ORI GIN AL PA PER

Numerical simulation of erosion and depositionat the Thailand Khao Lak coast during the 2004 IndianOcean tsunami

Linlin Li • Zhenhua Huang • Qiang Qiu

Received: 16 October 2013 / Accepted: 19 June 2014� Springer Science+Business Media Dordrecht 2014

Abstract A case study was conducted for the Thailand Khao Lak coast using a forward

numerical model to understand uncertainties associated with interpreting tsunami deposits

and relating them to their tsunami sources. We examined possible effects of the charac-

teristics of tsunami source, multiple waves, sediment supply and local land usages.

Numerical results showed that tsunami-deposit extent and thickness could be indicative of

the slip value in the source earthquake near the surveyed coastal locations, provided that

the sediment supply is unlimited and all the deposits are well preserved. Deposit thickness

was found to be largely controlled by the local topography and could be easily modified by

backwash flows or subsequent tsunami flows. Between deposit extent and deposit thick-

ness, using deposit extent to interpret the characteristics of a tsunami source is preferable.

The changing of land usages between two tsunami events could be another important factor

that can significantly alter deposit thickness. There is a need to develop inversion models

based on tsunami heights and/or run-up data for studying paleotsunamis.

Keywords Tsunami deposits � Sediment transport � Tsunami source � Numerical

simulations � Tsunami inundation � Coastal erosion

L. Li � Z. Huang (&) � Q. QiuEarth Observatory of Singapore, Nanyang Technological University, Singapore 639798, Singaporee-mail: zhhuang@ntu.edu.sg; zhenhua@hawaii.edu

Z. HuangSchool of Civil and Environmental Engineering, Nanyang Technological University,Singapore 639798, Singapore

Z. HuangDepartment of Ocean and Resources Engineering, School of Ocean and Earth Science and Technology,University of Hawaii at Manoa, Honolulu, HI 96822, USA

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Nat HazardsDOI 10.1007/s11069-014-1301-6

1 Introduction

Tsunami deposits have been increasingly investigated in the past several decades

(Dawson et al. 1996; Moore et al. 2007; Shi et al. 1995; Gelfenbaum and Jaffe 2003;

Peters et al. 2007; Richmond et al. 2012; Sato et al. 1995). The characteristics of tsunami

deposits (spatial distribution, thickness, grain size, etc.) are believed to be indicative of

the characteristics of tsunami flows and have been used to reconstruct tsunami-flow

patterns by establishing qualitative relationships between tsunami deposits and tsunami

hydrodynamic characteristics (Moore et al. 2007; Morton et al. 2007; Smith et al. 2007;

Spiske et al. 2010; Jaffe and Gelfenbuam 2007; Soulsby et al. 2007). With tsunami-flow

information derived from tsunami deposits, constraints could be further put on the

locations and nature of the corresponding source earthquakes (Martin et al. 2008; Nelson

et al. 2006; Bourgeois 2009). Previous studies have shown promising potential of using

tsunami deposits to reconstruct slip distributions of historic or prehistoric earthquakes,

and to infer the recurrence intervals and magnitudes of great earthquakes (Bourgeois

et al. 2006; Macinnes et al. 2010; Martin et al. 2008; Nanayama et al. 2003; Satake et al.

2005). In some instances, these kinds of inversion processes might be the only approach

to extend the short historical tsunami records in tsunami-prone coastal areas, and are

therefore of great importance in paleo-tsunami research. However, large uncertainties

may exist in the tsunami source derived from tsunami deposits using an inversion pro-

cedure. The uncertainties could be attributed to factors such as the complex mechanism

of rupture process, our lack of knowledge of the sedimentation process during each

tsunami event, the initial sediment setting, and the details of bathymetric and topographic

data at the tsunami attacking time.

Forward numerical models are particularly suitable for tackling issues of high uncer-

tainty and complexity, as they enable numerous and repeatable numerical tests in a highly

controlled environment. The aim of this study is to understand the uncertainties associated

with interpreting tsunami deposits and relating them to their tsunami sources through a

case study at the Thailand Khao Lak coast using a forward numerical model. Several sets

of numerical experiments were conducted to examine the influence of tsunami source,

multiple waves, sediment supply and bottom roughness. A thin layer of tsunami deposits

have been formed in Khao Lak area during the 2004 Indian Ocean tsunami, and the filed

data such as the grain size and thickness have been collected along several transects by

Fujino et al. (2010) and Hori et al. (2007). The availability of the filed data provides us

with an opportunity to compare simulation results with the field measurements and to

further our understanding of the following issues: (1) relationship between the earthquake

source parameters and the resulting tsunami heights, inundation extent, deposit distribution

and deposit thickness; (2) possible effects of multiple waves and backwash flows on the

horizontal variation of tsunami-deposit thickness; (3) effects of local morphology, sedi-

ment supply and local land use on the characteristics of tsunami deposits.

This paper is organized as follows: Sect. 2 briefly describes the capabilities of the

numerical model used in this study. In Sect. 3, we describe the impact of the 2004 Indian

Ocean tsunami on the studied area, which is followed by a description of model setup,

including the bathymetric and topographic data process, source model selection and initial

sediment setting. The model results are presented in Sect. 4. A discussion of the difficulties

in deriving tsunami source parameters from the characteristics of tsunami deposits is given

in Sect. 5, where issues in using inversion models and surveyed tsunami heights to infer the

source parameters are also discussed. Finally, Sect. 6 summarizes the main findings from

this study.

