This
implies that a robust tsunami warning system must integrate several systems
that monitor different potential triggers such as earthquakes and volcanoes,
among others. In the case of tsunamis generated by subduction earthquakes, it is
essential to detect and characterize the seismic source. Today, the
W-phase method is preferred for
accounting for large earthquakes in Chile, which provides a first moment tensor
solution within 5 min . As a matter of
fact, the regional W-phase method is now running in real time in less than
5 min . This method is based on waveform inversion theory;
therefore it is necessary to have an important number of broadband
seismometers in the regional field. The implementation of this method relies
on robust seismic networks. This paper tries to illustrate the possibility of
replication of these examples in other countries with tsunami threat produced
by earthquakes in the near field. It is well-known, however, that tsunami
heights are very sensitive to the spatial slip distribution of the seismic
source . Even after having a finite fault model (FFM), the
simulation of the tsunami propagation can take several hours depending on the
desired level of resolution. This is the reason why the tsunami forecasts of
many of the current warning systems are based on pre-computed scenarios
. Chile and Japan use this methodology for that
purpose
(https://www.jma.go.jp/jma/en/News/lists/tsunamisystem2006mar.pdf, last access: 5 December 2018). This methodology, however, ignores the
complexity of the seismic source and solves only for uniform slip models. We
propose a methodology applicable to near-field tsunamis triggered by
earthquakes that complements the monitoring systems in operation and helps
make better decisions during and after an emergency alert.
Methodology
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 .
Slip distribution model
Once a W-phase solution provides a characterization of an earthquake, we use
an elliptical slip distribution over a region determined by
applying the scaling law after . This serves as a preliminary
estimation while seismic waves are still traveling, and later finite fault
solutions are computed. This in turn allows us to model the near-field tsunami
for every finite fault model update. The elliptic model is discretized with
ny subfaults along-dip and nx=LWny, where L and W are the length and width of the fault
plane obtained with the scaling law. After setting ny=16, all the
earthquake cases analyzed in our study have enough resolution on the source
area.
Schematic showing the discretization of the calculation domain for
parallel computation.
Tsunami initial conditions
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 . This is obtained by applying the
Okada equations .
Near-field simulation of the 2015 Illapel earthquake with an
elliptical source (a) and a finite fault model (b). The
colors assigned to different areas indicate the expected run-ups in meters:
(1) red for run-ups larger than 3 m,
(2) orange for run-ups between 1 and 3 m, (3) yellow for run-ups between 0.3
and 1 m, and (4) green for run-ups smaller than 0.3 m.
Regional field simulation of the 2015 Illapel earthquake for an
elliptical source (a), and a finite fault model (b). The
colors assigned to different areas indicate the expected run-ups in meters:
(1) red for run-ups larger than 3 m, (2) orange for run-ups between 1 and
3 m, (3) yellow for run-ups between 0.3 and 1 m, and (4) green for run-ups
smaller than 0.3 m.
Tsunami modeling
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:
ηtt-g∇h∇η=0η(x,y,0)=η0(x,y)1ηt(x,y,0)=0,
where η(x,y,t) denotes the water surface, g the acceleration of
gravity, h(x,y) the bathymetry, and η0(x,y) the initial condition. In
the open boundaries, we set a radiation condition , whereas in
the solid boundaries (coasts) we impose full reflection in a vertical wall
placed at the 100 m isobath, before reaching the nonlinear zone. Here, a
Neumann boundary condition is applied: ∂η∂n^, where
n^ denotes the exterior unit normal vector. The linear
method (LM) allows us to obtain a faster estimation than a full tsunami code
since second-order terms are disregarded while still accounting for the same
main features. In addition, this approach does not require computation of the
velocity field, an added benefit that makes the computation programs even
faster. Each simulation is compared to its corresponding full nonlinear
shallow water equation propagation. We use the JAGURS code
written in Fortran90 using parallel arrays via OpenMP and OpenMP + MPI. This
code is based on the classic finite difference method of .
For each scenario, we run the simulation for the equivalent of 2 h of
tsunami travel time to obtain the main features of the run-up distributions,
despite the fact that later amplification of edge waves and resonance
effects can occur. The approximated run-up is obtained as the maximum from the
vertical wall reflection boundary condition. The resulting run-up values are on
the same order of the actual run-up for a sloping beach model .
Normalized run-up energy rate during the first 2 h of tsunami
simulation. Panel (a) shows the run-up rate along latitude and time, panel
(b) shows the final maximum run-up, and panel (c) shows the
normalized energy rate for the whole process as a time series.
Tsunami travel times across the Pacific basin for the 2015 Illapel
earthquake. Panel (a) shows the travel times after the shallow water
equations, while the travel times in (b) include the effects of
dispersion and the earth elasticity for a wave frequency of 2 mHz.
