deterministic strong ground motions

Deterministic Seismic Ground Motions and the PEER NGA Ground Motion Prediction Equations (GMPEs)

David M. Boore

EERI Utah Chapter Short Course on Seismic Ground MotionsWest Jordan, UtahMarch 05, 2015

1David M. Boore

http://www.daveboore.com/presentations.html

Contents of the Lecture• Overview of Ground‐Motion Prediction Equations (GMPEs)

• Predicted and Predictor Variables• The PEER NGA‐West2 GMPEs

• Data• Functions• Comparisons of median predictions• Aleatory and Epistemic Uncertainties

• Comparing Greek Data to NGA‐West2 Predictions• Present and Future Work• Resources

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Ground‐Motion Prediction Equations (GMPEs): What are they?

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Ground‐Motion Prediction Equations (GMPEs): How are they used?

• Engineering: Specify motions for seismic design (critical individual structures as well as building codes)

• Seismology: Convenient summary of average M and R variation of motion from many recordings

• Source scaling• Path effects• Site effects

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Developing GMPEs requires knowledge of:

• Data acquisition and processing• Source physics• Velocity determination• Linear and nonlinear wave propagation• Simulations of ground motion• Model building and regression analysis

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How are GMPEs derived?• Collect data

• Choose functions (keeping in mind the application of predicting motions in future earthquakes).

• Do regression fit

• Study residuals

• Revise functions if necessary

• Model building, not just curve fitting

P. Stafford 6David M. Boore

Considerations for the functions

• “…as simple as possible, but not simpler..” (A. Einstein)

• Give reasonable predictions in data‐poor but engineering‐important situations (e.g., close to M≈8 earthquakes)

• Use simulations to guide some functions and set some coefficients (an example of model building, not just curve fitting)

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Predicted and Predictor Variables• Ground‐motion intensity measures

– Peak acceleration– Peak velocity– Response spectra

• Basic predictor variables– Magnitude– Distance– Site characterization

• Additional predictor variables– Basin depth– Hanging wall/foot wall– Depth to top of rupture– etc.

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Input Parameters in PEER Spreadsheet: Source

• Moment magnitude• Fault Width• Fault Dip• Fault Type

– Unspecified– Strikeslip– Normal– Reverse

• Depth to Top of Rupture • Hypocentral Depth• Aftershock or Mainshock?

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Input Parameters in PEER Spreadsheet: Site

• VS30

• Was VS30 measured or inferred? (Needed for uncertainty calculation)• Depth to 1.0 km/s shear‐wave velocity• Depth to 2.5 km/s shear‐wave velocity

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Input Parameters in PEER Spreadsheet: Path

• Region• RJB• RRUP• RX• RY0

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Wave Type and Frequencies of Most Interest

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• Seismic shaking in range of resonant frequencies of structures

• Shaking often strongest on horizontal component:– Earthquakes radiate larger S waves than P waves– Refraction of incoming waves toward the vertical S waves primarily horizontal motion

• Buildings generally are weakest for horizontal shaking• GMPEs for horizontal components have received the most attention

Horizontal S waves are most important for engineering seismology:

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Frequencies of ground‐motion for engineering purposes

• 20 Hz ‐‐‐ 10 sec (usually less than about 3 sec)

• Resonant period of typical N story structure ≈ N/10 sec– What is the resonant period of the building in which we are located?

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What are response spectra?

• The maximum response of a suite of single degree of freedom (SDOF) damped oscillators with a range of resonant periods for a given input motion

• Why useful? Buildings can often be represented as SDOF oscillators, so a response spectrum provides the motion of an arbitrary structure to a given input motion

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Period = 0.2 s

0.5 s 1.0 s

Courtesy of J. Bommer16David M. Boore

Response Spectrum

Courtesy of J. Bommer17David M. Boore

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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:

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Design maps in building codes are for T=0.2 and T=1.0 s

• Design values at other periods are obtained by anchoring curves to the T=0.2 and T=1.0 s values, as shown in the next slide

• But PGA useful in liquefaction analysis (along with duration)