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2 Methodology

In this study, a two-way coupled model COMCOT-SED (Li et al. 2012) was used to

understand the sediment transportation and deposition process in Thailand Khao Lak coast

during the 2004 Indian Ocean tsunami. COMCOT-SED was based on two open source

codes: COMCOT (Liu et al. 1995; Wang 2009) and XBeach (Roelvink et al. 2008). This

model employs a nested grid system in which linear/nonlinear shallow-water equations are

solved on each grid using a finite difference method. The sediment transport module in

XBeach is incorporated into the innermost grid of COMCOT to model erosion and

deposition processes. Compared with other models (Apotsos et al. 2011a; Kihara and

Matsuyama 2010; Goto and Imamura 2007), which have been used in the past to simulate

tsunami-induced sediment movement, COMCOT-SED has the following advantages: (1)

The two-way coupling algorithm enables COMCOT-SED to simulate the entire lifespan of

a tsunami event seamlessly, from its generation, propagation, inundation on coastal

regions, to its resulting morphological changes; (2) The parallelized COMCOT-SED code

ensures high computational efficiency; (3) COMCOT-SED is also capable of handling

multiple sand layers with mixed grain sizes, which makes it possible to track the sediment

movement quantitatively. This model has been used to study the morphological change in

Lhoknga, west Banda Aceh, during the 2004 Indian Ocean tsunami (Li et al. 2012).

For completeness, the sediment transport model used in COMCOT-SED is outlined

below. For further details of COMCOT-SED the reader is referred to Li et al. (2012). The

sediment motion is modeled by a depth-averaged advection–diffusion equation, with a

source term formulated using the concept of equilibrium sediment concentration (Ga-

lappatti and Vreugdenhil 1985):

ohC

otþ ohCu

oxþ ohCv

oyþ o

oxDhh

oC

ox

� �þ o

oyDhh

oC

oy

� �¼ hCeq � hC

Ts

; ð1Þ

where h is the total water depth; u, v are the depth-averaged velocities in the x- and y-

directions, respectively; C is the depth-averaged concentration of suspended sediment; Dh

is the sediment diffusion coefficient; Ts is the adaptation time of sediment concentration,

given by the following approximation

Ts ¼ max fTs

h

ws

; 0:2

� �s: ð2Þ

The adaptation time Ts depends on the local water depth h, the sediment fall velocity ws

and a sediment transport depth factor fTs(default value is 0.1). As Ts approaches zero, the

sediment concentration responses to the change of flow instantaneously. Equation (1)

implies that both the entrainment and deposition of sediment are determined by the mis-

match between the actual sediment concentration C and the equilibrium concentration Ceq.

In this study, Ceq is calculated using the formula proposed by Van Rijn (1993). The

formulas for Ceq and ws can be found in the user manual of XBeach (Roelvink et al. 2008).

It is worth noting that the parameter Dh in Eq. (1) is related not only to turbulent flow

motion, but also to other factors such as numerical diffusion caused by coarse grids,

discretization of differential equations, and numerical dispersion introduced by depth-

averaging. The default value of Dh = 1.0 was adopted for all simulations presented in the

present study. A detailed discussion of the effects of key model parameters on the

numerical results can be found in Li and Huang (2013).

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The bottom elevation zb changes with time and is updated using the following

equations,

1� pð Þ ozb

otþ oSx

oxþ oSy

oy¼ 0; ð3Þ

Sx ¼ohCu

oxþ o

oxDhh

oC

ox

� �; ð4Þ

Sy ¼ohCv

oyþ o

oyDhh

oC

oy

� �; ð5Þ

with p being the porosity of bed material, and Sx and Sy being the sediment transport rates

in x- and y- directions, respectively.

3 Study area and model setup

3.1 The study area

Khao Lak coast is located in the coastal lowlands of south-western Thailand, which faces

the Andaman Sea. During the 2004 Indian Ocean tsunami, Khao Lak coast was reported as

one of the most severely damaged areas in south-western Thailand in terms of strong

erosion and coastal deformation. According to the post-tsunami field surveys carried out

along four transects (S1–S4 in Fig. 1) by Fujino et al. (2010) and Hori et al. (2007), the

tsunami heights in this area generally exceeded 5 m with a maximum up to 12 m, the

inundation extended about 2 km inland, and the tsunami deposits almost covered the whole

inundated area with a deposit thickness typically \10 cm.

3.2 Bathymetric and topographic data

The arrangement of the computational grids is shown in Fig. 2. Five nested grids (Grid 01

through Grid 05) were used, with the grid resolution varying from 1944 m in the source

region to 27 m in the Khao Lak area (see Table 1). In the deep-ocean area, a 30 arc-second

grid (ca. 925 m) derived from the GEBCO digital bathymetry/topography data set was

used to prepare the computational grids Grid 01 through Grid 04. For the innermost Grid

05, the ASTER topographic data was combined with GEBCO bathymetric data to produce

a uniform bathymetric and topographic data set with a spatial resolution of 27 m through

interpolation. Data gaps between the bathymetry and topography were interpolated and

filled up with nautical charts. The details of the five nested grids used in this study are

summarized in Table 1.

3.3 Selected source models

The characteristics of the great Sumatra–Andaman earthquake of 2004 have been only

partially understood due to its exceptionally complex nature. Data collected from different

sources (seismic waves, far- and near-field GPS data, remote sensing measurements of

uplift or subsidence using optical or synthetic aperture radar (SAR) images, tide gauges,

and satellite altimetry measurements) have been used to invert for fault geometry,

coseismic slip distribution, and rupture process of this event (Ammon et al. 2005; Banerjee

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et al. 2007; Chlieh et al. 2007; Fujii and Satake 2007; Meltzner et al. 2006; Piatanesi and

Lorito 2007). In this study, we selected four source models for the 2004 Sumatra–Andaman

earthquake event (Table 2). All the selected source models have been either inversed or

further constrained by tsunami data (e.g. Satellite altimetry data or tide-gauge data).

