1. GROUND MOTION VARIABILITY: COMPARISON OF SURFACE AND DOWNHOLE GROUND MOTIONS Adrian Rodriguez-Marek, Washington State University, USA Fabrice Cotton, LGIT, Grenoble, France Fabian Bonilla, IRSN, Fontenay aux Roses, France Presented at The Next Generation of Research on Earthquake- induced Landslides: An International Conference in Commemoration of the 10th Anniversary of the Chi-Chi Earthquake Taiwan, September, 2009

2. OUTLINE Motivation – site specific estimates of ground motion uncertainty Ground motion database Regression analyses Uncertainty at surface vs. depth Analysis of residuals Single station uncertainty Implications for seismic design

3. Ground Motion Predictions SOURCE (e.g. magnitude, style of faulting) PATH (e.g. decay rate) SITE (e.g. Vs30, depth to bedrock) Ground Motion Parameters (e.g. – Spectral Acceleration) ln(Ground Motion Parameter) pdf MOTIVATION

4. Ground Motion Predictions y mean = f (M,R,etc) + f(site) +   is a zero mean, standard normal random variable variability is typically broken down into intra- and inter- event components:  =  intra  intra +  inter  inter  accounts for inherent or aleatoric variability MOTIVATION

5. Ground Motion Predictions y mean = f (M,R,etc) + f(site) +  Question: Is  from attenuation relationships usable in all cases? Atkinson (2006) – Lower  when considering single stations Morikawa et al. (2008) – Lower for single source, path  estimates are function of parameterization Consideration of multiple-stations, multiple source-paths combinations implies a mixing of epistemic uncertainty in  estimates (ergodicity assumption, Anderson and Brune 1999) MOTIVATION

6. Ground Motion Predictions y mean = f (M,R,etc) + f(site) +  s-s  s-s +  e-e  e-e +  o  o (  e-e Event to event variability (intra-event) (  s-s Site-to-site variability (  o Remaining (unexplained) variability MOTIVATION

7. Ground Motion Predictions y mean = f (M,R,etc) + f(site) +  s-s  s-s +  e-e  e-e +  o  o For a given site i, (  s-s assumes a given value  i (no more a random variable), hence... y mean = f (M,R,etc) + f(site) +  i  s-s +  e-e  e-e +  o  o MOTIVATION Standard normal random variables Site Term

8. Ground Motion Predictions y mean = f (M,R,etc) + f(site) +  s-s  s-s +  e-e  e-e +  o  o For a given site i, (  s-s assumes a given value  i (no more a random variable), hence... y mean = f (M,R,etc) + f(site) +  i  s-s +  e-e  e-e +  o  o MOTIVATION Standard normal random variables Site Term

9. Site-specific ground motion predictions y mean = f (M,R,etc) + f(site) +  i  s-s +  e-e  e-e +  o  o With site specific information:  i can be estimated Analytically (Site Response Analyses) Multiple recordings (rarely) Estimates of  i must include epistemic uncertainty (hopefully lower than (  s-s The remaining uncertainty can be captured with single-station estimates of variability MOTIVATION

10. Site Response Analysis When site-specific site amplification studies are conducted, the starting point is bedrock ground motion, then... Questions: Are  amp and  input uncorrelated (implicit assumption)? What is  input ?  amp ? MOTIVATION

11. OPPORTUNITY!! KiK-net database: Large number of digital strong motion records 320 Events, 3784 Records Records screened and processed (G.Pousse, F. Bonilla) Surface and Downhole recordings Shear-wave measurements at each site DATABASE

12. KiK-net Database DATABASE

13. OBJECTIVES Develop a GMPE from Kik-Net data using both surface and downhole recordings Compare different estimates of uncertainty Surface vs. downhole Single-station estimates Obtain an estimate of standard deviation for site specific analyses OBJECTIVES

14. Previous work Cotton et al. (2008) On average, the site effects originated in the upper 100– 200 m are responsible for only about 9% of the total uncertainty.

15. REGRESSION METHODOLOGY - Functional form: Boore and Atkinson (2008) ln(y) = Fm + Fd + Fsite + Fborehole Fd = [c1 + c2(M-Mref)]ln(R/Rref) + c3(R-Rref) R = sqrt(R 2 + h 2 ) Fm = e1 + e5(M-Mh) + e6(M-Mh) for M<Mh Fm = e1 + e7(M-Mh) for M>Mh Fsite = blin*ln(Vs30/Vref) Fborehole = a + b*ln(Vs30/Vref) + c*ln(Vshole/3000) - Separate uncertainty into intra-event and inter-event (Random effects) ln(y ij ) = mean_estimate ij +  ij  intra +  i  inter REGRESSION ANALYSIS

16. Notes on regression methodology Use a single magnitude and distance scaling for surface and downhole data (regression from all the data) Inter-event terms are assumed to be the same for the surface and the borehole. The dependency of the intra-event term on depth, Vs30, or magnitude is obtained from an analysis of residuals. Linear Vs30 dependency, no nonlinear effects REGRESSION ANALYSIS

17. Comparison with Boore and Atkinson NGA Relationship REGRESSION ANALYSIS

18. Vs30 dependency REGRESSION ANALYSIS

19. Raw results : 3784 intra-events residuals REGRESSION ANALYSIS

20. Can the site term be improved? Surface Residuals at T = 1.0 s plotted versus site period from H/V of record itself  intra = 0.608   intra = 0.580 (4.6% reduction) REGRESSION ANALYSIS

21. Can the site term be improved? Surface Residuals at T = 1.0 s plotted baserock shear wave velocity  intra = 0.608   intra = 0.581 (4.4% reduction) REGRESSION ANALYSIS

22. For PGA, there is no apparent strong trend of standard deviations with Vs30 at depth.

23. At the surface, there appears to be a slight trend of increasing standard deviations with increasing Vs30 (This trend of increasing standard deviation with Vs30 is neutralized for T=0.2 and reversed for higher periods).

