Empirical Ground Motion Prediction Equations

1. Empirical Ground Motion Prediction Equations Introduction to Strong Motion Seismology Day 2, Lecture 3 Nay Pyi Taw, Myanmar Tuesday, 29 January 2013

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

3. Overview • Empirical ground-motion prediction equations (GMPEs) • 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 • Example: PEER NGA-West2 GMPEs USGS - DAVID BOORE

4. The Engineering Approach • Use physically based empirical relationships • Take a large suite of recorded earthquake motions and perform regression analysis to obtain models that may be used for the estimation of the distribution of future ground-motions • Simple models that only require knowledge of a few parameters • Significant variability associated with the estimates of these equations • Partly reflects the simplicity of the models • Partly reflects the inherent variability of earthquake ground-motions • The treatment of this variability is crucial for hazard analysis USGS - DAVID BOORE P. Stafford

5. 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. USGS - DAVID BOORE

6. 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). USGS - DAVID BOORE

7. 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. USGS - DAVID BOORE

8. Observed data adequate for regression except close to large ‘quakes Observed data not adequate for regression, use simulated data USGS - DAVID BOORE

9. 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 USGS - DAVID BOORE

10. 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 (gmroti50) • Use orientation-independent, non-geometric mean (rotd50) USGS - DAVID BOORE

11. 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) • A measure of local site geology USGS - DAVID BOORE

12. 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 USGS - DAVID BOORE

13. 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 USGS - DAVID BOORE

14. Most Commonly Used: Rrup RJB USGS - DAVID BOORE

15. 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 USGS - DAVID BOORE

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17. 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 USGS - DAVID BOORE

18. M and R dependence shown by data USGS - DAVID BOORE

19. The scatter remaining after removing magnitude and distance dependence is large • Can it be reduced by introducing other factors? • The most obvious additional factor tries to capture the effect of site response USGS - DAVID BOORE

20. Uncertainty after Mag & Dist Correction (E. Field)

21. Simplest: Rock vs Soil (E. Field)

22. Time-averaged shear-wave velocity to depth z: Average shear-wave slowness to depth z: USGS - DAVID BOORE

23. Site Classifications for Use With Ground-Motion Prediction Equations 1. Rock/Soil • Rock = less than 5m soil over “granite”, “limestone”, etc. • Soil= everything else 2. NEHRP Site Classes (based on VS30) 620 m/s = typical rock 310 m/s = typical soil 3. Continuous Variable (VS30) USGS - DAVID BOORE

24. VS30 as continuous variable Note period dependence of site response USGS - DAVID BOORE

25. Why VS30? • Most data available when the idea of using average Vs was developed were from 30 m holes, the average depth that could be drilled in one day • Better would be Vsz, where z corresponds to a quarter-wavelength for the period of interest, but • Few observations of Vs are available for greater depths • Vsz correlates quite well with Vs30 for a wide range of z greater than 30 m (see next slide, from Boore et al., BSSA, 2011, pp. 3046—3059) USGS - DAVID BOORE

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27. Effect of different site characterizations for a small subset of data for which V30 values are available • No site characterization • Rock/soil • NEHRP class • V30 (continuous variable) USGS - DAVID BOORE

28. σ=0.25 σ=0.25 USGS - DAVID BOORE

29. σ=0.21 σ=0.20 USGS - DAVID BOORE

30. Nonlinear Soil Response • Clearly seen in studies of pairs of records • Not as large as found in lab experiments • Account for in regression equations by looking for systematic variation of soil amplitudes relative to predicted rock amplitudes at given distance and magnitude USGS - DAVID BOORE

31. 2-stage Regression • Use 2 stage regression • Use weighted least-squares (random effects model) USGS - DAVID BOORE

32. Stage 1 Regression: Determine the distance function and event offsets USGS - DAVID BOORE

33. Stage 2 Regression: Determine the magnitude scaling USGS - DAVID BOORE

34. Quantifying the Uncertainty • The GMPEs predict the distribution of motions for a given set of predictor variables • The dispersion about the median motions can be crucial for low annual-frequency-of-exceedance hazard estimates (rare occurrences for highly critical sites, such as nuclear power plants, nuclear waste repositories) • Must be clear on type of uncertainty • The scatter is very large; can it be reduced? USGS - DAVID BOORE

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36. Two types of Aleatory Uncertainty • Within event (intraevent) (φ) (event-to-event variation has been removed) • Event-to-event (interevent) (τ): generally smaller than φ • Total (σ): USGS - DAVID BOORE

37. 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 USGS - DAVID BOORE

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41. Modeling Considerations • Not too simple • Not too complex (over paramerized) • Reasonable extrapolations to data-poor but engineering-important regions of predictor variable space (e.g., close to M~8 earthquakes) USGS - DAVID BOORE

42. Represent M-scaling by joined quadratic and linear or simple quadratic? USGS - DAVID BOORE

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44. Pacific Earthquake Engineering Research Center (PEER) NGA Projects:NGA (2008)NGA-West2 (2013) Abrahamson & Silva Boore, Stewart, Seyhan, and Atkinson Campbell & Bozorgnia Chiou & Youngs Idriss USGS - DAVID BOORE

45. NGA Project Details • All developers used subsets of data chosen from a common database • Metadata (e.g., magnitude, distance, etc.) • Uniformly processed strong-motion recordings • U.S. and foreign earthquakes • Active tectonic regions • The database development was a major time-consuming effort USGS - DAVID BOORE

46. 1264 (173) worldwide shallow crustal events from active tectonic regions 19409 (3551) recordings (mostly 3-components each) uniformly processed strong motion stations M3.0 (4.2) to 7.9 (7.9) PEER NGA-West2 Strong-Motion Database Blue = Previous NGA USGS - DAVID BOORE

47. BSSA13 GMPEs Dave Boore, Jon Stewart, Emel Seyhan, Gail Atkinson

48. Boore, Stewart, Seyhan, and Atkinson (BSSA13) Ground-Motion Prediction Equations (GMPEs) USGS - DAVID BOORE

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