Estimating seismic moments and Lg Q using Lg spectra

Vol. 17 Supp. (22~31) ACTA SEISMOLOGICA SINICA

Article ID: 1000-9116(2004)Supp.-0022-10

Nov., 2004

Estimating seismic moments and Lg Q using Lg spectra* J I N P i n g ( - ~ --~) X I A O W e i - g u o ( ~ ] ) D U A N K e - m i n ( ~ )

Northwest Institute of Nuclear Technology, Xi'an 710613, China

Abstract

A multi-event and multi-station inverse method is presented in the paper to simultaneously estimate the seismic

moments (Mo)and source comer frequencies (fc) of several Jiashi (Xinjiang, China) earthquakes, as well as the apparent Lg Q models for the paths from Jiashi to eight seismic stations (WMQ, AAK, TLG~ MAKZ, KUR, VOS, ZRN and CHK) in Central Asia. The resultant seismic moments correlate well with the M0 values obtained by Har- vard University using the centroid moment tensor (CMT) inversion and the surface-wave magnitudes as well. After the correction by a typical value of average radiation coefficient for regional SV waves, the M0 values from Lg spectral inversion are still close to the corresponding values obtained from CMT inversion. The obtained apparent QoLg values (Lg Q at 1 Hz) are consistent with the tectonic features of corresponding propagation paths. The QoLg values are 351+87, 349+86 and 300i-_27 for the paths from Jiashi to AAK, TLG and MAKZ, respectively. They are

smaller than QoLg values for the paths to KUR, VOS, ZRN and CHK, which are 553+72, 569&_58, 550+_57 and 603+65, respectively. These results agree with the condition that the paths to AAK, TLG and MAKZ mainly propagate through the mountainous Tianshan area where relatively strong seismic activities and large variations of

topography are exhibited, while the paths to KUR, VOS, ZRN and CHK mainly propagate through the stable area of Kazak platform. The QoLg value for the path to WMQ is 462+56. This is also in agreement with the condition that the path to WMQ is basically along the border area between Tianshan Mountain and Tarim Basin, and along this path the variations of topography and crustal thickness are moderate in comparison with that along the path to MAKZ.

Key words: spectral inversion; seismic moment; Lg Q; Jiashi earthquakes CLC number: P315.3+1 Document code: A

Introduction

The seismic Lg wave train propagates in the continental crust and can be considered as either the guided S waves (Bouchon, 1982) or a sum of overtone (higher order) surface waves (Knopoff, et al, 1973). In the stable continental area, Lg is very prominent and often exhibits largest ampli-

tude on regional seismograms. Since Nuttli's early investigation on its attenuation and utilization for measuring earthquake magnitude by a scale now known as mbLg (Nullti, 1973), Lg has been widely used for estimating magnitude of earthquakes and yield of underground nuclear explosions (Nuttli, 1986; Patton, 1988; Israelsson, 1994; GE, et al, 1992).

The attenuation of Lg exhibits large regionalized variations due to its way of propagation. The spectra of Lg waves contain the information of both source spectra and path characteristics of attenuation. In the past decade, some so-called spectral inversion algorithms were developed to

* Received date: 2003-07-29; revised date: 2004-02-20; accepted date: 2004-04-12. Foundation item: Foundation of Verification Researches for Army Control Technology (413290102).

Supp. Jin Ping, et al: ESTIMATING SEISMIC MOMENTS AND LG Q USING LG SPECIRA 23

simultaneously extract seismic moments (M0), source comer frequencies (fc) of earthquakes or underground nuclear explosions, as well as path-variable Lg Q models (Sereno, et al, 1988; Xie, 1993, 1998; Xie, Mitchell, 1996; Cong, et al, 1996; A1-Eqabi, et al, 2001). One obvious advantage of these algorithms is that little a priori information about path characteristics is needed for inversion. At the same time, some of the above-mentioned researches also suggest that Lg spectral inversion may have good application prospects in magnitude estimation and event discrimination. Additionally, it may also provide independent measurements for studying regional characteristics of Lg attenuation.

