Proceedings of the Ninth Pacific Conference on Earthquake Engineering

Building an Earthquake-Resilient Society

14-16 April, 2011, Auckland, New Zealand

Paper Number 008

Comparison of attenuation characteristics between the data from two distant regions: New Zealand and Japan

John X. Zhao and Matt C. Gerstenberger

GNS Science, Lower Hut, New Zealand.

ABSTRACT: Empirical prediction equations for response spectra are critical for seismic

hazard analysis and models have been developed for many regions. However, the

number of high-quality strong-motion records varies enormously based on the region.

For example, as many as 90% of the globally-available high quality strong-motion

records from subduction earthquakes are from Japan and New Zealand. Even with over

3000 strong-motion records, the distribution with respect to magnitude, source distance

and focal depth of the New Zealand data is poorer than that of the dataset from Japan.

For shallow earthquakes, the effect of possible Moho reflections, which were observed in

the dataset from Japan, are also prominent in the New Zealand data. For deep New

Zealand earthquakes, the variation of geometric attenuation with depth and source

distance, which was found in the Japanese data, was not recognized because of the

narrow distance range of the records for each deep earthquake. A careful re-examination

revealed that the effect of wave-propagation paths was prominent in the New Zealand

data set, but that the ‘error’ migrated into the inter-event error and an upwardly estimated

depth term from deep New Zealand earthquakes. Our results suggest that the attenuation

characteristics between New Zealand and Japan are remarkably similar but differ in

anelastic attenuation rates.

1 INTRODUCTION

A set of reliable ground-motion prediction equations is a vital part of seismic hazard analyses and is

often used to estimate seismic demand for a given engineering structure. Many models have been de-

veloped, including recent Next Generation Attenuation (NGA) models (Abrahamson and Silva 2008,

Boore and Atkinson 2008, Campbell & Bozorgnia 2008 and Choiu and Youngs 2008). Models have

also been developed for many parts of the world, for example, Akkar and Bommer (2010) for Europe,

the Mediterranean Region and the Middle East, Lin and Lee (2008) for Taiwan, McVerry et al. (2006)

for New Zealand, and Zhao et al. (2006) and many others for Japan. Deriving a ground-motion

prediction equation for a region from a small set of data can lead to seriously biased predictions at the

levels of ground shaking that cause damage to engineering structures. A careful investigation in the

present study will reveal the problem of data distribution and how this problem can be solved. It is

plausible to use local data to modify a set of attenuation models derived from regions that have a large

number of strong-motion records, as done by McVerry et al. (2006). We will illustrate this aspect in

the present study.

Zhao (2010) examined the geometric attenuation functions, using the dataset of Zhao et al. (2006).

With the large number of strong-motion records and their broad distribution with respect to magni-

tude, distance and depth, the Zhao (2010) study had three major findings: 1) possible effects of Moho

reflections were observed among the data from shallow crustal earthquakes; 2) the mantle wedge be-

tween the crust and the subducting plate appeared to have less attenuation than the portion of crust

above the mantle wedge; and 3) Ground motion from the deep subducting plate changed the attenua-

tion rates significantly at distances beyond about 200km. As Japan and New Zealand are considered

to have similar tectonic settings, we compare the attenuation characteristics of New Zealand data with

2

those of Japan to identify similarities and differences between two distant subduction regions.

2 STRONG MOTION DATASET

We assembled a set of New Zealand earthquake records from both the strong-motion and seismograph

networks. Focal depth is an important source parameter, and the depth in the GeoNet (New Zealand

seismograph and strong-motion recording network) catalogue is likely to be poor for earthquakes with

a depth of less than 50km. We used the depths determined by Eberhart-Phillips et al. (for 230 events

3.5<ML<7.3 between 2001 and June 2009), which were the most preferred hypocentral locations. For

events before 2001, we used the relocated ISC-EHB hypocentral locations which were the second

most preferred locations (127 events). For those events that were not available in either the dataset of

Eberhart-Phillips et al. (2010) or the relocated ISC catalogue, we used the depth in the dataset of

McVerry et al. (2006). For the rest of the events, the hypocentral location in the GeoNet catalogue was

used. Earthquakes in New Zealand and Japan are often classified as shallow crustal (with a depth of

25km or less for Japan, Zhao et al. 2006), subduction interface (less than 50km) and subduction intra-

slab earthquakes. Unfortunately, only a small number of earthquakes were reliably classified, and as

an alternative, we divided the earthquakes into three groups according to their focal depth: h ≤ 25km,