Referring to Table 2, the fault model M1 was proposed by Piatanesi and Lorito (2007)

by inverting the slip distribution from 14 tsunami waveforms recorded in the Indian Ocean

in consideration of the non-linearity of tsunami propagation. The fault geometry in this

model is the same as that in Banerjee et al. (2007), who subdivided the fault plane into 16

sub-faults. The fault model M2 was proposed by Chlieh et al. (2007), who took the fault

geometry from Ammon et al. (2005) and subdivided the fault into three main segments

(these segments were further discretized into 661 smaller cells). M2 took into account the

near-field GPS data from north-western Sumatra and along the Nicobar–Andaman islands,

far-field GPS data from Thailand and Malaysia, and both the in situ and remotely sensed

observations of the vertical motion of coral reefs. The simulation results predicted by this

Fig. 1 The study area in Phang-nga province, southwestern Thailand. Surveyed locations are marked byblack dots. The locations along transects S1, S3 and S4 were surveyed by Fujino et al. (2010), the locationsalong transect S2 were surveyed by Hori et al. (2007). The runup-limit line (marked by red dots) wasdigitized from Srisutam and Wagner (2010)

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fault model were proved to fit relatively well with the altimetric measurements made by the

JASON and TOPEX satellites. The fault geometry of the fault model M3 was inferred from

the tectonic setting with a total rupture area of 1,155 km by 150 km and the entire rupture

area was subdivided into six fault segments dipping eastward (Koshimura et al. 2009); for

model constraints, they mainly used two kinds of data to determine the fault dislocations:

JASON-1 altimetry data for the southern three sub-faults and the vertical displacement

field revealed by satellite radar imagery (Tobita et al. 2006) and field measurement (Ra-

jendran et al. 2007) for the entire rupture area (Koshimura et al. 2009). The fault model M4

has five fault segments, which are divided along 1,200 km of the Andaman-Sunda trench

based on the geometry that is identified from the bathymetry of the subduction zone. The

slip distributions of the rupture and aftershocks were provided by initial seismic inversion

models (Tanioka et al. 2006), and the slip distribution was then iteratively refined by

further constraining the source and simulating tsunami to match salient features of tide

gauge and satellite altimetry data (Grilli et al. 2007).

Fig. 2 Nested grids for COMCOT-SED simulations

Table 1 Information on the five grids for COMCOT-SED simulations

Grid 01 Grid 02 Grid 03 Grid 04 Grid 05

Lati. (�) 88E–101E 96E–99.5E 97E–99E 97.96E–98.6E 98.11E–98.27E

Longi. (degree) 0–17N 7.0N–10N 7.5N–9.54N 8.2N–9.14N 8.64N–8.72N

Grid size (m) 1944 648 216 108 27

Parent grid (None) Grid 01 Grid 02 Grid 03 Grid 04

Grid size ratio (None) 3 3 2 4

Time step (in s) 0.01 0.01 0.01 0.01 0.01

Coordinate system Spherical Spherical Spherical Spherical Cartesian

SWE Linear Linear Linear Linear Nonlinear

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3.4 Initial sand distribution and composition

After the 2004 Indian Ocean tsunami, Di Geronimo et al. (2009) conducted a post-tsunami

field survey and created a detailed map of sediment distribution in Khao Lak area. According

to their survey, a shallow sandy seafloor (\10 m deep) with scattered basement outcrops

extended for 3–4 km offshore from the Khao Lak area. Except the coral reef surrounding the

Pakarang cape, the offshore area was basically covered by sand, mud and gravelly sand. We

used the topographical and sedimentological maps given in Di Geronimo et al. (2009) (Fig. 2

in their paper) and digitized the sand distribution extent. We roughly divided the simulation

domain into four types: Area_gravel, Area_sand, Area_mud and Area_rock (Fig. 3), and

specified the grain size D50 as 1.0, 0.2, 0.1 mm and non-erodible for these four types of

simulation areas, respectively. The thickness of the erodible bed can be assumed to be

unlimited, i.e., there is an adequate supply of sediment in the computation domain.

4 Simulation results

4.1 Influences of fault characteristics on tsunami height, tsunami deposit

and inundation limit

In this study, the seafloor displacement was calculated using Okada’s model (1985), which

assumes that the initial surface elevation will simply follow the sea floor deformation

instantaneously. The maps of the initial sea surface elevations corresponding to the four

rupture models used in this study are shown in Fig. 4. These four source models were used

to study the tsunami height, inundation extent, characteristics of tsunami deposits, and the

relationship among the aforementioned features.

4.1.1 Tsunami heights

Referring to Fig. 5, the four source models all predict that the northern tip of North

Sumatra and Thailand’s southwest Andaman coast are the two most affected areas, even

Table 2 Key characteristics of the four source models used in this study

Sourcemodel

Reference The numberof segments

Data used for inversion Data used for furtherconstraint

M1 (Mw 9.1) Piatanesi andLorito (2007)

16 Tide gauge data GPS Static offsets (near- andfar-field)

M2 (Mw 9.15) Chlieh et al.(2007)

661 GPS static offsets (near-and far- field) ? coralreefs uplift

Seismic data ? very far-fieldGPS data ? Jason-1 andTOPEX/Poseidon altimetrydata

M3 (Mw 9.08) DCRC 6 / Jason-1 altimetrydata ? satellite radarimageries after Tobita et al.(2006)

M4 (Mw 9.22) Grilli et al.(2007)

5 Offshore bathymetry ?initial seismicinversion model

Tide gauge data ? Jason-1altimetry data

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though the severity differs significantly. Large tsunami heights ([4 m) predicted by M1

cover the scattered offshore islands north to 12�N and extend to the southern tip of Phuket

Island. M2 predicts a much smaller region of large wave height near Phra Thong Islands.

Compared with the tsunami heights predicted by M1, M3 gives a much more concentrated

area of large tsunami height, covering only the coastal region from Phra Thong Island to

Phuket Island. Similarly, the large tsunami heights ([4 m) predicted by M4 are also

concentrated in the coastal areas between Phra Thong Island and Phuket Island. Note that

the tsunami heights predicted by M4 are much larger than those predicted by M3. Figure 6

shows a comparison between the simulated tsunami heights with the measured data along

the Thai Andaman coast. Clearly, M4 produces much larger tsunami heights in this area,

followed by M3 and M1. M2 gives the weakest tsunami waves among the four source

models.

