Chiou and Youngs PEER-NGA Empirical Ground Motion Model for ...

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data are plotted as a function of station elevation in Figure C-2. Except for a few outliers, the correlation of Vs30 with elevation is clearly shown, particularly within Geomatrix-D category. The bimodal distribution observed in Figures 1 can be adequately modeled by the station elevation. Mapping Vs30 by C3 and Elevation Based on the trend noted in Figure C-2, the following functional form is selected to model Vs30 as a function of station elevation (Elv, in meters), ln( Vs 30 ) = ln( φ1 ) + 1+ e ln( φ2 ) − ln( φ1 ) . (ln( φ ) − ln( Elv )) / φ 3 Interpretations of the unknown coefficients are as followed: φ 1 and φ 2 are the asymptotic Vs30 as the elevation approaches 0 and ∞, respectively; at the elevation of φ3 meters, Vs30 is the (geometric) average of the two asymptotes. The above model was used to fit Vs30 data in each of the five Geomatrix categories. The estimated coefficients (φi, i=1, 4) are listed in Table C-1 and the fitted curves are shown on the left hand plot in Figure C-3. To show the difference between this mapping scheme and that used in California, Vs30 estimates of the non-measurement sites are plotted in the right panel of Figure C-3. The solid lines are Vs30 mapped by the new model; circles are Vs30 mapped by California’s model (Silva, 2004; see Note #34 in the site file NGA_Site_V017.XLS). In most cases the difference is not large. The larger difference occurs in Geomatrix-D category at elevation higher than 70m, as expected. REFERENCES: 4 Lee, C.T., Cheng, C.T., Liao, C.W., and Tsai, T.B., 2001, Site classfication of Taiwan free-field strong-motion stations: Bulletin of the Seismological Society of America, v. 91, no. 5, p 1283-1297. Wills, C.J., Petersen, M.D., Bryant, W.A., Reichle, M.S., Saucedo, G.J., Tan, S.S, Taylor, G.C, and Treiman J.A., 2000, A site conditions map for California based on geology and shear wave velocity: Bulletin of the Seismological Society of America, v. 90, no. 6b, p S187-S208. Wills, C.J. and Silva, W., 1998, Shear wave velocity characteristics of geologic units in California: Earthquake Spectra, v. 14, p. 533-556. Wills C.J. and Clahan K., 2005, NGA site condition metadata from geology, report to PEER-LL, 2005. C&Y2006, Appendix C C-2
Percent of Total 50 40 30 20 10 0 Geomatrix 3 rd Letter Table C-1. Estimated Coefficients. φ 1 φ 2 φ 3 φ 4 σ A 552 680 1 Number of Data Points 244 0.1154 0.3174 15 B 418 579 107.1 0.3850 0.2294 35 C - - - - - 4 2 D 228 509 39.4 0.373 0.2953 91 E 201 405 38.2 0.087 0.1810 18 Total = 163 3 1: This parameter is fixed by judgment. 2: There is insufficient number of data to derive a relationship. To estimate Vs30 of category C site, one could use the relationship for category D. 3: Two data points in Geomtrix-B category were removed. A 500 1000 1500 Geomatrix C3 D E 500 1000 1500 Figure C-1. Histogram of measured Vs30 grouped by Geomatrix’s 3 C&Y2006, Appendix C C-3 rd letter C3. The thick blue line is the Vs30 distribution model of California data (Silva, 2004) B Vs30 C 50 40 30 20 10 0
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Chiou and Youngs PEER-NGA Empirical
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data are consistent with strong mot
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Figure 1: Magnitude-distance-region
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Figure 2: Empirical ground motion d
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EQID Earthquake M Table 3: Inferred
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Site Average Shear Wave Velocity: A
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Figure 6: Relationship between VS30
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1 ) ∝ C2 × M + ( C2 − C ) × l
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Figure 9: Peak acceleration data fr
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C4+C5M slowly and the value of the
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allows the interpretation of the co
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Figure 13: Coefficients resulting f
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the top of rupture located at x = 0
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Figure 18: Intra-event residuals fo
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Figure 21: Variation of HW* with ma
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The interpretation of the parameter
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to the PEER-NGA pga data selected f
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EFFECT OF DATA TRUNCATION The initi
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term [ 1 Φ( y ( θ ) + τ ⋅ z ,
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Table 4: Estimate of Anelastic Atte
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data truncated at a maximum distanc
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faulting earthquakes at long period
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Slope -1.5 -1.0 -0.5 0.0 0.5 1.0 0.
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C&Y2006 Page 46 Table 5: Coefficien
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c1 of T0.010S c1 of T1.000S MODEL R
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esid 1 0 -1 -2 resid resid 1 0 -1 -
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esid resid resid 1 0 -1 -2 1 0 -1 -
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esid 2 1 0 -1 -2 SCEC Version 2 0 2
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Amplification w.r.t. Vs30 = 1130 m/
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Sa(g) Sa(g) 10 1 0.1 0.01 10 1 0.1
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Sa (g) Sa (g) 1 0.1 0.01 0.001 0.00
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Sa (g) Sa (g) 1 0.1 0.01 0.001 1 0.
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EXAMPLE CALCULATIONS FORTRAN routin
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Table 6: Example Calculations Perio
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REFERENCES Abrahamson, N.A., and Si
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Frankel, A., A. McGarr, J. Bicknell
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Appendix A Recordings from PEER-NGA
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RSN EQID Earthquake M Station No, S
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Page 121 and 122: Appendix B Estimation of Distance a
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Page 127: Appendix C Estimation of Vs30 at CW
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T0.200S 1 0.1 0.01 1 0.1 0.01 1130
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T0.200S 1 0.1 0.01 1 0.1 0.01 1130
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T0.200S 1 0.1 0.01 1 0.1 0.01 1130
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T0.200S 1 0.1 0.01 1 0.1 0.01 1130
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1 0.1 0.01
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T1.000S 1 0.1 0.01 0.001 1130 m/s 5
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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T3.000S 0.1 0.01 0.001 0.1 0.01 0.0
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