Most of the above-mentioned studies discuss the inverse algorithms applicable to single-event and multi-station situations, except for Sereno, et al (1988) who discussed an algorithm for multi-event and single-station situation. For the situation of a cluster of earthquakes occurred within the same source area, a multi-event and multi-station algorithm is presented in the paper to simultaneously extract source parameters of earthquakes and attenuation parameters for paths. The algorithm is applied to analyzing some Jiashi earthquakes recorded at several stations in Central Asia. Preliminary results show that this algorithm is applicable to Lg spectral inversion in the case of multi-events and multi-stations.

1 Inverse algorithm

Assume J seismic events within the same source area and N recording stations. According to Xie (1993), the displacement spectrum of Lg wave train of the jth event recorded at the ith station can be expressed as

S~(f)R(O~:) nfr U aiLg(f) - ~ exp(-Q-~--~)Xi( f )ro( f ) (1)

where ~Lg(f) is displacement spectrum, f is frequency, Sj( f) is source spectrum of thejth event,

R(0~) is source radiation coefficient, 0~j, A o and ~j are azimuth, distance and mean Lg travel time

from thejth event to the ith station, A0 is reference distance and may be taken as 100 km (Street, et al, 1975; Herrmann, Kijko, 1983); Qi(f) is the mean Lg quality factor for the path to the ith station, Xi( f ) is site response of the ith station, and rij(f) represents randomness of other effects.

Street, et al (1975) pointed out that the later portions of Lg wave train are primarily com- posed of scattered waves that average out the radiation effects. The investigation of Xie (1998) also showed that radiation patterns of Lg waves vary modestly. Therefore, like some former researches (Sereno, et al, 1988; Cong, et al, 1996; A1-Eqabi, et al, 2001), the term of radiation pattern is ignored for inversion in the paper. Additionally, site responses are generally unknown and it is difficult to inverse Sj( f ) , Qi( f ) , and Xi ( f ) simultaneously. So similar to Xie (1993), we

define e x p ( - ~ f r l J ~ =exp( ~ f r ° l QTJ)) x'(:) o:(:) J

where Q[(f)is the apparent Lg quality factor and is assumed to have a power-law frequency de-

pendence, that is

Q;(f) = Qo~f": (3)

where Qo~ and ;7: represent apparent Lg Q at 1 Hz and its power-law frequency dependence,

24 A C T A S E I S M O L O G I C A SINICA Vol. 17

respectively. Nevertheless, it is worth pointing out that if this assumption is invalid, extra errors will enter into the results of inversion.

Based on these simplifications or assumptions, the expression of Lg spectrum for practical inversion is

Si(f) ( nf'-~'rij I A~*(I) = ~ e x p / r0(f) (4) /Ao4, Oo, )

for simplicity, the superscript symbols ' in Q~i and r/: are omitted. According to Sereno, et al (1988), the source spectrum S2(f) may be expressed as

M0i 1

1+

where M0j andfcj are the seismic moment and source corner frequency of the jth earthquake, and p and Vs are medium density and shear-wave velocity, respectively.

Based on equation (4), Xie (1993) presented a single-event and multi-station algorithm to

simultaneously inverse M0 and fi of an event as well as Qo and r/for the paths to different recording stations. This method can be shortly described as: carry out an exhaustive search in the (Mo, fi) space by looping over all possible Mo andfi values. For fixed M0 andfi, reformulate equa-

tion (4) into linear equations of I"//and lnQ0/and solve these equations to obtain []i and In Qoi using the least square residual method. Under the multi-event and multi-station situation, this algorithm needs to carry out an exhaustive search in the space of source parameters (M01,fil, Mo2,fi2, • -', Moj, fcA, which is of 2xJ dimensions. Obviously this would be very time-consuming and im- practical in many cases. In addition, because this algorithm has to take double logarithm opera- tions on both sides of equation (4) to reformulate it into linear equations of r/i and lnQ0i, random fluctuations in Lg spectra may lead to numerical instabilities in inverse solutions (Xie, 1998).

