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# Empirical Specification of Ground Motions

Empirical Specification of Ground Motions. Ground-motion prediction equations Collections of ground-motion values (and time series) for magnitude and distance bins. Developing Equations. When have data (rare for most of the world): Regression analysis of observed data

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## Empirical Specification of Ground Motions

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1. Empirical Specification of Ground Motions • Ground-motion prediction equations • Collections of ground-motion values (and time series) for magnitude and distance bins

2. Developing Equations • When have data (rare for most of the world): • Regression analysis of observed data • When adequate data are lacking: • Regression analysis of simulated data (making use of motions from smaller events if available to constrain distance dependence of motions). • Hybrid methods, capturing complex source effects from observed data and modifying for regional differences.

3. Overview • Empirical ground-motion prediction equations • What they are and how they are used • The database • Processing of data • Combining horizontal components • Expected dependency on magnitude and distance • What functional form to use • What to use for the explanatory variables

4. Overview • Empirical ground-motion prediction equations • Possible biases and how to avoid them • Site characterization • Basin depth • Nonlinear response • Testing the results • Results and comparisons of various prediction equations

5. Overview • Empirical ground-motion prediction equations • Scatter • Complications and future directions

6. Ground-Motion Prediction Equations Gives mean and standard deviation of response-spectrum ordinate (at a particular frequency) as a function of magnitude distance, site conditions, and perhaps other variables.

7. Call them “Ground-Motion Prediction Equations” (GMPEs) • “Attenuation Equations” is a poor term • The equations describe the INCREASE of amplitude with magnitude at a given distance • The equations describe the CHANGE of amplitude with distance for a given magnitude (usually, but not necessarily, a DECREASE of amplitude with increasing distance).

8. Deriving the Equations • Regression analysis of observed data if have adequate observations (rare for most of the world). • Regression analysis of simulated data for regions with inadequate data (making use of motions from smaller events if available to constrain distance dependence of motions). • Hybrid methods, capturing complex source effects from observed data and modifying for regional differences.

9. Observed data adequate for regression except close to large ‘quakes Observed data not adequate for regression, use simulated data

10. What Measure of Seismic Intensity to Use? • PSA (derived from SD) • SD? Need for displacement-based design • Can be derived from PSA, so GMPEs in terms of PSA also give equations for SD • If use SA, then need separate GMPEs for PSA and SD • Usually horizontal component

11. How to Use Two Horizontal Components • Use both independently • Use larger component as recorded • Use larger component after rotation to find maximum • Use vector sum • Use geometric mean as recorded • Use orientation-independent geometric mean

12. The geometric means of these two sets of records differ by a factor of 2 at T = 1 s

13. Measure of Ground-Motion Intensity:GMRotI50 Boore, D. M., J. Watson-Lamprey, and N. A. Abrahamson (2006). Orientation-independent measures of ground motion, BSSA 96, 1502-1511.

14. How does the motion depend on magnitude? • Source scaling theory predicts a general increase with magnitude for a fixed distance, with more sensitivity to magnitude for long periods and possible nonlinear dependence on magnitude

15. Shape depends strongly on magnitude; for this reason scaling spectral shapes by peak acceleration is not advised

16. How does the motion depend on distance? • Generally, it will decrease (attenuate) with distance • But wave propagation in a layered earth predicts more complicated behavior (e.g., increase at some distances due to critical angle reflections (“Moho-bounce”) • Equations assume average over various crustal structures

17. What functional form to use? • Motivated by waves propagating from a point source • Add more terms to capture effects not included in simple functional form

18. What to use for the Predictor Variables? • Moment magnitude • Some distance measure that helps account for the extended fault rupture surface (remember that the functional form is motivated by a point source, yet the equations are used for non-point sources) • Distance must be estimated for future event (leaves out distance to energy center, hypocentral distance)

19. Moment Magnitude • Best single measure of overall size of an earthquake • Can be determined from ground deformation or seismic waves • Can be estimated from paleoseismological studies • Can be related to slip rates on faults

20. May need to convert magnitudes • Use empirical and/or theoretical relations • Important to use a common magnitude measure • This is essential in comparing ground-motion prediction equations • Moment magnitude is now the standard

21. Many distance measures are used • There is no standard, although the closest distance to the rupture surface is probably the distance most commonly used • The distance measure must be something that can be estimated for a future earthquake

22. Limitations in the dataset can produce biased results • Data censuring (lack of data from operational non-triggered recorders) can lead to attenuation with distance that is too small • Non-uniform distribution of data on M-D space can lead to tradeoffs in the magnitude scaling and the distance decay

23. Avoiding the magnitude-distance tradeoff • Use 2 stage regression • Use weighted least-squares (random effects model)

24. An Example of a Recent Major Effort to Derive New Ground-Motion Prediction Equations (GMPEs): Next Generation Attenuation (NGA) Project David M. Boore U. S. Geological Survey

25. NGA Project • NGA-E (empirical) • New ground motion models based primarily on empirical data • Use analytical models (seismological and geotechnical) to guide extrapolation outside of empirical data • Results used only in terms of scaling

26. NGA Project Details • Five developer teams • Ed Idriss • Brian Chiou and Bob Youngs • Dave Boore and Gail Atkinson • Norm Abrahamson and Walt Silva • Ken Campbell and Yousef Bozorgnia

27. Supporting Working Groups • Data Processing • Ground Motion Database • Validation of 1-D Rock Motion Simulation • Source/Path Effects • Site Classification & Site Effects • Statistical Modeling of Data • Parameterization to capture directivity effects

28. NGA Project Details • All developers used a common database (175 earthquakes, 3551 recordings) • Metadata (e.g., magnitude, distance, etc.) • Uniformly processed strong-motion recordings • U.S. and foreign earthquakes • Active tectonic regions • The database development took much longer than anticipated, resulting in at least a year delay in the project completion

29. Some earthquakes not included: 1987 Elmore Ranch, CA (add USGS data) 1992 Cape Mendocino, CA (add USGS data) 1997 Umbria-Marche, Italy, events 2002 Molise, Italy 2003 Zemmouri, Algeria (M 6.8) 2003 San Simeon, CA (M 6.4) 2003 Bam, Iran (M 6.5) 2004 Parkfield, CA (M 6.0) 2004 Chuetsu, Japan (M 6.6 + AS) 2005 Zarand, Iran (M 6.3)

30. NGA Project Details • Developers applied their own selection criteria to the common database • Selection criteria explicitly defined • Selection criteria shared with other developers • Defensible reason for excluding data • Other developers notified if metadata modified

31. Developer Scope • Ground motion model • Model for median estimate • Model for aleatory standard deviation • Ground motion parameters • Horizontal components (Average, FN and FP) • PGA, PGV and PGD • Spectral acceleration (5% damping, 0-10 sec period) • Applicable moment magnitude range • 5.0 – 8.5 (strike-slip faulting) • 5.0 – 8.0 (reverse faulting)

32. Developer Scope • Applicable distance range • 0 – 200 km • Fault types • Strike slip • Reverse • Normal • Site classification scheme • Developers select their preferred classification scheme • Provide a translation scheme to NEHRP categories • Need not include soft soil

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