433

A Finite – Fault Modeling of the 1755 Lisbon

Earthquake Sources

A. Carvalho1, A. Campos Costa, C. S. Oliveira

.

Introduction

In Portugal, being located at a moderate/low seismicity intraplate area, insufficient accelerograms

have been recorded to satisfactory undertake any regional empirical study. The number of

accelerograms is not only small but also refers to low-magnitude earthquakes located in only some

parts of its entire seismic area. For that reason, most prediction techniques of ground motion in

Portugal have been based on international empirical laws and not on regional data to quantify the

characteristics of ground motions. However, differences in the regional geology can led to

variations in ground motions characteristics and the use of empirical laws of other regions is

questionable and may not be appropriate for Portugal. As prediction cannot be based on empirical

analyses, theoretical models must be used as the basis for the predictions of strong motion in

Portugal. The development of stochastic based ground motion synthesis associated to a

seismological finite-fault modeling is a worldwide approach that can be used for representation of

1 A.. Carvalho (*)

LNEC, Laborato´ rio Nacional de Engenharia Civil, Lisboa, Portugal e-mail: xana.carvalho@lnec.pt L.A. Mendes-Victor et al. (eds.), The 1755 Lisbon Earthquake: Revisited, Geotechnical, Geological, and Earthquake Engineering 7,

DOI 10.1007/978-1-4020-8609-0_28, _ Springer ScienceþBusiness Media B.V. 2009

434

future large magnitude earthquakes occurring in Portugal, allowing the reproducing of specific

source effects like directivity and asperities distribution.

The strong ground motion prediction based on finite-fault simulation requires the identification of

the fault (strike, dip, length and width), source kinematics parameters (stress drop, velocity of

rupture, slip distribution), regional crustal properties (geometrical spreading, anelastic structure,

amplification and attenuation upper crust parameters) and the determination of amplification

effects due to the local site geology.

The model parameters calibration has been obtained with a dataset that includes horizontal

components of ground acceleration records (at rock sites) obtained by the Portuguese digital

accelerometer network. Validation and comparison are entirely in terms of 5% damped pseudo

absolute response spectra for acceleration.

The demonstrated agreement between model and data for low to moderate events in Portugal

provides strong grounds for accepting the stochastic-process model predictions for this type of

events and to use it as the basis for characterization of stronger earthquakes considering a finite

fault rupture modeled as a sum of a number of point sources distributed spatially and temporally.

Being so, the calibrated model is used to simulate ground motion acceleration for the 1755 Lisbon

earthquake, considering different source models proposed in literature. For each possible source

model several simulations were performed varying nucleation points. The soil effect was taken

into account considering a nonlinear behaviour of the stratified geotechnical sites conditions. The

simulated intensity is compared with the observed intensity values.

Numerical approach

The non-stationary stochastic finite fault simulation method, herein called RSSIM (Carvalho et al.,

2004; 2007) has been implemented starting from the classic simulation code FINSIM (Beresnev

and Atkinson, 1998), widely employed in the seismological literature for simulation of the ground

motion from both moderate and high magnitude earthquakes. However, it differs from the classic

FINSIM as it avoids the computation of acceleration time series representing the contribution of

each sub-fault, but synthesizes the ground motion due to the entire fault from the Power Spectral

Density Function (PSDF) radiated by each sub-fault, using the random vibration theory and the

extreme values statistics (ex. Vanmarcke, 1976; Boore & Joyner, 1984; Boore, 2003).

Like FINSIM, the RSSIM method assumes that the fault plane is a rectangle, subdivided into an

appropriate number of sub-faults, which are modelled as point sources characterized by an ω2

spectrum.

The method starts estimating, for each subfault, the amplitude of the acceleration Fourier

spectrum, ( , )A R :

2( , ) ( ) ( ) ( , ) ( ) ( )ZA R C S G R An R P F (1)

435

where C is a scaling factor including the free surface amplification factor, the radiaton pattern of

shear waves and the energy partition into the two horizontal components, S() is the amplitude

displacement source spectrum, G(R) is the geometric spreading factor, An(,R) is the anelastic

path attenuation factor, P() accounts for the upper crust attenuation and FZ() is a crustal

amplification function. The functional form of all these factors and the respective physical

meaning can be found elsewhere [eg. Boore, 2003; Carvalho et al., 2004; Ferrer& Sanchez-

Carratalá, 2004] and in the modeling parameters section of this text.