Fig. 3 Initial sand distribution in the computational domain

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From the early studies on how earthquake-source parameters affect tsunamis, one might

naturally attribute the differences among these model results to two key factors of the first-

order importance in determining tsunami height: seismic moment and slip distribution

(Abe 1979; Geist 1998; Okal 1988). After analyzing a large number of seismic parameters

influencing tsunami generation, Okal (1988) suggested that tsunami height should have a

Fig. 4 The initial surface elevations derived from four fault models: a Piatanesi and Lorito (2007) (sourcemodel M1), b Chlieh et al. (2007) (source model M2), c Tohoku University Disaster Control ResearchCenter (DCRC) (Koshimura et al. 2009) (source model M3), d Grilli et al. (2007) (source model M4)

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direct relationship with seismic moment M0. This conclusion was proved basically true by

our simulation results but with one exception. The tsunami heights along the Thai And-

aman coast are roughly correlated to the magnitudes of the selected source models, except

for M2, which ranks the second largest among the four fault models; however, much

smaller tsunami heights are generated compared to M1 and M3. The exceptional low

tsunami heights generated by M2 might be understood from the following two aspects: the

rupture length of the 2004 Sumatra–Andaman earthquake is extremely long and only the

northern portion of the rupture contributes significantly to the tsunami height along the

Thai Andaman coast. Since the seismic moment is linearly proportional to the slip value,

spatial variations in the amount of slip should be the most likely reason for the low tsunami

heights associated with M2.

The slip distribution of the northern part of the 2004 Sumatra–Andaman rupture, which

starts from the southern tip of Nicobar Islands and ends to the northern tip of Andaman

Islands, may directly affect the tsunami heights near the Thai Andaman coast. The fol-

lowing aspects may have contributed to the differences in the simulated tsunami heights in

this area:

Fig. 5 Maximum sea surface elevations during the whole life span of the tsunamis generated by the fourfault models: a Piatanesi and Lorito (2007) (source model M1), b Chlieh et al. (2007) (source model M2),c Tohoku University Disaster Control Research Center (DCRC) (Koshimura et al. 2009) (source model M3),d Grilli et al. (2007) (source model M4)

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1. The rupture lengths in the four fault models are different and vary in the range of

1,155–1,300 km. The number of the sub-faults and the size of each sub-fault are

different among the four fault models. Along the rupture length, 16 sub-faults are

divided for M1, 661 for M2, 6 for M3, and 5 for M4. Except for M2, the other three

fault models assume that the slip is distributed uniformly over the sub-faults in the dip

direction. According to Geist and Dmowska (1999), this assumption may significantly

Fig. 6 The calculated tsunami heights (blue bars) and surveyed data (black dots) along Thai Andamancoast (the blue dots indicate the survey locations): a Piatanesi and Lorito (2007) (source model M1),b Chlieh et al. (2007) (source model M2), c Tohoku University Disaster Control Research Center (DCRC)(Koshimura et al. 2009) (source model M3), d Grilli et al. (2007) (source model M4). The red rectangularon the maps marks the Khao Lak coast shown in Fig. 7

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underestimate the maximum tsunami height and the leading wave steepness of local

tsunamis in most cases, leading to an underestimation of local tsunami run-up.

2. The values of slip vary among these fault models. The average slip value of the

northern portion of the rupture is 7.8 m for M1,\5 m for M2, 8.7 m for M3 and 12 m

for M4. The simulation results shown in Fig. 6 indicate that the calculated tsunami

heights are proportional to the average slip values in the corresponding rupture areas.

3. The locations of the rupture are not exactly the same. Compared with other fault

models, the main rupture zone of M3 is farther away from the Andaman and Nicobar

islands to the southwest. Even though the exact rupture location has limited influence

on far-field tsunami heights, it may pose considerable influence on local tsunami

height (Okal and Synolakis 2008).

In spite of a possible underestimation of the tsunami heights predicted by M1, M3 and M4

due to the assumption of uniform slip in the dip direction, these three models still generate

much larger tsunami heights in the coastal zones of interest, emphasizing the significance

of the slip value in determining tsunami heights.

In addition to seismic moment and slip distribution, other factors such as directivity,

focusing and defocusing effects may also affect tsunami heights. It has long been known

that the directivity plays an extremely important role in determining the tsunami height in

an area, especially in the far-field area (Okal 1988). The directivity effect suggests that

tsunami height is a strong function of the direction of tsunami path from its parent

earthquake. According to Kajiura(1972), the difference in azimuths for long rupture

sources is related to the geometric shapes of tsunami sources. In this study, the four fault

models all have similar geometries and fault orientations, suggesting that the directivity

effect is not the main reason for the discrepancy in the calculated tsunami heights.

Irregularity in bathymetry also plays an important role in determining the tsunami heights

in far fields for a tsunami generated with a given total energy (Satake 1988). It is because

the velocity of a tsunami (C ¼ffiffiffiffiffighp

under the shallow water approximation) varies with

the water depth h, a zone of reduced bathymetry (ridge, plateau) can spatially redistribute

wave energy (Okal and Synolakis 2008).

The average tsunami heights measured in the far-field regions seem to be more related

to the size of the parent earthquake, represented by its moment magnitude, than the exact

rupture location and slip distribution (Okal 1988; Okal and Synolakis 2008). Apparently,

directivity effect and wave focusing/defocusing by bathymetry during the propagation of a

tsunami play a more significant role in far-field than in near-field. By contrast, local

tsunami heights are controlled mainly by the magnitude and spatial variations of slip (Geist

1998). Along Thai Andaman coast, the tsunami heights are controlled mainly by the slip

value in the rupture area. As suggested by Okal (2008), the excitation of a tsunami should

grow linearly with the slip on the fault plane, and so should the final run-up, provided that

everything else are the same. When the rupture length is long, field survey data should

cover all the affected coastal areas since the constraints put on the magnitude and slip

values of the tsunami source by the tsunami heights are only limited to the near-field

regions.

4.1.2 Relationship between maximum extent of tsunami deposit and inundation limit

Figure 7 shows the inundation maps and the near shore tsunami heights along the Khao

Lak shoreline obtained by the four fault models. M4 gives the largest tsunami heights,

which are overestimated compared with the measured data. M1 and M3 give comparable

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tsunami heights and similar inundation maps. Both the tsunami height and inundation limit

are significantly underestimated by M2.

