Predicting Ground Motion from Earthquakes

1. Predicting Ground Motion from Earthquakes Art McGarr “If we know where a major earthquake is likely to occur, how large will the ground motion be at a particular site?”

2. Summary of Strong Ground Motion from Earthquakes • Measured using PGA, PGV, pseudo-spectral acceleration or velocity PSA or PSV, and intensity. • Increases with magnitude. • Enhanced in direction of rupture propagation (directivity). • Generally decreases with epicentral distance. • Low-velocity soil site gives much higher ground motion than rock site. Vs30 is a good predictor of site response.

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

4. Ground Motion Prediction Equations • Empirical regressions of recorded data • Estimate ground shaking parameter (peak ground acceleration, peak velocity, spectral acceleration or velocity response) as a function of (1) magnitude (2) distance (3) site • May consider fault type (strike-slip, normal, reverse)

5. 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.

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

7. 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) • Site terms • Maybe style of faulting

8. 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 • Of the many magnitude scales, which is the most useful for ground motion prediction?

9. 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

13. 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 • Many different measures of distance

14. Source to Site Distances

15. Path effects • Wave types • Body (P, S) • Surface (Love, Rayleigh) • Amplitude changes due to wave propagation • Geometrical spreading (1/r in uniform media, more rapid decay for velocity increasing with depth) • Critical angle reflections • Waveguide effects • Amplitude changes due to intrinsic (conversion to heat) and scattering attenuation [exp(-kr)]

16. Characteristics of Data • Change of amplitude with distance for fixed magnitude • Change of amplitude with magnitude after removing distance dependence • Site dependence • Scatter

17. Spatial Variability "It is an easy matter to select two stations within 1,000 feet of each other where the average range of horizontal motion at the one station shall be five times, and even ten times, greater than it is at the other” John Milne, (1898, Seismology)

18. 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

23. People have known for a long time that motions on soil are greater than on rock • e.g., Daniel Drake (1815) on the 1811-1812 New Madrid sequence: • "The convulsion was greater along the Mississippi, as well as along the Ohio, than in the uplands. The strata in both valleys are loose. The more tenacious layers of clay and loam spread over the adjoining hills … suffered but little derangement."

25. 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 620 m/s = typical rock 310 m/s = typical soil 3. Continuous Variable (V30)

26. Empirically-based Prediction Equations: Results and Comparisons

29. A&S, sS, Vs=600

31. Strong-motion Recordings from the 1994 M6.7 Northridge Earthquake

32. 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.

34. Illustrating distance and magnitude dependence Chi-Chi data are low at short periods (note also scatter, distance dependence)

35. An Extreme Site Effect -1985 M8.1 Michoacan Earthquake

36. Site Response: 1985 Michoacan, Mexico Earthquake

37. Mexico City ・ 350 km from earthquake epicenter ・　9000 deaths ・　collapse of 371 high rise structures, especially 10-14 story buildings

38. Strong-motion Records from Mexico City hard rock hills old lake bed Anderson et al., 1986

39. Mexico City Acceleration Response Spectrum Recorded data Expected ground motions Resonance Period of 10 to 14 story buildings

40. PGA generally a poor measure of ground-motion intensity. All of these time series have the same PGA:

41. But the response spectra (and consequences for structures) are quite different (lin-lin and log-log plots to emphasize different periods of motion):

42. Perception of results depends on type of plot (linear, log)

43. Ground Motion Prediction • Intended to predict PGA, PGV, or spectral response at periods of engineering interest • logY=a1+a2(M-Mr1)+a3(M-Mr2)+a4R+a5LogR+site+a6F • Coefficients ai are determined by regression fits to ground motion data sets. • Ground motion generally increases with M and decreases with R • Site term mostly depends on near-surface shear-wave speed, usually expressed as Vs30 • Site effects sometimes dominate • Response spectra much more useful than PGA for predicting structural damage