Methods for regression analysis of strong-motion data

We introduce a new computational method for implementing Brillinger and Preisler's (1984, 1985) one-stage maximum-likelihood analysis of strong-motion data. We also reexamine two-stage methods and agree with Masuda and Ohtake (1992) that rigorous analysis requires off-diagonal terms in the weighting matrix for the second-stage regression but note that Masuda and Ohtake failed to account for the earthquake-to-earthquake component of variance. Analysis by Monte Carlo methods shows that both one-stage and two-stage methods, properly applied, are unbiased and that they have comparable uncertainties. Both give the same correct results when applied to the data that Fukushima and Tanaka (1990) have shown cannot be satisfactorily analyzed by ordinary least squares. The two-stage method is more efficient computationally, but for typical problems neither method requires enough time to make efficiency important. Of the two methods, only the two-stage method can readily be used with the techniques described by Toro (1981) and McLaughlin (1991) for overcoming the bias due to instruments that do not trigger.

[1]  C. Richter.  An instrumental earthquake magnitude scale , 1935 .

[2]  F. B. Hildebrand,et al.  Methods of Applied Mathematics , 1966 .

[3]  N. Draper,et al.  Applied Regression Analysis , 1966 .

[4]  S. R. Searle.  Linear Models , 1971 .

[5]  H. Kanamori,et al.  A moment magnitude scale , 1979 .

[6]  David M. Boore,et al.  Peak horizontal acceleration and velocity from strong motion records including records from the 1979 Imperial Valley, California, earthquake , 1981 .

[7]  Kenneth W. Campbell,et al.  Near-source attenuation of peak horizontal acceleration , 1981 .

[8]  David M. Boore,et al.  Prediction of earthquake response spectra , 1982 .

[9]  David R. Brillinger,et al.  An exploratory analysis of the Joyner-Boore attenuation data , 1984 .

[10]  David R. Brillinger,et al.  Further analysis of the Joyner-Boore attenuation data , 1985 .

[11]  W. B. Joyner,et al.  Measurement, Characterization, and Prediction of Strong Ground Motion , 1988 .

[12]  Kenneth W. Campbell,et al.  Empirical Prediction of Near-Source Ground Motion For the Diablo Canyon Power Plant Site, San Luis Obispo County, California , 1989 .

[13]  William H. Press,et al.  Numerical recipes , 1990 .

[14]  K. L. McLaughlin.  Maximum Likelihood Estimation of Strong-Motion Attenuation Relationships , 1991 .

[15]  Comment on “a new attenuation relation for peak horizontal acceleration of strong earthquake ground motion in Japan” by Y. Fukushima and T. Tanaka , 1992, Bulletin of the Seismological Society of America.

[16]  Y. Fukushima,et al.  Reply to T. Masuda and M. Ohtake's “Comment on ‘A new attenuation relation for peak horizontal acceleration of strong earthquake ground motion in Japan’” , 1990, Bulletin of the Seismological Society of America.

[17]  N. A. Abrahamson,et al.  A stable algorithm for regression analyses using the random effects model , 1992, Bulletin of the Seismological Society of America.