1. Characteristics of Ground Motions
Chu-Chuan Peter Tsai1
1
Associate Research Fellow, Inst. Earth Sciences, Academia Sinica, PO Box 1-55, Nankang, Taipei,
115, Republic of China.
1、、、、Introduction
Ground motion at a particular site due to earthquakes is influenced by source, travel path,
and local site conditions. The first relates to the size and source mechanism of the earthquake.
The second describes the path effect of the earth as waves travel at some depth from the
source to the site. The third describes the effects of the upper hundreds of meters of rock and
soil and the surface topography at the site. Strong ground shakings cause severe damages to
man-made facilities and unfortunately, sometimes, induce losses of human lives. Studies of
the characteristics of observed accelerograms from earthquake events upgrade one’s capability
in seismic hazard mitigation.
This article serves to introduce and outline some selected materials in the literature,
which relate to the present topic, rather than to give details of it. Readers who are interested
in more details are referred to the references given herein.
2、、、、Some Basics
Direct Information from An Accelerogram
The information which can be directly obtained from an accelerogram by visual
inspection and simple scaling (Hudson, 1979) includes:
peak acceleration
time duration of strong shaking
frequency of predominant waves and rough idea of frequency range
amplitude and frequency relationships between vertical and horizontal motions
approximate distance from recording site to earthquake hypocenter
Wave Types Involved in Strong Ground Motion
Horizontal ground motion is produced by S body waves (shear waves that travel through
the earth) and by surface waves (waves that propagate along the surface).
Typical Earthquake Accelerograms
The overall visual impression reveals that earthquake recordings come in many different
shapes and sizes, due to various conditions of distance, site geology, transmission path, and
source. In general, characterizing an accelerogram would be based on amplitude of peak
value, duration of strong shaking, approximate frequency contents, and general envelope
shape, which indicates the way in which the peak amplitudes vary over the length of the
record.
Factors that affect strong ground motion
magnitude (Hanks and Kanamori, 1979)
distance
site
fault type, depth, and repeat time
directivity and radiation pattern
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2. Detailed Information from An Accelerogram
Processed accelerograms will recover more information from the record:
routine processing and double integration of records
response spectra
calculation of Fourier amplitude spectrum
Various parameters may be used to characterize strong ground motion for purpose of
seismic design (Joyner and Boore, 1988). These include peak acceleration, peak velocity,
response spectral values, and Fourier amplitude values. Peak displacement has also been
suggested, but it is too sensitive to the choice of high-pass filter used in record processing.
The most useful one among these parameters is the response spectrum value because it is the
basis of most earthquake-resistant design. It may be used in the dynamic analysis of structures,
and it is the basis for the relation, in building codes, between the lateral-design-force
coefficient and the period of the building.
However, the search of a single parameter to characterize ground motion is doomed to
failure.
3、、、、Empirical Prediction
Well-designed regression analyses of an available data set are in general used for the
empirical prediction of strong ground motion. It is important to choose a form of the
predictive equation based on physical grounds. If data were plentiful, it would matter less
what form were chosen; either the form would fit the data, or the lack of fit would be obvious.
A key feature of the data set is the scarcity of data points for distances less than about 20 km
and magnitudes greater than 7.0. Confident predictions can simply not be made in that range
of magnitude and distance, which is, unfortunately, where predictions are most needed. Some
examples are:
Joyner and Boore (1981, 1982)
skrrdMcMbay +++−+−+= log)6()6(log 2
2/122
0 )( hrr += (1)
Campbell (1981, 1985)
skrMhhrdbMay +++++= )]exp(ln[ln 21 (2)
Sadigh et al (1997)
)]exp(ln[)5.8(ln 211
2
MhhrdMcbMay c
++−++= (3)
The standard deviation, ylnσ , of an individual prediction of yln is some what in the
range of 0.35-0.75, depending on the data set used for regression analysis.
4、、、、Theoretical Prediction
Stochastic Source Models
the barrier model of Papageorgiou and Aki (1983)
the asperity model of Tsai (1997)
the stochastic ω -square model of Hanks and McGuire (1981)
Green’s function (Spudich and Ascher, 1983)
Stochastic simulations and random vibration theory (Boore, 1983)

3. 5、、、、Hybrid Prediction
Empirical Green’s function
A method of summing up recordings of small earthquakes, which are considered as
Green’s functions, in an attempt to simulate the ground motion from larger events (e.g.,
Hartzell, 1978, 1982; Wu, 1978).
6、、、、Description of Fourier Amplitude Spectrum
Hanks (1982)
Anderson and Hough (1984)
Tsai and Chen (2000)
7、、、、Uncertainty
How the uncertainty can be accurately obtained and adequately be narrowed down is an
important issue in ground motion prediction. Source, site, and path effects all contribute to
the uncertainties of ground motions.
Epistemic Uncertainty vs. Aleatory Uncertainty
Toro et al., (1997) suggested that there are two types of uncertainty in ground motion
prediction (also SSHAC, 1997): epistemic and aleatory. Epistemic uncertainty is that
attributable to incomplete knowledge and data about the physics of the earthquake
phenomenon, whereas aleatory uncertainty is that inherent in the unpredictable nature of
future earthquake events. In principle, the former can be reduced by the accumulation of
additional information; the latter cannot, however, be reduced by the accumulation of more
data or additional information.
Decompose of Uncertainty
variance components technique (Tsai and Chen, 2001; Chen and Tsai, 2001)
8、、、、Probabilistic Seismic Hazard Analysis (PSHA)
A probabilistic seismic hazard analysis is widely regarded as the most general way to
combine and present the large quantities and diverse types of information involved in the
strong ground motions.
Conventional PSHA
Cornell (1968)
PSHA Considering Nonlinear Site Effect
Wen et al. (1994)
Beresnev and Wen (1996)
Tsai (2000)
9、、、、Reference
Anderson, J. G. and S. E. Hough “A model for the shape of the Fourier amplitude spectrum of
acceleration at high frequencies, Bull. Seism. Soc. Am. 74, p.1969-1993, (1984).
Beresnev, I. A. and K-L. Wen “The possibility of observing nonlinear path effect in
earthquake-induced seismic wave propagation”, Bull. Seism. Soc. Am. 86, p.1028-1041,
(1996).
Boore, D. M. “Stochastic simulation of high-frequency ground motions based on
seismological models of the radiated spectra”, Bull. Seism. Soc. Am. 73, p.1865-1894,
(1983).