25km < h ≤ 50km, and h > 50km. Using 25km to define shallow earthquakes does not suggest that the

crustal thickness is 25km in New Zealand; we used this depth for a consistent comparison with the

models developed from data in Japan (25km was used by Zhao et al. 2006 and Zhao 2010 as a cut-off

depth for crustal earthquakes). The 50km depth boundary was used because earthquakes in a subduc-

tion zone at a depth of over 50km were all classified as subduction slab earthquakes. For 168 earth-

quakes since August 2003, Ristau (2009) estimated the moment magnitude and focal mechanisms

which were the most preferred source parameters. Focal mechanisms and moment magnitudes from

the Harvard catalogue were the second most preferred source parameters, and moment magnitude and

focal mechanisms for events in the McVerry et al. (2006) catalogue were used for the remaining

events (many of the moment magnitudes in the McVerry et al. 2006 catalogue were from the Harvard

catalogue). For all events that were not in these catalogues, we used local magnitudes in the GeoNet

catalogue to derive moment magnitudes via an empirical equation by Zhao and Gerstenberger (2010)

and their focal mechanisms were assigned as unknown.

0

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3.5 4 4.5 5 5.5 6 6.5 7 7.5 8

So

urc

e d

ista

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km

)

Magnitude

SC A

SC B

SC C

SC D

SC E

(a)

0

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0 20 40 60 80 100 120 140 160 180 200

So

urc

e d

ista

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km

)

Focal Depth (km)

SC ASC BSC CSC DSC E

(b)

Figure 1 The distribution of earthquake records with respect to (a) magnitude and source distance

and (b) depth and source distance for 5 site classes

Figure 1(a) presents the distribution of earthquake records with respect to magnitude and distance. The

magnitude range for deep earthquakes is 4.3-6.7. Figure 1(b) shows the distribution of strong-motion

records with respect to magnitude and focal depth. We used the shortest distance from a recording sta-

tion to the fault rupture plane for large earthquakes and hypocentral distance for others. The distance

range for deep earthquakes is limited with many fewer records than for shallow earthquakes. Because

of the very small number of records within a distance of 10km, we introduced a set of strong motion

records from Californian shallow crustal earthquakes. The site classes for the overseas data are the

NEHRP site classes from the NGA dataset. We used 30km as the cut-off distance for the overseas

events; this comes from the consideration that this distance range will be suitable to constrain near-

source terms in the attenuation model while the possible effect of different anelastic attenuation rates

3

among different regions will have a minimal effect on the model parameters derived for New Zealand

data.

3. SIMPLE ATTENUATION MODELS FOR NEW ZEALAND STRONG-MOTION REC-

ORDS

In the present study we fitted an identical set of attenuation models to those in Equation (1) of Zhao

(2010) so as to compare the distribution of residuals for New Zealand data. The prediction functions

have the following form:

ijikDPDPUNUNNNSSRRijVOCiVOC

jiDPDPjiSHSHjieSHCiWCWijie

SFFFFFehxb

xbxbrMMaMay

ηξδδδδδ

δδδ

+++++++++

+++−−+=

,,

,,,2

21, )(log)()(log(1)

where

=

=

=

=

−

=

=

eventsotherallfor0

50kmoverdepthwitheventdeepfor1

eventsotherallfor0

25kmofdepthawithineventshallowfor1

eventsotherallfor0

faultingunknownwitheventcrustalshallowfor1

eventsotherallfor0

faultingnormalwitheventcrustalshallowfor1

eventsotherallfor0

faultingslipstrikewitheventshallowfor1

eventsotherallfor0

faultingreversewitheventshallowfor1

DP

SH

UN

N

S

R

δ

δ

δ

δ

δ

δ

(2)

)exp( + 21,, iWjiji Mccxr += (3)

The ground motion parameter y is either peak ground acceleration (PGA), peak ground velocity (PGV)

or 5% damped response spectral acceleration (the geometric mean of the two horizontal components)

for a given spectral period T. Distance x is the closest distance to a fault rupture plane for large events

and hypocentral distance for other events. Parameters a1 and a2C represent magnitude scaling. MC is a

magnitude constant, coefficients b and d are, respectively, anelastic and geometric attenuation rates,

and Sk is the term for kth site-class. Subscript i denotes event number and j denotes record number from

the ith event. FR is the term for reverse faulting earthquakes, FS is the term for strike-slip events, FN is

the term for normal faulting events and FUN is the term for earthquakes with unknown focal mecha-

nisms. The focal mechanism terms in Equation (1) are applicable only to earthquakes within the top

