Earthquake Research in China
Volume 26，Number 3，2012
Methods for Estimating Mean
Annual Rate of Earthquakes in
Moderate and Low Seismicity
Regions1
Peng Yanju，Zhang Lifang，Lv Yuejun，and Xie Zhuojuan
Institute of Crustal Dynamics，China Earthquake Administration， Beijing 100085，China
Two kinds of methods for determining seismic parameters are presented，that is，the
potential seismic source zoning method and grid-spatially smoothing method． The Gaussian
smoothing method and the modified Gaussian smoothing method are described in detail，
and a comprehensive analysis of the advantages and disadvantages of these methods is
made． Then，we take central China as the study region，and use the Gaussian smoothing
method and potential seismic source zoning method to build seismic models to calculate the
mean annual seismic rate． Seismic hazard is calculated using the probabilistic seismic
hazard analysis method to construct the ground motion acceleration zoning maps． The
differences between the maps and these models are discussed and the causes are
investigated． The results show that the spatial smoothing method is suitable for estimating
the seismic hazard over the moderate and low seismicity regions or the hazard caused by
background seismicity; while the potential seismic source zoning method is suitable for
estimating the seismic hazard in well-defined seismotectonics． Combining the spatial
smoothing method and the potential seismic source zoning method with an integrated
account of the seismicity and known seismotectonics is a feasible approach to estimate the
seismic hazard in moderate and low seismicity regions．
Key words: Moderate and low seismicity regions; Annual seismic activity rate; Gridspatially smoothing method; Potential seismic source zoning method
INTRODUCTION
Seismicity in the moderate seismic region is characterized by scattering and clustering．
The scattering characteristic means a dispersed spatial distribution of earthquakes，and for
most parts of the region，the possibility of occurrence of moderate-strong earthquake cannot be
1
Received on May 5，2011． This project was sponsored by the National Key Technology R＆D Program，China
(2006BAC13B01) ．
336
Earthquake Research in China
ruled out． Clustering means an inhomogeneous spatial distribution of earthquakes，and there
is a higher possibility of occurrence of earthquakes for certain areas，while lower possibility for
other areas ( Gao Mengtan，et al． ，2008 ) ． Earthquakes in a moderate and low seismicity
region are usually of magnitude lower than 6. 0 ， which do not produce obvious surface
displacement，thus，the evidence of faulting used to identify the seismogenic structures is
indistinct．
According to the current seismic design and prevention principles，seismic design is not
necessarily required for regions with design peak ground acceleration less than 0. 05 g．
However，most of these regions are located in the densely populated and economically
developed provinces and metropolis in eastern China． Once an earthquake occurs，it will
cause serious economic loss and social unrest． Many moderate-strong earthquakes have
occurred in eastern China in recent years，causing serious damage． The highest epicentral
intensity of these earthquakes reached Ⅶ degrees，and the direct economic losses from an
earthquake could reach tens of millions of Yuan ( RMB) ． For instance，the M5. 7 earthquake
in November 2005 in Jiujiang-Ruichang，Jiangxi Province left millions of people affected，
more than ten people dead and nearly 20 ，000 homes destroyed in Jiangxi，Hubei，Anhui
Provinces，with a direct economic loss of more than 2 billion Yuan ( RMB) ． The June 23 ，
2001 M4. 9 Rongchang，Chongqing earthquake caused a direct economic loss of nearly 40
million Yuan ( RMB) ． Thus，seismic hazard in low and moderate seismicity regions cannot
be ignored，and in-depth study on the relevant technology of seismic hazard zoning and
seismic fortification should be carried out．
Seismic hazard analysis method， with the spatio-temporal inhomogeneity taken into
consideration，is used in seismic hazard zoning in China． The essence of the technology is to
delineate the potential seismic source zones and determine the relevant seismicity parameters，
e． g． b-value，upper limit magnitude and mean annual seismic rate，etc． One of the major
criteria for potential source delineation is to find whether or not late Pleistocene active faults
are present． However，for low and moderate seismicity regions dominated by earthquakes of
M ≤6. 0 ，this criterion is difficult to apply． And owing to the low earthquake frequency and
small sample size，there is great uncertainty in the determination of the parameters，especially
