Paper No. TS-4-1

SOURCE INVERSION AND INUNDATION MODELINGTECHNOLOGIES FOR TSUNAMI HAZARD ASSESSMENT, CASESTUDY: 2001 PERU TSUNAMI
Bruno Adriano1, Shunichi Koshimura2 and Yushiro Fujii 3

ABSTRACTThe source of the Peru tsunami of June 23, 2001, which was generated due to a large earthquake (Mw= 8.4 by USGS) at the southern part of Peru, is estimated by the inversion of 10 tsunami waveforms
that were recorded at ten tide gauge stations around the Pacific Ocean. Then, we perform the tsunami
numerical inundation modeling to investigate the validity of this source model through comparison interm of the run-up height with field survey data measured around Camana city. As a results, thewaveform inversion shows that large slips were estimated at the deeper part (> 29 km) of the fault
plane, located more than 50 km from the trench axis, with a largest slip value about 9.96 m. The total
seismic moment is calculated as 3.7x1021Nm (Mw = 8.3) for 12-subfault model. The inundation
modeling result is consistent in terms of the run-up height data measured around Camana city.

INTRODUCTION
Peru has experienced some of the largest tsunamis that have occurred around the world. As anexample, an earthquake off the southern coast of Peru (16.265°S 73.641°W, Mw = 8.4 at 20:33:14
UTC according to US Geological Survey, USGS) on June 23, 2001 generated a tsunami that as statedby the post-tsunami report done by the Directorate of Hydrography and Navigation (DHN), Peru
Navy, the coastal cities of Ocoña, Camana, Quilca and Matarani, located at the southern part of Peru,
were significantly affected. In Camana the tsunami wave penetrated more than one kilometer causing
destruction and death. This tsunami event was recorded in several tide gauge stations placed in
Hawaii, Japan, Australia, New Zealand and Chile with tsunami heights between 5 m and 20 cm. At
the tide gauge station located at Callao, Lima-Peru, the tsunami wave was recorded 90 minutes after
the mainshock with an initial tsunami height of 40 cm.

1 Laboratory of Remote Sensing and Geoinformatics for Disaster Management, International Research Instituteof Disaster Science, Tohoku University, Japan. Email: badrianoo@geoinfo.civil.tohoku.ac.jp2 Professor, Laboratory of Remote Sensing and Geoinformatics for Disaster Management, International
Research Institute of Disaster Science, Tohoku University, Japan. Email: koshimura@irides.tohoku.ac.jp
3 Research Scientist, Building Research Institute, International Institute of Seismology and Earthquake
Engineering, Japan. Email: fujii@kenken.go.jp

DATA AND METHOD
Bathymetry and Topography Data
To perform the tsunami inundation modeling the computational area is divided into four domains toconstruct the nested grid system. The bathymetry/topography data for the first and second domains are
re-sampled from General Bathymetry Chart of the Ocean (GEBCO) 30 arc-seconds grid data. Thebathymetry data for the third and fourth domains are constructed from the nautical chart provided by
DHN and the topography data are merged from the Thermal Emission and Reflection Radiometer(ASTER) 1 arc-second resolution and 50 m resolution contour line data from Camana LocalGovernment. The grid size varies from 810 m to 30 m (see Fig. 1ab). In order to conduct the tsunami
waveform inversion the bathymetry data are taken from GEBCO 30 arc-seconds grid data for thecomputation domain (see Fig. 1c).
Field Survey Data
The International Tsunami Survey Team (ITST) conducted a field survey along the area affected by
the tsunami with the main purpose to examine the tsunami damage, to measure the tsunami run-up
height and the extent of inundation and also to interview the eyewitnesses of the event. The measured
tsunami run-up around Camana city done by the ITST is used in this study to validate the tsunami
inundation model.

Fig. 1 (a) Domains scheme to construct the nested grid system. (b) Smaller domain used in the tsunami
inundation modeling (c) Computational domain used in the tsunami waveform inversion. Green rectangles
indicate the location of the tide gauge stations. Red star shows the epicenter (USGS). Lower hemisphere
projection is the Global Centroid Moment Tensor (GCMT) solution.