Figure 8 compares the spatial distribution of the simulated tsunami deposit with the

corresponding inundation-limit line for each fault model. The simulation results indicate

that the tsunami deposits are roughly correlated to the inundation limit, which is consistent

with the observations of most post-tsunami field surveys along the low-lying coastal areas,

i.e. tsunami deposits commonly extend to over 90 % of the actual inundation limit (Gel-

fenbaum and Jaffe 2003; Moore et al. 2006; MacInnes et al. 2009). It should be pointed out

that the simulation results in Fig. 8 were obtained by assuming an unlimited sediment

supply in the simulation domain. In reality, the existence of coral reef and outcrops in

nearshore regions and the presence of concrete roads and coastal structures may make the

occupied area non-erodible, affecting the resultant distribution of tsunami deposits (the

influence of sediment supply will be discussed in Sect. 4.3). Recent field survey on the

inundation and tsunami deposits due to the 2011 Tohoku-oki tsunami from Sendai Plain

provides one exception (Abe et al. 2012; Chague-Goff et al. 2012; Goto et al. 2011, 2012).

After surveying seven shore-normal transects along the Sendai Coastal Plain, Abe et al.

(2012) found that sand layers of thickness [0.5 cm could extend to over 90 % of the

inundation distance in places where the inundation distance was\2.5 km. However, in the

places where the inundation distance was up to 4.5–5.0 km, sand layers of thickness

Fig. 7 The inundation maps, calculated tsunami heights (blue lines) and surveyed data (black dots) alongthe Khao Lak shoreline for the four source models: a Piatanesi and Lorito (2007) (source model M1),b Chlieh et al. (2007) (source model M2), c Tohoku University Disaster Control Research Center (DCRC)(Koshimura et al. 2009) (source model M3), d Grilli et al. (2007) (source model M4). The white line in eachmap indicates the measured run-up limit

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[0.5 cm extended only to 3 km, which is only 57–76 % of the inundation distance;

beyond 3 km landward, the tsunami deposits continued as a mud layer to the inundation

limit. High concentrations of water-leachable chloride contained in the mud deposit

indicate that the geochemical markers may prove to be useful in identifying the maximum

inundation limit of paleotsunamis that could extend well beyond any preserved sand layer

(Goto et al. 2011). Therefore, the maximum landward extent of sand deposit can be only

assumed to represent the minimum inundation limit.

4.1.3 Thickness of tsunami deposit

Figure 9 compares the predicted thicknesses of tsunami deposit with those measured along

the four transects shown in Fig. 1. Three fault models (M1, M2 and M3) underestimate the

deposit thickness along all four transects. Only M4 gives comparable results, especially

along transects S2 and S3. The deposit thickness is roughly proportional to the tsunami

height along the coast, which determines the inundation depth and velocity inland. M2

predicts negligible tsunami deposits in the surveyed regions due to the low tsunami heights

and the limited inundation depth; M4 gives the largest tsunami heights and the thickest

deposit thickness. Figure 9 suggests that tsunami deposit thicknesses could be indicative of

nearshore tsunami heights, provided that other parameters (topography, initial sand dis-

tribution, etc.) are kept the same.

Figure 10 shows the spatial distributions of tsunami deposit along transects S1–S4

predicted by M4. A strong correlation between the topography and the deposit thickness is

demonstrated in Fig. 10. Thick deposits are found in the topographic lows but less deposit

in topographical highs. The distribution of tsunami-deposit thickness has been described in

many published papers, which have suggested that the thick deposits usually occur locally

in low-lying areas or in front of topographical highs (Peters et al. 2007; Moore et al. 2007;

Smith et al. 2007). The relationship between topography and deposit thickness underlines

that the deposit thickness is highly sensitive to the local topography in a studied area.

Therefore, the discrepancy between the simulated and measured deposit thicknesses is due

partly to the relatively coarse topography data we used in this study.

Fig. 8 The spatial distributions of tsunami deposit thickness: a Piatanesi and Lorito (2007) (source modelM1), b Chlieh et al. (2007) (source model M2), c Tohoku University Disaster Control Research Center(DCRC) (Koshimura et al. 2009) (source model M3), d Grilli et al. (2007) (source model M4). In each map,the blue line marks the run-up limit, and the red dots indicates the survey locations along the four transects.The color in the map indicates the deposit thickness and the unit of the color bar is meter

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Characteristics of tsunami deposits are linked to tsunami source parameters through

tsunami heights and inundation limit in a study area. Aside from bathymetric variation and

the effect of directivity, tsunami heights along the coast of a study area are basically

controlled by two key source parameters: seismic moment and slip distribution. Local

tsunami heights are directly proportional to the slip value in the corresponding rupture

area. Far-field tsunami heights have a positive relationship with the seismic moment, which

determines the total volume of seawater displaced. Greater tsunami heights along a coast

could result in a larger inundation extent, giving a higher possibility that a larger portion of

the inundation area would be covered by thicker tsunami deposits. Our simulation results

also suggest that thicker deposits may correspond to larger earthquakes if multiple historic

or pre-historic tsunami-deposit layers are found in the same location, assuming that the sea

level hasn’t changed much between those events and all the deposits are well preserved.

From a comparison between the simulation results given by the four fault models and

the measured tsunami deposits and tsunamis heights along Thailand Khao Lak coast, it

seems that the fault model M4 is more reasonable. In the following discussion of possible

influences of other factors on tsunami deposits, only the fault model M4 is used.

4.2 Influence of multiple waves

As shown in Fig. 11a, the Khao Lak coast may see multiple waves according to the fault

model M4: the first peak is 13 m high, the second about 5 m high, the third \3 m, and

others are even smaller than the third wave. The time histories of tsunami height in

locations P1 and P2 (Fig. 11a) indicate that transect-S3 is mostly affected by the first wave.