the annual seismic rate，and whether the parameters are reasonable or not directly affects the
results of seismic hazard zoning． Therefore， seismic hazard analysis is one of the key
techniques for seismic zoning studies in low and moderate seismicity region ( Yan Jiaquan et
al． ，1996 ) ．
In this paper，two methods for determining annual seismic rate for low and moderate
seismicity regions are compared and analyzed． One is to deal with the spatial inhomogeneity of
seismicity by delineating the potential seismic source zone with the aid of geological and
seismic data，but the probability of occurrence of earthquakes in the potential source zone is
assumed to be equal． The other kind of method is to directly calculate the mean annual rate
based on the practical spatial inhomogeneity of earthquakes， such as the grid smoothing
method and the smoothing of epicenters of historical earthquakes． This paper takes the central
China region， where the seismicity level is low， as an example and uses the Gaussian
smoothing algorithm to calculate the annual seismic rate and the seismic hazard． Then，the
results are compared with those obtained by the potential seismic source zoning method and
the causes for the differences arising there from are analyzed． Meanwhile， the PGA
exceedance probability curves are calculated for the two cities of Qianjiang and Changde using
two seismicity models， and the similarities and differences between them are analyzed．
Finally， the authors draw some conclusions on the seismicity modeling in the low and
moderate seismicity regions．
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337
1 COMPARISON OF THE METHODS FOR ESTIMATING MEAN ANNUAL SEISMIC
RATE
1. 1
Potential Seismic Source Area Zoning Method
The concept of potential seismic source zone was brought forward by Cornell in 1968． He
assumed that seismicity was not distributed randomly in space but in a certain range of space，
namely，the potential seismic source zone，and the future earthquake would occur in this potential
source zone． The scaling of small to large earthquakes in the potential seismic source zone
satisfies the G-R relation，and the distribution of the seismicity satisfies the Poisson distribution
temporally，and the homogeneous distribution spatially．
Taking into account the spatial inhomogeneity of seismicity，the third-generation seismic
zoning map of China adopts the two-level zoning method． Firstly，to divide the areas，where the
intensity，frequency and spatial distribution of earthquake activity are obviously correlated with
the seismotectonic settings，into different seismic regions according to the regional seismicity，
seismo-geological conditions，and geophysical field data，then，delineate the potential seismic
source zones of various upper limit magnitudes in the seismic regions． Based on the statistical b
values and the annual rate of earthquakes with magnitude greater than a certain magnitude interval
in the seismic regions，and using the multifactor comprehensive evaluation method，the spatial
distribution function is determined for each potential seismic source zone，then the annual seismic
rate of each magnitude interval is allocated to the potential source zones ( Gao Mengtan，1988) ．
As the earthquake distribution in the potential seismic source zone is assumed to be
homogeneous， when the potential source zone delineated is too large， the homogeneous
distribution will dilute and lead to underestimation of the seismic hazard; while if the area
delineated is too small，it will result in the future earthquakes exceeding the upper limit of
magnitude ( Xu Guangyin et al． ，1996) ． Since the potential source area zoning is based mainly
on the characteristics of spatial distribution of seismicity and the geological structures，for the
regions with indistinct seismogeological structures and lower seismicity level，the bases for the
delineation of potential source areas are inadequate，therefore，it contains great uncertainties．
Nowadays，the study of the seismicity models in seismically inactive regions has attracted
more and more interest from scientists． The gridded smoothing method，which makes it possible to
avoid potential seismic source zonation and take due consideration of the spatial inhomogeneity of
seismicity，has become a hot point in the research of seismicity parameters in the world．
Numerous studies have been carried out in USA，France and China ( Frankel，1995; Beauval，et
al． ，2006; Xu Guangyin，2003; Zhang Lifang et al． ，2008) ．
1. 2
G ridded Spatially Smoothing Method
Frankel ( 1995 ) put forward a spatially smoothed seismicity approach to construct the
seismicity models for areas with indistinct seismogenic structures and low seismicity． The method