Implementation and benchmarking
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 . The details of the propagation
and run-up distribution of the 12 events tested are presented in the
supporting information. For these examples we used the finite fault models
provided by the USGS (), as they have proven operationally
robust for real-time operations in the context of global monitoring. All the
computations were performed on a Dell Precision 7920, with two Intel Xeon
Gold 6136 processors, each with 12 physical cores, for a total of 24 physical
cores, and two threads each. For each time iteration, the domain is divided
into 48 subdomains that are computed in different threads, for a parallel
array (Fig. ). To compute the tsunami initial condition, the Okada
equations were implemented in the C programming language using threading,
together with the finite difference scheme for the LM. The C code uses the
pthread library to define a C data structure containing a pthread, and then
calls a function that sends each grid subdomain to threads running in
different cores for computation. This method is as reliable as any other
linear scheme method, as it solves the same equations. The only significant
difference is in the thread distribution for time optimization. When a
thread finishes, it computes for a certain time step and it joins with the
others in order to avoid miscomputations. For instance, on the system used to
run our computations for a regular grid of 4 million points with an FFM of
300 subfaults, the vertical and horizontal seafloor displacements can be
calculated almost instantly (less than 5 s), and 2 h of tsunami wave
propagation for the 2011 Tohoku, Japan, earthquake can be solved in 60 s.
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 Mw 7.7 Nicaragua earthquake and the 2006
Mw 7.6 Java earthquake. The geometry of the earthquakes causative
fault varies from L=150 km to L=500 km; the range of peak
displacement at the source varies from 3 to 40 m. Therefore, we have tested
as many earthquakes and as many source features as possible for this study:
the 1992 Mw 7.7 Nicaragua Tsunami earthquake
the 2001 Mw 8.4 Southern Peru earthquake
the 2003 Mw 8.3 Hokkaido earthquake
the 2006 Mw 7.6 Java earthquake
the 2007 Mw 8.1 Solomon Islands earthquake
the 2007 Mw 8.0 Pisco earthquake
the 2009 Mw 8.1 Samoa Islands region earthquake
the 2010 Mw 8.8 Maule earthquake
the 2011 Mw 9.0 Tohoku earthquake
the 2012 Mw 7.8 British Columbia earthquake
the 2014 Mw 8.2 Iquique earthquake
the 2015 Mw 8.3 Illapel earthquake.
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 , where the linear method predicts 0.39 m for the
elliptic source and 0.12 m for the FFM, whereas JAGURS gives 0.55 m for the
elliptic source and 0.15 m for the FFM.
Summary of the CPU time in seconds for the 12 events.
tIC indicates the time needed to compute the initial conditions,
tPr the processing time, tTP the time to compute the
tsunami propagation, and tT the total time.
Flow chart of the methodology proposed in this study.
Application to compliment tsunami alert. Case study: the 2015 Illapel earthquake
On 16 September 2017 an 8.3 Mw earthquake occurred in the
Coquimbo region, Chile . The characteristics of this
event made it an ideal case study for tsunami generation. The national
agencies implemented the established protocols for evacuating the whole
Chilean coast, even the more distant insular territories (SNAM, bulletin 1,
16 September, 23:02 UTC -5). Such
decisions have to be made within minutes of origin time. In general, an
accurate prediction of the tsunami run-up heights requires a precise image of
the seismic source, which at present is not available within 5 min for
real time after adding the tsunami simulation times. Nevertheless, we can
come close to a quasi-real-time approach by triggering a first estimation
assuming an elliptical slip distribution. This only takes a few seconds, and
can at present be performed instead of searching a pre-computed database of
scenarios that are usually limited. For monitoring purposes, the results can
be updated every time a seismic source image is received, for both the near
field (at 15 arcsec) and regional field (at 60 arcsec). All this
information is summarized in a color-coded map following the official coding
used by the Chilean institutions . Color-coded maps are
self-explanatory, which makes them easy to interpret (Figs. and
). Each region can then be rapidly assigned a color linked to a
specific evacuation protocol. All the simulations were performed for 2 h of tsunami propagation where the main energy content plays a key role
on the inundation process. Figure illustrates the normalized
energy rate that generates the run-up history along the coast, showing that
the majority of the global energy is concentrated within the first hour. We
can also observe that the first estimation obtained for an elliptical fault
predicts the same levels of inundation as the full finite fault model in the
near field, while we can observe minor differences in the regional field.
This makes sense since finite fault model results become available during
the tsunami monitoring stage, when time is not as critical as in the very
first minutes after origin time. Note it is possible to
increase the number of warning levels, allowing us to find the optimal number of
states for emitting and communicating the warning bulletin. In this study we
choose the UNESCO standard. For completeness, we computed the travel time
isochrones across the Pacific basin (Fig. ). These computations
use a dense set of rays following , which allows us to
include dispersive effects. We have also included the effect of the earth
elasticity as shown in . These kinds of maps can be computed
instantly together with the very first estimation of the moment tensor and
then updated.
Conclusions
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. . Taking into account the results of our study we can list
the following as the most noteworthy results.
Although other tsunami warning centers use linear theory as part of their operations, for instance at the Pacific Tsunami Warning Center (PTWC) (http://unesdoc.unesco.org/images/0022/002203/220368e.pdf, last access: 20 December 2018), in this study we have combined it with the use of more complex sources and faster algorithms to generate a unique and simple product easy to interpret.
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 it is possible to instantaneously calculate the tsunami arrival times from sources generated in the far field with enough accuracy. This can also be done via tsunami modeling, but at the expense of longer computation times.
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.
Data availability
No data sets were used in this article.
The supplement related to this article is available online at: https://doi.org/10.5194/nhess-19-1297-2019-supplement.
Author contributions
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.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
This study was enterally supported by the Programa de Riesgo Sśmico.
Review statement
This paper was edited by Maria Ana Baptista and reviewed by
Victor Sardina and three anonymous referees.
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