According to our numerical simulations, the wave front reaches the inundation-limit line

0 2 4 6 80

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S1

0 2 4 6 8 10 120

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S2

Measured dataM1M2M3M4

0 2 4 6 8 10 120

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S3

0 2 4 6 8 10 120

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S4

Fig. 9 Comparisons of the simulated tsunami-deposit thicknesses with the survey data

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around 2 h 40 min after the earthquake. We define the stage before 2 h 40 min as the up-

rushing stage and the rest the backwash stage. Figure 11b shows three snapshots of tsunami

deposit thickness along transect-S3; these snapshots clearly show that the tsunami deposits

along transect-S3 are formed mostly by the first wave during the up-rushing stage and

reworked by the receding flow during the backwash stage. Two large deposition zones (one

between 250 and 450 m inland, and the other between 500 and 700 m inland) are formed

0 200 400 600 800 1000 12000

4

8

12

16

Distance (m)

Ele

vatio

n (m

)Transect S1

0 200 400 600 800 1000 12000

10

20

30

Distance (m)

Dep

osit

thic

knes

s (c

m)

Model ResultsMeasurement

200 400 600 800 10000

4

8

12

16

Distance (m)

Ele

vatio

n (m

)

Transect S2

200 400 600 800 10000

10

20

30

Distance (m)

Dep

osit

thic

knes

s (c

m)

0 200 400 600 800 10000

4

8

12

16

Distance (m)

Ele

vatio

n (m

)

Transect S3

0 200 400 600 800 10000

10

20

30

Distance (m)

Dep

osit

thic

knes

s (c

m)

0 200 400 6000

4

8

12

16

Distance (m)

Ele

vatio

n (m

)

Transect S4

0 200 400 6000

10

20

30

Distance (m)

Dep

osit

thic

knes

s (c

m)

Fig. 10 Spatial distributions of tsunami deposits along the four surveyed transects. Left topographicprofiles, maximum tsunami heights, and tsunami deposits (with a 10-times exaggeration in the layerthickness) along the transects S1–S4 (see Fig. 1 for their locations). Right comparisons between thecalculated tsunami-deposit thicknesses and the survey data along the four transects S1–S4

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during the up-rushing stage of the first wave, indicating that most sand in the deposits is

entrained locally by the wavefront and then transported inland. When the first wave reaches

the inundation limit, overland water starts to retreat, and part of the deposits in the large

deposition zone between 250 and 450 m are eroded and transported seaward to the coastal

area near the coastline, forming a smaller deposition zone near the coastline (between 10

and 200 m). The second and third waves are not large enough to modify the shapes of the

deposition zones. This is the case when the successive tsunami waves are smaller than the

first wave. In other cases where some of the successive tsunami waves are larger than the

preceding wave, pre-existing tsunami deposits could be completely removed by the large

successive waves, leaving no trace of tsunami deposits, as discussed by many previous

studies (Apotsos et al. 2011a; Dawson and Shi 2000; Li et al. 2012). These studies all

pointed out the possible changes in deposit thickness and distribution caused by backwash

flows or one of the subsequent multiple waves during a tsunami event. Due to the fact that

the tsunami-deposit thickness measured by geologists after an event records only the final

stage of sediment erosion–deposition process at a surveyed location, existing inverse

models (Jaffe and Gelfenbuam 2007; Soulsby et al. 2007) using deposit thickness as a main

parameter have to assume that successive tsunami waves are smaller than the first wave;

otherwise, the inverse models might underestimate the strength of the tsunami flow.

Wav

e el

evat

ion(

m)

0 200 400 600 800 10000

5

10

15

20

Distance (m)

Dep

osit

thic

knes

s (c

m) t=2h 35min

t=2h 40mint=2h 45min

Before backwash

After backwash

Uprushing stage

2 2.5 3 3.5 4-10

01020

Point P2

2 2.5 3 3.5 4-10

0

10

20Point G

2 2.5 3 3.5 4-10

0

10

20Point P1

Time(hour)

(a)

(b)

Fig. 11 The influence of multiple waves on the tsunami deposit thickness along transect S3: a the timeseries of tsunami height at locations G, P1 and P2 (the exact locations are shown in Fig. 1); b threesnapshots of deposit thickness along transect S3

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4.3 Influence of sediment supply

To further understand effects of different local sediment distributions, two more cases

were simulated with three different initial sediment distributions: sediment distributions

DA, DB and DC. The differences among these three distributions are summarized

below:

1. For the distribution DA, sand classes with grain sizes of 0.1, 0.2 and 1.0 mm were

specified for the muddy area, the sandy area, and the inland gravel area, respectively.

The rocky area was non-erodible.

2. For the distribution DB, the grain size in the inland gravel area was specified as

0.5 mm instead of 1.0 mm.

3. For the distribution DC, the inland area was assumed to be densely covered by

vegetation or buildings (i.e. non-erodible).

Figure 12 shows the maps of tsunami-deposit thickness, obtained by using the fault

model M4, for the three initial sediment distributions. The tsunami-deposit extents still

follow more or less the inundation extents even though the deposit thicknesses are sig-

nificantly different. Since the sediment distribution DB has finer sand available in the

inland area, it gives rise to a layer of tsunami deposits thicker than the other two distri-

butions. As shown in Fig. 13, the deposit thickness given by the sediment distribution DA

is 30–50 % thicker than those given by the sediment distribution DA in most of the

surveyed locations. The deposit thickness is significantly smaller for the sediment distri-

bution DC, and only in several surveyed locations can the deposits be observed. In other

words, if an inland region is non-erodible, the tsunami deposits may not be detectable in

most of the inundated areas.