uses the models obtained respectively from the modern moderate and small earthquake regions，
the historical destructive earthquake regions and the homogeneous background seismicity regions
to calculate the seismicity parameters with some weighting． The basic assumption of this method is
that future destructive earthquakes will take place near the historical earthquakes． The first model
represents the distribution of modern moderate and small earthquakes which may reflect the
tectonic characteristics of future large earthquakes． The second model points out that a future
destructive earthquake may recur in the vicinity of historical earthquakes; and the third model
represents the probability of occurrence of moderate strong earthquakes in areas without historical
earthquakes． Firstly，we divide the study area into a grid and calculate the rate of earthquakes
Earthquake Research in China
338
larger than the threshold magnitude n i in each grid cell， then， using Herrmann's formula
( Herrmann，1977) ，convert the accumulative earthquake rate to the rate of increments of each
magnitude interval，and perform the spatial smoothing of seismic rates in a grid by the Gaussian
function，expressed as:
2 2
Σj n j e －Δij / c
n珘i =
(1)
2 2
Σ e －Δij / c
j
Where，n珘i is the earthquake rate in the ith grid cell，c is the correlation distance，Δ is the
smoothed radius，taken as 3c，j represents the number of grids around the ith grid within the
smoothed radius of 3c．
The Gaussian function represents，to a certain extent，the spatial inhomogeneity of seismicity
and the randomness of earthquake occurrence． This method avoids the delineation of the potential
seismic source zones and embodies the spatial inhomogeneity of seismicity． It has been applied to
the compilation of the US National Seismic Hazard Maps of 1996，2002 and 2007．
In light of the basic assumption of Frankel (1995) ，Cao et al． (1996) built the background
seismicity models with magnitudes less than 6. 5 for southern California，using the exponential
smoothing function and the Gaussian smoothing function，respectively． They calculated the annual
rate of background seismicity and systematically analyzed the differences between the results
obtained by the two functions． The results show that in high seismicity areas，the result obtained
by a Gaussian function is higher than that by an exponential function． However，in lower
seismicity areas，the exponential function produced a slightly higher result，which is attributed to
the inherent characteristics of the function itself． The author would suggest: For higher seismicity
areas，since the earthquake distribution itself is fairly smooth，it doesn't require too much
smoothing． Exponential smoothing processing is enough，and a Gaussian function will lead to
excessive smoothing． On the other hand，in moderate and low seismicity areas with sparse
distribution of earthquakes，it will need more smoothing，so the Gaussian function will be
suitable．
In view of the characteristics of seismicity in the low and moderate seismicity areas，Lapajne
et al． (2003) improved the circular Gaussian smoothing method by proposing a two-stage circular
and elliptical smoothing algorithm and equivalent circular smoothing algorithm． With a two-stage
circular and elliptical smoothing algorithm，we first perform the circular Gaussian smoothing and
determine the smoothed radius according to the epicenter error． The correlation distance is chosen
as 1 /3 of the smoothed radius． The second stage is to assume that the earthquake occurs on the
fault． Though the scattering seismicity doesn't have a direct or definite relationship to the known
fault or the historical earthquake event，the hypothetical fault length can be determined according
to the empirical relationship． Then，the fault's type and direction are determined from geological
data，the major axis of the ellipse is determined from the fault's length，and its minor axis from
the width of the seismogenic structure． The lengths of the semi-major axis and semi-minor axis are
equivalent to the correlation distance in a circular smoothing; the equivalent circular smoothing is
a variant of the traditional circular smoothing． In the event that tectonic data is not available，this
method can approximately replace elliptical smoothing． Under the assumption that the equivalent
smoothing area is equal to the elliptical smoothing area，the correlation distance is determined
objectively according to the epicenter error and the size of the hypothetical fault，then the
calculation is done according to the circular smoothing algorithm． Results show that both methods
are suitable for constructing seismic models in low and moderate seismicity regions．
Kagan et al． (1980) studied the epicenter distribution of earthquakes in low and moderate
