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A new method for estimation of the attenuation relationship with variance components

Yi-Hau Chen and Chu-Chuan Peter Tsai
A new method for estimation of the attenuation relationship with variance components
Bulletin of the Seismological Society of America (June 2002) 92 (5): 1984-1991


A new approach to estimation of strong-motion attenuation relations with multiple variance components is proposed. In the terminology of Abrahamson and Youngs (1992), the attenuation relationship considered is a "mixed" model, where the regression coefficients are treated as the "fixed effects" and the components of deviations are treated as the "random effects." Following Dempster et al. (1981), an MLR procedure is adopted, which performs the maximum likelihood (ML) estimation of mixed models where the fixed effects are treated as random (R) effects with infinite variance. Both the fixed and random effects are estimated in a unified framework via an expectation-maximization (EM) algorithm. A modification of the MLR procedure is performed to accommodate nonlinear attenuation models. Compared with other methods, our proposal requires no additional regression or searching procedures and hence is neat and simple. Explicit formulae are provided for the variance estimates of the estimated model parameters. Two types of the strong-motion prediction are discussed: the unconditional prediction without accounting for the site-specific deviation, and the conditional prediction that further incorporates that deviation. A simulation study shows that the proposed procedure yields estimates with smallest biases and least computation time, compared with the EM procedure in Brillinger and Preisler (1985) and with the two-stage method in Joyner and Boore (1993). The new method is applied to a dataset of Taiwan's ground motions for illustration. This application reveals that the site-to-site variability in this dataset is remarkable; hence, the ergodic assumption ignoring "the spatial variability of ground motions" (Anderson and Brune, 1999) may not be suitable for probabilistic seismic hazard analyses in Taiwan. Also, in this application the conditional prediction is shown to be much more accurate than the unconditional prediction.

ISSN: 0037-1106
EISSN: 1943-3573
Serial Title: Bulletin of the Seismological Society of America
Serial Volume: 92
Serial Issue: 5
Title: A new method for estimation of the attenuation relationship with variance components
Affiliation: Academia Sinica, Institute of Statistical Science, Taipei, Taiwan
Pages: 1984-1991
Published: 200206
Text Language: English
Publisher: Seismological Society of America, Berkeley, CA, United States
References: 15
Accession Number: 2002-076555
Categories: Seismology
Document Type: Serial
Bibliographic Level: Analytic
Illustration Description: illus. incl. 2 tables
N22°00'00" - N25°30'00", E119°15'00" - E122°00'00"
Country of Publication: United States
Secondary Affiliation: GeoRef, Copyright 2018, American Geosciences Institute.
Update Code: 200223
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