1. Ground Motion Parameters Measured by triaxial accelerographs 2 orthogonal horizontal components 1 vertical component Digitized to time step of 0.005 - 0.01 sec For 60 sec record, N = 3 x 60 / 0.01 = 18,000 values Important characteristics Amplitude Frequency content Duration

2. Ground Motion Parameters Amplitude parameters Peak acceleration Peak velocity Peak displacement Sustained maximum acceleration 3-cycle 5-cycle

3. Ground Motion Parameters Amplitude parameters Rock site Rock site Soil site Soil site Highest a max Highest v max Fault Normal Fault Parallel

4. Frequency content parameters Fourier spectrum Plot of c n vs  n gives Fourier spectrum c n Ground Motion Parameters nn Example from ProShake

5. Frequency content parameters Response spectrum Ground Motion Parameters Examples from ProShake

6. Frequency content parameters Spectral parameters Predominant period Bandwidth Ground Motion Parameters

7. Duration Bracketed duration Trifunac duration Ground Motion Parameters +0.05g -0.05g 5% 95% TdTd TdTd

8. Other ground motion parameters rms acceleration Arias intensity Spectral intensity Ground Motion Parameters All are influenced by amplitude, frequency content, and duration All are influenced by amplitude, frequency content, and duration

9. Effects of source parameters on ground motions Magnitude Ground Motion Parameters

10. Effects of source parameters on ground motions Magnitude Ground Motion Parameters

11. Prediction Predictive relationships (attenuation relationships) Establish database Select form of predictive equation Perform regression analyses Evaluate uncertainty Ground Motion Parameters

12. Prediction Examples: Ground Motion Parameters

13. Prediction Standard error -  ln Y Ground Motion Parameters log R ln Y M = M* R = R* ln Y  ln Y Accounts for uncertainty in prediction of effects of earthquake Accounts for uncertainty in prediction of effects of earthquake

14. Prediction Standard error -  ln Y Ground Motion Parameters log R ln Y M = M* median +  ln Y median -  ln Y

15. Prediction Standard error Ground Motion Parameters log R ln Y M = M* R = R* ln Y Y = Y*

16. Prediction Standard error Ground Motion Parameters log R ln Y M = M* R = R* ln Y Y = Y* Most ground motion parameters are lognormally distributed

17. Lognormal distribution Ground Motion Parameters x ln x The logarithm of a lognormally distributed random variable is normally distributed Median of ln x is equal to mean of ln x Median of x is less than mean of x

18. Standard normal distribution Standard normal variate, z Mean: z = 0 Standard deviation:  z = 1 Ground Motion Parameters Values of probability distribution for z obtained from widely used tables

19. Prediction Standard error Ground Motion Parameters log R ln Y M = M* R = R* ln Y Y = Y* P[Y > Y*| M=M*, R=R*]

20. Prediction Standard error Ground Motion Parameters log R ln Y M = M* R = R* ln Y Y = Y* P[Y > Y*| M=M*, R=R*]

21. Prediction Common parameters Peak acceleration Spectral accelerations Ground Motion Parameters T SaSa 0 a max

22. Prediction Common parameters Peak acceleration Spectral accelerations Ground Motion Parameters T SaSa 0 median median + 