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Tectonophysics 390
Depth variation of seismic source scaling relations: implications
for earthquake hazard in southeastern Australia
Trevor I. Allena,*, Gary Gibsona,b, Amy Brownb,1, James P. Culla
aSchool of Geosciences, Monash University, P.O. Box 28E, VIC 3800, AustraliabES&S Seismology Research Centre, 8 River St., Richmond, VIC 3121, Australia
Received 12 February 2002; received in revised form 25 September 2002; accepted 9 March 2004
Available online 5 October 2004
Abstract
Advances in earthquake data acquisition and processing techniques have allowed for improved quantification of source
parameters for local Australian earthquakes. Until recently, only hypocentral locations and local magnitudes (ML) had been
determined routinely, with little attention given to the inversion of additional source parameters. The present study uses these
new source data (e.g. seismic moment, stress drop, source dimensions) to further extend our understanding of seismicity and the
continental stress regime of the Australian landmass and its peripheral regions.
Earthquake activity within Australia is typically low, and the proportion of small to large events (i.e. the b value) is also low.
It is observed that average stress drops for southeastern Australian earthquakes appear to increase with seismic moment to
relatively high levels, up to approximately 10 MPa for ML 5.0 earthquakes. This is thought to be indicative of high compressive
crustal stress, coupled with strong rocks and fault asperities. Furthermore, the data indicates that shallow focus earthquakes
(shallower than 6 km) appear to produce lower than average stress drops than deeper earthquakes (between 6 and 20 km) with
similar moment.
Recurrence estimates were obtained for a discrete seismogenic zone in southeastern Australia. Decreasing b values with
increasing focal depth for this zone indicate that larger earthquakes (with high stress drops) tend to occur deeper in the crust.
This may offer an explanation for the apparent increase of stress drop with hypocentral depth. Consequently, earthquake hazard
estimates that assume a uniform Gutenburg–Richter distribution with depth (i.e. constant b value) may be too conservative and
therefore slightly overestimate seismic hazard for surface sites in southeastern Australia.
D 2004 Published by Elsevier B.V.
Keywords: Depth variation; Seismic source scaling; Earthquake hazard
0040-1951/$ - see front matter D 2004 Published by Elsevier B.V.
doi:10.1016/j.tecto.2004.03.018
* Corresponding author. Present address: Geoscience Australia,
GPO Box 378, Canberra, ACT 2601, Australia. Tel.: +61 2 6249
9864; fax: +61 2 6249 9986.
E-mail address: [email protected] (T.I. Allen).1 Present address: FM Global, Level 37, 140 William Street,
Melbourne, VIC 3000, Australia.
1. Introduction
It has long been recognised that the stress field of
continental Australia is of high horizontal compres-
(2004) 5–24
T.I. Allen et al. / Tectonophysics 390 (2004) 5–246
sion (Worotnicki and Denham, 1976; Denham et al.,
1979; and others). At the inception of the of the World
Stress Map compilation (Zoback et al., 1989; Zoback,
1992), knowledge of the stress regime of the continent
was still poorly constrained. However, recent initia-
tives to compile stress orientation data from analysis
of in situ measurements coupled with earthquake focal
mechanisms now provide a more detailed account of
the continental stress field in Australia and its
peripheral regions (Hillis and Reynolds, 2000; and
others). Unlike most stable continental regions,
Australia does not exhibit uniform horizontal com-
pressive stress parallel to the direction of absolute
plate motion (Zoback et al., 1989; Richardson, 1992;
Hillis and Reynolds, 2000; Reynolds et al., 002).
Observational measurements of in situ stress demon-
strate high horizontal stress at shallow depths (Den-
ham et al., 1979).
Historically, knowledge of Australian seismicity
has been limited by the relatively short recording
period and the sparse seismograph network, especially
prior to the 1960s (Gibson et al., 1981). As a result,
many smaller earthquakes were not recorded, heavily
biasing the Australian earthquake catalogue with a
greater proportion of larger events relative to small
events. If the catalogue deficiencies are not considered
in earthquake hazard estimates, apparent b values
become too low (i.e. having a comparatively low
proportion of small to large events), giving erroneously
high hazard when ground shaking is extrapolated to
moderate-to-long return periods. With the expansion of
seismic networks in the mid 1970s, the seismograph
coverage in eastern Australia has become quite good
by world standards. An increased number of low
magnitude events can now be detected and located,
giving more accurate estimates for the recurrence of
small to moderate earthquakes in these areas. Seismo-
graph coverage in the remote western and central
regions of the continent is still relatively poor.
Most of the earthquakes recorded in Australia tend
to be shallow and are restricted to a seismogenic zone
within the upper 20 km of the crust (Denham, 1988).
Given that the earthquakes are shallow, it is not
uncommon for the larger events to be associated with
surface rupture, as was observed with the 1968 MS 6.8
Meckering earthquake (Denham, 1988) and the MS
6.3, 6.4 and 6.7 earthquakes of the 1988 Tennant
Creek sequence (Jones et al., 1991). There have been
some documented earthquakes within continental
Australia that are reported to have focal depths in
excess of 30 km (e.g. McCue and Michael-Leiba,
1993; Michael-Leiba et al., 1994). However, these
occurrences have been rare and are not representative
of the continent-wide trend.
In contrast to most stable continental regions,
where the largest earthquakes are concentrated in
failed rifts or passive margins, Australia’s largest
onshore earthquakes have occurred in the unrifted
ancient Proterozoic and Archean terranes of western
and central Australia (Johnston and Kanter, 1990).
More complex earthquake distributions are observed
in the younger terranes of the Phanerozoic eastern
margins (Fig. 1).
The purpose of the current study is to firstly
examine any possible variation of source scaling
relations of southeastern Australian earthquakes with
respect to focal depth. Secondly, we investigate the
Gutenburg–Richter distribution for well-located events
in terms of hypocentral depth and local stress, and
consider any implications for earthquake source scal-
ing and discuss any consequences for hazard estimates.
2. Earthquake source parameters
2.1. Theory of earthquake source scaling
Resolving earthquake source parameters from the
measurement of elastic wave energy propagating
through complex geological terrains remains the
fundamental challenge facing seismologists. Conse-
quently, appropriate care must be taken when evaluat-
ing earthquake source parameters; e.g. seismic
moment, rupture size, stress drop and magnitude.
2.2. Seismic moment
The seismic moment M0 is one of the most robust
measures of an earthquake’s size and is defined
following (Aki and Richards, 1980)
M0 ¼ luA; ð1Þ
where l is the shear modulus at the source, u is the
average displacement across the rupture, and A is the
fault area. M0 can occasionally be calculated using
Fig. 1. Distribution of documented Australian earthquakes of magnitude ML 4.0 and greater, 1801–2002, overlying the major orogenic domains
and covers. Note the relative number of Australian earthquakes compared to the Indonesian subduction zone events to the north. (Adapted after
Foster and Gray, 2000; Betts et al., 2002).