To avoid these problems, we employ the Gauss-Newton method for the spectral inversion of Lg in the case of multi-events and multi-stations. Sereno, et al (1988) employed a similar ap- proach for Lg spectral inversion in the case of multi-events and single-station. For a given set of

Qoj, rb, Moj, fi~ values (i=1, ..., N, j=I , -.., J) , according to equation (4), the fitting error (residual)

for A~g(f) at the kth sampling frequencyfi can be expressed as

dij k = In A~g(fk )4A°Aij + 7Ifkl-rlirij (6)

Sj(fk) Qo,

The inverse problem then is to find a set of Q.oj,O:,f/lo:, L values, so that the sum of square re-

siduals is minimized, that is N J K

Res = E Z Z ai~ k =min. (7) i=l j=l k=l

where K is the number of sampling frequencies for each spectrum. For convenience, define

m=[Qol,rl~,'",QoN,rlN,lnMo~, f~,'",lnMoj, f ~ = [ m l , m 2 , . - . , mq]V

Supp. Jin Ping, et al: ESTIMATING SEISMIC MOMENTS AND LG Q USING LG SPECTRA 25

as the model vector of q=2x(N+J) dimensions. Let m0 be a starting point in the model space, and then the solution to equation (7) may be approached using the following iterative procedure, that is

d ( m r ) = - - - G ( m r ) i ~ i r (8 )

(9)

where

mr+ 1 : m~ + ~m r

d(mr) = ( d i l l , dH2, "", dtcj/¢) T = ( d l , d2, ' - .def t

is a vector ofp=N><J×K dimensions, and

G(m r ) = (Od~ / Oms )

is a matrix ofp×q dimensions. Elements of G(m~) can be easily obtained from the following par- tial derivatives, that is

In practice, the iteration stops when

Odi:_ nfk'-~'rij4, Odok_ rtf~-~'r01gfkr/'

0Q0 ̀ Q02~ Dr/, Q0,

Odu~ - 8j,

OlnMoj

118m ll

(10)

Odok _ 2f] 1 6st (11)

is less than a pre-set small number and the conse-

quent result my is taken to be the solution. Assuming that the random factor r 0 in equation (4) obey a logarithmic normal distribution, then the uncertainty of mi is

gvn 2 = c2F~(1, p-1)Cm(i, i) (12)

where e~=Res2/(p-q), Fa(1, p - I ) is an F statistic with 1 andp-1 degrees of freedom for the critical

level ~z, and Cm(i, i) is the ith diagonal element of matrix Cm=(GTG) -l. This algorithm has been tested with the synthetic Lg spectra in the range of 0.1 ~5 Hz for six

imaginary co-located earthquakes recorded by two virtual stations. Source and path parameters for these virtual earthquakes and stations are listed in Table 1, respectively. The synthetic Lg spectra were computed using equations (4) and (5), and the random factor rij(f) in equation (4) was rep- resented by a factor e e where e is a random number obeying the normal distribution N(0, o2). For comparison, the average inversion results with uncertainties of twice standard deviation derived

from one hundred numerical tests with cr =0.2 are listed in Table 1, while more viewable com- parisons between inversion results and real model parameters are illustrated in Figure 1. It can be

Table 1 Compar ison be tween mode /pa rame te r s and inversion results for numerical tests

Model parameters Inversion results

Station 1 (A=500 km) Qo=500; r/=0.3 Q0=519-±115; r/=0.28i-0.10

Station 2 (A=300 km) Qo=350; r/=0.5 Q0=366+90; r/=0.49±0.09

1 Mo=lXl0~N.m f, =1.0 Hz M 0 =(0.98±0.15) 10 j~ N-m

2 M0=5xl015 N.m fe --0.6 Hz M 0 = (4.95±0.69) 1015 N.m

3 M0=2×1016 N.m fc =0.4 Hz M o = (19.8+2.9) 1015 N-m

4 Mo=lxl017 N-m f¢ =0.2 Hz M o = (102±19) 1015 N.m

5 M0=5xl0 t7 N.m fc =0.15Hz M 0 = (511±117) 1015 N.m

6 M0=2.5×1018m fc =0.07 Hz M 0 = (3 144+2 027) 1015N-m

fc =(1.00-i-0.08) Hz

L = (0.6o±o.05) nz f~ = (0.40-L-0.04) Hz

f~ = (0.20-£-0.03) Hz

f¢ = (0.15±-0.02) Hz

f~ = (0.067:1--0.03) Hz

26 ACTA SEISMOLOGICA SINICA Vol. 17

seen that both source and path parameters can generally be well estimated using the algorithm described above, except for the case when the source corner frequency is below the lower limit of frequency band of the data (such as in the case of event 6 in Table 1). Under this situation, the uncertainty in resultant seismic moment would become very large and great errors would be intro- duced.