Taking into account the Fourier amplitude spectrum, ( , )A R , and a given source duration, Ts, the

one-sided power spectral density function (PSDF) of acceleration can be derived by means of:

2( , )1

( )

s

A RSa

T (2)

The PSDF of the response of the oscillator with a circular frequency n and a damping ratio

assuming a stationary process is calculated as:

2( , , ) ( ) ( , , ) x n x nS Sa H (3)

in which ( , , ) x nH is the complex displacement frequency response function relative to the

input absolute base acceleration and given by

2

2 2( , , )

2

nx n

n n

Hi

(4)

To cope with the non stationary of the intensity of the response of the oscillator, a intensity time-

modulating response function, , is specified directly in a way that the evolutionary response

moment of order k is obtained by the modulating function and the stationary response moment of

order k as:

2, , , , , ( , , ) k n n k nt t (5)

in which

0

, , ( , , )kk n x nS d

(6)

and , the response modulating function, is obviously dependent of frequency and damping of the

one degree of freedom system and can be found in Duarte (1978).:

1

2 11 2

2 22 12

0

1( t t )n

n

( t t ) ( t t )n n

t t

( t , , ) e t t t

e e t t

. (7)

436

where t1 represents the starting time of the strong motion part of the accelerogram and t2 gives the

starting time of the decay part being t2 = T + t1 , T the duration of the strong motion.

For a finite source, subdivided into N sub-faults, and considering that stochastic process associated

to all the N subfaults are independent, the final evolutionary finite–fault response moment, Tk ,

can be estimated as the sum of all subfault response moments. Therefore:

2

1

, , , , , , ,

N

Tk n j n k nj

j

t t (8)

Considering the extreme values statistics and taking T as the duration of the earthquake, the

displacement non-stationary response spectrum, RS, that synthesizes the integration over the fault

of all the delayed sub-sources can be estimated (Vanmarcke, 1976):

0 00

0.577216, , , 2 ln(2 ) , , ,

2 ln(2 )

Tn nRS T f T T

f T

(9)

Where fo is the central frequency of the response written as

Tn

0 Tn

Tf

T

12

2

0

( , , , )1

2 ( , , , ) (10)

Comparison of response spectra obtained with the non-stationary stochastic finite fault simulation

method, RSSIM, and with classic FINSIM can be seen in Zonno et al. [2005] and Carvalho et al.

[2007].

Once the non-stationary response spectra have been achieved, an equivalent stationary PSDF can

be iteratively estimated, following the classical theory of stationary random process. This approach

was adopted in an automatic seismic loss estimate methodology (LNECLoss – Sousa et al., 2004)

that was developed at LNEC. This PSDF will be the input for the 1D analysis of soil effects.

In order to define scenarios at locations where different geotechnical conditions prevail, an

adequate transfer function must be defined to cope with the filtering effect and dissipative nature

of local soil propagation medium. The complex transfer function iH ( | h, , ,G ) ς from rock

outcrop acceleration to shear strain of each layer i is obtained, which allows to write the shear

strain PSDF as function of the independent variable associated with the circular frequency :

*i i ro iS ( ) H ( | h, , ,G ) S ( ) H ( | h, , ,G ) ς ς (11)

in which andh, , G ς are parameters vectors of n+1 dimension, representing the height, density,

viscous proportional damping ratio and the elasticity distortion modulus, of each stratified soil

layer i, respectively. and *i iH ( ) H ( ) are complex conjugate functions.

437

This last equation is only valid under the hypothesis of elastic linear behaviour of soil meaning

that, parameters ( ,G)iς should be kept constant even if they depend on the value of shear strain .

However, even for low amplitude input motion, soil tends to exhibit a non-linear behaviour. In this

case an equivalent iterative linear secant stiffness approach was adopted as it is frequently used in

other soil dynamics computer codes (SHAKE, FLUSH). For that purpose it will be necessary to

have estimates of the peak shear strain vector peaki, j whose members i vary from 1 to n for each

soil layer, and j stands for the interaction cycle

Extreme Statistics determines the estimates of peakj based on the hypothesis that the PSDFs

i, jS ( ) are a Gaussian zero mean random processes. In that case estimates of peaki, j can be

obtained by:

22 0 2

2 0

i, jpeaki, ji, j

i, j

Tln ln(ln( )

(12)

where the stationary moments of 1st and 2nd orders of the strain are defined as defined in eq. 6 but

for the PSDFs S ( )i , j defined in equation 11.