T.I. Allen et al. / Tectonophysics 390 (2004) 5–24 7
relation (1) whenever the average displacement across
the fault can be quantified by surface rupture. In
practice, seismic moment is evaluated from the
asymptote of low-frequency earthquake motion, esti-
mated from the low-frequency spectral level X0 of the
far-field displacement spectrum A( f ). The displace-
ment spectrum can be modelled following
A fð Þ ¼ X0
1þ f =fcð Þc ; ð2Þ
where fc is the corner frequency and c is the
asymptotic high-frequency spectral decay exponent.
c is a value typically bound to at least 1.5 (required to
obey conservation of energy laws) and 3; given
M0~fc�3 (assuming constant source scaling; Hough,
1996). Observationally, c is usually found to be about
2. The Brune (1970) model relates the spectral
amplitude of P- or S-wave coda to the seismic
moment by
M0 ¼4pq0c
30G rð ÞX0
U/h; ð3Þ
where q0 is the density of the source medium, c0 is
either the P- or S-wave velocity at the source, U/h is
T.I. Allen et al. / Tectonophysics 390 (2004) 5–248
the mean radiation pattern (0.52 and 0.63 for P- and
S-waves, respectively; Boore and Boatwright, 1984)
and the geometric spreading coefficient G(r) is given
by the relations (Herrmann and Kijko, 1983)
G rð Þ ¼ r r V r0r0rð Þ1=2 r N r0
;
�ð4Þ
where r0 is typically taken to be 80 km; the
approximate distance where geometrical spreading
becomes less severe owing to surface-wave arrivals
(Castro et al., 1997).
2.2.1. Source dimensions
Unlike the seismic moment calculation from Eq.
(3), estimates of earthquake source dimensions are
highly model dependent and can be susceptible to
systematic errors (Beresnev, 2001), particularly in the
underestimation of the corner frequency from far-field
displacement spectra owing to the attenuation of high-
frequency perturbations. The Brune (1970) model
represents a circular dislocation with instantaneous
stress release. The radius R0 of a circular fault is
inversely related to the corner frequency following
R0 ¼Kcb0
2pfc; ð5Þ
where b0 is the shear-wave velocity in the source area
and Kc is a constant depending on the source model,
where Kc=2.34 (Brune, 1971).
2.2.2. Stress drop
Stress drop Dr is defined as the difference between
the initial and final stress levels averaged over the
fault plane and is given by (Brune, 1970, 1971)
Dr ¼ 7
16
M0
R30
: ð6Þ
The relationship represents a uniform decrease in
shear stress acting to produce seismic slip over a
circular fault.
It is generally accepted that the seismic stress
drops are relatively uniform over a wide magnitude
range and have observationally been found to be
independent of earthquake size; therefore following
the scaling law M0~fc�3 (e.g. Aki, 1967; McGarr
et al., 1981; Somerville et al., 1987; Urbancic et
al., 1992; Abercrombie and Leary, 1993; Aber-
crombie, 1995; and others). These findings suggest
that earthquakes of all magnitudes exhibit self-
similarity and are scaled at constant stress drop.
However, the debate as to the validity of earth-
quake scaling at constant stress drop over all
magnitudes is a controversial issue in observational
seismology. Many authors have observed a break-
down in earthquake self-similarity for small magni-
tude earthquakes (e.g. Molnar and Wyss, 1972;
Garcıa-Garcıa et al., 1996; Shi et al., 1998; and
others). Gibowicz et al. (1991) calculated source
parameters for very small events of magnitude MW
�3.6 to �1.9 from active seismicity at the Under-
ground Research Laboratory, Canada. They also
observed stress drop to increase with increasing
seismic moment, although they and others have
suggested that the apparent breakdown at low
magnitudes does not agree with predicted models
(Aki, 1967), and is simply an artefact of severe
attenuation of the high-frequency energy obscuring
the corner frequency in the upper few kilometres of
the crust (e.g. Abercrombie and Leary, 1993;
Abercrombie, 1995; Prejean and Ellsworth, 2001)
and limitations in sampling bandwidth (Hough,
1996; Ide and Beroza, 2001; Hiramatsu et al.,
2002). Abercrombie and Leary (1993), and Aber-
crombie (1995) have compared seismograms
recorded at a 2.5-km depth to those recorded at
the surface for the same events and have demon-
strated this near-surface attenuation.
The attenuation of high-frequency energy is a
particular concern when evaluating stress drop for
crustal earthquakes. Shi et al. (1998) demonstrated
that they can simulate corner frequencies by spectral
fitting, typically higher than those obtained via
conventional asymptote methods that are consistent
with hypocentral distance. These estimates are based
largely on the evaluation of seismic moment
obtained employing local attenuation relations.
Accounting for discrepancies in conventional and
simulated corner frequencies, Shi et al. still observed
an apparent breakdown of constant source scaling for
small magnitude earthquakes in eastern North
America.
T.I. Allen et al. / Tectonophysics 390 (2004) 5–24 9
Nuttli (1983a) has previously suggested that earth-
quakes within stable continental regions are suscep-
tible to systematic increases of average stress drop
with seismic moment (e.g. Nuttli, 1983b; Bungum et
al., 1992). In contrast, he adds, earthquakes near plate
margins have nearly constant stress drop, consistent
with constant earthquake source scaling.
Several studies have shown intraplate earth-
quakes to have higher stress drops than interplate
earthquakes with similar moment (e.g. Molnar and
Wyss, 1972; Kanamori and Anderson, 1975; Scholz
et al., 1986; Houston, 2001). It is suspected that
near plate margins where high levels of earthquake
activity are common, fault rheology is typically
uniformly weak, consequently Dj appears to be
low. In contrast, the effect of fault healing over
time is more apparent in intraplate regions of low
seismicity. Consequently, we observe higher levels
of stress release resulting from the initiation of
rupture on new growth surfaces or healed fault
asperities (e.g. Molnar and Wyss, 1972). Johnston
(1992), however, argued that there was insufficient
evidence to confirm any significant disparity
between the magnitude of stress drop of intraplate
and interplate earthquakes. Recent evaluations of
source parameters from the 2001 MW 7.6 Bhuj,
India earthquake, however, indicate that this was a
high stress drop event (Antolik and Dreger, 2003).
The earthquake, which occurred in stable continen-
tal crust, possessed relatively high-frequency ground
motion and a short rupture duration which suggests
a relatively small rupture size. Tightly clustered
hypocentral locations from the aftershock sequence
reinforce the assumed small rupture size of the
main shock (Johnston, personal communication,
2002).
Average stress drops for intraplate earthquakes
have been reported to range from 0.1 to about 100
MPa (Johnston, 1992; Abercrombie and Leary, 1993)
although most do not exceed 10 MPa.
2.2.3. Earthquake magnitude
There are several different definitions of earth-
quake magnitude, each evaluated taking advantage of
different characteristics of recorded ground motion.
Some magnitude scales perform better for different
sized earthquakes at different distances, however, all
are scaled to some degree to give approximately
equivalent solutions for any specific earthquake. The
local magnitude scale, ML (Richter, 1935), provided
the first convenient measure of earthquake size from
instrumental recordings and may be calculated
following
ML ¼ logA� logA0 rð Þ þ Sj; ð7Þ
where Sj is the site correction factor, A is the recorded
trace amplitude at hypocentral distance r and the
�log A0(r) term is scaled such that for an event of
ML 3.0, A=1 mm recorded at an epicentral distance of
100 km on a standard horizontal-component Wood–
Anderson seismograph (Richter, 1935, 1958). The
local magnitude scale has since been redefined for
southeastern Australia by Michael-Leiba and Mala-
fant (1992), and subsequently extended by Wilkie et
al. (1994).