0.0 0.5 1.0 1.5 2.0Period

0.0

0.5

1.0

1.5

2.0

2.5

Spec

tralR

espo

nse

Acce

lera

tion 0.0 0.5 1.0 1.5 2.0

0.0

0.5

1.0

1.5

2.0

2.5

Construct response spectrum at all periods using T = 0.2 and 1.0 sec values

Computing RotD50• Project the two as‐recorded horizontal time series into azimuth Az

• For each period, compute PSA, store Az, PSA pairs in an array

• Increment Az by δα and repeat first two steps until Az=180

• Sort array over PSA values• RotD50 is the median value• RotD00, RotD100 are the minimum and maximum values

• NO geometric means are used

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25

To convert GMPEs using random component as the IM (essentially, the as‐recorded geometric mean), multiply by RotD50/GM_AR

To convert GMPEs using GMRotI50 as the IM (e.g., 2008 NGA GMPEs), multiply by RotD50/GMRotI50

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Strike-normal (also known as “fault-normal”) motion only close to maximum

motion within about 3 km of the fault

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What to use for the basic predictor variables?

• Moment magnitude– Best single measure of overall size of an earthquake (it does not saturate)

– It can be estimated from geological observations– Can be estimated from paleoseismological studies– Can be related to slip rates on faults

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• Distance – many measures can be defined

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• Distance– The distance measure should help account for the extended fault rupture surface

– The distance measure must be something that can be estimated for a future earthquake

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• Distance – not all measures useful for future events

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Most Commonly Used:RRUP

RJB (0.0 for station over the fault)

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Courtesy: Jennifer Donahue


• A measure of local site geology

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Site Classifications for Use WithGround-Motion Prediction Equations

• Rock = less than 5m soil over “granite”, “limestone”, etc.• Soil= everything else

2. NEHRP Site Classes (based on VS30)

3. Continuous Variable (VS30)

1. Rock/Soil

620 m/s = typical rock

310 m/s = typical soil

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0 ( )

SZ z

S

zVd

V

0

1 1 ( )z

SZ SSZ

S S dV z

Time-averaged shear-wave velocity to depth z:

Average shear-wave slowness to depth z:

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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)

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Vsz correlates quite well with Vs30 for a wide range of z greater than 30 m

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But regional differences exist

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VS Profiles for VS30=270 (± 5%)

CALIFORNIA JAPAN

From Kamai et al (2015)Abrahamson (2015)

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0 500 1000 15000.1

0.2

1

2

10

index (sorted by V30)

obse

rved

/pre

dict

ed(n

osi

teco

rrect

ion)

class Dclass Cclass B

T = 2.0 sec, rjb < 80 km

File

:C:\p

eer_

nga\

team

x\re

sids

_dm

b_m

r6_6

_by_

clas

s_t2

p0.d

raw

;D

ate:

2005

-04-

20;T

ime:

16:3

7:55

Large scatter would remain after removing site effect based on site class

Knowing site class shifts aleatory to epistemic uncertainty

This figure is also a good representation of the data availability for various site classes: most data are from class D, very few from class B (rock) 42David M. Boore

200 1000 20000.40.5

1

2

345

V30, m/sec

Am

plifi

catio

n

T=0.10 s

slope = bv, where Y (V30)bV

200 1000 20000.40.5

1

2

345

V30, m/sec

T=2.00 s

VS30 as continuous variable

Note period dependence of site response43David M. Boore

Effect of different site characterizationsfor a small subset of data for which V30values are available

• No site characterization• Rock/soil• NEHRP class• V30 (continuous variable)

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-0.5

0

0.5

1

1.5

Obs

-BJF

(M,R

) RockSoil

T = 2.0 secResiduals computed as obs-bjf (with no site correction,which is the same as assuming BJF class A or V30 = VA).