Tsunami Source Models
The source model of the 2001 Peru earthquake has been estimated from two different seismologicalanalyses, the Global Centroid Moment Tensor (GCMT) and Kikuchi and Yamanaka [1]. The resultsof these studies are used for two different source models Uniform Slip Model (USM) andHeterogeneous Slip Model (HSM), respectively. In addition, in this study a third model calledTsunami Waveform Inversion Model (TWIM) is estimated. It is the result of the inversion ofobserved tsunami waveforms.
Tsunami Waveform Inversion
In order to estimate the extent of the rupture area and the slip amount distribution, we divided thesource into 12 sub-faults that cover the aftershock area during one month after the mainshock (seeFig. 2). The sub-fault size is 50 km x 50 km. The top depths are 14.15 km and 29.60 km for shallow
and deep, respectively. The epicenter is located on the northern sub-fault. The focal mechanisms forall the sub-faults are strike = 308°, dip angle = 18° and slip angle = 63° from the GCMT solution of
the mainshock (Table 1).
To calculate the tsunami propagation initiated at each sub-fault, the lineal shallow-water or long-wave

equations were numerically solved by finite-difference method (Satake [2]). The governing equations
are described in Fujii and Satake [3]. The previous Fig 2c shows the computation area, there are 1800
x 3600 grid point along the longitude and latitude, respectively. For the initial condition, static
deformation of the seafloor is calculated by using the rectangular dislocation model (Okada [4]). We
also take into consideration the effect of the seismic horizontal displacement in region of steep
bathymetry slope (Tanioka and Satake [5]).

Fig. 2 Spatial locations and order numbers of sub-fault planes. Red star shows the mainshock epicenter. Redcircles indicate aftershocks within one month after the mainshock.

Tsunami Inundation Modeling
The numerical simulation is conducted by using TUNAMI-N2 (Tohoku University’s Numerical
Analysis Model for Investigation of Near-filed tsunami No.2) code based on shallow water theory andCartesian coordinate system, which was developed by Disaster Control Research Center (DCRC),
Tohoku University, Japan. The set of nonlinear shallow water Eqns. (1)-(3) is discretized using a
staggered leap-frog finite difference scheme (Imamura [6]). The computation time for the tsunami
propagation is 3.5 hour. In order to satisfy the stability condition the time step is 0.2 s. The tsunami
inundation is calculated on the fourth domain using 1 arc-second of bathymetry and topography griddata, and in this domain there are 1200 x 900 grid points along the longitude and latitude directions,respectively. The value of the Manning’s roughness coefficient is assumed to be equal to 0.025(Koshimura [7]).
∂η ∂M ∂N++=0∂t
∂x
∂y(1)

∂M∂  M 2  ∂  MN ∂η gη 2+ −M M2 + N2+  = − gD∂t∂x  D  ∂y  D ∂x D 7 / 3(2)∂N ∂  MN  ∂  N 2 ∂η gη 2gD
N M2 + N2+ +=−−∂t ∂x  D  ∂y  D ∂y D 7 / 3(3)Therein, the follow definitions are used:ηM = ∫ udz

(4)

−hη

N = ∫ υ dz

(5)

−hD =η + h(6)In these equations, M and N are the discharge flux of x- and y-directions, respectively; η is the waterlevel, and h is the water depth to the mean sea level.

RESULTS AND DISCUSSION
Source Models
The USM is a single fault based on the GCMT solution which proposes the magnitude, strike, slip
angles and centroid latitude/longitude for this event. The slip amount, length and width of the fault areestimated through scale law proposed by Papazachos [8]. Table 1 shows the magnitude and source
parameters for this model. Fig. 3.1a shows the spatial location of the fault area
Table 1 Sub-fault parameters obtained by tsunami waveform inversion of tide gauge data.

Magnitude Strike(Mw)
angle
8.4
310º

Dip
angle
18º

Slip Length
angle (km)63º270

Width(km)95

Slip(m)4.0

Top depth(km)29.6

The source parameters for the HSM are taken from the seismic inversion results of Kikuchi andYamanaka [1] available at http://wwweic.eri.u-tokyo.ac.jp/EIC/EIC_News/105E.html. They analyzed
teleseismic broadband P waves retrieved from 24 seismic stations to determine the general source
parameters. They determined the slip distribution in detail of 40 sub-fault segments in the rupture areaof 150 km by 240 km and each sub-fault segment area is 30 km x 30 km. Fig. 3b shows the slip
distribution for the HSM. The dislocation value reach up to ~5 m and the largest slip amounts arelocated on the southern area. However, the fault plane proposed does not include the location of themainshock which correspond to the epicenter.

Fig. 3 (a) Location of the fault plane for the USM. (b) Slip distribution estimated by inversion analysis ofteleseismic record by Kikuchi and Yamanaka [1]. Blue star shows the mainshock epicenter. Red circles indicate
aftershocks within one month after the mainshock.

Fig. 4 Slip distribution estimated by inversion analysis of tide gauge data. Blue star shows the mainshock
epicenter. Red circles indicate aftershocks within one month after the mainshock.