Once convergence is attained, the transfer function H ( )a between rock outcrop acceleration and

site specific acceleration is defined, and the PSDF of this acceleration can be computed as:

2a ro aS ( ) S ( ) H ( ) (13)

in which 2

aH ( ) represents the transfer function between outcrop acceleration and the absolute

acceleration at the top of the 1D vertically S wave propagation column of stratified soil medium.

This approach allows a significant saving of calculation time, roughly a factor of twenty with

respect to the usual approach based on the traditional methods, can be achieved.

Resuming, each seismic input is defined by the rock outcrop power spectral density function of

acceleration and, given a stratified soil profile, the new PSDF is computed at the surface level

using procedure described above.

Modeling parameters

Finite-fault simulations require that the fault-plane geometry (length, width, strike, dip, number of

subfaults considered and depth to the upper edge), the source parameters (seismic moment, slip

distribution, stress drop, nucleation point, rupture velocity), the crustal properties of the region

(geometrical spreading coefficient and anelastic attenuation) and the site-specific soil response

information be previously specified.

438

Carvalho et al [ 2005, 2007] estimated most of this parameters using previous information from

several regional studies and a least square sense, comparing synthetic and observed response

acceleration spectra, to obtain a set of parameters that best fit data. In the last months a progress

has been made towards understanding the source and crustal characteristics, estimating source

parameters based on source spectra of S waves of 12 earthquakes records (corresponding to a total

of 25 records) and the upper crustal attenuation parameter from the high-frequency decay of the

acceleration spectra, after correcting observed spectra from geometrical spreading and anelastic

attenuation effect. Here we report the results of that study.

The dataset used includes horizontal components of 25 ground acceleration records obtained by

the portuguese digital accelerographic network, on rock sites. The regional distribution of the

earthquakes epicenters and magnitudes are illustrated in Figure 1. Some of the events were

recorded in more than one station.

Mag nitud e

ÊÚ 3.3

ÊÚ 3.4

ÊÚ 3.6

ÊÚ 3.9

ÊÚ 4.0

ÊÚ 4.1

ÊÚ 4.2

ÊÚ 4.4

ÊÚ 4.5

ÊÚ 5.4

5.9ÊÚ

36° 36°

38° 38°

40° 40°

42° 42°

11°

11°

9°

9°

7°

7°

ÊÚÊÚ

ÊÚ

ÊÚ

ÊÚ

ÊÚ

ÊÚ

ÊÚÊÚ

ÊÚÊÚÊÚ

ÊÚÊÚ

N

#5#10

#7#12

#11

#6

#4

#1

#8

#9

#2

#3

Mag nitud e

ÊÚ 3.3

ÊÚ 3.4

ÊÚ 3.6

ÊÚ 3.9

ÊÚ 4.0

ÊÚ 4.1

ÊÚ 4.2

ÊÚ 4.4

ÊÚ 4.5

ÊÚ 5.4

5.9ÊÚ

36° 36°

38° 38°

40° 40°

42° 42°

11°

11°

9°

9°

7°

7°

ÊÚÊÚ

ÊÚ

ÊÚ

ÊÚ

ÊÚ

ÊÚ

ÊÚÊÚ

ÊÚÊÚÊÚ

ÊÚÊÚ

N

#5#10

#7#12

#11

#6

#4

#1

#8

#9

#2

#3

Fig. 1- Epicentral distribution of earthquakes of portuguese accelerographic data base

As two physical mechanisms of earthquake generations exists in Portugal, namely events

originated by the movement between the Eurasian and African plates (here in called interplates

events) and events originated in faults inside the Eurasian plate (herein called intraplate events),

calibration of model parameters was done separately with data corresponding to intraplate and

interplates events.

439

The horizontal components of the accelerations at each station were windowed, using a time

window that included the main S-wave arrival and 90% of total energy, and then Fourier

transformed to obtain acceleration and displacement-amplitude spectra.

The observed spectra

In RSSIM approach, the source term (S(ω) in eq. 1)is assumed as an omega-square (ω2) model

specified by [Brune, 1971]:

2

( )1

o

c

MS

(14)

where Mo and c stand for seismic moment and circular corner frequency respectively.