seismicity regions and found that their arrangement patterns are very complicated，as characterized
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339
by seismic gaps，clusters or stripes． Accordingly，Woo (1996) thought that earthquakes could be
distributed in groups，showing fractal characteristics． The seismic rate R per unit area at a
distance from any earthquake has a proportional relationship of R － λ ，the exponent λ is related to
the fractal dimension D，and according to the fractal characteristics of the spatial distribution of
seismicity，an approach of spatially smoothed epicenters of historical earthquakes is developed，
with its smoothing function expressed as:
－λ
r2
λ －1 1
K( m，r) =
2． 0］
(2)
1 + 2
λ ∈ ［1． 5，
2
π r s ( m)
r s ( m)
r s ( m) = He km
(3)
where，m is earthquake magnitude， λ is the control of the degree of smoothing，and r s is
magnitude-dependent smoothed radius． For each magnitude interval，we count the distance of
each earthquake to its nearest one，average them to get the mean distance，then get H and k from
regression of the mean distance and the magnitudes in the same magnitude interval．
The introduction of magnitude-dependent probability density function in the method has the
following advantages: It can calculate the annual seismic rate of earthquakes with magnitudes
higher than the historical maximum magnitude of earthquake based on neotectonic data or expert
system judgment，and can include the uncertainties in earthquake magnitudes and the randomness
of the relationship between the magnitude itself and fault． Meanwhile，by constructing the
magnitude-dependent probability density function，the frequency and intensity of the actual
earthquakes can be used to characterize the seismicity of the study area，instead of the expression
by the strict G-R relationship，thus avoiding counting and computing b value，while objectively
embodying the characteristics of seismic activity in the study area．
Using the methods of spatially smoothed epicenters of historical earthquakes and the
delineation of potential seismic source zones，Beauval et al． ( 2006 ) constructed two different
seismic models to compare the differences in the seismic hazards obtained from the two models．
Results show that in the low and moderate seismicity area，the seismic hazards obtained by the
two models are equivalent to each other，but in the high seismicity area，the hazard obtained by
the spatial smoothing method is lower than that by the potential seismic source zoning method．
The above-mentioned smoothing methods involve mainly earthquake catalog data，and there
is a high requirement for the completeness of the data． Therefore，we need to construct the
catalogue with a certain threshold magnitude of completeness from the original earthquake
catalogue for the calculation． However，in a low and moderate seismicity area，the earthquake
samples themselves are small in quantity，so if rejecting the data of the incompleteness intervals，
we cannot make use of the data of large earthquakes from the remote history． Moreover，the
earthquake data of high magnitude intervals are less in itself，and is inadequate to completely
determine the area of the future strong earthquake merely from the moderate and small earthquake
data． In order to solve this problem，Lapajne et al． (1997) suggested a seismicity model based
on released seismic energy，that is，the high seismic energy release area shall be the area where
future large earthquakes may occur． Assuming there is no missing of any earthquakes in the high
magnitude intervals in the entire data period，i． e． the large earthquake catalogue is regarded to
be complete，the energy released by moderate and small earthquakes is negligible，and therefore
their completeness can be neglected． The total energy released by all earthquakes during the study
period is converted to the seismic rate of earthquakes of a certain magnitude interval，and then，
the hazard is calculated using the weighted multi-model means in combination with other
seismicity models．
(
)
340
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Earthquake Research in China
APPLICATION EXAMPLES
In this section，we choose the central China region (106. 5° ～ 114. 5°E，24. 5° ～ 30. 7°N)
as the study region and use the spatially smoothed seismicity model to calculate its ground motion
parameters，estimate the seismic hazard and obtain the PGA distribution maps． Then the maps are
compared with the results in the Seismic Ground Motion Parameter Zonation Map of China
( GB18306-2001) derived from the method of potential seismic source area delineation．
Topographically，the study region includes Hunan Province，eastern Guizhou Province，