4. Campbell, K.W. “Near-source attenuation of peak horizontal acceleration”, Bull. Seism. Soc.
Am. 71, p.2039-2070, (1981).
Campbell, K.W. “Strong motion attenuation relations: a ten-year perspective”, Earthquake
Spectra, 1, p.759-804, (1985).
Chen, Y. H. and C.-C. P. Tsai “A new method for estimation of the attenuation relationship
with variance components”, submitted to Bull. Seism. Soc. Am. (2001).
Hanks, T. C. and R. K. McGuire “The character of high-frequency strong ground motion”,
Bull. Seism. Soc. Am. 71, p.2071-2095, (1981).
Hanks, T. C. “fmax”, Bull. Seism. Soc. Am. 72, p.1867-1879, (1982).
Hartzell, S. H. “Earthquake aftershocks as Green’s functions”, Geophys. Res. Lett. 5, p.1-4,
(1978).
Hartzell, S. H. “Simulation of ground accelerations for the May 1980 Mammoth Lakes,
California, earthquakes”, Bull. Seism. Soc. Am. 72, p.2381-2387, (1982).
Hudson, D. E. “Reading and interpreting strong motion accelerograms”, Earthquake
Engineering Research Institute, 112 pp., (1979).
Joyner, W. B. and D. M. Boore “Peak horizontal acceleration and velocity from strong-
motion records including records from the 1979 Imperial Valley, California, earthquake”,
Bull. Seism. Soc. Am. 71, p.2011-2038, (1981).
Joyner, W. B. and D. M. Boore “Prediction of earthquake response spectra”, U.S. Geological
Survey, Open-File Report 82-977, 16 pp., (1982).
Joyner, W. B. and D. M. Boore “Measurement, characterization, and prediction of strong
ground motion”, Proc. of Earthquake Engineering Soil Dynamics II, GT Div/ASCE,
Park City, Utah, June 27-30, p.43-102, (1988).
Papageorgiou, A. S. and K. Aki “A specific barrier model for the quantitative description of
inhomogeneous faulting and the prediction of strong ground motion. Part I. Description of
the model”, Bull. Seism. Soc. Am. 73, p.693-722, (1983).
Sadigh, K., C.-Y. Chang, J. A. Egan, F. Makdisi, and R. R. Youngs “Attenuation relationships
for shallow crustal earthquakes based on California strong motion data”, Seism. Res. Lett.
68, p.180-189, (1997).
Senior Seismic Hazard Analysis Committee (SSHAC) “Recommendations for probabilistic
seismic hazard analysis: guidance on uncertainty and use of experts, Main Report”, R. J.
Budnitz (Chairman), G. Apostolakis, D. M. Boore, L. S. Cluff, K. J. Coppersmith, C. A.
Cornell, and P. A. Morris, Lawrence Livermore National Laboratory, NUREG/CR-6372,
Vol. 1, 256 pp. (1997).
Spudich, P. and U. Ascher “Calculation of complete theoretical seismograms in vertically
varying media using collocation methods, Geophys. J. R. Astron. Soc. 75, p.101-124,
(1983).
Toro, G. R., N. A. Abrahamson, and J. F. Schneider “Model of strong ground motions from
earthquakes in Central and Eastern North America: best estimates and uncertainties”,
Seism. Res. Lett. 68, p.41-57, (1997).
Tsai, C.-C. P. “Ground motion modeling for seismic hazard analysis in the near-source regime:
An asperity model”, Pure appl. geophys. 149, p.265-297, (1997).
Tsai, C.-C. P. “Probabilistic seismic hazard analysis considering nonlinear site effect”, Bull.
Seism. Soc. Am. 90, p.66-72, (2000).
Tsai, C.-C. P. and K. C. Chen “A model for the high-cut process of strong-motion
accelerations in terms of distance, magnitude, and site condition: An example from the
SMART 1 array, Lotung, Taiwan”, Bull. Seism. Soc. Am. 90, p.1535-1542, (2000).
Tsai, C.-C. P. and Y. H. Chen “Variance components analysis of ground-motion variability
for rock sites in Taiwan”, Abstracts of the 96th
Annual Meeting, SSA 2001, Seism. Res.

5. Lett. P.285, (2001).
Wen, K.-L., I. A. Beresnev, and Y. T. Yeh “Nonlinear soil amplification inferred from
downhole strong seismic motion data”, Geophys. Res. Lett. 21, p.2625-2628, (1994).
Wu, F. T. “Prediction of strong ground motion and using small earthquakes”, Proc. of 2nd
Internat. Microzonation Conf. 2, San Francisco, p.701-704, (1978).