Moment magnitude MW can be derived from
seismic moment M0 employing the following empiri-
cal definition proposed by Hanks and Kanamori
(1979)
MW ¼ 2
3logM0 � 6:07; ð8Þ
where M0 is in N-m.
2.3. Data selection
Given the relatively low levels of seismicity and a
wide distribution of epicentres, coupled with a sparse
seismograph network, constraining depths for many
Australian earthquakes can be difficult. Earthquakes
chosen for the present study were all selected from
southeastern Australia where, due to the development
of much of the nation’s infrastructure and higher than
average earthquake activity, the seismograph network
is well developed. Data for this project were recorded
and located by the ES&S Seismology Research
Centre, Melbourne. Most of the earthquakes selected
were well-located, having well-constrained focal
depths with uncertainties of about F4 km or less.
Of the many thousands of events in the catalogue, 93
events which met these criteria were chosen. These
events occurred from 1993 to 2001 and magnitudes
ranged from ML 1.6 to ML 5.0.
T.I. Allen et al. / Tectonophysics 390 (2004) 5–2410
Some exceptions to these criteria were made. To
maximise the earthquake magnitude range for the
study given the small number of moderate-large
events recorded at close range (necessary to obtain
good depth control), several larger earthquakes with
slightly less well-defined focal depths were included.
In addition, several deeper events with slightly higher
depth uncertainties were also added to the study
catalogue to give improved constraints for any
possible depth dependence of earthquake source
scaling parameters. Fig. 2 shows a schematic map of
the selected earthquakes together with the local
seismograph network.
2.4. Methodology
All seismograms used in the analysis were digitally
recorded on three-component seismographs at a sample
Fig. 2. Schematic map of selected earthquakes with respect to the lo
rate of 100 Hz, with an anti-alias filter at 25 Hz. Fourier
spectra of the S-wave coda for each event were
calculated and corrected for instrumental response
and attenuation from anelastic and scattering processes.
Attenuation was corrected using the apparent
quality factor Qa( f,r) recently derived for south-
eastern Australia (Allen, 2004). Owing to complex
heterogeneities in the structure of the Earth’s litho-
sphere and upper mantle (e.g. Kennett, 1989), it is
often insufficient to use a discrete Q( f ) function to
evaluate earthquake source parameters for local earth-
quakes. The apparent quality factor Qa( f,r) proposed
by Allen (2004) therefore extends on conventional
Q( f ) functions by allowing for additional complexity
in the variation of crustal structure with depth, and
considers factors such as variable velocity gradients
and anomalous large-amplitude reflections from the
Moho. Following the form Qa( f,r)=Qr(r)g(r), the
cation of the Australian seismograph network (open triangles).
Fig. 3. Attenuation model of the form Qa( f,r)=Qr(r)fg(r) used to
evaluate earthquake source parameters.
Table 1
Site corrections Sj and standard errors (in ML) for the vertica
component of the 56 seismographs for which more than one record
was used in the present study
Site Correction nk Site Correction nk
ABEM �0.04F0.08 36 KOWA �0.10F0.25 3
APN +0.15F0.08 16 KTLM �0.31F0.10 25
AVD �0.05F0.13 8 LBXM +0.26F0.08 19
AVO �0.04F0.08 25 LGT +0.21F0.12 20
BANM �0.13F0.04 3 MACM +0.35F0.10 11
BJEM �0.04F0.08 33 MCV +0.24F0.14 26
BUDM +0.02F0.04 26 MDRM �0.13F0.27 3
CCRM �0.02F0.25 8 MITM �0.20F0.15 26
CDNM +0.05F0.15 22 MLWM �0.26F0.25 6
COP +0.07F0.39 2 MTL �0.01F0.10 17
CPXM +0.01F0.07 34 NARM �0.11F0.10 22
CTBM +0.13F0.07 16 NATM �0.14F0.07 38
DDC �0.24F0.73 3 PAT �0.16F0.10 34
DON +0.04F0.12 15 ROYM �0.19F0.08 42
DRAM �0.05F0.07 48 RUSM �0.09F0.18 14
DTMM �0.17F0.08 37 SGTH +0.32F0.71 2
DVBX �0.00F0.12 21 SMBT +0.17F0.41 2
EUGM +0.12F0.24 13 STN �0.38F0.09 2
FSHM +0.26F0.12 25 TALM +0.09F0.08 37
FTZM +0.15F0.06 22 TAT +0.06F0.25 4
GOGM �0.35F0.19 7 TOMM �0.05F0.11 25
GRVM �0.12F0.10 17 TYR +0.23F0.10 37
GVL +0.06F0.12 22 WAH �0.23F0.20 2
HOPM �0.09F0.27 5 WER �0.23F0.10 28
IVSM +0.01F0.10 29 WGBM �0.11F0.08 27
JBD +0.03F0.20 7 WILL +0.50F0.28 3
JBRM �0.06F0.09 19 WRNM +0.12F0.29 4
KANM +0.08F0.09 42 YERM +0.14F0.08 35
All corrections are additive and nk is the number of records at site
used to calculate Sj. Standard errors are given to a 95% confidence
interval.
T.I. Allen et al. / Tectonophysics 390 (2004) 5–24 11
attenuation model used in the present study is defined
as (Allen, 2004) (Fig. 3);
Qa f ; rð ÞrV150 ¼ ð1:85r þ 10e�r10Þf 0:96�0:0039rð Þ
Qa f ; rð ÞrN150 ¼ 0:42r þ 212:11ð Þf 0:50�0:0003rð Þ ð9Þ
The term Qr increases systematically with hypo-
central distance and gives an apparent quality factor
which must be used to estimate seismic wave
amplitude at distance r from the source. Because
Australian earthquakes are shallow, at present, it is
assumed that Qa( f,r) does not vary with focal depth.
This new attenuation model further extends prior
estimates of Q( f ) by Wilkie and Gibson (1994) and
more recent studies presented by Allen et al. (2002).
Following Brune’s (1970, 1971) model, earthquake
source parameters [i.e. seismic moment M0, rupture
radius r0, and stress drop Dr; Eqs. (3, 5 and 6),
respectively] were subsequently calculated from ver-
tical component seismograms employing an S-wave
velocity of 3.58 km s�1 and density of 2.67 g cm�3.
In addition, local magnitudes ML were estimated
from synthesized Wood–Anderson seismograms. Ini-
tially setting the site correction factor Sj=0 [Eq. (7)],
we calculate an average magnitude Mi for the ith
event following the relations of Wilkie et al. (1994).
Using vertical component seismograms, site correc-
tions were subsequently derived following
Sj ¼
Xnkk¼1
ðMi �MijÞ
nk; ð10Þ
where Mij is the magnitude at the jth site and nk is the
number of records recorded at j. Evaluation of site
corrections for 56 of the sites used in this study (with
at least two records) coupled with their standard errors
is shown in Table 1.