200 300 400 1000-1

-0.5

0

0.5

1

V30 (m/sec)

Obs

-BJF

(M,R

)-S

ite(r

ock,

soil)

RockSoil

T = 2.0 secrock & soil site classification

File

:C:\p

sv\D

EVEL

OP\

RSD

L2A_

B_pp

t.dra

w;

Dat

e:20

03-0

6-13

;Ti

me:

19:0

7:42

σ=0.25

σ=0.25

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-1

-0.5

0

0.5

1

Obs

-BJF

(M,R

)-S

ite(B

,C,D

)

RockSoil

T = 2.0 secNEHRP B,C,D site classification

200 300 400 1000-1

-0.5

0

0.5

1

V30 (m/sec)

Obs

-BJF

(M,R

)-S

ite(V

30) Rock

Soil

T = 2.0 secV30 site classification (continuous)

File

:C:\p

sv\D

EVEL

OP\

RSD

L2C

_D_p

pt.d

raw

;D

ate:

2003

-06-

13;T

ime:

19:0

8:04

σ=0.21

σ=0.20

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2002 M 7.9 Denali Fault

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K2-16

1741

K2-03

K2-06K2-09

K2-11K2-12

K2-14

K2-22

1744

1751

K2-02

K2-13

1734

1737

K2-01

K2-04

K2-05

K2-07

K2-19

1397

1731

1736

K2-08

K2-20K2-21

-150 -149.8

61.1

61.2

Longitude (oE)

Latit

ude

(o N)

D

C/D C

Chu

gach

Mts

.

Site Classes are based on the average shear-wave velocity in the upper 30 m

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Remove high frequencies by filtering to emphasize similarity of longer‐period waveforms

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0.1 1 100.001

0.01

0.1

1

10

100

Frequency (Hz)

Four

ier

Acc

eler

atio

n(c

m/s

ec)

Denali: EWclass Dclass C/Dclass Cclass B (one site)

range of previous site response studies

0.1 1 100.1

0.2

1

2

Frequency (Hz)R

atio

(rel

ativ

eto

avg

C)

Denali: EWclass Dclass C/Dclass Cclass B (one site)

range of previous site response studies

File

:C:\a

ncho

rage

_gm

\fas_

and_

ratio

_EW

_avg

_ref

_cc_

4ppt

.dra

w;

Dat

e:20

05-0

4-19

;Ti

me:

17:1

9:5

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•Strong correlation between Ztor and M

•Most M>7 earthquakes reach the surface (but no data for normal-fault earthquakes with M>7)

Correlation between Ztor, mechanism, and M

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Stewart et al., PEER 2013/22; Courtesy of Y. Bozorgnia

GMPEs: The Past

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The large epistemic variations in predicted motions are not decreasing with time

From Douglas (2010)

Mw6 strike-slip earthquake at rjb = 20 km on a NEHRP C site

55

(M=6, R=20 km)

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GMPEs: The Present

• Illustrate Empirical GMPEs with PEER NGA‐West 2

• (NGA = Next Generation Attenuation relations, although the older term “attenuation relations” has been replaced by “ground‐motion prediction equations”)

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PEER NGA‐West 2 Project Overview• Developer Teams (each developed their own GMPEs)

• Supporting Working Groups– Directivity– Site Response– Database– Directionality– Uncertainty– Vertical Component– Adjustment for Damping

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NGA-West2 Developer Teams:

• Abrahamson, Silva, & Kamai (ASK14)• Boore, Stewart, Seyhan, & Atkinson (BSSA14)• Campbell & Bozorgnia (CB14)• Chiou & Youngs (CY14)• Idriss (I14)

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PEER NGA‐West 2 Project Overview

• All developers used subsets of data chosen from a common database – Metadata– Uniformly processed strong‐motion recordings– U.S. and foreign earthquakes– Active tectonic regions (subduction, stable continental regions are separate projects)

• The database development was a major time‐consuming effort

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Observed data generally adequate for regression, but note relative lack of data for distances less than 10 km. Data are available for few large magnitude events.

NGA-West2 database includes over 21,000 three-component recordings

from more than 600 earthquakes

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Observed data not adequate for regression, use simulated data (the subject of a different lecture)

Observed data adequate for regression exceptclose to large ‘quakes

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Restricted to data within 80 km with at least 4 recordings per event

NGA‐West2 PSAs for ss events (adjusted to Vs30=760 m/s) vs. RRUP

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nrecs = 11,318 for TOSC=0.2 s; nrecs = 3,359 for TOSC=6.0 s

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There is significant scatter in the data, with scatter being larger for small earthquakes.

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For a single magnitude and for all periods the motions tend to saturate for large earthquakes as the distance from the fault rupture to the observation point decreases.

