本文旨在探討NGA-West2 GMPE 的偏差和誤差，採用的指標為加權後殘
值的平均數和標準化殘值的標準差。首先詳細介紹NGA-West2 GMPE 和其標準差，接著依據I14、BSSA14、CB14 及ASK14 的篩選準則，從NGA-West2 Flatfile擷取各GMPE的測站資料，然後計算並檢視加權後殘值的平均數接近0，以及標準化殘值的標準差接近1 的程度，以分析各GMPE的適用性。最後採用與I14 相同的測站紀錄，針對I14 的函數型式，重新進行非線性迴歸分析，估計一套新的參數，以驗證加權後殘值的平均數和標準化殘值的標準差等兩項評估指標的有效性。本文結論為：(1)由I14、BSSA14、CB14 和ASK14 所得的加權後殘值之平均數通常為負值，在長週期的PSA 甚至是偏低的負值，代表這四條GMPE高估了PSA，將高估地震危害度分析的結果。(2)由I14、BSSA14、CB14和ASK14所得的標準化殘值之標準差絕大部份大於1，代表這四條GMPE低估了標準差，將低估地震危害度分析在高PSA的結果。(3)這四條GMPE 引用了為數不多的台灣測站紀錄，分別以所有測站紀錄和台灣測站紀錄進行殘值分析，結果明顯不同，因此這四條GMPE 在台灣地震危害度分析的適用性值得商榷。(4)這四條GMPE 所得的加權後殘值之局部平均數隨規模起伏的幅度最為明顯，表示這四條GMPE在某些規模的局部偏差比起任何Rrup和
VS30來得大。(5)這四條GMPE 的標準差隨規模而減少的趨勢並不特別明顯，短週期PSA 的標準差與規模略呈減函數關係，長週期PSA 的標準差則接近常數。(6)週期愈大，這四條GMPE 的標準差有增加的趨勢，但仍非週期的線性遞增函數。(7)新參數GMPE 的加權後殘值平均數非常接近0，標準化殘值的標準差非常接近1，且誤差平方和比原始I14 來得小。

SUMMARY
The purpose of this study is to discuss the biases and errors in NGA-West2 GMPEs with indices of the mean of weighted residuals and the standard deviation of standardized residuals. Station records are screened out form the NGA-West2 Flatfile in order for calculating the weighted residuals and standardized residuals. If the mean of weighted residuals approaches to 0 and the standard deviation of standardized residuals approaches
to 1, then the GMPE is unbiased and its standard deviation is correct, respectively. Finally, new parameters in the same form of I14 are estimated through a nonlinear regression analysis with the identical station records of I14 to verify the effectiveness of these two evaluation indices. The conclusions are as follows: (1) The means of weighted residualsform I14, BSSA14, CB14, and ASK14 are always negative. These 4 GMPEs would overestimate PSA and the results of PSHA. (2) The standard deviations of standardized residuals form I14, BSSA14, CB14, and ASK14 are almost larger than 1. These 4 GMPEs would underestimate their standard deviations and the results of PSHA at high PSA. (3) The local averages of weighted residuals form these 4 GMPEs vary with the magnitude more obviously than with the rupture distance and the shear-wave velocity over the top 30 m. (4) For the GMPE with new parameters, the mean of weighted residuals is very close to 0, the standard deviation of standardized residuals is very close to 1, and the sum of squared residuals is less than that
from I14.

INTRODUCTION
NGA-West2 GMPE project was sponsored by the California Earthquake Authority,the California Department of Transportation, and the Pacific Gas & Electric Company.
The project was executed by the Pacific Earthquake Engineering Research, the Southern California Earthquake Center, and the United States Geological Survey. In 2013, the fivework teams proposed I14 GMPE, BSSA14 GMPE, CB14 GMPE, ASK14 GMPE, and CY14 GMPE.

The parameters of GMPE can be estimated by different methods. Most of the NGA-West2 GMPE referred to a mixed-effect model proposed by Abrahamson and Young to analyze between-event residuals and within-event residuals, and processed several times of the nonlinear regression analysis to estimate the related parameters.