2.5. Analysis of data
Typically, far-field displacement spectra obeyed
Brune’s (1970) source model of decreasing amplitude
as x�2 for frequencies above fc, where x=2pf and f is
the frequency of the ground perturbation (Fig. 4).
Resulting earthquake source parameters are presented
in Table 2.
Average Brune stress drop for southeastern Austral-
ian earthquakes appear to increase with seismic
l
j
Fig. 4. Typical S-wave far-field displacement spectra for four southeastern Australian earthquakes calculated from vertical component
seismograms. Spectra are corrected for the effects of anelastic attenuation and scattering following the relations of Allen (2004).
T.I. Allen et al. / Tectonophysics 390 (2004) 5–2412
Table 2
Source parameters from southeastern Australian earthquakes
Place Date HHMM Longitude
(8E)Latitude
(8N)Depth
(km)
M0
(Nm)
MW ML R0
(km)
Dr(MPa)
fc(Hz)
ni
Katoomba 1993-03-22 0806 150.346 �33.826 17 5.06e+12 2.41 2.53 0.16 0.50 8.12 12
Mt St Gwear 1993-05-03 1523 146.327 �37.782 7 8.31e+11 1.88 1.68 0.16 0.20 10.28 5
Churchill 1993-07-24 1333 146.485 �38.353 15 2.01e+13 2.82 3.00 0.28 0.41 4.79 5
Taralgon South 1993-09-25 0240 146.530 �38.311 10 2.32e+13 2.83 3.03 0.21 1.02 6.45 5
Mullengrove 1993-10-10 1606 149.174 �34.505 19 3.82e+12 2.33 2.48 0.12 0.89 10.80 6
Moe 1993-10-31 1004 146.268 �38.150 12 1.45e+12 2.07 1.80 0.17 0.14 8.03 3
Boolarra South 1994-02-01 0553 146.350 �38.536 17 1.20e+14 3.31 4.00 0.32 1.70 4.13 14
Mullengrove 1994-04-19 1823 149.241 �34.592 3 4.66e+12 2.40 2.43 0.11 1.41 11.79 6
Mullengrove 1994-04-29 0749 149.225 �34.579 5 9.63e+12 2.59 2.86 0.20 0.52 6.63 7
Ettamogah 1994-05-21 0859 146.962 �36.034 3 1.52e+13 2.73 3.10 0.21 0.68 6.22 8
Lapstone 1994-06-06 0802 150.527 �33.784 20 2.94e+12 2.25 2.21 0.14 0.49 9.68 10
Fish Creek 1994-06-27 0152 145.962 �38.722 12 1.56e+13 2.74 2.98 0.19 0.96 6.95 5
Ellalong 1994-08-06 1104 151.292 �32.917 1 7.01e+15 4.53 5.58 0.75 7.82 1.79 12
Walhalla 1994-12-26 0344 146.548 �38.008 17 2.17e+12 2.17 2.05 0.15 0.28 8.93 6
Bowral 1995-01-03 1351 150.484 �34.534 7 1.11e+13 2.65 2.81 0.19 0.76 7.18 12
Warragul 1995-01-11 0711 145.992 �38.165 9 2.44e+13 2.86 3.27 0.17 2.23 7.91 7
Boolarra South 1995-02-01 1021 146.259 �38.462 10 2.45e+13 2.87 3.23 0.28 0.51 4.81 6
Dora Dora 1995-03-26 0653 147.233 �35.958 4 2.41e+13 2.86 3.18 0.27 0.57 5.03 10
Newnes 1995-05-03 0424 150.249 �33.186 11 3.54e+13 2.96 3.38 0.20 2.01 6.75 21
Boolarra South 1995-05-03 1748 146.283 �38.472 15 3.54e+13 2.95 3.20 0.25 1.05 5.43 6
Jenolan Caves 1995-05-20 1129 150.083 �33.868 14 8.70e+13 3.22 3.71 0.25 2.59 5.41 17
Glendon Brook 1995-05-28 2313 151.549 �32.543 14 1.14e+14 3.31 4.05 0.32 1.47 4.12 17
Adaminaby 1995-07-21 1426 148.859 �36.031 5 4.46e+13 3.04 3.65 0.26 1.09 5.10 14
Frogmore 1995-07-29 1343 148.735 �34.283 3 1.59e+13 2.74 3.06 0.25 0.45 5.35 12
Benambra 1995-07-30 0441 147.658 �36.761 11 8.79e+13 3.23 3.71 0.33 1.05 4.02 12
Boorawa 1995-08-17 0141 148.739 �34.313 4 1.85e+13 2.78 3.25 0.25 0.53 5.39 19
Boorawa 1995-08-19 0901 148.741 �34.312 1 2.39e+13 2.85 3.39 0.20 1.36 6.76 22
Boorawa 1995-09-12 1024 148.720 �34.310 1 3.04e+13 2.93 3.43 0.22 1.31 6.16 22
Frogmore 1995-10-14 0411 148.761 �34.317 3 3.56e+13 2.98 3.50 0.24 1.18 5.64 24
Katoomba 1995-11-05 1053 150.355 �33.830 17 1.39e+12 2.01 1.87 0.12 0.40 11.55 7
Tooborac 1995-11-18 0932 144.764 �37.114 13 6.77e+13 3.15 3.89 0.25 1.95 5.38 19
Mt Martha 1996-01-16 1030 145.070 �38.284 11 9.17e+12 2.56 2.74 0.22 0.40 6.16 8
Eucumbene 1996-02-18 1934 148.666 �36.152 13 7.29e+13 3.18 3.74 0.28 1.53 4.85 6
Toorongo 1996-05-10 0548 146.145 �37.733 11 8.96e+12 2.58 2.78 0.23 0.37 5.70 12
Yerranderie 1996-05-21 1008 150.323 �34.174 17 1.59e+12 2.07 1.95 0.17 0.13 7.67 11
Lake Burragorang 1996-06-06 0254 150.288 �34.128 20 4.86e+12 2.41 2.47 0.15 0.64 8.91 15
Dalton 1996-08-13 1233 149.214 �34.749 1 1.80e+13 2.78 3.17 0.27 0.43 5.04 22
Thomson Reservoir 1996-09-25 0453 146.425 �37.859 11 6.04e+13 3.13 3.44 0.36 0.55 3.67 16
Thomson Reservoir 1996-09-25 0749 146.422 �37.863 11 2.36e+15 4.18 5.02 0.48 9.52 2.80 22
Thomson Reservoir 1996-09-25 0756 146.438 �37.855 12 5.13e+12 2.40 2.52 0.21 0.26 6.47 6
Thomson Reservoir 1996-09-25 1920 146.421 �37.856 11 4.31e+12 2.36 2.42 0.21 0.20 6.34 8
Thomson Reservoir 1996-09-29 1652 146.432 �37.865 11 1.25e+12 2.01 1.80 0.13 0.22 9.92 7