Chongqing，and southern Hubei Province． The faults there have low Quaternary activity． Most of
them are early and mid Pleistocene，small-sized and buried faults． The thickness of the crust in
the area is small，mostly 35 ～ 40km，the foci of earthquakes are shallow，generally from a few
kilometers to 20km． This is also one of the major reasons why the moderate and small sized
earthquakes of this region are more likely to cause damage．
3
44 historical seismic events of M≥4
have been recorded in the study area，including 20
4
3
of M S 5. 0 ～ 5. 9，and 2 of M S 6. 0，which are the August 1631 M6
Hunan Changde earthquake
4
1
and the 1856 M6
earthquake between Hubei Xianfeng and Sichuan Qianjiang． There have
4
been 1696 earthquakes of M L ≥2. 0 recorded in the period from 1970 to December 2008，among
which，219 events of M L3. 0 ～ 3. 9，27 of M L 4. 0 ～ 4. 9，and 4 of M L 5. 0，with the largest being
M = 5. 7． Fig． 1 shows the spatial distribution of epicenters of these earthquakes． It is clear that
both historical and modern seismicity have low intensity and frequency， and their spatial
distributions are relatively scattered，but meanwhile show certain clustering characteristics．
Completeness analysis was performed for the historical earthquake catalogues and the modern
moderate and small earthquake catalogues，and the foreshocks and aftershocks were removed．
Then，the seismic data in the completeness periods were chosen to establish the historical
seismicity model and the modern seismicity model of small to moderate earthquakes，respectively．
The mean annual seismic rate of M ≥4. 0 in the study region was calculated using the Gaussian
spatial smoothing approach introduced by Frankel ( 1995 ) ． Detailed steps are as follows: We
divide the study region into 0. 2° N × 0. 2° E grid cells according to the distribution of sample
quantities，calculate the number of M ≥ M0 earthquakes n i in each grid cell i，then perform
smoothing on n i using Gaussian smoothing function ( namely，the aforementioned formula (1) ) to
obtain the spatial distribution of n珘i ． Fig． 2 shows the distribution of mean annual seismic rates
calculated from historical earthquake catalogue．
Then，choosing the same ground motion attenuation relationship with that used in the Seismic
Ground Motion Parameter Zonation Map of China ( GB18306-2001) ，we perform the calculation
based on the two above-constructed seismicity models using the probabilistic seismic hazard
estimation method． Detailed steps are as follows:
(1) Use Herrmann (1977) formula to convert the accumulative number of earthquakes n珘i
into the incremental value N i ( M) of the number of earthquakes at the magnitude interval ( M +
ΔM) in the grid cell; ΔM is an increment of earthquake magnitude，taken as 0. 2 in this study．
(2) Allot N i ( M) of all grids in the range of distance from site D x to D x + Δ，and define the
summation of N i ( M) in the torus centered at the site as N x ．
(3) Summate all earthquake magnitude intervals and distances，and calculate the annual
exceeding probability P( μ ＞ μ0 ) of the ground motion μ exceeding μ0 :
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341
Fig． 1
Epicenter distribution of historical earthquakes and modern
moderate and small earthquakes in the study region
P( μ ＞ μ0 ) =
ΣD ΣM
10［log( N x / T) －bM y］
p( μ ＞ μ0 | D x ，M y )
(4)
Where，T is time in the calatogue，p( μ ＞ μ0 | D x ，M y ) is in the place D x where earthquake of M y
oceurred，the condition probability of ground motion μ exceediny μ0 ，D is obtained in 0 ～ 150km，
M value depends on earthquake Magnitude up and down limit．
The calculations yield a distribution of peak ground acceleration ( PGA ) with 10%
probabilities of exceedence in 50 years，and by weighting the results obtained from the two
seismicity models，we get the seismic zoning results，as shown in Fig． 3( a) ．
For comparison purposes，Fig． 3( b) presents the results of seismic zoning by the method of
potential seismic source area delineation．
Compared with Fig. 3( b) ，the general patterns of the PGA zoning maps obtained by the two
methods are roughly consistent，but there are still certain differences between them． The map
from the spatial smoothing method shows obviously continuous changes， which embody the
characteristic of spatial smoothing． For example，the area from Shaoyang to Huaihua sees a
gradually decreased PGA，but in Fig. 3 ( b ) ，since a NE-directed potential source of M5. 5
earthquake is delineated in the Huaihua area，the region sees a slight increase in PGA，as 0. 05g
in part of the area and an indication of the tectonic effect． Similarly，in the vicinity of Yueyang，
since tectonic factors are taken into account in delineating the potential seismic source，we get a