A visual inspection of the displacement-amplitude spectra of S-waves for the 12 events (see figure

2 for an example) leads to the conclusion that the spectral shapes for all events appear to be

similar, showing a plateau at lower frequencies, a decrease of the spectral amplitudes as f-2 at

higher frequencies and one corner frequency (the interception of both plateau and f-2 lines), as

predicted by the ω2 model.. However this feature seems to begin to change as magnitude nears 5.4

and the spectral shape of the 6.0 earthquake has two corner frequencies, where the spectral

envelope changes its general trend. This observational result implies that the shape of the source as

described by the ω2 model ceases to be valid as magnitude increases up to 5.5.

Another feature showed is that for frequencies greater than a certain frequency the spectral

amplitudes decay more rapidly as f-2. This decay is modeled as the high-cut filter P(ω) in eq. 1 and

in this study is described as 2

kP( ) exp( ) [Anderson & Hough, 1984], being k the

attenuation upper crustal parameter.

#4

1.E-08

1.E-06

1.E-04

1.E-02

0.1 1 10 100

Freq. [Hz]

AF

[c

m.s

]

#6

1.E-08

1.E-06

1.E-04

1.E-02

0.1 1 10 100

Freq. [Hz]

AF

[c

m.s

]

Fig. 2 Observed displacement-amplitude spectra of S-waves (for earthquakes #4 and #6, as in

figure 1) and lines of ω2 model.

440

Path parameters:

W adopted the frequency-dependent quality factor, Q(f)=250f 0.7 of Pujades et al. [1990] for the

inelastic attenuation ( , ) exp( ( ) ) An R fR Q f and the tri-piece-wise geometric attenuation

function described by Atkinson & Boore [1995] defined by assuming a crustal seismogenic

thickness of 31 km for the intraplate events [Jiménez-Munt et al, 2001] and 20 km for the

interplates events [Dezes & Ziegler, 2001].

Upper crustal parameter:

The term ( ) exp( ) P f is a high cut filter to account for near-surface attenuation effects,

which describes the observed rapid spectral decay at high frequencies. The k parameter is

estimated by fitting the high-frequency decay of the acceleration spectrum with a straight line in a

log-linear scale (Anderson & Hough, 1984), as illustrated in Figure 3. k was measured separately

for the two horizontal components of all the 25 records of our database. A suitable frequency band

(depending on quality of data, generally ranging from 5-10 Hz to 20-25 Hz) was chosen in order to

perform reliable regressions. A value of k=(0.032 ± 0.005) s was inferred from the analysis of all

records.

#7

1.E-03

1.E-02

1.E-01

1.E+00

1.E+01

0 5 10 15 20 25

Freq. [Hz]

SVF_X

AF

[c

m/s

]

#4

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0 5 10 15 20 25

Freq. [Hz]

SVF_X

AF

[c

m/s

]

Fig. 3 Example of k estimations from the amplitude Fourier spectra of acceleration. SVF_X: x

horizontal component of the S.Vicente Fora (SVF) station

As regard to site-specific amplification, we expressed the factor Fz(ω) in eq. 1, as a function that

takes into account of density and S wave velocity changes respect to an homogeneous propagation

model:

2

2

1

F ( )z zi

zi

(15)

We employed the impedance function with fzi=0.5Hz, for interplates events, accordingly to

Carvalho [2007].

441

Source parameter

Having a better understanding of attenuation, we can correct the observed spectrum back to the

source, obtaining the source displacement-amplitude spectrum as:

/ ( )2 2

( , ) ( , )( )

(2 ) ( , ) ( ) ( ) (2 )

f k R f Q fA f R A f RS f e R e

f An f R G R P f f

(16)

where A(f,R) is the S-wave spectrum of ground acceleration observed, the two exponential terms

are used to correct both upper crust and path and attenuation and the terms Rα corrects the

amplitude decrease due to geometric spreading.

In the w2 model, the high-frequency level of the source model is controlled by stress drop, Δσ, that

is correlated with frequency corner frequency in terms of the relation

136

04.91 10cf M

(17)

where Δσ is in bars, β in km/sec and M0 in dyne.cm.

As stress drop increases for an earthquake of a given moment, so does fc and the high-frequency

level of the source spectrum. Being so, the parameters that take values appropriate to each

earthquake source spectrum are seismic moment and stress drop.