Thomson Reservoir 1996-10-01 1815 146.430 �37.862 11 1.05e+12 1.95 1.77 0.15 0.15 9.13 6
Katoomba 1996-10-01 2142 150.393 �33.830 9 2.64e+13 2.88 3.09 0.21 1.33 6.48 21
Yinnar 1996-10-30 1222 146.366 �38.308 19 7.18e+12 2.51 2.43 0.19 0.46 7.02 7
Thirlmere 1996-12-10 1254 150.501 �34.153 12 1.75e+13 2.76 3.02 0.17 1.52 7.79 19
Thirlmere 1996-12-10 1258 150.504 �34.152 12 8.33e+12 2.57 2.78 0.16 0.90 8.35 19
Thomson Reservoir 1996-12-24 0844 146.440 �37.857 12 4.25e+12 2.36 2.42 0.19 0.28 7.10 10
Cape Paterson 1996-12-24 2228 145.534 �38.696 17 4.14e+13 3.01 3.37 0.22 1.62 5.96 11
Red Hill 1997-01-20 1103 145.031 �38.379 19 5.64e+13 3.10 3.56 0.24 1.85 5.62 8
Thomson Reservoir 1997-02-03 2314 146.427 �37.866 11 6.17e+12 2.48 2.42 0.22 0.25 6.06 8
(continued on next page)
T.I. Allen et al. / Tectonophysics 390 (2004) 5–24 13
Place Date HHMM Longitude
(8E)Latitude
(8N)Depth
(km)
M0
(Nm)
MW ML R0
(km)
Dr(MPa)
fc(Hz)
ni
Pakenham 1997-04-03 1632 145.470 �38.102 9 3.33e+12 2.29 2.26 0.16 0.38 8.55 7
Warragul 1997-05-04 2233 145.959 �38.135 14 3.18e+13 2.94 3.18 0.25 0.89 5.33 12
Murrindindi 1997-05-23 0040 145.442 �37.318 12 4.35e+12 2.36 2.50 0.13 0.78 9.92 8
Tatong 1997-06-27 0320 146.094 �36.781 9 3.82e+14 3.67 4.27 0.41 2.40 3.24 20
Cootamundra 1997-08-23 0012 148.197 �34.627 4 2.98e+13 2.91 3.57 0.24 0.93 5.53 19
Brindabella 1998-02-14 1823 148.702 �35.375 9 2.96e+14 3.59 4.47 0.31 4.22 4.26 23
Merriwa 1998-03-09 1241 150.055 �32.171 4 4.67e+13 3.05 3.79 0.32 0.63 4.18 11
Fish Creek 1998-04-04 0955 146.124 �38.709 16 5.71e+13 3.12 3.60 0.27 1.27 4.94 11
Corryong 1998-07-17 0122 148.005 �36.441 12 5.77e+14 3.79 4.65 0.31 8.14 4.24 10
Thomson Reservoir 1998-09-19 0534 146.379 �37.842 2 1.99e+12 2.16 1.97 0.17 0.17 7.86 7
Thomson Reservoir 1998-09-19 0548 146.381 �37.835 4 5.40e+12 2.41 2.31 0.20 0.30 6.67 8
Barmedman 1998-09-27 0147 147.437 �34.218 4 1.11e+13 2.62 3.12 0.19 0.74 7.12 6
Portsea 1998-09-27 2232 144.741 �38.290 21 9.83e+13 3.27 3.77 0.22 4.24 6.16 8
Junee 1998-10-16 1346 147.457 �34.751 16 1.35e+14 3.37 4.12 0.22 5.36 6.00 6
Wee Jasper 1998-11-07 2242 148.893 �35.144 7 2.17e+13 2.83 3.27 0.24 0.67 5.51 17
Michelago 1998-12-31 0611 149.154 �35.783 4 3.47e+13 2.98 3.46 0.27 0.81 5.03 16
Yallourn North 1999-01-13 0940 146.317 �38.097 12 1.31e+14 3.35 3.89 0.32 1.82 4.22 17
West Wyalong 1999-03-14 0013 147.070 �34.009 12 6.65e+14 3.83 4.44 0.34 7.20 3.88 11
Appin 1999-03-17 0158 150.748 �34.253 5 1.20e+15 3.99 4.54 0.47 4.38 2.83 12
Lake Mountain 1999-04-16 1051 145.984 �37.413 4 2.63e+13 2.88 3.13 0.24 0.86 5.61 14
Lake Mountain 1999-04-16 1108 145.973 �37.415 4 1.14e+13 2.66 2.81 0.20 0.59 6.56 13
Frogmore 1999-07-13 0142 148.976 �34.286 4 3.17e+13 2.94 3.37 0.20 1.80 6.75 19
Whouroly South 1999-08-03 0347 146.562 �36.554 3 4.85e+12 2.40 2.54 0.15 0.66 9.05 7
Lake Mountain 1999-08-15 1320 146.026 �37.495 12 2.32e+12 2.17 2.17 0.13 0.44 10.07 6
Epping 1999-08-19 1710 144.993 �37.495 4 8.14e+12 2.54 2.73 0.18 0.64 7.54 10
Dalton 1999-09-27 0929 149.163 �34.753 4 8.94e+12 2.57 2.73 0.23 0.34 5.88 12
Bowral 1999-09-29 0042 150.492 �34.523 7 6.43e+12 2.48 2.56 0.21 0.33 6.49 18
Warrawaralong 1999-10-11 2024 150.459 �33.521 12 3.45e+12 2.31 2.36 0.14 0.54 9.44 16
Lake Burragorang 1999-10-18 0307 150.352 �34.162 16 9.60e+11 1.91 1.78 0.16 0.11 8.52 12
Young 2000-02-27 1749 148.392 �34.472 4 1.77e+13 2.77 3.30 0.18 1.40 7.54 7
Rochester 2000-03-11 1501 144.713 �36.308 23 6.55e+12 2.47 2.73 0.16 0.71 8.36 6
Gaffneys Creek 2000-03-16 1326 146.103 �37.496 8 9.16e+13 3.25 3.78 0.22 3.64 5.99 13
Lapstone 2000-05-15 1011 150.567 �33.798 13 7.89e+11 1.88 1.58 0.18 0.06 7.44 4
Boolarra South 2000-06-11 1840 146.302 �38.425 17 7.48e+12 2.54 2.69 0.21 0.34 6.26 9
Graytown 2000-06-22 1813 144.864 �36.815 6 3.80e+13 2.98 3.35 0.30 0.60 4.41 13
Dandenong 2000-07-24 0747 145.272 �37.958 20 1.97e+13 2.79 3.04 0.22 0.79 6.02 11
Fish Creek 2000-08-03 1128 145.987 �38.752 16 3.46e+13 2.97 3.25 0.36 0.32 3.67 12
Boolarra South 2000-08-29 1020 146.236 �38.391 15 1.62e+13 2.75 2.76 0.28 0.34 4.85 12
Boolarra South 2000-08-29 1205 146.245 �38.402 15 6.92e+14 3.82 4.78 0.37 6.33 3.60 21
Mt. Worth 2001-01-05 1604 146.012 �38.256 8 8.81e+12 2.58 2.70 0.22 0.35 6.00 10
ni is the number of records used to obtain average source parameters for the ith event.
