GROUND MOTION VARIABILITY: GROUND MOTION VARIABILITY: COMPARISON OF SURFACE AND COMPARISON OF SURFACE AND DOWNHOLE GROUND MOTIONSDOWNHOLE GROUND MOTIONS

Adrian Rodriguez-Marek, Washington State University, USA

Fabrice Cotton, LGIT, Grenoble, FranceFabian 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

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

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

Ground Motion Predictions

ymean = 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

intra2

inter2

Ground Motion Predictions

ymean = 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

Ground Motion Predictions

ymean = 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

Ground Motion Predictions

ymean = 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 ...

ymean = f (M,R,etc) + f(site) + i s-s + e-e e-e

+o o

MOTIVATION

Standard normal random variables

Site Term

Ground Motion Predictions

ymean = 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 ...

ymean = f (M,R,etc) + f(site) + i s-s + e-e e-e

+o o

MOTIVATION

Standard normal random variables

Site Term

Site-specific ground motion predictions

ymean = 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

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 ?

Ampinputsurface22

MOTIVATION

OPPORTUNITY!!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

KiK-net DatabaseKiK-net Database

100

101

102

103

4

4.5

5

5.5

6

6.5

7

7.5

Distance, km

Mag

nitu

de

DATABASE

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

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(R2 + h2)

Fm = e1 + e5(M-Mh) + e6(M-Mh) for M<MhFm = 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(yij) = mean_estimateij + ij intra + i inter

REGRESSION ANALYSIS

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

Comparison with Boore and Atkinson NGA Relationship

101

102

103

10-5

100

Distance, km

PG

A (

g)

BA

This Study

REGRESSION ANALYSIS

Vs30 dependency

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

Period (s)

linea

r V

s30

term

Surface

-100m-200m

REGRESSION ANALYSIS

-4

-2

0

2

4SURFACE (Mean = -0.0018 StdDev = 0.6746)

-4

-2

0

2

4BOREHOLE at 100m (Mean = -0.0015 StdDev = 0.5522)

-4

-2

0

2

4BOREHOLE at 200m (Mean = -0.0006 StdDev = 0.5543)

Raw results : 3784 intra-events residuals

REGRESSION ANALYSIS

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)

10-2

10-1

100

101

-4

-2

0

2

4

Site Period (s)

log r

esid

uals

REGRESSION ANALYSIS

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

0 500 1000 1500 2000 2500 3000 3500-3

-2

-1

0

1

2

3

Baserock Shear Wave Velocity (m/s)

log

resi

dual

s

Surface standard deviations

Vs30Vs30 and

H800Vs30 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

Surface standard deviations

Vs30Vs30 and

H800Vs30

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)

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

Surface vs. Downhole comparison: Intra-Event Residuals

Average

18% reductionMaximum of

24% at 0.1s

ANALYSIS OF RESIDUALS

Implications

Lower residuals at depth: Various hypothesis1) Site effects are responsible for larger residuals

at surface2) 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

Single-Station Residuals

44 stations with at least 15 recordings(995 records)

ANALYSIS OF RESIDUALS

100

101

102

103

4

4.5

5

5.5

6

6.5

7

7.5

Distance (km)

Mag

nitu

de, M

w

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

0 5 10 15 20 25 30 35 40 450

0.5

1

1.5single station standard deviations

surface

borehole

0 0.2 0.4 0.6 0.8 1 1.2 1.40

0.5

1

surface std

bore

hole

std

Mean Res: Surf = 0.63190 BH = 0.62551

Results for PGA

ANALYSIS OF RESIDUALS

Single Station Standard Deviation

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20.5

0.6

0.7

0.8

0.9

1

Period (s)

Tota

l Sig

ma

(log

units

)

Surface, Regression

Borehole, Regression

Surface, Single StationBorehole, Single Station

Atkinson (2006)

ANALYSIS OF RESIDUALS

Single Station Standard Deviation

ANALYSIS OF RESIDUALS

Single Station standard deviation removing event term

0 0.5 1 1.5 2 2.5 3

0.4

0.5

0.6

0.7Single Station Sigmas Removing Event Term

Period (s)

Tot

al S

igm

a (lo

g un

its)

Surface

Borehole

Atkinson

0 0.2 0.4 0.6 0.8 1 1.2 1.40

2

4

6

8

Period (s)

Per

cent

age

Red

uctio

n at

dep

th

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

Implications

Surface and Depth single-station residuals are more or less equal1) Site effects are responsible for larger residuals

at surface2) Site parameterization is better at depth than

at surface (more site variability at surface)3) Surface-waves, non 1-D effects responsible for

larger residuals4) Surface estimates of single station variability

can apply to borehole variability

IMPLICATIONS

Implications for site-specific analyses: use of single station residuals

ymean = 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

Surface Borehole Surface Borehole

PGA 0.63 0.63 0.48 0.47

T=0.1s 0.65 0.63 0.52 0.48

T=1.0 s 0.63 0.64 0.44 0.41

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 = ??

FBHsurface22

IMPLICATIONS

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

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

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.