On the basis of w2 model, the seismic moment and the corner frequency can be obtained by the

horizontal and f-2 lines from the Source displacement-amplitude spectra. Rovelli et al [1991]

suggests that one should avoid visual inspection or the simultaneous inversion of the ground

motion spectrum in terms of both seismic moment and corner frequency and computed the corner

frequency by means of an objective technique using the expression of Andrews (1986):

2

0

2

0

( )1

2( )

c

V f df

f

D f df

(18)

where V (f) and D (f) are the source velocity and displacement spectra. Knowing fc and the seismic

moment, the stress drop can be obtained using eq. 17.

Another technique is to estimate simultaneously seismic moment and stress drop using the

theoretical function of the source spectrum (eq 14) and fit it to the source spectra of S waves for an

assumed seismic moment with a constant stress drop (example in Figure 4). The seismic moment

is obtained from the source spectral amplitude at low frequency while searching to obtain Δσ at

high frequencies.

We have used the three techniques (visual inspection, eq. 18 and the fit of source theoretical

function to the source S-wave spectra) to obtain source parameters for each earthquake.

442

For the set of earthquakes the average stress drop is 101 bars for intraplate events and 66 bars for

interplates events.

#4

1.E-05

1.E-04

1.E-03

1.E-02

1.E-01

0.1 1 10 100

Freq. [Hz]

AF

[m

.s]

SVF

#6

1.E-04

1.E-03

1.E-02

1.E-01

1.E+00

0.1 1 10 100

Freq. [Hz]

AF

[m

.s]

SVF

7

Fig. 4 Example of the source spectra of two events. The smooth curve represents the theoretical

model of eq. 14 that was fit to the envelope of the source spectrum.

Duration:

The duration T of an earthquake signal at a hypocentral distance R can be represented as [Atkinson

& Boore, 1995]

0( ) T R T bR (19)

where T0 is the source duration (here taken as 1/fc) and b is a coefficient controlling the increase of

duration with distance. Carvalho [2007] obtained b=0.1 for intraplate events and b=0.015 for

interplates events.

Results of model parameters are represented in table 1 and figure 5 shows some examples of

response spectra comparison between synthetic and observed. In general, the synthetics are in

good agreement with observations for at least one of the recorded horizontal components.

Table1: Model parameters

Intraplate Interplate

Crustal thickness, D [km] 31 20

Quality factor, Q(f) 250*f0.7

Geometric attenuation 1/R (R 1.5D km)

1/R0 (1.5D km< R 2.5D km) 1/R0.5 ( R > 2.5D km)

Distance-dependent duration 0.1 R 0.015 R

k [s] 0.032

Shear-wave velocity, [km/s]

3.5

Crustal density, [g/cm3] 2.8

Stress drop, [bars] 101 66

Amplification function Fzi(ω)

2

2( )

1

zi zi

zi

F

fzi=0.5HZ

443

0.01

0.1

1

10

0.01 0.1 1 10

Períod [s]

Acc [

cm

/s^2]

#4

SVF0.01

0.1

1

10

100

0.01 0.1 1 10

Períod [s]

Acc [

cm

/s^2]

#3

SVF0.01

0.1

1

10

100

0.01 0.1 1 10

Períod [s]

Acc [

cm

/s^2]

#8

BEN

0.01

0.1

1

10

100

0.01 0.1 1 10

Períod [s]

Acc [

cm

/s^2]

#6

SVF

0.01

0.1

1

10

100

0.01 0.1 1 10

Period [s]

Acc [

cm

/s^2]

#7

BEN

0.01

0.1

1

10

100

0.01 0.1 1 10

Period [s]

Acc [

cm

/s^2]

#6

SVI

Fig. 5 Example of response spectra comparison between synthetic and observed data. Black lines

are the simulated results, gray lines are both horizontal components of the recorded accelerogram.

(simple line: component N-S; bold line: component E-W). Stations: SVF – S. Vicente Fora

(Lisbon); BEN – Benavente (Benavente); SVI – S. Vicente (Algarve).

1755 Lisbon earthquake

Source models

The 1755.11.01 earthquake, known as the 1755 Lisbon earthquake, generated the largest known

tsunami in SW Europe and its magnitude has been estimated as Mw= 8.5 – 8.9 by several authors

[e.g. Abe, 1979; Moreira, 1984]. The exact location remains controversial, even though the

earthquake epicentre is know to have been offshore. For the localization of the major seismogenic

zones in the SW Iberia Margin, please refer to figure 1 of Ribeiro et al. [2008] (this volume).

