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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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)

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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).

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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,

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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).

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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).

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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.

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