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. 8
Western North America
Moment Magnitude
7
Observed data adequate
for regression except
close to large ‘quakes
6
File: D:metu_03regressm_d_wna_ena_pga.draw; Date: 2005-04-20; Time: 20:29:49
5
Used by BJF93 for pga
1 10 100 1000
8
Eastern North America
7
Moment Magnitude
Observed data not
adequate for regression,
6 use simulated data
5
Accelerographs
Seismographic Stations
1 10 100 1000
Distance (km)

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

11. Fourier acceleration spectrum (cm/sec)
0.01
100
0.1
1.0
10
1 10 -1
Frequency (Hz)
R = 20 km
101
M 5 to 8 in steps of 0.5
102
File: C:metu_03regressfas_range_of_m.draw; Date: 2003-09-02; Time: 21:23:19

12. PSA (cm/sec 2)
1000
10
100
0.1
1
4
5
T = 1.0 sec
T = 0.20 sec
6
M
7
T = 2.0 sec
R = 20 km
8
File: C:metu_03regresspsa_vs_m_t0p2_1p0_2p0.draw; Date: 2005-05-05; Time: 14:48:34

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

27. Date: 2005-03-29; Time: 16:48:28
Western North America (used by BJF93, 97 for pga) World (NGA, with BA exclusions)
8 8
File: C:atc_portland_2005m_d_wna_bjf_peer_pga_with_big_text.draw;
7 7
Moment Magnitude
Includes
02 Denali Fault (M 7.9)
99 Chi-Chi (M 7.6)
6 6
99 Kocaeli (M 7.5)
78 Tabas (M 7.4)
86 Taiwan (M 7.3)
99 Duzce (M 7.1)
5 5
valid region for using BJF equations
1 10 100 1000 1 10 100 1000
Distance (km) Distance (km)

28. File: C:metu_03regressPAPVVSD.draw; Date: 2003-09-03; Time: 16:32:45
1
Peak Acceleration (g)
10 -1 M 7.5
M 6.5
NEHRP Class D
M 5.5
10 -1 1 10 1 10 2
Distance (km)
5 % damped PSV (cm/s)
5 % damped PSV (cm/s)
102
102
101 M 7.5
M 7.5
NEHRP Class D
M 6.5 101 M 6.5
T = 0.3 sec M 5.5 NEHRP Class D
T = 1.0 sec M 5.5
1
1 101 102 1 101 102
Distance (km) Distance (km)

29. 1
A&S, sS, Vs=600
5
5.5
6
6.5
7
7.5
0.1 M8, AR=2
M8, AR=4
PGA (g)
M8, AR=8
M8, AR>15
0.01
0.001
1 10 100 1000
Rupture Distance (km)

30. 1.2
1
File: C:metu_03regresspgam7vsd.draw; Date: 2003-09-05; Time: 12:36:40
BJF93, random, NEHRP D, M=7.0
peak horizontal acceleration (g)
1 shaded: median/10 , median*10
0.8
0.3
0.6 0.2
0.4 0.1
0.2
BJF93, random, NEHRP D, M=7.0
shaded: median/10 , median*10
0
0 20 40 60 80 100 0.1 1 10 100
djb djb

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

32. Ground-Motion Prediction Equations
Gives mean and 1.0
standard deviation of
response-spectrum
Larger Horizontal Peak Accel (g)
ordinate (at a
File: D:metu_03regressBJFLNDNR.draw; Date: 2005-04-20; Time: 20:25:26
particular frequency)
as a function of
magnitude distance, 0.1
site conditions, and
perhaps other
variables.
1992 Landers, M = 7.3
1994 NR, M=6.7 (reduced by RS-->SS factor)
Boore et al., Strike Slip, M = 7.3, NEHRP Class D
0.01 +
_
10-1 1 101 102
Shortest Horiz. Dist. to Map View of Rupture Surface (km)

33. Soil
M = 7.5
Date: 2003-09-03; Time: 18:47:06
D = 0 km
102 D = 10 km
Pseudo Relative Velocity (cm/s)
File: C:metu_03regressFIG8_srl_fault_type.draw;
D = 20 km
D = 40 km
D = 80 km
101
Mechanism: strike slip
Mechanism: reverse slip
1
0.1 0.2 1 2
Period (sec)

34. Illustrating distance and magnitude dependence
10000
T = 0.1 sec T = 2 sec
File: C:peer_ngateamxrs_t0p1_t2p0_chi_chi_lp89_nr94.draw; Date: 2005-05-03; Time: 12:07:50
1000
PSA (cm/sec 2)
100
Chi-Chi (M 7.6) Chi-Chi (M 7.6)
Loma Prieta (M 6.9) Loma Prieta (M 6.9)
Northridge (M 6.7) Northridge (M 6.7)
10
0.1 1 10 100 0.1 1 10 100
Rjb (set values less than 0.1 to 0.1 km) Rjb (set values less than 0.1 to 0.1 km)
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. 0.2
Peru, 5 Jan 1974, Transverse Comp., Zarate
Acceleration (g)
0.1 M = 6.6, rhyp = 118 km
PGA generally a 0
poor measure of -0.1
ground-motion -0.2
0 50 100 150
intensity. All of 0.2
Montenegro, 15 April 1979, NS Component, Ulcinj
Acceleration (g)
M = 6.9, rhyp = 29 km
these time series
0.1
File: D:encyclopedia_bommeraccel_same_pga.draw; Date: 2005-04-20; Time: 19:44:33
0
have the same -0.1
PGA: -0.2
0 50 100 150
0.2
Mexico, 19 Sept. 1985, EW Component, SCT1
Acceleration (g)
M = 8.0, rhyp = 399 km
0.1
0
-0.1
-0.2
0 50 100 150
0.2
Romania, 4 March 1977 EW Component, INCERC-1
Acceleration (g)
0.1 M = 7.5, rhyp = 183 km
0
-0.1
-0.2
0 50 100 150
Time (sec)

41. But the response spectra (and consequences for structures)
are quite different (lin-lin and log-log plots to emphasize
different periods of motion):
5%-Damped, Pseudo-Absolute Acceleration (g)
Peru (M=6.6,r hyp=118km)
1
File: D:encyclopedia_bommerpsa_same_pga.draw; Date: 2005-04-20; Time: 19:34:16
Montenegro (M=6.9,r hyp=29km)
1
Mexico (M=8.0,r hyp=399km)
Romania (M=7.5,r hyp=183km)
0.1
0.8
0.6 0.01
0.4 0.001
Peru (M=6.6,r hyp=118km)
-4 Montenegro (M=6.9,r hyp=29km)
0.2 10
Mexico (M=8.0,r hyp=399km)
Romania (M=7.5,r hyp=183km)
0 10-5
0 2 4 6 8 10 0.1 1 10
Period (sec) Period (sec)

42. Boore, Joyner, and Fumal (1997); rjb = 10 km
5%-Damped, Pseudo-Absolute Acceleration (cm/sec 2)
1500
File: C:metu_03regresspsa_bjf_m55_m75_class_b_c_d.draw; Date: 2003-09-06; Time: 12:16:49
M=7.5, NEHRP classes B, C, D
2000
M=5.5, NEHRP classes B, C, D
1000
1000
200
100
500
D
C 20 M=7.5, NEHRP classes B, C, D
B M=5.5, NEHRP classes B, C, D
0 10
0 0.5 1 1.5 2 2.5 0.1 0.2 0.3 1 2
Period (sec) Period (sec)
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