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At any fixed distance the ground motion increases with magnitude in a nonlinear fashion, with a tendency to saturate for large magnitudes, particularly for shorter period motions. To show this, plot PSA within the bands vs. M.

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At any fixed distance (centered on 50 km here, including PSA in the 40 km to 62.5 km range) the ground motion increases with magnitude in a nonlinear fashion, with a tendency to saturate for large magnitudes, particularly for shorter period motions. PSA for larger magnitudes is more sensitive to M for long‐period motions than for short‐period motions David M. Boore

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For a given period and magnitude the median ground motions decay with distance; this decay shows curvature at greater distances, more pronounced for short than long periods.

(lines are drawn by eye and are intended to give a qualitative indication of the trends)David M. Boore

Characteristics of Data that GMPEs need to capture

• Magnitude‐distance distribution depends on region• Change of amplitude with distance for fixed magnitude• Change of amplitude with magnitude after removing distance dependence

• Site dependence (including basin depth dependence and nonlinear response)

• Earthquake type, hanging wall, depth to top of rupture, etc.

• Scatter

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In 1994• Typical functional form of GMPEs

(Courtesy of Yousef Bozorgnia)

(Boore, Joyner, and Fumal, 1994)

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In 2014

(Courtesy of Yousef Bozorgnia)74David M. Boore

Boore, Stewart, Seyhan, and Atkinson (BSSA14) GMPEs• General form:

• M scaling

• Distance scaling:

20 1 2 3 4 5, E h hF mech e U e SS e NS e RS e eM M M M M

0 1 2 3 6,E hF mech e U e SS e NS e RS e M M M

M ≤ Mh:

M >Mh:

30 1

30

ln , , , , , , ,

, ,E P JB S S JB

n JB S

Y F mech F R region F V R region z

R V

M M M

M

75Modified from a slide by E. Seyhan

1 2 3 3, , ln /P JB ref ref refF R region c c R R c c R R M M M

2 2JBR R h

• General form:

• M scaling




M ≤ Mh:

M >Mh:

30 1

30

ln , , , , , , ,

, ,E P JB S S JB

n JB S


R V

M M M

M



2 2JBR R h

focal mechanism quadratic M-scaling

linear M-scaling

Boore, Stewart, Seyhan, and Atkinson (BSSA14) GMPEs

BSSA14 GMPEs

• General form:

• M scaling




M ≤ Mh:

M >Mh:

30 1

30

ln , , , , , , ,

, ,E P JB S S JB

n JB S


R V

M M M

M



2 2JBR R h

M-indep.

M-dependent distance decay

pseudo depth

BSSA14 GMPEs

• General form:

• M scaling




M ≤ Mh:

M >Mh:

30 1

30

ln , , , , , , ,

, ,E P JB S S JB

n JB S


R V

M M M

M



2 2JBR R h anelastic attenuation

regional corrections

BSSA14 GMPEs

• Site term

Linear site term

Nonlinear site term

31 2

3

2 30 4 5 30 5

ln( ) *ln

, ( ) exp ( )* min ,760 360 exp ( )* 760 360

nl

s s

PGAr fF f ff

f V T f T f T V f T

3030

30

ln

ln

ln

SS c

ref

lin

cS c

ref

Vc V VV

FVc V VV

130 1 1 , , , , ln ln ( , )S S JB lin nl zF V R z region F F F z region M

VS30-scaling

Break velocity

Slope of nonlinearity

Vs30 (m/s)

ln(F

lin)

PGAc

1

Vc

PGAr (g)ln

(Fnl

)

soft soil

stiff soil

PGA

f2 1


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Why ln Y? Residuals are log-normally distributed

Adding BSSA14 curves to data plots shown before

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• Need complicated equations to capture effects of:– M: 3 to 8.5 (strike‐slip)– Distance: 0 to 300km– Hanging wall and footwall sites– Soil VS30: 150‐1500 m/sec– Soil nonlinearity– Deep basins– Strike‐slip, Reverse, Normal faulting mechanisms– Period: 0‐10 seconds

• The BSSA14 GMPEs are probably the simplest, but there may be situations where they should be used with caution.