Table 2 (continued)
T.I. Allen et al. / Tectonophysics 390 (2004) 5–2414
moment to the highest magnitudes in the data set (i.e. to
at least ML 5.0; Fig. 5) to relatively high levels (up to
approximately 10 MPa). These observations are con-
trary to the belief that stress drop is independent of
earthquake size. The non-uniformity of average stress
drop with magnitude is further demonstrated by
plotting stress drop against corner frequency, super-
imposed with lines of constant stress drop (Fig. 6). For
moderate to large events (with characteristically lower
fc), Dr appears to plateau near 10 MPa (i.e. for fcb3
Hz). If we consider that disparities observed in earth-
quake scaling are an artefact of high-frequency
attenuation, then compensation for losses of high-
frequency ground motion would force corner frequen-
cies higher, particularly for low magnitude earth-
quakes. This would, to some extent, improve the
uniformity of scaling parameters for earthquakes in
southeastern Australia. Unfortunately the argument
Fig. 5. Relationship between Dr and M0 for the selected data, showing a systematic increase in average Brune stress drop with seismic moment
for the 0bhV6 km, 6bhV14 km and hN14 km depth ranges respectively (a–c). The combined data indicates a subtle increase in Dr with
increasing depth (d).
T.I. Allen et al. / Tectonophysics 390 (2004) 5–24 15
over scaling at constant Dr versus increasing Dr with
seismic moment is presently limited by the absence of
high quality records from largeMLN5.0 earthquakes in
southeastern Australia. Stress drops that plateau for
fcb3 Hz may indicate a breakdown in self-similarity for
smaller earthquakes with higher corner frequencies.
The present are classified into three depth win-
dows, 0bhV6 km, 6bhV14 km and hN14 km
representing shallow, moderate and the deeper focus
events respectively. These categories were selected to
preserve approximately equal depth increments down
to the base of the seismogenic zone (about 20 km).
Fig. 6. Source scaling relationship betweenM0 and fc for earthquakes
in southeastern Australia, illustrating an increase of stress drop with
seismic moment. Lines of constant stress drop were obtained from
Eqs. (4) and (5), employing a S-wave velocity of 3.58 km s�1. This
plot indicates that at low corner frequency (e.g. fcb3 Hz), Dr may
plateau to constant levels near 10 MPa.
Fig. 7. Relationship between MW and ML for selected southeas
Australian earthquakes. Local magnitudes ML are calculated
following the �log A0 relations of Wilkie et al. (1994).
T.I. Allen et al. / Tectonophysics 390 (2004) 5–2416
Regression analysis of each depth window sug-
gests that Dr increases slightly from shallow events to
the moderate and deeper events at focal depths greater
than 6 km (Fig. 5d). This may indicate that higher
deviatoric stresses are required to initiate fault rupture
at greater depths. The authors recognise that these data
are not well constrained for moderate to large
magnitude earthquakes. Consequently, more data are
required to validate these apparent trends.
Following Eq. (6), we assume source dimensions
to be inversely proportional to the cube root of stress
drop. Given calculated values of Dr for southeastern
Australia are relatively high, we can infer that fault
rupture length for any given seismic moment will be
more compact than usual (Table 2). These data agree
with the shorter duration, events with high-frequency
motion typically observed in Australia (Sinadinovski
et al., 2000; Allen et al., 2003). Enrichment of high-
frequency perturbations for intraplate eastern North
American earthquakes has also been noted when
compared to western North American earthquakes
(Boore and Atkinson, 1987; and others).
ML was calculated from the peak trace amplitude
of synthetic displacement seismograms equivalent to
the output from a standard Wood–Anderson torsion
seismograph (following Uhrhammer and Collins,
1990). All magnitudes were calculated from vertical
component records (including a vertical component
correction) with relevant attenuation corrections were
applied following the �log A0 relations of Wilkie et
al. (1994).
Fig. 7 indicates a comparison between MW, derived
from the empirical relation of Hanks and Kanamori
(1979) [Eq. (8)] and ML to test the equivalence of the
two magnitude scales in Australia. Inspection of the
data reveals a strong linear correlation between the
magnitude scales. It was shown that magnitudes for
both MW and ML tend to be equivalent around
magnitude 2.5, however, they tend to diverge signifi-
cantly at higher magnitudes. Linear regression gives
the empirical relationship between the magnitudes
scales as
MW ¼ 0:64ML þ 0:83 ð11Þ
The relatively high stress drops observed for
earthquakes in southeastern Australia may provide
an explanation for the observed inconsistency
between MW and ML values. The Hanks and
t
T.I. Allen et al. / Tectonophysics 390 (2004) 5–24 17
Kanamori (1979) relation was originally defined using
mostly large to great interplate earthquakes assuming
a constant stress drop of about 5 MPa (Singh and
Havskov, 1980), significantly lower than stress drops
observed for moderate-to-large intraplate Australian
earthquakes.
3. Earthquake recurrence parameters
3.1. Theory
Earthquake size distribution can usually be
described by the Gutenburg–Richter magnitude–fre-
quency law (Gutenburg and Richter, 1944) for a
discrete seismogenic zone
logN ¼ a� bm; ð12Þ
where N is the number of earthquakes having a
magnitude zm, and a and b are constants. a is the rate
of occurrence of earthquakes, or the level of seis-
micity, while the bb valueQ is a convenient means of
describing the relative proportion of small to large
earthquakes. These parameters are an essential input
for probabilistic earthquake hazard analysis. Follow-
ing Eq. (12), a b value of 1.0 would correspond to ten
times as many earthquakes exceeding magnitude m as
would exceed magnitude m+1. A large b value (e.g.
bN1.0) implies a higher proportion of small events
with respect to large events, whereas a lower
proportion of small events will give rise to a low b.
Most earthquake catalogues are complete for larger
earthquakes, but incomplete for smaller events, so
considerable care must be taken to avoid systematic
error when estimating b. The earthquake magnitude
above which a catalogue is complete normally varies
with both time and place.
Frohlich and Davis (1993) suggested that for
teleseismic earthquakes at least, b has a value of
1.0, in the sense that it is usually between 0.7 and 1.4.
The b value is a statistical measure and given it is
resolved from the gradient of a log–log distribution,
these bounds represent a dramatic variation in the
nature of seismicity. Some authors have shown that
the b value may be susceptible to significant regional
lateral and vertical variation (Karnık and Klıma, 1993;
Wiemer and Benoit, 1996; Mori and Abercrombie,
1997; Wiemer and Wyss, 1997; Gerstenburger et al.,
2001) and that its value may vary with time (Urbancic
et al., 1992).
It has been shown, both experimentally (Scholz,
1968) and observationally in underground excavations
(Urbancic et al., 1992), that b demonstrates an inverse
relationship to stress. Urbancic et al. (1992) also noted
that spatial and temporal variations in decreasing b
values were well correlated with increasing stress
estimates for time intervals prior to rockbursts in
mines. Furthermore, Urbancic et al. found that at the
completion of an aftershock sequence (which facili-
tates stress redistribution subsequent to a rockburst
and leads to a temporary increase of b), the b values
were again observed to decrease. Moreover, Wiemer
and Wyss (1997) observed that b values on fault
asperities are significantly lower than for the rest of
the fault zone. This observation is consistent with the
findings of Urbancic et al. (1992). Consequently, it is
reasonable to suggest that investigations into the
temporal and spatial variability of b can provide
limited information for earthquake prediction. Con-
sistently low b values can simply mean that both the
rocks and fault asperities are strong.
