Predicting Ground Motion from Earthquakes

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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?

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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.

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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).

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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)

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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.

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

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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?

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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

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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

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Source to Site Distances
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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)

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Characteristics of Data

• Change of amplitude with distance for fixed
  magnitude
• Change of amplitude with magnitude after removing
  distance dependence
• Site dependence
• Scatter

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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)
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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

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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."

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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)
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Empirically-based Prediction Equations Results
and Comparisons
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AS, sS, Vs600
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Strong-motion Recordings from the 1994 M6.7
Northridge Earthquake
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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.
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Illustrating distance and magnitude dependence
Chi-Chi data are low at short periods (note also
scatter, distance dependence)
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An Extreme Site Effect -1985 M8.1 Michoacan
Earthquake
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Site Response 1985 Michoacan, Mexico Earthquake
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Mexico City 350 km from earthquake epicenter
9000 deaths collapse of 371 high rise
structures, especially 10-14 story buildings
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Strong-motion Records from Mexico City
hard rock hills
old lake bed
Anderson et al., 1986
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Mexico City Acceleration Response Spectrum
Recorded data
Expected ground motions
Resonance Period of 10 to 14 story buildings
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PGA generally a poor measure of ground-motion
intensity. All of these time series have the
same PGA
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But the response spectra (and consequences for
structures) are quite different (lin-lin and
log-log plots to emphasize different periods of
motion)
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Perception of results depends on type of plot
(linear, log)
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Ground Motion Prediction

• Intended to predict PGA, PGV, or spectral
  response at periods of engineering interest
• logYa1a2(M-Mr1)a3(M-Mr2)a4Ra5LogRsitea6F
• 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