Pergamon

Phys. Chem. Earth, Vol. 21, No. 12, pp. 71-74, 1996 Copyright © 1997 Elsevier Science Ltd

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PII: S0079-1946(97)00012-8

A Comparison of the Spectral Characteristics of Observed and Simulated Tsunamis

J. M. Miranda 1, P. M. A. Miranda 1, M. A. Baptista 2 and L. Mendes Victor 1

1 Centro de Geofisica da Universidade de Lisboa - R. da Escola Polit6cnica 58, 1250 - Lisboa, Portugal 2 Department de Engenharia Civil - Inst. Superior de Engenharia de Lisboa, Lisboa, Portugal

Received 5 August 1996; accepted 15 December 1996

Abstract. The spectra of real tsunamis depend on the source characteristics, propagation effects on the deep ocean, shelf topography and harbour geometry. The separation between all these effects is possible if a large number of instrumental tsunami data is available and, in that case, the source parameters may be computed by cancellation of path and instrumental effects. This is not generally the case in the SW Iberian region, where, in spite of some very large historical events there is only a small number of instrumental tsunamis. A good case study for that methodology is given by the 28.02.1969 tsunami, which has been previously studied with rather encouraging results in terms of the comparison of arrival times and amplitudes between observed and simulated tsunamis. The aim of the present study is the comparison between the spectral characteristics of instrumental tide records and the synthetic wave forms computed with a shallow water model. © 1997 Elsevier Science Ltd. All rights reserved

1 Introduction

The observed tsunami data are highly convoluted time series where the tsunami signal is modified by different effects, including harbour resonance, coastal wave trapping, wave diffraction and so on. Comer (1982) proposed a method for estimation of source characteristics by computation of spectral amplitude ratios. This procedure is possible for regions where several tsunamis are generated at the same source region; for regions like SW Iberia this is not the case because, while there are some large historical tsunamis, only a small number of events is well described and the number of instrumental

Correspondence to: Pedro Miranda, Centro de Geofisica, R. Escola Polit6cnica 58, 1250 Lisboa, PORTUGAL. E- Mail: fmiranda@cc.fc.ul.pt. Fax: +351 1 3953327.

tsunamis with a reasonable amount of tide gauge data is even smaller.

The best documented of those tsunamis followed the 28.02.1969 earthquake, which occurred at 2:40:32.5 (UTC), with epicentre at 36.01N, 10.57W, in the Horseshoe Abyssal Plain (Southwest Iberia). The focal mechanism of the 28.02.1969 earthquake was a thrust with a small strike-slip component, oriented N55E, and the fault plane dimensions, obtained through the analysis of the aftershock sequence were 80 km long and 50 km wide (Fukao, 1973). The earthquake generated a small tsunami that was clearly recorded at the tide stations of Portugal, Spain and Morocco. The availability of a considerable amount of instrumental data, from this event, allows for the determination of arrival times and amplitudes and for the study of the spectral content of the mareogram data. Because this was a large earthquake in a region which is generally associated with the strong long term seismicity, the 1969 earthquake deserved a lot of interest in the literature. On the other hand, the associated tsunami has also been studied in a series of papers, which focused on the spectral characteristics of the observed time series (Baptista et al. 1992), on different aspects of shallow water simulations of the tsunami propagation (Heinrich et al 1994, Gjevik et al. 1996) and on the use of backward ray- tracing techniques to locate the tsunami source (Gjevik et al 1996). The results of the two latter studies have been quite encouraging in terms of the comparison of arrival times and amplitudes between observed and simulated tsunamis.

One of the referred studies (Baptista et al., 1992) tried to infer the source characteristics of the 28.02.69 event from a comparison between the spectra of the "quiet days" (days without tsunami) and the spectra of tsunami days, at four stations Cascais, Lagos, Cadiz, Horta (Azores Islands). The nmin conclusion from that study was that the occurrence of a tsunami does not change significantly the peaks observed in the spectra of the "quiet days", although

71

72

their amplitudes are clearly amplified; it was also concluded that each station presented quite well defined peaks that should correspond to the bathymetric signature of the harbour where the tide gauge is located.