Evaluation of b is highly dependent on the accurate
measurement of magnitudes. Frohlich and Davis
(1993) remarked that despite being a logarithmic
scale, magnitudes for individual events can still vary
by up to 0.5 over a network of seismograph sites. This
is to be expected given that many attenuation
relationships used to calculate magnitudes do not
consider many effects on ground motion by factors
such as radiation pattern, soft surface sediments,
topography, etc. It was shown earlier that different
magnitude scales are not necessarily equivalent over
all magnitude ranges (Fig. 7) and this may result in
increased uncertainties when converting between
scales. Consequently, the robustness of b is dependent
on which magnitude definition is chosen, and on any
combinations of magnitude scales used. Some seis-
mologists argue that the b value is essentially constant
and any studies to the contrary suffer from statistical
or observational inadequacies (Frohlich and Davis,
1993; Kagan, 1999). Nevertheless, we believe that the
b value can exhibit spatial variation and must be
considered to give reasonable estimates of earthquake
recurrence.
T.I. Allen et al. / Tectonophysics 390 (2004) 5–2418
3.2. Data selection
Given that the determination of b value can be
sensitive to relatively minor idiosyncrasies in earth-
quake catalogues, it was necessary to be more
inclusive and thus less rigorous in our selection criteria
than for the source parameter data, especially given
Australia’s relatively low levels of seismicity. For this
component of the study, a seismogenic region in
southeastern Australia, with good seismograph cover-
Fig. 8. Schematic map of the study area showing the location of seismic rec
0bhV6 km, 6bhV14 km and hN14 km depth ranges, respectively (b–d). I
Basins (BB) with respect to the underlying Lachlan Fold Belt (LFB) sys
proportion of small events from the shallow to the deep focus earthquake
age, was selected. The region, delineated in Fig. 8, has
an area of approximately 43,400 km2 and partially
encompasses the Gippsland Basin to the south and the
Southern Highlands of the Lachlan Fold Belt (Fig. 8a).
The data were extracted from the ES&S Seismol-
ogy Research Centre’s earthquake catalogue, which
has had a level of completeness down to below ML
2.0 in this region since 1976 (see Fig. 9a). All events
with calculated hypocentral depths encompassed
within the selected zone were included and the list
orders (a) with respect to the epicentral locations of the events for the
ndicated in the map are the Gippsland (GB), Otway (OB) and Bass
tem. Note the differences in spatial distribution and the decreasing
s.
Fig. 9. Earthquake recurrence from Gutenburg–Richter magnitude–frequency relations determined using the maximum likelihood fitting method
for all events in the study area (a) and the 0bhV6 km, 6bhV14 km and hN14 km depth ranges, respectively (b–d). The segments that are defined
by 10 or fewer events are shown as heavy dashed lines in black. The fine dashed lines model the a and b values which best fit the sample data.
T.I. Allen et al. / Tectonophysics 390 (2004) 5–24 19
declustered by the removal of foreshocks and after-
shocks. The b values were subsequently calculated
from these data. The same depth increments were
applied as for the source parameter investigation
above. Although many earthquake depths were well-
constrained, a large number have depth uncertainties
T.I. Allen et al. / Tectonophysics 390 (2004) 5–2420
in the order of 5 to 10 km, consequently introducing
unavoidable uncertainties in the following analysis.
3.3. Methodology and results
Fig. 8b–d gives earthquake locations for the 0bhV6km, 6bhV14 km and hN14 km depth ranges within the
region, respectively. From visual inspection, it appears
that the earthquakes in the upper depth range (Fig. 8b)
tend to be scattered relatively uniformly over the
region. For the moderately deep focus events, the
majority of seismicity seems to be more concentrated
in the southeast (Fig. 8c), and delineation of active
seismogenic zones, typically trending NE–SW,
becomes more obvious. For the deeper focus events
(Fig. 8d), we again see further concentration of
earthquakes in the southeast. In addition, the shallow
focus earthquakes in Fig. 8b appear to have a higher
proportion of small events relative to large events
when compared to the moderate and deeper focus
earthquakes (Fig. 8c–d).
Individual b values were calculated employing the
maximum likelihood method as described by Aki
(1965), who gave a relation equivalent to
1
b¼ ln 10ð Þ m� m0Þð ð13Þ
where m is the sample’s mean magnitude, and m0 is
the lowest magnitude for which the event catalogue is
complete.
An overall b value was firstly calculated for the
combined data (Fig. 9a). The b values for the three
depth ranges were subsequently calculated. Fig. 9
illustrates the average recurrence relationships deter-
mined using the maximum likelihood method
described above assuming a maximum magnitude
Mmax of 7.5. The b values evaluated in Table 3 were
Table 3
Local magnitude b values for the combined and 0bhV6 km, 6bhV14km and hN14 km and depth ranges, respectively
Depth range Number of events m0 b Value
All depths 2340 1.4 0.88F0.02
0Vhb6 km 1036 1.8 1.06F0.13
6Vhb14 km 842 1.8 1.00F0.06
hN14 km 462 1.5 0.77F0.06
The table includes the number of events and the lowest magnitude
for which the catalogue is complete for each depth range.
resolved from local magnitudes ML only. These plots
indicate a systematic decrease in b value with depth.
This implies that larger earthquakes tend to occur at
greater hypocentral depths. If moment magnitudes
were used for comparison, then computed b values
would be higher given that MW appears to be lower
than ML for moderate-to-high magnitude events (see
Fig. 7).
It should be noted that the b value calculation for
the 0- to 6-km depth range was influenced by the
largest earthquake in this region and depth range only
having a magnitude of ML 3.1. This observation in
itself reinforces our suggestion that larger earthquakes
tend to be deeper.
4. Discussion
4.1. Earthquake source parameters in southeastern
Australia
Source parameters evaluated for southeastern
Australian earthquakes associated with well-con-
strained hypocentres indicate that stress drop appears
to increase systematically to relatively high levels for
the largest events used in the study. There may be
some evidence to suggest that stress drops plateau
for larger events and the apparent magnitude depend-
ence of stress drop is a result of a breakdown in
constant source scaling at lower magnitudes. How-
ever, this argument is difficult to quantify in south-
eastern Australia given the deficiency of quality
ground motion records from large nearby MLN5.0
earthquakes.
Unlike western and central Australia, relatively
high levels of crustal attenuation characterise south-
eastern Australia (Allen et al., 2002; Allen, 2004).
Attenuation of high-frequency elastic energy, critical
for the measurement of fc, may therefore provide an
explanation for the apparent increase of Dr with
seismic moment. The high stress drops observed for
southeastern Australia imply higher frequency ground
motion and that earthquake source dimensions are
more compact than usual. Response spectra calculated
for some Australian earthquakes indicate enrichment
of high-frequency ground motion, consistent with the
relatively high stress drops evaluated in the present
study (Sinadinovski et al., 2000; Allen et al., 2003).
