Árbók VFÍ/TFÍ - 01.01.1997, Blaðsíða 236

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Árbók VFÍ/TFÍ 1995/96
the shape function is picked from the smoothed average Fourier spectrum (the 15 order
polynomial approximation).
2. Simulation of the arrival times according to scheme in Eqs. (22) with v0a constant, as
the stationary process Eq. (25) is being simulated.
3. Each wave is calculated according to Eq. (25) and amplitude modulated using the
envelope function shown in Fig. 4. The parameters of the envelope function were
selected as t,— l ,5sec, t^^G.O sec and c=0.18. The thus modulated shape functions are
then ordered and summed according to Eq. (25) to provide a simulated record. In order
to ensure a correct scaling of the amplitude of the simulated record, the standard devia-
tion of the entire record was computed and set equal to the standard deviation of the
original record measured at Minni Núpur. Thus, the simulated record has been given
a proper scale for the amplitudes. The simulated record thus adjusted is shown in Fig.
7. Obviously, it does not look identical to the measured record since a smoothed aver-
age spectrum was used for the simulation. The artificial record, however, can be inter-
preted as being descriptive of earthquakes of magnitude close to 6, which might later
be recorded at the same station.
Finally, the frequency content of the artificial earthquake was compared with the
smoothed average Fourier spectrum, which was the basis of the frequency simulation.
Fig. 8 shows a histogram of the simulated frequencies together with the smoothed aver-
age Fourier spectrum of the recorded earthquake. Apparently, the simulated frequen-
cies cover the spectral range fairly well.
Conclusion
It has been shown that a non-homogeneous compound Poisson process can represent real earth-
quake motion processes with satisfactory accuracy. Using the amplitude-modulated version of
the homogeneous Poisson process, where the envelope function is applied at the time of arrival
of each wave form, an equivalent non-homogeneous form is obtained for which sample
functions are more easily generated. It is discussed how suitable wave forms can be wave forms
is essential for succesful simulation of artificial earthquakes in this manner. In a numerical
example it is shown how such information can be extracted from available earthquake records,
which allows the generation of artificial records of similar character as the nreasured records.
Time has not allowed a more detailed study of the simulation process, which will be the
subject of another paper. It would be of interest to generate a number of records using the
above model and study the parameter statistics as well as the derived average Fourier
spectrum in comparison with the smoothed real spectrum used in the analysis. Generalion of
earlhquake records using theoretical earthquake spectra modelled for the Minni Núpur site
along the lines indicated by Eq. (15) is also of interest.
Acknowledgement
Special thanks are extended towards the staff members of the Engineering Research Institule
of the University of Iceland, who made records from the Vatnafjöll earthquake of 25th May
1987 available for this study. Mr Benedikt Halldórsson helped with the simulation process by
writing a MATLAB programme to handle the numerical calculations. Without his assistance,