25km so as to be consistent with the model by Zhao (2010). Term bVOC is the anelastic attenuation rate

in the volcano zone of the North Island and xVOC is the portion of the straight line distance from a re-

cording station to the hypocentre or the closest part of a fault rupture plane passing through the central

volcanic zone defined by Cousins et al. (1999). Variables ξi,j and ηi with zero means and standard de-

viations of σ and τ, represent the intra- and inter-event errors of a particular record respectively. We

capped the maximum focal depth at hcut, i.e., when hi> hcut, hi = hcut. The near-source term c2 in Equa-

tion (3h) was fixed as 1.15, corresponding to 0.5 in log10 scale, i.e., 0.5loge(10) (Zhao 2010), for all

spectral periods. Zhao and Gerstenberger (2010) showed that the optimal model parameters were

derived for hcut=170km when an anelastic attenuation rate inversely proportional to depth (see Eber-

hart-Phillips and McVerry, 2003) was used. In order to carry out a fair comparison with the model by

Zhao (2010), we used hcut=100km and a constant anelastic attenuation rate for deep earthquakes. Equa-

4

tion (1) of Zhao (2010) had magnitude-squared terms for crustal and subduction interface earthquakes

and a magnitude-cubed term for subduction slab earthquakes together with linear magnitude terms.

The coefficients for the magnitude-squared term and magnitude-cubed term were negative, to ensure

that the response spectra did not increase in a linear, or more rapid, manner with increasing magnitude.

The magnitude distribution of NZ data from deep earthquakes (50km or deeper) with respect to mag-

nitude does not allow for deriving a higher magnitude term and therefore only a linear magnitude term

was used for deep earthquakes. The site classification for New Zealand strong-motion recording sta-

tions is largely based on surface geology but borehole data are used for some. We used 5 site classes,

from A to E defined in NZS1170.5, broadly similar to the NEHRP site classes. Site classes A and B

were taken as equivalent to SC I class used in the Zhao (2010) study, C corresponds to SC II class, D

to SC III and E to SC IV classes.

4 ANALYSYS OF RESIDUALS

The intra-event residuals from the simple model in Equation (1) are defined as the natural logarithm of the recorded spectrum minus the predicted value and the inter-event residuals. The distribution of in-tra-event residuals with respect to distance usually reflects the adequacy of the attenuation functions (Zhao 2010). Because of the large scatter of the residuals, it is not possible to judge the distribution without a trend line. For a perfect distribution the trend line fitted to the residuals has a zero at all dis-tances. Negative residuals mean that the recorded spectrum is over-predicted and positive residuals mean it is under-predicted. The details of the residuals are discussed in the following section.

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Intr

a-e

ven

t re

sid

uals

Source distance (km)

Data from Japan

PGA(b)

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a-e

ven

t re

sid

uals

Source distance (km)

Data from Japan

0.5s(d)

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a-e

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t re

sid

uals

Source distance (km)

NZ data

PGA(a)

Over-predicted region

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Intr

a-e

ven

t re

sid

uals

Source distance (km)

NZ data

0.5s(c)

Figure 2 Comparison between the distribution of intra-event residuals for shallow earthquakes in

New Zealand (left panel) and Japan (right panel), The top row is for PGA; the second row

is for acceleration spectra at 0.5s.

4.1 Shallow crustal earthquakes

Figure 2 compares the intra-event residuals from shallow New Zealand earthquakes with those of shal-low crustal events from Japan (Zhao 2010). For PGA and spectral acceleration at 0.5s, the trend lines fitted to the residuals have an almost identical variation pattern, with respect to source distance, to those of the Japanese data derived from Equation (1) in Zhao (2010). Zhao (2010) interpreted these trend-line variations as possible effects of Moho reflection. The similarity is remarkable, considering that the depth of the Moho discontinuity in Japan can differ significantly from that of New Zealand. The variations of the trend lines fitted to the New Zealand data at 1s and 2s are similar to those at short periods, while the effect of Moho reflection for data from Japan becomes subtle at long periods.