600

d 4oc

- ( a ) o o

0 . 6

o 0 .4

I ~0.2 200 t I

Stationl Station2

I 10 ~

(c) o E

10 ~

10~ I

10 ~ I I 10 t~ 10 ~ 10 L~

M~ ( Real ) / N . m

~ 0 .

- (b) t

I Stationl Station2

(d)

0 .2 0 .4 0 .6 0 . 8 1.0 J~ ( Real ) / t lz

Figure 1 Results o f numerical tests (a) Distribution of inverted Q0 values; (b) Distribution of inverted 77 values; (c) Inverted/140 values versus respective real values; (d) Invertedfe values versus respective real values. More details about the tests are given in the text

Because the algorithm used in this paper does not need to transform equation (4) into linear equations of In Q0i, the numerical instability occurring in the algorithm of Xie (1993) due to random fluctuations in Lg spectra is naturally avoided.

2 Data and analyses

The data analyzed in the paper are recordings of eight Jiashi (Xinjiang, China) earthquakes registered at eight stations in Central Asia, i.e. WMQ, AAK, TLC~ MAKZ, KUR, VOS, ZRN and CHK. Locations of these earthquakes or stations are given in Figure 2. The epicentral distances from these earthquakes to the stations are about 300 km to 1 600 km. The source parameters for the earthquakes are given in Table 2 and the coordinates of stations in Table 3.

Analyses were based on the recordings of vertical components. The spectra used for inversion were computed by the way explained as follows. Lg wave trains were isolated using a 3.0-3.6 km/s velocity window (Figure 3). For each isolated Lg recording, we removed its linear trend and computed its amplitude spectrum using the 4 096 points FFT; smoothed the spectrum by five-point averaging and then removed the instrument response for displacement input from it. In practice, only samples with frequencies greater than 0.1 Hz and signal-to-noise ratio more than 2 were used for inversion. Additionally, because the spectra obtained by FFT were of linearly equal frequency interval, for the balance between high and low frequency samples, they were resampled to be of logarithmically equal frequency interval by interpolation.


Table 2 Source parameters of Jiashi earthquakes studied

No. Date Time ~) Epicenter ~) Depth~ ) MagnitudeS) Moment2~ Moment3~ Comer frequency 3~

a-mo-d h:min:s ~1(o) ,~j(o) /kin Ms M0/1017 N.m MollO 15 N.m fdHz

1 1997-10-17 17:35:14.5 39.44 76.86 24.2 5.1 1.2 38.2-+-5.9 0.374-0.05

2 1998-03-19 13:51:33.7 39.92 76.73 33 5.6 3.3 144±20 0.394-0.05

3 1998-08-02 04:40:39.3 39.57 77.03 9.8 5.6 3.3 113±16 0.464-0.06

4 1998-08-02 05:48:38.7 39.58 77.34 21.1 4.0 - - 2.0-'-*0.4 1.27___0.19

5 1998-08-03 15:15:22.5 39.55 77.10 24 4.4 - - 3.9-+0.7 1.084-0.15

6 1998-09-03 06:43:02.3 39.49 77.32 23.2 4.4 0.33 17.8±2.9 0.644-0.09

7 1998-10-02 17:01:57.7 39.51 77.59 33 4.2 - - 5.1-+0.8 0.794-0.11

8 1998-12-23 19:23:33.6 39.77 76.90 3.7 4.2 - - 9.6+1.4 0.47___0.06

Note: I) Intemationai Seismology Center (ISC); 2) Harvard University; 3) This

8O ° 85 ° I i 55°N

65°E 70 ° 75 ° I I

ZRN A CHK

\ \ T L (

KUR

MAKZ

WMQ

50 *

45 °

,10*

I i I i 3 5 °

Figure 2 Locations of earthquakes (dark dots) and

stations used in the paper

study.