1700

1600

1500

1100 ~ ~(

1000

17"00 1800 1900 2000 21~ 2200 2300 2600 krn I¢

F i g u r e 1 - B a t h y m e t r y and location of stations.

The numerical simulation of the 28.02.1969 event was presented in two previous papers (Heiurich et a1.1994, Gjevik et al. 1996), where arrival times and wave amplitudes between the available tide gauge data and simulated waveforms for the 28.02.1969 tsunami were compared. The results obtained showed a reasonable agreement for most of the stations located along the coast of Iberia (cf. figure 2), in terms of arrival times and amplitudes, That work is pursued here with an analysis of the spectra of observed and simulated tsunamis.

2 Data Processing

The analysis of mareogram data for the 28.02.1969 tsunami was carried out by Baptism et al. (1992). The instrumental data were analysed in three steps: digitisation, linear interpolation between sampled values and filtering. The sampling interval chosen was 18 seconds; the separation between the tsunami signal and the tide was obtained using a high pass Butterworth filter with a cutoff frequency of 16 m i n -1 .

The synthetic tsunami data used in this study were obtained using a non-linear shallow water model based on the SWAN code, after Mader (1988). Synthetic tsunami time series were produced for some coastal stations in the area: Cascais, Lagos, and Faro (Portugal), Cadiz (Spain) and Casablanca (Morocco). The tsunami source was simulated with an initial displacement above the assumed epicentre location given by a simple analytical formula,

J. M. Miranda el al.

which implies a region of upward movement in one side of the fault and a smaller region of downward movement on the other side, with an exponential decay of the displacement away from the fault. The dimensions of the source area were chosen according to Fukao's parameters 80kin long by 50 km wide with an azimuth of N55E (Fukao, 1973); a total vertical displacement of 2.5 meter was imposed at the source region. For each tide station a synthetic record was produced, with a sampling interval of 2 sec and a length of 12 h.

The amplitude spectra of observed and simulated tsunamis at each station were obtained by Fourier analysis, using the Welch method (see for example Oppenheim, 1975). This method is a standard procedure to reduce the variance of the spectrum. Each data record of length N is divided into K segments of M samples such that K = N / M .

then each segment is convoluted with an appropriate window, w ( N ) , before computation of the spectrum:

] M-I 2

t~(oJ) = - ~ _ _ l ~ x ( ' ) ( n ) e - " i = 12. . . .K (1) MU I-=o I •

where M - 1 /

u = .--L S ' w : ( N ) (2) ~-=--o

and the spectrum estimate is defined as: 1 K

= x tg>(o . , ) (3)

The observed tsunami records, consisting of time series with 2400 data points each, were produced; each time series was then divided into 4 segments and Hamming windows were applied to each segment; finally the corresponding FFT was computed and the average of the FFFs was obtained. To use the same number of data points in each data window of both the synthetic and observed wave forms, each segment of the simulated data records was interpolated with the same sampling rate of the observed data. The procedure, described above, was then applied to the synthetic tsunami data to obtain the amplitude spectra.

3 Results and conclusions

The comparison between observed and simulated waveforms is shown in figure 2. As previously mentioned there is a good agreement in terms of arrival times and maximum amplitudes, except for the case of Casablanca. There are, though, obvious discrepancies between the observed and simulated series, which will reflect on the comparison of the spectra.

The comparison between the spectra, shown in figure 3 shows that: (i) for each station the broad shape of spectra of observed and simulated tsunamis is similar; (ii) the main peaks of the simulated spectra are well located but their relative amplitude does not fit with observations.

Spectral Characteristics of Observed Sim ulated Tsunamis 73

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C l m ~ s . C~rnpm~sort of ~ and simUletod tsunamis

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Amplitude Spectra - Faro

3 - Spectra ol'o~e~ed mind slmulmted tsumumdso

74

Looking at individual spectra, it can be found that both in the case of Cascais and Lagos, there is good amplitude agreement in the low frequency domain (below 0.05 min~), there is a deficit of energy in the high frequency range (above 0.1 or 0.15 min l ) and an excess of energy in the mid range. In the case of Cadiz the simulated series shows excess of energy for frequencies below 0.1 min -~. The Casablanca simulation shows the best spectral comparison. The lack of energy in the high frequency domain of all spectra is surely related with the model resolution, which is at 2.5 km in all the simulations shown so far.