The source model of the 2001 Peru earthquake has been estimated by a tsunami waveform inversionfrom tide gauge data (Satake [9]). We used non-negative least square method and delete-halfjackknife method to estimate the slip and error, respectively (Fujii and Satake [3]). The observed
tsunami waveforms at tide gauge were sampled at 1 min interval, hence the synthetic waveform arealso computed at 1 min interval. We used the first cycle of tsunami waveform because the spatial
resolution of the bathymetry data may prevent accurate modeling of later phases such as reflectedwaves. The inversion results are shown in Fig. 4. The largest slips are estimated on the southern partof the source region, at the deeper region of the fault. The two largest slip amounts (8.72 m and 9.96m) are located in front of coastal area of Camana city, less than 50 km, which is responsible forgenerating abnormal large tsunami in this area. The total seismic moment is calculated from this slip
distribution as 3.7x1021Nm (Mw 8.3) for 12-subfault model.
The obtained slip distribution is similar to the proposed by Kikuchi and Yamanaka [1]. Their result(seismic moment is calculated as 2.2x1021 Nm, Mw = 8.2) shows that the largest slip of 3 m to 5 m islocated at the southern part of the epicenter approximately 75 km south of Camana city. Our subfaults 3, 8 and 9 may correspond to their asperities.

Tsunami Inundation Modeling
The inundation result from our source models are validated through the comparison with field survey
data from ITST [10], [11] and [12] in terms of the run-up height. It is performed by using K and k
proposed by the equations (7), (8) and (9) (Aida [13]). Where Ri and Hi are the measured and modeled
values of tsunami runup height at point i, respectively.
Ki =RiHi(7)log K =

1 n
∑ log Ki
n i =1(8)log k =

1 n
∑ (log Ki )2 − (log K )2n i =1

(9)

The local inundation depth is the result of measuring water marks on structures or debris on trees
above the ground while the inundation height is the result of measuring water marks or debris above
the astronomical tide level when the tsunami arrived. We calculate the computed runup height basedon the local inundation depth result and the topography data used in the inundation modeling.
According to the ITST[10], [11] and [12] approximately 20 points were obtained for tsunami run-up
height. JSCE [14] empirically provides the guideline for a tsunami numerical modeling suggestingthat 0.95 < K < 1.05 and κ < 1.45 as the threshold of valid tsunami source to develop the tsunami
hazard assessment.
Based on the previous analysis, our best source model is the TWIM, this model satisfies the K and kvalues (K=1.00 and k=1.40) recommended by JSCE [14], excluding the higher values which might be
the result of the lack of bathymetry and topography data in the tsunami modeling. Fig. 5 and Table 2
show the analysis results between observed and computed tsunami run-up for our three source models
where it is conclusive that The TWIM’s result are better approximation compare with the rest twomodels.

Table 2 Numerical model results validation in term of tsunami run-up.

ModelUSM
HSM
TWIM

K
0.85
1.18
1.00

k
1.53
1.83
1.40

8USM7HSMTWIM6)5(mled4oml3cairem2uN
100

1234

5Observed (m)678 012345Observed (m)678 012345678Observed (m)Fig. 5 Comparison between the observed and the numerical model results in term of tsunami run-up heightaround Camana city.

Fig. 6 shows the inundation result map using our best source model. In general, the computed tsunami
inundation area along the coastline of Camana city agrees well with the observed inundation area.
Although, on the northern part the inundation results are slightly overestimate the field survey data.
This might indicate the limitation of the tsunami inundation model using the shallow water
approximation, and the possibility that the field data represents the extreme feature of tsunami run-up
height, or lack of bathymetry and topography features in the model (Koshimura et al, 2009).

Fig. 6 Maximum computed tsunami run-up height based on the TWIM. Background satellite image LandSsat(path=4, row=71)

CONCLUSIONS
We performed tsunami inundation modeling based on the shallow water approximation and by using
four computational domains that are connected with nested grid system and three different source
models, which two of them were estimated by seismological analysis and the third model calculatedby the inversion of tsunami waveform shows that large slips were estimated at the deeper part of thefault plane, with a largest slip value as 9.96 m. The total seismic moment is calculated as 3.7x1021Nm(Mw = 8.3) for 12-subfault model. The inundation modeling result based in the TWIM is more
appropriate approximation compared to the field survey in terms of the run-up height compared withthe USM and HSM. Considering the accuracy of the bathymetry and topography data, the third model
can be used as tsunami source of June 23, Peru earthquake.

ACKNOWLEDGEMENT
The authors acknowledge support from the Japan Ministry of Education, Culture, Sports, Science andTechnology (MEXT) and JST-JICA SATREPS project for the financial support throughout the study.
These supports make possible the forthcoming international conference, as well as international joint
research projects and exchange programs with overseas universities.

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