The several isoseismal maps published led to the conclusion that the source location of this event

was in the vicinity of Gorringe Bank (GBF) [Martinez Solares, 1979; Levret, 1991]. This location

was further supported by the occurrence of a tsunamigenic earthquake on 1969.02.28. Johnston

[1996] suggested that a NE-SW trending fault, at the base of the NW flank of Gorringe Bank,

could be responsible for the 1755 earthquake.

Baptista et al.[1998] performed a hydrodynamic modelling of the 1755 tsunami. Results from a

backward ray tracing simulations suggest a tsunami source located quite close to the Portuguese

444

coast. In order to precisely locate the 1755 seismogenic source, in 1998 the area between the

Gorringe Bank and the Cape St. Vicente has been surveyed within the framework of the European

BIGSETS projects (Big Sources of Earthquake and Tsunami in SW Iberia). One of the main

results [Zitellini et al., 2001] was the characterization of the active tectonic structure located

offshore Cape St. Vicente named as Marques Pombal Thrust fault (MPT) which, accordingly to

the authors, could be the generator of the 1755 Lisbon earthquake.

Terrinha et al. [2003] pointed out that additional rupture areas have to be associated with the MPT

system to generate such a destructive earthquake and that the 65 km long Pereira de Sousa Normal

Fault (PSNF) located along the Portuguese margin, to the north of MPT, could constitute the

northward prolongation of the MPT.

Baptista et al. [2003], based on new MCS (multi-channel seismic reflections surveys) data,

presented a new reappraisal of the 1755 source and proposed a possible composite source

including the Marques de Pombal Thrust fault and the Guadalquivir Bank (NGBF), which,

accordingly to authors, will act as a possible southeastward extension of the rupture area related to

the 1755 event.

Vilanova et al [2003] propose that, although the main shock was offshore, the resulting static

stress changes induced the rupture of the Lower Tagus Valley (LTVF), near Lisbon. They favour

this model, rather that site effects causing high intensities in the Lisbon area, because not only the

highest intensities show a negative correlation to soft soil but also because this local rupture can

explain other phenomena described in the eyewitness accounts like an internal tsunami in the

Tagus River, ground deformation affecting the course of the Tagus River, the spatial pattern of

damaging aftershocks, duration of the event and the number of shocks felt.

Gutscher [2004] proposed an alternative area for the 1755 event, a shallow east dipping fault plane

beneath the Gulf of Cadiz associated with subduction beneath Gibraltar.

Zitellini et al. [2004] and Ribeiro et al. [2006] proposed the Horseshoe Thrust Fault (HF) as an

additional source area to the Marquês de Pombal Thrust. They favour this solution for additional

area/slip for the 1755 event, given its orientation sub parallel to the MPT and the almost geometric

continuity between both fault zones that facilitates the strain/displacement transfer between them.

Gradin et al. [2007], using a velocity model valid for frequencies up to 0,3Hz and validated for the

1969.02.28 earthquake, proposed a regression to convert simulated values of Peak Ground

Velocity (PGV) into Modified Mercalli Intensity (MMI) in SW Iberia. They extrapolate the

method and the empirical relationship PGV-IMM to the case of the 1755 earthquake, and tested

three sources proposed by different authors, namely the Gorringe Bank solution, the Marques de

Pombal – Pereira de Sousa fault system and the subduction in the Gulf of Cádiz. The authors

concluded that rupture directivity plays a particularly important role and that a primary source

located at Gorringe Bank is the most realistic hypothesis to fit the observed isoseismal pattern.

445

Modeling geometry

Using the stochastic finite fault method explained above, we have tested the six different fault

source geometries for the source of the 1755 earthquake proposed by the different authors, and

mentioned in the previous section.

For all geometries, fault segments were divided into smaller subfaults, each one considered as a

point source. The slip distribution is randomized, and for each fault model three nucleation points

were considered, to take in account directivity studies. The geometry of each source model is

presented in Table 2 and the fault source geometries and the different nucleation points considered.

are presented in the next figures. The geometry named GBF considers the model of Johnston

[1996], MPT-PS considers the proposal of Terrinha et al. [2003], the model MPT-GqB considers

the study of Baptista et al. [2003], model off-LVTF, considers besides the main shock offshore

(Gorringe Bank or Marquês Pombal Fault), a second earthquake in Lower Tagus Valley Fault

(LTVF) as proposed by Vilanova et al. [2003], the MPT – HF considers the Horseshoe Thrust

Fault as an additional source area to the Marquês de Pombal Thrust Fault and the geometry model

GC considers the proposal of Gutscher [2004]. The numbers presented in each fault geometry

represent the different nucleation points considered in simulations.