Using the geometric attenuation functions proposed by Zhao (2010) to account for the Moho reflection effect for New Zealand data can eliminate the biased residual distribution; the left panel in Figure 3 shows the residuals from Equation (1) and the right panel shows the residuals corrected using the ge-ometric attenuation function in Equation (2) in Zhao (2010). The distance values for the changes in geometric attenuation rates and the depth terms are identical to those used by Zhao 2010. The distri-

5

bution of residuals in the right panel of Figure 3 is not biased, suggesting that the attenuation charac-teristics between New Zealand and Japan are very similar for shallow earthquakes, and that the geo-metric attenuation functions proposed by Zhao (2010) for crustal earthquakes from Japan can be used for New Zealand data.

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Depth ≤ 25km

0.4s(a)

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1.0s(c)

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a-e

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t re

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uals

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Depth ≤ 25km

1.0s(d)

Figure 3 Intra-event residuals for shallow earthquakes. The left panel is for the simple model and the right panel is for the residuals corrected by using the geometric attenuations proposed by Zhao (2010). The top row is for 0.4s and the second row for 1.0s

4.2 Deep earthquakes

All earthquakes with a depth greater than 50km are likely to be subduction slab earthquakes, except for some deep earthquakes at locations far away from the subduction zones. We found that that the in-tra-event residuals derived from the model with hcut=170km were well distributed with respect to source distance, for all spectral periods, while the distribution of the residuals for subduction slab earthquakes in Japan with depth greater than 50km had strong bias at large distances if a simple geo-metric attenuation function was used (Figure 12 in Zhao 2010). However, the total residuals at large distances are on average under-predicted as shown in the left panel of Figure 4 (with hcut=100km, as in Zhao 2010), similar to the total residuals for the data from Japan in the right panel (from Zhao 2010). Note that the distributions of intra-event and total residuals from Zhao (2010) are very similar because the distribution of inter-event residuals with respect to focal depth and magnitude from the simple model of Zhao (2010) was not biased. The biased distribution of total residuals in the New Zealand da-ta (the left panel in Figure 4) is a result of a biased distribution of inter-event residuals with respect to depth for deep events. The under-predicted data for deep earthquakes are all from large distances. The biased distribution of total residuals suggests that the observed effect of multiple wave propagation paths in subduction zones, illustrated by Figures 15 and 16 in Zhao (2010) are also likely among the New Zealand data. However, part of this effect is diminished by the upward bias in the estimated large depth term. Also, because of the narrow distance ranges for the New Zealand data from deep earthquakes, a part of the effect of the multiple wave-propagation paths in the subduction slab pro-posed by Zhao (2010) could migrate into the inter-event residuals. The total residuals, however, con-tain the “missing” part of the “intra-event” residuals that can be recovered from the inter-event residu-als, leading to evident under-estimates of the spectra for deep subduction earthquakes in the left panel of Figure 4. If we assume that the depth cap derived from the records in Japan (with excellent data dis-tribution with respect to magnitude, distance and depth) is also appropriate for New Zealand earth-quakes, we can, therefore, use the depth-dependent geometric attenuation functions defined in Equa-tion (4) of Zhao (2010) to correct the total residuals of the New Zealand records. Figure 5 shows the residuals of the data from New Zealand earthquakes with a depth of 50km or greater and those from earthquakes with a depth of 90km or greater. Figure 4(a) shows that the records at large distances are significantly under-predicted, while Figure 4(b) shows that the biased residuals can be corrected very well by the geometric attenuation functions developed by Zhao (2010). The results for other short-

6

period spectra (PGA, 0.05-0.3s) are very similar to those in Figure 5. We also found that adopting a inversely proportional anelastic attenuation rate to depth that was intended to account for the increase in the average Q values with increasing depth (Eberhart-Phillips and McVerry 2003) did not eliminate the biased distribution of residuals for New Zealand deep earthquakes.

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Data from Japan

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(b) PGA

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PGA(a) Under-predicted region

Over-predicted region

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tal r

esid

uals

Source distance (km)

NZ data

0.5s(c)

Figure 4 Comparison between the distribution of total residuals for deep earthquakes in New Zea-

land (left panel) and Japan (right panel). The top row in (a) and (b) is for PGA; the second

row in (c) and (d) is for 0.5s spectral period.