higher result than that by a spatial smoothing approach． At the left top of the study region，a NEdirected stripe of PGA less than 0. 05g appears in Fig. 3( a) ，and this trend also appears in Fig. 3
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Earthquake Research in China
( b) but with a higher result，due to the reason that the former does not have a potential seismic
source in this area，while the latter produces a higher result owing to the spatial smoothing of
seismicity around the area． In Fig. 3( b) ，a 0. 15 g zone appears in the Changde area，due to the
delineation of a potential seismic source with magnitude 7. 0 in this area in view of the fact that an
3
M6
earthquake took place there in 1631． Relatively，the result is lower in Fig. 3 ( a ) ．
4
Comparison between Fig. 3( a) and Fig. 3 ( b) indicates that the potential seismic source zoning
method has a greater effect on the seismic hazard estimates in the low and moderate seismicity
regions． In addition，the bases for the delineation of the potential sources in these regions are
inadequate，therefore，there is subjective uncertainty in the determination of the potential source
boundary and the upper limit magnitude introduced． The spatial smoothing method avoids this
kind of uncertainty． However，since the seismicity is smoothed over larger areas，the seismic
hazard will be diluted in high seismicity regions．
Then，using the seismicity models derived from the two methods，we calculate the PGA
exceeding probability curves for the two cities，Qianjiang and Changde，and the results are shown
in Fig． 4． As can be seen in the figure，the result from the spatial smoothing method is higher
than or approximate to that obtained from the potential source zoning method for regions with
higher exceeding probability，while in regions with a lower exceeding probability，the result
obtained from the spatial smoothing is small． The reason for this lies in the fact that the potential
seismic source area zoning method involves numerous geological data，which represents a longer
time period than that of the historical earthquake data，thus，contributes more greatly to the
hazard of low exceeding probability levels． This also confirms the statement suggested by Beauval
et al． ( 2006 ) that the seismic hazard estimate derived from the spatially smoothed gridded
seismicity modeling is the lower bound of the seismic hazard estimate of the region． When using
the spatially smoothed gridded models，tectonic information should be counted properly． For
example，we can first perform spatial smoothing，then take into account the relationship to the
potential source area and assign weights of geologic structure，or adopt an elliptical model to do the
smoothing according to the tectonic data． In this way，the method can produce a result which more
appropriately represents the future seismic hazard level． Fig． 4 also shows another phenomenon; a
big difference in the hazards estimated from the potential seismic source zoning method between the
two cities in the areas of low exceeding probability． This is because the earthquake background and
the upper limit magnitude are different between the two areas． The use of the potential source area
zoning method embodies the impact of potential seismic source delineation．
3
DISCUSSION AND CONCLUSION
The paper makes the comparative analysis of the currently widely used methods for
determining the mean annual seismic rate，and taking the central China region as an example，
compares the differences in seismic hazard estimates derived from Gaussian smoothing and
potential seismic source area zoning，and investigates the causes for the differences． We have
drawn the following conclusions on the estimation of mean annual seismic rate and seismic hazard
in the low and moderate seismicity regions:
(1) Method for Estimating Mean Annual Seismic Rate in Low and Moderate Seismicity
Regions
The gridded spatially smoothing method directly uses earthquake catalog data，especially
modern small and medium-sized earthquake catalogues． Seismic activity itself is a manifestation of
tectonic movement，and the epicenter distribution reflects，to some extent，the tectonic activity
information． Thus the method has implicitly considered the seismic structural factors，to some
extent，and can be used to estimate seismic hazard in low and moderate seismicity regions with
Volume 26，Number 3
Fig． 2
Contours of mean annual seismic rates of M L ≥4. 0 calculated from historical
earthquake catalog with a Gaussian smoothing function
Fig． 3( a)
Peak ground acceleration zoning map by Gaussian smoothing ( unit:gal)
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Earthquake Research in China
Fig． 3( b)