24. Note that the mean residuals are non-zero for low Vs30 values at the surface. That may be an indication of nonlinear effects.

25. Surface standard deviations Vs30 Vs30 and H800 Vs30 and To Vs30 and Vshole PGA.675.671.667.674 T=0.1 s.774.770.764.774 T=1.0 s.608.585.580.581

26. Surface standard deviations Vs30 Vs30 and H800 Vs30 and To Vs30 and Vshole PGA.675.671.667.674 T=0.1 s.774.770.764.774 T=1.0 s.608.585.580.581 About 4% decrease (only significant effect)

27. Surface vs. Downhole comparison: Total Residuals Average reduction of 11.5% at depth (over all periods from 0.01s to 1.36s) Maximum reduction of 16.2% for a period near 0.1s. ANALYSIS OF RESIDUALS

28. Surface vs. Downhole comparison: Intra-Event Residuals Average 18% reduction Maximum of 24% at 0.1s ANALYSIS OF RESIDUALS

29. Implications Lower residuals at depth: Various hypothesis 1)Site effects are responsible for larger residuals at surface 2)Site parameterization is better at depth than at surface (more site variability at surface) 3)Surface-waves, non 1-D effects responsible for larger residuals ANALYSIS OF RESIDUALS

30. Single-Station Residuals 44 stations with at least 15 recordings (995 records) ANALYSIS OF RESIDUALS

31. The strong reduction in standard deviation from surface to depth is not observed when looking at single-station estimates Stations with more than 15 recordings Results for PGA ANALYSIS OF RESIDUALS

32. Single Station Standard Deviation ANALYSIS OF RESIDUALS

33. Single Station Standard Deviation ANALYSIS OF RESIDUALS

34. Single Station standard deviation removing event term Average reduction of 4.9% at depth (over all periods from 0.01s to 1.36s) Maximum reduction of 7.6% for a period near 0.1s. ANALYSIS OF RESIDUALS

35. Implications Surface and Depth single-station residuals are more or less equal 1)Site effects are responsible for larger residuals at surface 2)Site parameterization is better at depth than at surface (more site variability at surface) 3)Surface-waves, non 1-D effects responsible for larger residuals 4)Surface estimates of single station variability can apply to borehole variability IMPLICATIONS

36. Implications for site-specific analyses: use of single station residuals y mean = f (M,R,etc) + f(site) +  i  s-s +  e-e  e-e +  o  o IMPLICATIONS Single Station Residuals Single Station Residuals extracting event term  e-e and  o oo SurfaceBoreholeSurfaceBorehole PGA 0.63 0.480.47 T=0.1s 0.650.630.520.48 T=1.0 s 0.630.640.440.41

37. For site response analyses Ln F = ln(Sa) surf – ln(Sa) bh Assumes independence of  bh and  F  bh =  o (single station variability removing event terms)  F = ?? IMPLICATIONS

38. Single station estimates of the amplification function standard deviations vary between 0.23 and 0.30, with an average value across periods of 0.26. ANALYSIS OF RESIDUALS

39. For a selected period (T=0.1s)  o = 0.477  F = 0.280  bh = sqrt(0.477^2 + 0.28^2) = 0.553 From database:  surf = 0.517  6% difference  o and  F are not independent... or  o and inter-event terms are not independent (path effects on both) ANALYSIS OF RESIDUALS

40. Conclusions There is an average reduction of 11.5% reduction in total sigma values at depth over all periods (from 0.01s to 1.36s), with a maximum reduction of 16.2% for a period near 0.1s (20% reduction in intra-event sigmas) The large reduction in standard deviation from surface to depth is not observed when looking at single-station estimates Single station estimates of standard deviation at the surface are in general applicable to larger depths.

41. Amplification function variability ? Method 1. the amplification function variability is due to different ray geometries in the last 100 meters of one station Method 1. the amplification function variability is due to different ray geometries in the last 100 meters of one station Method 2. the amplification function variability is due to different ray geometries in the last 100 meters of several stations due to several sources Method 2. the amplification function variability is due to different ray geometries in the last 100 meters of several stations due to several sources Method 3. the amplification function variability is due to different ray geometries (local and regional) between several source and several stations Method 3. the amplification function variability is due to different ray geometries (local and regional) between several source and several stations

42. Input variability Input variability Input variability for site specific studies : event to event variability + variability due to source- geometry effects (single site, at depth) Input variability for site specific studies : event to event variability + variability due to source- geometry effects (single site, at depth) Single station variability at depth = input variability ? Single station variability at depth = input variability ?

43. Questions : Some stations are more variable than others (regional 3D effects ?). How to take into account the single station median value variability (epistemic uncertainty ?)

44. Method 4.  total is composed of: (values for PGA)0.82 Inter-event (Event-to-event variability): (0.46) Intra-Event (0.67) Intra-station variability ?????(0.45) From single station standard deviation (0.64), removing inter-event variability (0.46) Inter-station (station-to-station) variability (0.51) ??   intra-event ) 2 =   intra-station ) 2 +   inter-station ) 2