Obviously, the biases and errors of GMPE would affect the results of PSHA.Therefore, it is necessary to verify the unbiasedness of the GMPE and its standard deviation. We proposed two indices to do such verification, i.e., the mean of weighted residuals and the standard deviation of standardized residuals.

MATERIALS AND METHODS
In the thesis, we get the station records from the NGA-West2 Flatfile according to different selection criteria proposed by each NGA-West2 GMPE. There were still some
quantitative differences between our records and the ones given in the NGA-West2 reports. Then we processed the residuals analysis. If the mean of weighted residuals is very close to zero, then the GMPE is unbiased. If the standard deviation of standardized residuals approaches to one, then the standard deviation of GMPE is unbiased. The weighted residual is the difference between the record in natural log unit and the predicted one by
the GMPE divided by the square of the estimated standard deviation of the GMPE. The standardized residual is the difference between the record in natural log unit and the
predicted one by the GMPE divided by the estimated standard deviation of the GMPE. We investigated the local variations of residuals and squared residuals over the magnitude, the rupture distance, and the averaged shear-wave velocity. The variation of the standard deviation across the period was also discussed. Finally, we used the same station records and the same form of I14 to perform the nonlinear regression analysis, and then the new parameters are estimated. The results of residual analysis to I14 and the new GMPE were compared.

RESULTS AND DISCUSSION
The means of weighted residuals from I14 at long-period PSA are less than zero so that I14 overestimates the PSA at long period. The standard deviation of standardized
residuals of I14 is more than one so that I14 underestimates the standard deviation of PSA at all periods. The means of weighting residuals from BSSA14 at most long-period PSA are less than zero so that BSSA14 also overestimates the PSA at most long period. The
standard deviation of standardized residuals from BSSA14 is more than one so that BSSA14 underestimates the standard deviation of PSA at all periods. The means of
weighted residuals from CB14 are less than zero so that CB14 overestimates the PSA at all periods. The standard deviation of standardized residuals from CB14 is more than one at long-period PSA but less than one at short-period PSA so that CB14 underestimates the standard deviation of PSA at long period but overestimates the
standard deviation of PSA at shorter period. The means of weighted residuals from ASK14 at most long-period PSA are less than zero so that ASK14 overestimates the PSA at most long period. The standard deviation of standardized residuals from ASK14 is more than one so that ASK14 underestimates the standard deviation of PSA at all periods.

It was found that at short-period PSA the standard deviation of I14 decreases when the magnitude increases, and so does BSSA14 in the interval of moderate magnitude. There was no obvious trend of the standard deviation of CB14 over the magnitude at short-period PSA and in the interval of moderate magnitude. The standard deviation of ASK14 decreases when the magnitude increases at short-period PSA and in the interval of moderate magnitude.
For the PSA at short period, the new GMPE and I14 are close, but for the PSA at 10-sec period, the new GMPE is better than I14 in catching the variation of records over
the rupture distance.

CONCLUSION
(1). The means of weighted residuals form I14, BSSA14, CB14, and ASK14 are always negative, especially for the cases of PSAs at long periods. These 4 GMPEs would overestimate PSA and the results of PSHA.
(2). The standard deviations of standardized residuals form I14, BSSA14, CB14, and ASK14 are almost larger than 1. These 4 GMPEs would underestimate their standard deviations and the results of PSHA at high PSA.
(3). Taiwan records used by these 4 GMPEs are so minor that the results of residual analysis are quite different. It is suspicious to use such GMPEs in Taiwan
PSHA.
(4). The local averages of weighted residuals form these 4 GMPEs vary with the magnitude more obviously than with the rupture distance and the shear-wave velocity over the top 30 m.
(5). For these 4 GMPEs, the standard deviations of PSAs at short periods decrease a little when the magnitude increases, but the standard deviations of PSAs at long
periods approach to a constant.
(6). The standard deviations of these 4 GMPEs increase as the period increases, but their relations are not linear.
(7). For the GMPE with new parameters at each period, the mean of weighted residuals is very close to 0, the standard deviation of standardized residuals is very close to 1, and the sum of squared residuals is less than that from I14.

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