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tal r

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Depth ≥ 90km

0.2s(d)

Figure 5 Total residuals for 0.2s spectral periods of the data from earthquakes with a depth over 50km in the top row and from earthquakes with depth over 90km in the bottom row. The left panel shows the residuals from the simple model and the right panel show the residuals corrected by the geometric attenuation functions proposed by Zhao (2010)

5. SUMMARY AND DISCUSSIONS

We used the residuals from a set of simple attenuation functions used by Zhao (2010) to examine the attenuation characteristics of New Zealand seismograms strong-motion records. We found that the distributions of intra-event residuals with respect to source distance from records of New Zealand shallow and deep earthquakes were remarkably similar to those found from a large strong-motion da-taset from Japan. We found good evidence of possible Moho reflection for shallow earthquakes and the effect of multiple-wave propagation in the subduction slab for deep earthquakes in New Zealand.

7

The features are remarkably similar to the attenuation characteristics in Japan. The geometric attenua-tion functions designed to account for possible Moho reflection for data from Japan by Zhao (2010) can be used to correct the bias in the distribution of residuals of the New Zealand data.

-1.4

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-1

-0.8

-0.6

-0.4

-0.2

0

0.01 0.1 1

10

0x

an

ela

cti

c a

tte

n.

rate

Spectral period (s)

NZ ShallowNZ Deep

(a)

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-0.8

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-0.2

0

0.01 0.1 1

10

0x

an

ela

cti

c a

tte

n.

rate

Spectral period (s)

Japan CrustalJapan Slab

(b)

Figure 6 Comparison of attenuation rates for (a) New Zealand data and (b) for data from Japan

0.001

0.01

0.1

1

1 10 100

No

rmalized

Sp

ectr

a

Source distance (km)

NZ model

Japan model

(b)0.5s

0.001

0.01

0.1

1

1 10 100

No

rmalized

PG

A

Source distance (km)

NZ modelJapan model

(a)PGA

Figure 7 Comparison of attenuation between New Zealand data and the data from Japan, (a)

normalized PGA and (b) spectral acceleration at 0.5s spectral period

However, the attenuation parameters between New Zealand and Japan are not identical. Figure 6 compares the anelastic attenuation rates b in Equation 1 between New Zealand and Japan. The anelas-tic attenuation rates shown in Figure 6(a) include the distance terms when the geometric attenuation functions proposed by Zhao (2010) were used. The anelastic attenuation rates for shallow and deep New Zealand earthquakes are very similar for spectral periods up to 0.7s (Figure 6a) while the anelas-tic attenuation rates for deep earthquakes in Japan are much larger (in absolute value) than those in New Zealand at short periods (Figure 6b). At short periods up to 0.2s, the anelastic attenuation rates for shallow earthquakes in New Zealand are similar to those of Japan, but considerably smaller than those for Japan at longer periods. Up to 1s spectral period, the anelastic attenuation rates for New Zealand deep earthquakes are considerably smaller than those of the subduction slab earthquakes in Japan, but they are similar at 2s. Note that the larger anelastic attenuation rate for subduction slab earthquakes than crustal earthquakes in Japan is caused by the relatively low Q values in the mantle, while the effect of high-Q along the propagation path in the subduction slab was incorporated in geo-metric attenuation functions (Zhao 2010). Figure 7 compares the attenuation curves of normalized PGA for shallow New Zealand earthquakes and crustal earthquakes from Japan. The differences be-tween the two models are caused by the difference in the anelastic attenuation rate, suggesting that the same geometric attenuation functions can be used for these earthquakes from two distant parts of the world.

Even though the number of records from New Zealand is large, the poor distribution in distance ranges for deep earthquakes leads to apparent ‘unbiased’ distribution of the intra-event residuals with respect to source distance for deep earthquakes. Without the results from the Zhao (2010) study, the effect of multiple-wave-propagation paths may not have been discovered, suggesting that developing models for a region with a small number of records, or a reasonably large number of records but with a poor distribution with respect to magnitude, source distance and focal depth, may not lead to optimal esti-mates of the model parameters. The approach used by McVerry et al. (2006) to establish a New Zea-land model by using a small New Zealand dataset to modify a set of attenuation models derived from regions with a large dataset would be more reasonable than developing a model from the poor dataset.

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ACKNOWLEDGEMENTS

We would like to thank Dr. David Rhoades and Dick Beetham for their reviews and comments. The work reposted here was supported by New Zealand Earthquake Commission and the Foundation for Research, Science and Technology, under programme CO5X0402. All records were from GeoNet.

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