Table2: Source parameters: fault geometry (strike, dip and dimensions) and magnitude considered

Source Strike Dip (L x W) [km] M

CBF N60ºE 40º 200 x 80 8.7

MPT

PSNF

N20ºE

N180ºE

24º

24º

100 x 70

100 x 120

8.3

8.45

MPT

GqB

N21,7ºE

N70ºE

24º

45º

100 x 55

96 x 55

8.3

8.3

HF

MPT

N60E

N20ºE

45º

24º

175 x 140

100 x 70 8.3

LVTF N38ºE 55º 40 x 28 6.7

GC

N11ºW

2,5º

5,0º

7,5º

162 x 68

174 x 68

198 x 6.8

8.4

8.45

8.5

Surface modeling

For each Portuguese council, the response spectrum derived from each source model, was

transformed into Power Spectrum Density Function (PSDF), at the bedrock, using the classical

theory of stationary random process already described. Site effects were, then, evaluated following

the numerical approach explained elsewhere in this paper and using an available data base (herein

DB1), containing information about soil classification for Portugal (classified as 0, 1 and 2 for

rock, medium and soft soil respectively – Oliveira et al., 1995) and a data base (DB2) with

stratified soil profile units for the Metropolitan Area of Lisbon (MAL). In DB2, each soil unit

considers the thickness of shallow layers, shear waves velocity, density and plastic index. This

446

data base was built in the framework of the project conducted by the Portuguese civil protection

authority, for which it was conducted a geological - geotechnical survey that allowed the

characterization of stratified soil profile units for MAL with a fair level of detail. Each classified

soil type (0, 1 or 2, accordingly to DB1) for MAL correspond to a particular stratified soil profile

accordingly to DB2 and we extrapolated this soil profile units for every Portuguese counties that

had the same soil type classification.

Results and discussion

For each fault geometry seismic action was computed at the bedrock level and surface. Results for

each source model considered, for each nucleation point, are shown in figures 6 to 10. PGAb and

PGAs means Peak Ground Acceleration at bedrock level and surface, respectively, PGVs stands for

Peak Ground Velocity at surface and IMM for the Modified Mercalli Intensity. Synthetic

isoseismal maps were built using the regression of Gradin et al. [2007] that convert PGV into

IMM in SW Iberia.

It is emphasized the primordial effects of rupture directions on strong ground motions, as also

shown in Gradin et al. [2007], which remarks the importance of using methodologies that can

account for directivity effects as already mentioned in Carvalho et al. [2007].

An important conclusion of these figures is that the soil effects play a particularly important role in

the pattern of isoseismals. In fact, even when peak ground values maps show a radial pattern, the

surface maps reproduce most features of the observed macroseismic field, for most of the source

models.

Our results do not sustained a solution of a source located below Gorringe Bank, which produce

too low values of IMM in south of Portugal. The composite models that considers the Marques the

Pombal fault and a additional source area ( MPT-GqB, MPT-PSNF, MPT-HF) seems good

hypothesis, considering an upward rupture, towards Lisbon City, the Guadalquivir Bank source

model reproducing higher intensities in Algarve. The subduction zone in Gulf of Cádiz fails to

reproduce the isoseismal features of the 1755 earthquake in western Portugal.

Considering a triggered rupture in Lower Tagus Valley Fault, a M6.7 seems a too high magnitude

for the inland earthquake (similar PGA values in Lisbon and Algarve) but a smaller magnitude, in

order of M6.5 can give satisfactory PGA values in Lisbon. Nevertheless, PGV values in Lisbon are

caused by the offshore source and not by local source which means, considering PGV the ideal

choice among the ground-motion parameters for damage direct relation, and as a consequence, that

correlates best with intensity [Atkinson & Kaka, 2007; Gerstenberg et al., 2005], that there is no

need to look for a trigger solution to justify high intensities in Lisbon area.