The Faro simulation is an exception to the previous conclusions. In this case there is a clear 15 min component present in the simulated spectrum, which is absent from the "observed" spectrum. Because Faro is located close to a region of sand dunes and very shallow water (a few meters deep for tens of kms) a small error in its location or in the representation of bottom topography and coastal geometry could lead to large changes in the simulated time series. To test that hypothesis another simulation was performed, using a 1 km resolution grid for the Faro area. Four alternative locations of the station were chosen along the coast line of that grid, all of them within a distance of a couple kms to the original location in the 2.5 km grid, but at somewhat different water depth (between 1 and 30 m). Figure 4 shows a zoom of the area close to Faro, in the 1 km grid, where the four stations are positioned. For comparison, the real tide gauge was located in the channel close to station 2 at a depth of around 5 m.

Figure 5 shows the time series of water height for those stations. It can clearly be seen that they are very different from each other, in spite of the small distance between the stations, not only in terms of arrival time but also in terms of spectra, shown in Figure 6. The difference between spectra and arrival times at the chosen locations is strongly related to the depth of those stations. An analysis of these data shows that as the there is a red-shift of the spectra when the depth of the analysis grid point is reduced. On the other hand, these results show the importance of high resolution bathymetric data for simulations in shallow waters and of corresponding precision in the location of the tide gauges. A similar analysis, not shown, for nearby grid points around the station of Cascais has produced similar results.

Finally a comment is required on the Casablanca results shown in figure 2. Besides what has been said in relation to the spectra of that series, which is the concern of the present paper, there is an obvious problem in the polarity of the first wave crest. This problem was found and discussed in Gjevik et al (1996) and is probably related to the tsunami source function chosen.

Acknowledgements. Suggestions made by two anonymous reviewers were used to improve the paper. This research was partially financed by the Commission of the European Communities under Contracts EV5V-CT92- 0175 (Project GITEC) and ENV4-CT96-0297 (GITECTWO).

J. M. Miranda et al.

1335

~ 13~

1325

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2180 2185 2190 2195 2200 2205 2210

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Figure 4 - Location of stations close to Faro in the 1 km grid.

1 2215

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Figure 5 - Simulated tsunamb in the stations shown in Figure 4.

Faro - simulations w i t h a grid of l k m r e s o l u t i o n 0.010

o

i 0.006 io.o.

0 . 0 ~ O 0 0.1 0.2 0.3 0.4 0 5

Frequency (m in 4 )

Figure 6 - Spectra of tsunamis shown in Figure 5

R e f e r e n c e s Baptista, M.A., Miranda, P.M.A., Mendes-Vietor, L., Maximum Entropy

Analysis of Portuguese tsunami data. The tsunamis of 28.02.1969 and 26.05.1976, Sc. of Tsunami Hazards, vol.10, n°l, pp 9-20, 1992.

Comer, R.P., Tsunami Generation by earthquakes, PhD thesis - M.I.T. 232 pp, 1982.

Fukao, Y., Thrust faulting at a lithospheric plate boundary, The Portugal earthquake of 1969, Earth andPlanet. SeL Lett., 18, pp 205-216, 1973.

Gjevik, B., Pedersen, G., Dybesland, E., Harbitz, C.B., Miranda, P.M.&, Baptism, M.A., Mendes-Vietor, L., Heinrieh, Ph., Roche, R. and Guesmia, M., Modeling tsunamis from earthquake sources near Gorringe Bank Southwest of Portugal, Submitted to the J. Geophys. Res., 1996.

Heinrieh, Ph., Baptista, M.A., Miranda, P.M.&, Numerical Simulation of the 1969 tsunami along the Potluguese coasts, Preliminary results, Se. Tsunami Hazards, 12, 1, pp3-24, 1994.

Mader, C., Numerical Modelling of water waves, University of California Press, Berkeley, California. 264 pp, 1988.

Oppenheim, A.V. and Schafer, R.W., Digital signal Processing, Prentice Hall, INC., Englewood Clifs, New Jersey (USA), 585 pp, 1975.