T.I. Allen et al. / Tectonophysics 390 (2004) 5–24 21
Depth characteristics of the stress drops described
above were investigated using the same data set (Fig.
5). Linear least squares regression for each depth
profile was performed and indicated that the stress
drop appears to increase slightly with depth for
southeastern Australian earthquakes of similar seis-
mic moment. It may be expected that higher
deviatoric stresses at greater depths have an influence
on stress drops of intraplate earthquakes. Indeed,
Hanks and Johnston (1992) reported the occurrence
of two deep crustal eastern North American earth-
quakes with well-constrained hypocentral depths
greater than 20 km having higher than average stress
drop (the MW 5.4 southern Illinois earthquake, 9
November 1968; and the MW 5.9 Saguenay, Quebec
earthquake, 25 November 1988). It is subjective to
draw conclusions on the basis of two earthquakes,
however, these occurrences in particular further
suggest that deeper focus earthquakes may possess
higher stress drops than earthquakes of similar
seismic moment at shallower depths. It is also
possible that the observed increase in average stress
drop with hypocentral depth is merely an artefact of
the larger events (assumed to have higher stress drop)
being more likely to occur at greater depths,
subsequently introducing a systematic bias into the
data set.
A comparison between ML and MW as calculated
using the Hanks and Kanamori (1979) function
reveals a strong linear correlation, as would be
expected. Regression analysis of the two parameters
demonstrated that the magnitude scales are roughly
equivalent at a magnitude of 2.5, however, ML
calculated employing the �log A0 relations of Wilkie
et al. (1994) increases more rapidly than MW. The
relationship between the two magnitude scales for
southeastern Australian earthquakes was empirically
evaluated as MW=0.64 ML+0.83 [Eq. (11)] for events
less than ML 5.0. The discrepancy between the
magnitude scales may result from the assumption of
a constant stress drop which is lower than that
observed in southeastern Australia, inherent within
the Hanks and Kanamori (1979) relation [Eq. (8)]
(e.g. Singh and Havskov, 1980). Allen (2004) inves-
tigates an alternative methodology for the evaluation
of ML employing the anelastic attenuation parameters
described in Eq. (9). Local magnitudes evaluated
using the method of Allen (2004) have significantly
lower uncertainties than ML’s evaluated using the
�log A0 relations of Wilkie et al. (1994) and
addresses the relatively poor comparison between
MW and ML observed in the present study. Employing
the attenuations of Wilkie et al., local magnitudes
calculated for individual events are observed to
increase systematically with r. In contrast, ML
residuals calculated using the methodologies of Allen
(2004) and averaged at uniform distance separation
define a linear relationship with a near zero gradient,
for rb~750 km. Allen (2004) suggests that local
magnitudes calculated using the attenuation relations
of Wilkie et al. may overestimate the size of an
earthquake by as much as 0.3 of a magnitudes unit,
particularly for moderate-to-large events recorded at
large hypocentral distances.
4.2. Earthquake recurrence parameters in southeast-
ern Australia
Despite errors which may have been introduced
due to uncertainties in hypocentral depth for many of
the less well-located earthquakes used in the recur-
rence calculations, a decrease in b value with
hypocentral depth was detected (Table 3). The differ-
ence between the shallow and moderate depth ranges
is small and could possibly be an artefact of catalogue
incompleteness or limitations in reliable earthquake
depth control. Although many well-located earth-
quakes occur within 6 km of the surface, no event
larger than ML 3.1, well-located or otherwise, had a
depth of less than 6 km in the study region. The
observed decrease of b for the deeper focus events is
well-defined, implying that a larger proportion of
moderate-large earthquakes occur at depth. As we are
limited by relatively low earthquake activity in
Australia, it is difficult to map lateral and/or vertical
variability of b, however, our data do agree with
previous studies of Mori and Abercrombie (1997),
Gerstenburger et al. (2001) and others, who also
demonstrate a systematic decrease of b value with
depth within the seismogenic zone.
Previous b value estimates for this region have
been obtained by Gaull et al. (1990). Although their
source zones differed from that of the current study,
for a similar region, they obtained an overall b value
of 0.77, compared to our 0.88 for the combined data.
This discrepancy may be due to the sensitivity of the
T.I. Allen et al. / Tectonophysics 390 (2004) 5–2422
b value to either difference of source zones, or
catalogue incompleteness for lower magnitude earth-
quakes. In addition, Koo et al. (2000) estimated a b
value of 0.81 for the Melbourne Metropolitan Area,
adjacent to our study area. Note that these b values are
all based on local magnitudes. If earthquake recur-
rence were based on the moment magnitudes as
calculated in this study, the b values would be a little
higher, subsequently increasing the recurrence inter-
val for large damaging earthquakes and lowering the
associated hazard.
Both Scholz (1968) and Urbancic et al. (1992)
showed that b demonstrates an inverse relationship to
stress. From these findings, it may be implied that
stress drops for earthquakes in regions of low b
should be higher than those of earthquakes of similar
seismic moment in regions of high b. Alternatively,
this similarity may simply imply that the larger
earthquakes that appear to have high stress drop
occur at greater depths.
5. Conclusions
The Qa( f,r) model employed in the our estimates
of the earthquake source parameters provides a simple
model for the variation of seismic attenuation at
varying source–receiver distances and allows for more
consistent estimates of source parameters in south-
eastern Australia compared to earlier Q models (e.g.
Wilkie and Gibson, 1994).
A systematic increase in Brune stress drop with
increasing magnitude to at least ML 5.0 was
observed. It remains to be seen whether stress drops
will continue to increase for earthquakes of MLN5.0.
The relatively high stress drops evaluated suggest
compact source dimensions and high-frequency
ground motion. In addition, stress drops were
observed to increase slightly with increasing hypo-
central depth.
For a discrete study area in southeastern Australia,
b values were observed to decrease with depth,
implying that both rock strength and thus yield stress
increase with depth. Decreasing b values with source
depth suggest that larger earthquakes (with high stress
drops) tend to occur deeper. Moreover, this observa-
tion may explain why stress drop appears to increase
with hypocentral depth. Consequently, current models
may slightly overestimate earthquake hazard for
surface sites in southeastern Australia.
The relationship between ML and MW has a
significant effect on current estimates of ground
motion recurrence, and consequently on earthquake
hazard estimates. If moment magnitude (as calcu-
lated in this study) were used in ground motion
recurrence estimates, it would have the effect of
increasing the b value, consequently lowering hazard
associated with southeastern Australian earthquakes.
Therefore, the quantification of earthquake magni-
tude for hazard studies remains a major source of
uncertainty and is a problem that must be addressed
in the future to achieve reliable probabilistic hazard
estimates.
Acknowledgments
The authors would like to thank the staff at the
Seismology Research Centre for access to resources
and their generous cooperation. Special thanks go to
Greg McPherson and Bradley White for their kind
assistance in the software development phase of this
research. We also acknowledge Heidi Houston for her
critical review and thoughtful suggestions on the
original manuscript. Dan Clark is thanked for provid-
ing the digital elevation model in Fig. 2. This research
was supported by a Monash University postgraduate
scholarship.
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