Results from the Seismic Ground Motion Parameter Zonation Map of China and potential
seismic source zonation ( adapted from the zonation map GB18306-2001)
Fig． 4
Exceeding probability curves of peak ground acceleration obtained by different methods
indistinct seismogenic structures or seismic hazard from background seismicity in strong
earthquake active regions．
The gridded spatially smoothing method avoids the uncertainties arising from the
determination of potential source boundary and introduction of upper limit magnitude． The
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345
spatially smoothing methods mainly make use of earthquake catalogue data． For the existing
seismiotectonic data，we can use the elliptical smoothing model to determine the major and minor
axes of ellipse according to the fault rupture zone so as to take account of the tectonic effect，as
done by Lapajne et al． (2003) ． Alternative we can use smoothed gridded data to delineate the
potential seismic sources in the regions with distinct seismogenic structures and assign different
weights to the grid cells in and outside the potential source area to completely embody the
geological tectonic information，as done by Xu Guangyin (2003) ． The gridded spatial smoothing
method and the potential seismic source area zoning method both have their respective
advantages． An appropriate combination of the two can supplement each other and produce results
that better describe the level of seismic hazard．
Regarding the correlation distance in the gridded spatially smoothing method，it can be
determined by the subjective empirical relations according to the precision of the historical and
modern earthquake data，or by the more objective method of statistical regression based on the
relationship of epicentral distribution of seismicity in the study region． For instance，Cao et al．
(1996) and Woo (1996) counted and calculated the average of the minimum distance between
the earthquake pairs in each magnitude interval according to the principle that the seismic rate at
a certain range of distance to an epicenter complies with the power-law relationship，and then
obtained the expressions for the magnitude-dependant smoothed radii．
Each of the gridded spatially smoothing methods has its own characteristics． The authors
think that the method of spatially smoothed epicenters of historical earthquakes proposed by Woo
(1996) is the most objective one． Besides the characteristic of determining different smoothed
radii by statistical regression of seismicity of different magnitude intervals，the introduction of the
magnitude-dependant probability density function allows this method to calculate the annual
seismic rate higher than the maximum magnitude of the past earthquakes according to the
neotectonic information or the expert judgment system，a solution to the shortage of earthquake
data of high magnitude intervals in the low and moderate seismicity regions． Meanwhile，the
magnitude-dependant probability density function itself includes the uncertainties of magnitude in
the earthquake catalogs， and the method directly uses the frequency and magnitude from
earthquake catalogs to characterize the seismic activity，which no longer needs to construct the
G-R model，thus，avoiding the uncertainties arising from b value calculation and reflecting the
real seismic activity of the study region．
(2) The Mean Annual Rate of Earthquakes in High Magnitude Intervals
Limited by the historical data，earthquake catalogues are restricted． Even in the historical
records rich region，the North China region，the completeness period of the M ≥4. 7 earthquake
catalog is only about 500 years． The periodicity of seismicity in this region is about 300 years
( Huang Weiqiong，et al． ，
1994) ; in other words，the completeness period of data cannot cover
two seismic active periods． This situation cannot be improved significantly in a short time．
At present，China is compiling seismic zoning maps with the aim of protecting buildings from
collapse in earthquake，which requests consideration of a lower probability of exceedance level of
ground motion parameters，that is，a probability of exceedance of 2% for 50 years，equivalent to
a return period of about 2，500 years of earthquakes． For a high level seismic hazard，its
controlling factors in general come from the surrounding or far-field high-magnitude earthquake
activity． However，in the low and moderate seismic activity areas，the period of historical records
has only about 500 years，its seismic frequency and intensity are low，and the sample size of
earthquakes in high-magnitude intervals is small． Thus，uncertainty can be imagined in the
ground motion parameters calculated from the data of earthquakes once every 2，500 years．