447

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

PN PGAb PGAs PGVs IMM

1

2

3

1

2

3

1

2

3

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

300 - 45 0

PGA [cm /s^2 ]

N

Fig. 6. Synthetic PGAb, PGAs, PGVs and isoseismal maps, for nucleation points 1 to 3, using the

source model GBF.

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

448

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

PGAb PGAs PGVs IMM

1

2

3

1

2

3

1

2

3

1

2

3

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

300 - 45 0

PGA [cm /s^2 ]

N

Fig. 7. Synthetic PGAb, PGAs, PGVs and isoseismal maps, for nucleation points 1 to 3, using the

source model MPT-PSNF.

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

449

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

PN PGAb PGAs PGVs IMM

1

2

3

12

3

12

3

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

300 - 45 0

PGA [cm /s^2 ]

N

Fig. 8. Synthetic PGAb, PGAs, PGVs and isoseismal maps, for nucleation points 1 to 3, using the

source model MPT-GqB.

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

450

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

PN PGAb PGAs PGVs IMM

1

2

3

1

2

3

1

2

3

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

300 - 45 0

PGA [cm /s^2 ]

N

Fig. 9. Synthetic PGAb, PGAs, PGVs and isoseismal maps, for nucleation points 1 to 3, using the

source model MPT-HF.

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

451

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

PN PGAb PGAs PGVs IMM

1

2

12

12

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

300 - 45 0

PGA [cm /s^2 ]

N

Fig. 10. Synthetic PGAb, PGAs, PGVs and isoseismal maps, for nucleation points 1 and 2, using

UP: the source model GC; DOWN: the source model Off-LVT

PN PGAb PGAs PGVs IMM

1

2

2 12 1

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

300 - 45 0

PGA [cm /s^2 ]

N

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

IMM

< 6,0

6,0 - 6,5

6,5 - 7,0

7,0 - 7,5

7,5 - 8,0

8,0 - 8,5

8,5 - 9,0

9,0 - 9,5

9,5 - 10 ,0

0 - 1 00

100 - 15 0

150 - 20 0

200 - 25 0

250 - 30 0

PGA [cm /s^2 ]PGA [cm /s^2 ]

>3 00

250 - 30 0

200 - 25 0

150 - 20 0

100 - 15 0

0 - 1 00

PGV [cm /s]

>3 0

25 - 30

20 - 25

15 - 20

10- 1 5

0 - 1 0

452

Conclusions

A non – stationary stochastic method was applied to test four different models that have been

taken as possible for the source of the 1755 earthquake. Source parameters of the model (corner

frequency, stress drop) were estimated based on source spectra of S waves of 12 earthquakes

records (corresponding to a total of 25 records) and the upper crustal attenuation parameter was

estimated from the high-frequency decay of the acceleration spectra, after correcting observed

spectra from geometrical spreading and anelastic attenuation effect.

Site effects were evaluated by means of an equivalent stochastic non-linear one-dimensional

ground response analysis of stratified soil profile using the LNECloss system and using an

available data base (herein DB1), containing information about soil classification for Portugal and

a data base with stratified soil profile units for the Metropolitan Area of Lisbon (MAL).

Analyzing the most complete study performed here and its results we conclude that (i) the soil

effects play a particularly important role in the pattern of isoseismals; (ii) the composite models

that considers the Marques the Pombal fault and a additional source area ( MPT-GqB, MPT-PSNF,

MPT-HF) seems good hypothesis, considering an upward rupture, towards Lisbon City, the

Guadalquivir Bank source model reproducing higher intensities in Algarve; (iii) The subduction

zone in Gulf of Cádiz fails to reproduce the isoseismal features of the 1755 earthquake in western

Portugal; (iv) The high intensities in Lisbon area, in Lusitania Basisn and Lower Tagus valley

Basin can be explained as site effects, together with a directivity effect (upward direction) from an

offshore source, considering that PGV correlates best with intensity.

Other considerations, namely the possibility of each source to produce a tsunami, the time arrivals

of tsunami, the geological evidences, the consequent damage and so on, are left to others.

Current methods of predicting ground motions for future earthquakes in Portugal will/should be

based on an assumed seismological model of source and propagation processes.

Acknowledgments

This study was performed in the framework of the European Commission through the LESSLOSS

FP6 Integrated Project Risk Mitigation for Earthquakes and Landslides, No.: GOCE-CT-2003-

505488.

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