Table 3 Coordinates and parameters of Lg Q of

stations used for inversion

Station ~/(o) 2el(o) QOLg

WMQ 4 3 . 8 2 1 8 7 . 6 9 5 462±56 0.51±0.04

AAK 4 2 . 6 3 9 74.494 3 5 1 + 8 7 0.3620.10 TLG 43.230 77.230 3495:86 0.3220.10

MAKZ 4 6 . 8 0 8 8 1 . 9 7 7 3002:27 0.4420.04 KUR 5 0 . 7 1 5 78.620 553±72 0.1420.08

VOS 52.723 70.980 5 6 9 + 5 8 0.1720.06 ZRN 52.951 69.004 550:i:57 0.19-2-0.06

CHK 5 3 . 6 7 6 70 .615 6032:65 0.1120.07

The method described in section 2 was used to inverse M0 and fi values of all eight earthquakes as well as QoLg and values for the paths from Jiashi to all eight stations simultaneously. The model parameters that should

be inversed totaled 32. For the calculation of source spectra using equation (5), p and Vs were taken to be 3.0 g/cm 3 and 3.75 km/s (equivalent to S-wave velocity of the lower crust), respec

I I I t I I I ] 0 ~ 0 100 200 300 400 500 600 10 3

t / s

10-4

i0_~

~ I0 ~

10.~c

10o-~ 10-~ 10 o 10 z .f / Hz

I 10 z

Figure 3 Illustration of data used for inversion Left: Velocity window used to isolate Lg wave trains. The seismogram demonstrated here is the ZRN recording of 1998-10-02 Jiashi earthquake (see Table 1). The epicentral distance to ZRN is approximately 14.5 °. Right: Respective Lg displacement spectrum versus noise spectrum. The noise spectrum was obtained using the noise recording within the time window just prior to the P arrival time and of the same length as the Lg window


tively. The results of inversion of source and path attenuation parameters are given in Table 2 and 3, respectively.

Results of inversion can fit the observed Lg displacement spectra quite well. As an example, Figure 4 illustrates the fitting for spectra of one of the earthquakes. It can be seen that Lg spectra of various stations are all well fitted.

10

E I0 ~

1 0 "

I0"4

'.'2 e

- . , I 0 ~

10 ~

w,

10-~ A A K TLG

i I I I l l i i l I I I I I I I I l l t I I

10 ° 1 0 ~ 10 ° f~ Hz f~ Hz

M A K Z

I I I I J I I I J I 1 0 " 10 °

f /Hz

10 '~

10-~

10 ~

l O l

l O ~

E - . . ] 0 6

lO -~

I0 4

E 1 0 ~

10 ~

I I i , , ~ , , ] t

] 0° f /Hz

WMQ I I I I I I I l l [

I0 ~ 10 ° f ! Hz

J , , , ,,,,I ,

1 0 t 10 o

f / H z

i0 ~

w.

E

QIO ~ %

i0-8

10 - I

~ o 10 '

2 ZRN '~ I 0 ~

I I I I I l i l t I

1 0 °

f / t f z

CHK ~'~ I I I I I I I 1 [ I

1 0 i lO o f~ l l z

Figure 4 Synthetic Lg spectra (real lines) for the Jiashi earthquake occurred at 04:40:39.3 on August 2, 1998 recorded at all the eight stations in Central Asia v e r s u s the observed (dashed lines) Synthetic Lg spectra were computed using the respective inversion results