It can be concluded from Figs. 12 and 13 that the initial sediment distribution, espe-

cially the inland sediment supply, can significantly affect the distribution of the resultant

Fig. 12 The predicted tsunami deposit thicknesses for different initial sand distributions : a distributionDA, b distribution DB, and c distribution DC. The color in the map indicates the deposit thickness and theunit of the color bar is meter

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tsunami deposits. This conclusion is in agreement with what was observed during several

modern post-tsunami field surveys (Smith et al. 2007; Sato et al. 1995; Shi et al. 1995;

Richmond et al. 2012): the main source of tsunami deposits came from beach areas or local

sand. Similar conclusions were also mentioned by Apotsos et al. (2011b) who simulated

tsunami inundation and sediment transport in a sediment-limited embayment on American

Samoa; their simulations showed that the amount of sediment available for transport could

affect the onshore deposition thickness by more than 50 % by.

4.4 Influence of bottom roughness

Three distributions of bottom roughness in the inland areas, described by Manning’s

roughness coefficient, were simulated to understand the influence of bottom roughness on the

resulting tsunami deposits. The sediment distribution described in Sect. 3.4 was adopted here,

the fault model M4 was used to generate the initial tsunami, and a fixed value of n = 0.013

was chosen for the water area. The three distributions of bottom roughness in the inland area

are: n = 0.03 for Case NA, n = 0.06 for Case NB, and a viable value of n for Case NC. For

Case NC, the roughness was determined by considering the different land uses/covers (see

Fig. 14), and six different types of land uses/covers were identified in the inland region

according to the geo-referenced high-resolution satellite image Ikonos (CRISP 2004) in Khao

Lak area: grass land, young plantation, dense forest, urban area, mangrove forest, and water

areas. For each area, a different Manning’s coefficient was specified according to the

guideline for selecting the Manning’s coefficients for natural channels and floodplains (Ar-

cement and Schneider 1989). A large roughness value (n = 0.06) was chosen for the urban

0 2 4 6 80

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S1

0 2 4 6 8 10 120

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S2

Measured dataDADBDC

0 2 4 6 8 10 120

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S3

0 2 4 6 8 10 120

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S4

Fig. 13 Comparisons of the simulated tsunami-deposit thicknesses with the survey data for different initialsediment distributions

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areas. Similarly, larger roughness values were also specified for dense forest (n = 0.065) and

mangrove forest (n = 0.08).

Referring to Fig. 15, which shows the maps of deposit thickness for the three distri-

butions of bottom roughness, the effects of bottom roughness on sediment transportation

and deposition are significant. As shown in Fig. 16, larger bottom roughness helps dissi-

pate wave energy more quickly, and consequently leads to a smaller inundation area, lower

inundation depth, slower flow velocity and thinner deposit zone. Although the deposit

thicknesses have been dramatically decreased by larger values of bottom roughness

Fig. 14 The map of bottom roughness based on the land-cover classification of a 2003 Ikonos image forKhao Lak

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(n C 0.06), tsunami deposits still cover most part of the inundation area. If this thin deposit

layer is recognizable in urban areas or dense forest areas, the chance to identify tsunami

inundation extent still remains.

Fig. 15 The predicted tsunami-deposit thicknesses for different types of land coverage: a case NA; b caseNB; c case NC. The color in the map indicates the deposit thickness and the unit of the color bar is meter

0 2 4 6 80

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S1

0 2 4 6 8 10 120

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S2

Measured dataNANBNC

0 2 4 6 8 10 120

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S3

0 2 4 6 8 10 120

10

20

30

Sample location

Dep

osit

thic

knes

s (c

m)

Transect S4

Fig. 16 Comparisons of the simulated tsunami-deposit thicknesses with the survey data for different typesof land coverage

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5 Discussion

5.1 Uncertainties associated with inverting tsunami source parameters

from the characteristics of tsunami deposits

The characteristics of tsunami deposits such as landward extent and deposit thickness have

been used to infer the recurrence intervals and magnitudes of great tsunami earthquakes,

slip distributions of historic or prehistoric tsunami earthquakes in some specific areas

(Bourgeois et al. 2006; Macinnes et al. 2010; Martin et al. 2008; Nanayama et al. 2003;

Satake et al. 2005). From the extents of prehistoric tsunami deposits, Nanayama et al.

(2003) inferred that large tsunamis unusually occurred about every 500 years on average

over the past 2,000–7,000 years along the Kuril trench. Using tsunami-deposit distribution,

Macinnes et al. (2010) further determined the magnitude and slip distribution of the 1952

Kamchatka great earthquake. Martin et al. (2008) untangled the 1969 Ozernoi and 1971

Kamchatskii tsunamis using a combination of field mapping of tsunami deposits and

tsunami modeling; they differentiated these two tsunamis in some localities, and elucidated

the earthquakes’ focal mechanisms and rupture areas. The commonality of the approaches

used in these studies is the use of forward numerical models: a series of hypothetical

rupture models are proposed based first on known information such as tectonic setting of

the source region, existing catalogs of the earthquake, paleoseismological evidences in the

stratigraphic record, and then forward numerical models are used to simulate the tsunami

propagation and inundation in the interested coastal areas based on these hypothetical

rupture models. The simulated inundation extents are compared with the observed deposit

extents to see whether the initial tsunami heights suffice to inundate the whole area covered

by tsunami deposits. Obviously, the trial-and-error procedure could be totally hopeless and

questionable when we have no clue or little information on the location and the geometry

of the source earthquake. However, when the characteristics of tsunami deposits are used

as proxies to infer the tsunami source parameters, we should always bear in mind the

following points:

1. In some instances, the evidence for tsunami deposits on a coast simply may not be well

preserved due to subsequent flooding or bio- and cryoturbation (Bourgeois et al. 2006).

2. The characteristics of tsunami deposits are very site-specific and may be

significantly affected by local conditions. It is necessary to have a good

understanding of the local conditions such as topography, land uses and sediment

availability. According to the aforementioned numerical experiments, the thickness

of tsunami deposits is more easily affected by local conditions. Compared with

deposit thickness, the deposit landward extent is more robust: if a thin deposit still

could be detected, its extent would be indicative of the tsunami inundation area,

thus the tsunami size.