Courtesy of Yousef Bozorgnia)82David M. Boore

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Model Applicability

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Developer M R Vs30

ASK14 3.0‐8.5 0‐300 180‐1000

BSSA14 3.0‐8.5 0‐400 150‐1500

3.0‐7.0 (NS) 0‐400 150‐1500

CB14 3.3‐8.5 (SS) 0‐300 150‐1500

3.3‐8.0 (RS) 0‐300 150‐1500

3.3‐7.5 (NS) 0‐300 150‐1500

CY14 3.5‐8.5 (SS) 0‐300 180‐1500

3.5‐8.0 (RS, NS) 0‐300 180‐1500

I14 >=5.0 0‐150 >=450

Comparisons of NGA‐West1 and NGA‐West2 results for each developer

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Comparisons of NGA‐West2 results for the five developer teams

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Surface outcrop, 45 degree dip to right, to 15 km depth99David M. Boore

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?

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BSSA14 GMPEs

• Aleatory uncertainty

2 230 30 , , , ,JB S JB SR V R V M M M

1

1 2 1

2

4.5 4.5 4.5 5.5

5.5

MM M M

M

30, ,JB SR V M

between-event aleatoryuncertainty

within-event aleatory uncertainty

Total aleatory uncertainty


Stage 1 Regression: Determine the distance function and event offsets

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Stage 2 Regression: Determine the magnitude scaling

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Example of comparison of total standard deviations

Gregor et al., 2014)

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108

Al Atik and Youngs, 2014)

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Epistemic uncertainty for normal faults

Model-to-model variability is generally larger than the uncertainty in the medians of each model

Comparisons of Greek Data and the NGA‐W2 GMPEs

• Residual = ln Observed – ln Predicted from NGA‐W2

• For each period, use mixed effects regression to separate residuals into – 1) overall bias– 2) earthquake‐to‐earthquake (inter‐earthquake) variation

– 3) within earthquake (intra‐earthquake) variation

109David M. Boore

Mixed effects regressions

i<0

ij

iji>0

EQID: 1

EQID: 2

ij

30ln , , ,

| EQID

The random part fits a mean to each of the random groups defined in EQID( ) 0 var( )

ij ij ij JB S

ij k i ij

ij ij ij

R Y M mech R V

R c

vector IID randomerror terms with mean E and Z

110

Greek Data compared with NGA‐W2 GMPEs

Residual=ln Observed – ln NGA‐W2

Except for Vs30 dependence for small Vs30, overall dependence of Greek and NGA‐W2 predictions are similar

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Significant overall bias for sort periods (max factor=0.68)—due to filtering effects of structures from which records were obtained?

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GMPEs: The Future

• Future PEER NGA Work • Using simulations to fill in gaps in existing recorded motions

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NGA-West2/3

Vertical component (finished)

Add directivity

NGA-East

For stable continental regions

2015

NGA-Sub

For subduction regions

2016

NGA: 2014 and beyond

Slide from Y. Bozorgnia114David M. Boore

Vertical/Horizontal (from SBSA14/BSSA14)

115

Magnitude Dependence VS30 Dependence

NOTE: Rule of thumbV/H=2/3 OK only for RJB=70 km, VS30= 760 m/s

New data may not fill in gaps in data in the near term, particularly close to large earthquakes and for important fault‐site geometries, such as over the hanging wall of a reverse‐slip fault.

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Use of Simulated Motions

• Supplement observed data and derive GMPEs from the combined observed and simulated motions

• Constrain/adjust GMPEs for things such as:– Hanging wall– Saturation– Directivity– Splay faults and complex fault geometry– Nonlinear soil response

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Resources

• Web Sites– peer.berkeley.edu/ngawest2/

• peer.berkeley.edu/ngawest2/final-products/• peer.berkeley.edu/ngawest2/databases/

– www.daveboore.com• Papers• Software for evaluating GMPEs

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Resources

• Paper and Reports – 2013 PEER Reports (from PEER web site)– 2014 Earthquake Spectra Papers (H

component papers published in vol. 30(3), August, 2014)

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Resources

• Programs to evaluate GMPEs– NGA-West2 GMPEs Excel file (from

databases page of NGA-West2 web site)– http://www.daveboore.com/pubs_online.ht

ml (Fortran programs available under the entry for BSSA14)

– Matlab code for ASK14 from EqSsupplement

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Thank You

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deterministic strong ground motions

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