Resulted values of apparent QoLg and #7 are consistent with tectonic features of various paths. As guided waves in the crust, the amplitudes of Lg wave trains are affected not only by the intrin- sic attenuation due to nonelasticity of rocks under the earth, but also by variations of topography and crustal thickness along propagation paths. In mountainous regions where variations of topography and crustal thickness are large, Lg waves attenuate quickly due to energy leakage; while in


platform regions where variations of topography and crustal thickness are small, Lg waves attenuate slowly. For the eight stations studied in the paper, the paths to AAK, TLG and MAKZ mainly propagate through the mountainous and tectonically active area of Tianshan Mountain. The obtained apparent QoLg values for the three paths are relatively small and comparable to each other if their uncertainties are considered. The path to WMQ mainly propagates through the border region between Tarim Basin and Tianshan Mountain. In this region, the gradient direction of crustal thickness is approximately perpendicular to the extension direction of Tianshan Mountain. So the variation of crustal thickness along the path to WMQ is smaller than that along the paths to MAKZ, AAK and TLG. Consequently, QoLg value for the path to WMQ is significantly bigger than that for paths to MAKZ, AAK and TLG. Additionally, the obtained Qoeg value for the path from Jiashi to WMQ is comparable to the QoLg values for the paths with similar tectonic characteristics obtained by Xie, et al (1996) and Cong, et al (1996). After crossing the Tianshan Mountain, the paths to stations KUR, VOS, ZRN and CHK largely propagate through the stable area of Kazak platform where variations of crustal thickness are small; consequently the apparent QoLg values for

these paths are relatively big and comparable to each other. Based on r/values obtained, it seems that Lg Q is more dependent upon frequency in the Tianshan Mountain than in the Kazak platform.

However, Xie (1998) pointed out that apparent 7] values obtained by Lg spectral inversion could tend to decrease with increasing epicentral distance. This needs further investigation in the future.

The seismic moments obtained in the 10 ~

paper correlate well with that obtained by Harvard University using the so-called centroid moment tensor (CMT) inversion (Figure 5). However, the M0 values obtained by Lg .~ spectral inversion are systematically smaller z lo" than the values obtained by CMT. The former ones are averagely and approximately about 40% of the later ones. Similar result was also obtained by Xie (1998). This is probably due 10,~ to the fact that seismic moment estimated by 1°" CMT inversion measures the maximum radiation strength of source in different directions, while seismic moment estimated by Lg spectral inversion measures the average radiation strength. It may be loosely assumed that

M0(Lg) = M0(CMT)-Ro~ where M0(Lg) and

Figure 5

• O

i0 'r i0,~

M0 ( C M T ) / N m

Logarithm of M0(Lg) versus logarithm of M0(CMT) • denotes the result before correction by average SV radiation coefficients; o indi-

cates the result after correction. More de-

tails are explained in the text

M0(CMT) are seismic moments estimated by Lg spectral and CMT inversions respectively, and

Ra~ is average radiation coefficient of source. Only the vertical component of Lg waves at re-

gional stations was involved here, so Ro, is likely to take average radiation coefficient of re-

gional SV waves as discussed by Boore and Boatwright (1984). They computed R~of re-

gional SV waves for three kinds of typical focal mechanisms, i.e. the strike slip on a vertical fault, dip slip on a 30 ° dipping fault and oblique slip (rake angle=45 °) on a 45 ° dip ping fault.

The Ro, of regional SV waves for three kinds of focal mechanisms are 0.20, 0.46 and 0.43, re-

spectively. The focal mechanisms derived from CMT solutions for some of the earthquakes in

Table 2 are listed in Table 4. Based on these solutions, it seems that Ro, =0.40 can reasonably


Table 4 Focal mechanisms of some of earthquakes studied account for the systematic deviation between M0(Lg) and M0(CMT). Figure 5

Nodal plane 1 Nodal plane 2 No. shows that M0(Lg) agrees well with

Strike Dip Slip Strike Dip Slip M0(CMT) after the correction by average

1 339° 81° 178° 70° 88° 9° r a d i a t i o n c o e f f i c i e n t . However, t h e r e s u l t 2 243 ° 23 ° 79 ° 75 ° 68 ° 95 ° 3 231 ° 30 ° _5 ° 13 ° 66 ° _]08 ° also has the implication that possibly there 6 234 ° 32 ° -90 ° 54 ° 58 ° - 9 0 ° is no obvious difference in Lg excitation

Note: (1) Numbers in the first column refer to event indices in Table 2; between strike-slip and dip-slip earth- (2) The focal mechanisms are from CMT solutions of Harvard quakes. University. The relationship between uncorrected