3. Information on the local sea-level and geomorphic history of a coastline under

investigation is essential when reconstructing a tsunami history for a specific

location. On a stable coast, it is possible to take the current elevation and extent of a

tsunami deposit as an indicator of run-up and inundation; however, on an unstable

coast, changes in relative sea level and shoreline location must be taken into

account. Even for young tsunami deposits, run-up estimates might be inaccurate if

there had been uplift or subsidence associated with recent earthquakes (Bourgeois

et al. 2006).

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5.2 Forward numerical models versus inversion models

The application of forward numerical models described in Sect. 5.1 relies heavily on the

availability of the location and geometry of a source earthquake, which could be

unavailable for pre-historic tsunamis. In addition to forward numerical models, there are

other types of inverse models that could directly calculate the slip distribution of a fault

model from available tsunami data. These types of inverse models are briefly reviewed

here, and followed by a discussion of possible difficulties in using inland tsunami-height

data to infer slip distribution.

The characteristics of a tsunami wave, including wave heights recorded by DARTs in

deep sea, waveforms recorded by tide gauges, and runup heights measured during post-

tsunami surveys, are useful to constrain some fault parameters (Geist and Dmowska 1999;

Okal and Titov 2007; Piatanesi and Lorito 2007; Pires and Miranda 2001; Satake 1987; Wu

and Ho 2011; Abe 1973). Different methods for tsunami-waveform inversion have been

proposed in the past. Various types of data are required by these methods. Abe (1973)

employed a backward ray-tracing technique to locate the boundaries of a tsunami source.

In this method, only the tsunami arrival time at each observation point is required to start

the backward tracing computation. This technique applies only to linear long waves and

can only locate the tsunami source, without giving any information about its shape and

amplitude. Satake (1987) proposed a method to invert the slip distribution using tsunami

waveforms recorded by tide gauges. In this method, the fault area is divided into sub-faults,

and synthetic waveform is calculated at each tide gauge for each sub-fault. By using the

technique of Green’s function and the waveforms recorded by available tide gauges, they

treated the observed waveform as a linear superposition of the Green’s functions so that the

displacement on each sub-fault can be determined by solving a linear equation (Satake

1987; Johnson and Satake 1993). Piatanesi et al. (1996) proposed a very similar approach

to retrieve the information on slip distribution. They used Green’s function technique and

solved shallow water equations using a finite-element method instead of finite-difference

method; their results showed that the local run-up heights collected during the post-event

field surveys could be used for the inversion when tide-gauge records are not available/

sufficient. Instead of applying a least-square procedure to minimize the difference between

the recorded tide-gauge waveforms and the calculated synthetic waveforms, they applied a

least-square procedure to minimize the difference between the observed run-up values and

the computed maximum water levels along the coast.

For methods based on linear long waves, using surveyed tsunami-height and run-up data

in inland areas or some tide-gauge data in very shallow areas can be problematic. It is

evident that the assumption of linear waves holds only in deep seas where tsunami heights

are far less than water depth. However, linearity of water waves is no longer valid in an

inundated area or in nearshore waters where the water depth is usually comparable to

tsunami height. In reality, the nonlinearity of tsunami waves and the effects of local

bathymetry and topography cannot be neglected. To address this difficulty, an adjoint

method proposed by Pires and Miranda (2001) may be very promising. As an alternative to

the approaches based on linear long waves, the joint method has the advantage of being

able to use either linear or non-linear forward propagation models that can account for non-

linear advection and run-up effects. This method is particularly useful for pre-historic

tsunamis or even some historic and modern tsunamis for which the tide-gauge records are

not available or scarce. For pre-historic tsunamis, the available information could only be

tsunami deposits, which may be scattered in some coastal lowland areas. With this method,

the tsunami heights must be first inferred directly or indirectly from the characteristics of

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tsunami deposits before they are used as input data to the inversion model. However, the

adjoint method has only been tested using tide-gauge records for the tsunami caused by the

28th February 1969 Gorringe Bank earthquake. The capability of using tsunami heights or

run-ups as the only input data to an inversion model is still yet to be proved.

Compared with the trial-and-error approach used in forward numerical models, the

reliability of inversion models depends mostly on the quality and quantity of surveyed

tsunami data. To derive reasonable inversion results, a large number of tide-gage stations

with good azimuthal coverage is desirable. For pre-historic tsunamis, the inference from

tsunami deposits to tsunami heights could be promising but very challenging.

6 Conclusions

In this paper, numerical experiments were conducted for the Thailand’s Khao Lak region to

understand the uncertainties associated with inverting tsunami source parameters from the

characteristics of tsunami deposits. Two key characteristics of tsunami deposits were

examined: deposit extent and thickness. The influences of tsunami source parameters,

multiple waves, sediment supply and bottom roughness on deposit extent and thickness

were discussed. Our main conclusions are summarized as follows:

1. For near-field tsunami deposits (close to the source area), the deposit extent and

thickness are more indicative of the slip values close to the tsunami deposit area. For

far-field tsunami deposits, the deposit extent and thickness are more indicative of the

magnitude of the source earthquake.

2. Compared with deposit thickness, the deposit landward extent is more robust: if a thin

deposit layer can be detected, the extent is indicative of the tsunami inundation area,

thus the tsunami size.

3. The extent and thickness of tsunami deposits may be further used to quantify some

parameters of the corresponding source earthquake through two possible approaches:

forward numerical models based on a large number of hypothetical rupture models,

and direct inverse models. Forward numerical models require considerable compu-

tational resources, and existing direct inverse models are for linear long waves. There

is a need to extend direct inverse models to handle nonlinear effects.

4. To reconstruct a tsunami history for a specific location, it is important to know the

local conditions, the preservation of tsunami deposits, the local sea-level and

geomorphic history of the coastline.

Acknowledgments The authors would like to thank Dr. Shigehiro Fujino for generously sharing with usthe detailed tsunami-deposit data using in this study. This work was supported by the Earth Observatory ofSingapore, Nanyang Technological University, Singapore, through the project ‘‘Understanding TsunamiSources from Surveyed Tsunami Heights and Sediment Deposits’’. This is EOS Contribution No. 63.

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