Moreover，the high-magnitude interval seismicity parameters play a decisive role in determining
the ground motion parameters of low probability of exceedance level． Therefore，the annual
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Earthquake Research in China
seismic rate of earthquakes in high magnitude intervals remains a hard nut to crack in the ground
motion parameter zoning in low and moderate seismicity regions．
At present，only by resorting to the earthquake catalogs from the modern instrumental seismic
records，improving the recognition techniques of seismogenic structures of strong earthquakes and
combiningthese with historical earthquake research can we determine the parameters of seismic
activity． The study of seismogenic structures is not merely limited to analogy to seismogenic
structures，but has been developed to a stage of investigating the relationship of seismic activity
with buried structures， geophysical fields， and the lateral heterogeneity of the deep crust
structures． Some studies found that for certain M6. 0 earthquakes，though there are no obvious
signs of surface structures observed，there are a certain relationships with the buried fold activity．
The combination of various means will be the trend for determining ground motion parameters in
the low and moderate seismicity regions．
REFERENCES
Beauval C． ，Scotti O． and Bonilla E． The role of seismicity models in probabilistic seismic hazard estimation:
comparison of a zoning and a smoothing approach ［J］． Geophys． J． I． ，2006，65(2) : 584 ～ 595．
Cao T． Q． ，Petersen，M． D． ，Reichle，M． J． Seismic hazard estimate from background seismicity in Southern
California ［J］． Bull． Seism． Soc． Am． ，1996，86(5) :1372 ～ 1381．
Cornell C． A． Engineering seismic risk analysis ［J］． Bull． Seism． Soc． Am． ，1968，58:1583 ～ 1606．
Frankel A． Mapping seismic hazard in the central and eastern United States ［J］． Seism． Res． Lett． ，1995，6
(4) : 8 ～ 12．
Gao Mengtan，Xiao Heping，Yan Weimin，et al． The importance of seismic zonation in moderate earthquake area
and the recent technical progress ［J］． Technology for Earthquake Disaster Prevention，2008，3(1) :1 ～ 7 ( in
Chinese with English Abstract) ．
Gao Mengtan． A discussion on the mean annual rate of large earthquakes ［J］． Recent Development in World
Seismology，1988，(1) : 1 ～ 5( in Chinese with English Abstract) ．
Herrmann R． B． Recurrence relations ［J］． Earthquake Notes，1977，48:47 ～ 49．
Huang Weiqiong，Li Wenxiang，Cao Xuefeng． Research on the completeness of earthquake data in the Chinese
mainland ( Ⅰ) : Taking the North China region as an example ［J］． Acta Seismologica Sinica，1994，16(3) :
273 ～ 280 ( in Chinese with English abstract) ．
Kagan Y． Y． ，Knopoff，L． Spatial distribution of earthquakes: the two point correlation function ［J］． Geophys．
J． R． Astr． Soc． ，1980，62:303 ～ 320．
Lapajne J． K． ，Motnikar B． S． ，Zabukovec B． ，Zupancic P． Spatially smoothed seismicity modeling of seismic
hazard in Slovenia ［J］． J． Seism． ，1997，1: 73 ～ 85．
Lapajne J． K． ， Motnikar， B． S． ， Zupancic， P． Probabilistic seismic hazard assessment methodology for
distributed seismicity ［J］． Bull． Seism． Soc． Am． ，2003，93(6) :2502 ～ 2515．
Shen Dexiu． A Study on Identification of Seismogenic Structure of Moderate-strong Earthquakes in South China and
Its Application ［D］． ( Master's degree thesis) In: Institute of Geology，China Earthquake Administration，
2007 ( in Chinese with English abstract) ．
Woo G． Kernel estimation methods for seismic hazard area source modeling ［J］． Bull． Seism． Soc． Am． ，1996，
86(2) :353 ～ 362．
Xu Guangyin，Gao Mengtan． The study on the characters of non-uniform earthquake distribution within the
potential source areas ［J］． Earthquake Research in China，1996，12 ( 3 ) : 294 ～ 299 ( in Chinese with
English abstract) ．
Xu Guangyin． Study on 3-D Potential Seismic Source Models and Their Applications on Probabilistic Seismic Hazard
Analysis［D］． In: Institute of Geophysics，China Earthquake Administration，2003 ( in Chinese with English
abstract) ．
Yan Jiaquan，Jia Sujuan． The principle and methodology of delineation of potential seismic source for moderate
earthquakes in Northeast and North China ［J］． Earthquake Research in China，1996，12(2) :173 ～ 194 ( in
Chinese with English abstract) ．
Zhang Lifang，Lv Yuejun，Peng Yanju，et al． Estimate of seismic parameters in low seismicity region by using
spatially smoothing approach ［J］． Technology for Earthquake Disaster Prevention，2008，3(1) :27 ～ 36 ( in
Volume 26，Number 3
347
Chinese with English Abstract) ．
About the Author
Peng Yanju，born in 1976，is Ph．D and associate research professor of the Institute of Crustal
Dynamics， CEA． Her major is research of seismicity， earthquake disasters， etc． E-mail:
pengyj408@ 126． com