M0(Lg) and surface wave magnitude Ms is illustrated in Figure 6a, which shows that M0(Lg) and Ms are linearly correlated. The preliminary result about the relationship between M0(Lg) and Ms obtained by regression is

lg(M 0) = (1.00 + 0.27)M s + (11.54 + 1.28) (10)

where lg is the logarithm operation to the base 10, and Mo is measured in N-m. As illustrated in Figure 6b, the obtained f¢ values generally tend to decrease as seismic mo-

ment increases. The preliminary result about the scaling relationship between f~ and M0 is

fc o¢ M0 -0'42!'0"22 " Some earlier researches suggested that approximately fc is inversely proportional

to the 1/4 power (Xie, et al, 1996; Cong, et al, 1996) or 1/3 power (A1-Egabi, et al, 2001) of M0. Due to large uncertainty of power exponent in our result, further researches based on more events are needed to resolve the ambiguity inf¢ and M0 scaling.

(a) 1 .51 (b) _. 1°~'[ " lg(M0 ) = 1.00Ms + 11, 54 • I. 0 0.42 lg(tVL,) q- 7.47

1 0 ~ q I I I I I 0 I 4.0 5.0 6.0 10" 10 ~ 10 ~

Ms MJN.m

Figure 6 Logarithm of M0 versus Ms (a); Logarithm off¢ values versus logarithm of Mo for the earthquakes studied (b)

3 Conclusions

Using Lg displacement spectra of clustered earthquakes occurred within the same source area and recorded by various regional seismic stations, a multi-event and multi-station inversion method has been presented in the paper to simultaneously estimate seismic moments and source comer frequencies of these earthquakes as well as path-variable apparent Lg Q models. Numerical tests have shown that this method may be applied to Lg spectral inversions in the case like this.

Using this method we have calculated M0 and f¢ values of eight Jiashi earthquakes as well as

QOL~ and 77 values for the paths from Jiashi to eight stations in Central Asia. The obtained QoLg values are consistent with the tectonic features of corresponding propagation paths. The paths from Jiashi to AAK, TLG and MAKZ mainly propagate through the mountainous Tianshan area.

Relatively smaller values of QoLg, i.e. 351+87, 349+86 and 300+27 were obtained for the paths to these three stations, respectively. The paths to stations KUR, VOS, ZRN and CHK largely propa-

Supp. Jin Ping, et al: ESTIMATING SEISMIC M O M E N T S A N D L G Q USING L G SPECTRA 31

gate through the stable area of Kazak platform. Consequently, relatively bigger QOLg values, i.e.

553_+72, 569+_58, 550+_57 and 603_+65 were obtained for the paths to these four stations, respectively. The path to WMQ is basically along the border region between Tianshan Mountain and Tarim Basin. As a consequence, an intermediate QOLg value of 462+_56 was obtained for this path. For the power-law frequency dependence of Lg Q, r/values were estimated to be around 0.4 for the paths to AAK, TLG~ MAKZ and WMQ and 0.1 ~0.2 for the paths to KUR, VOS, ZRN and CHK.

M0 values obtained by Lg spectral inversion correlate well with CMT results. However, M0 values from Lg spectra are averagely and approximately about 40% of the values from CMT. This is probably due to the fact that seismic moment estimated by Lg spectral inversion measures the average radiation strength of source, while seismic moment estimated by CMT inversion measures the maximum radiation strength of source in different directions. After the correction by a typical value of average radiation coefficient for regional SV waves as discussed by Boore and Boat- wright (1984), M0 values obtained by Lg spectral inversion agree well with those obtained by CMT inversion.

The preliminary results also have shown that lg(M0) is approximately proportional to the surface wave magnitude Ms. The work in the future is try to process more events; then on the basis of more extensive inversion results, the relationships between lg(Mo) and magnitudes in various defi- nitions may be further approached; and at the same time, the utilization of Lg spectral inversion in magnitude estimation and event identification for regional seismic events may be further investi- gated as well.

Acknowledgements: Heartfelt thanks to the anonymous reviewers of the paper for their valuable advices.

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Estimating seismic moments and Lg Q using Lg spectra