The study of the dynamic parameters of earthquakesources, such as the seismic moment
å
0
, the corner fre-quency
f
c,
and the drop in stress
Δ
, makes it possible tounderstand better the nature of the processes of accu-mulation and relaxation of tectonic stresses in the seis-moactive regions. The stress drop during the seismicevent is very sensitive to the type of regional stressesand the strength characteristics of a medium, and thelocal temporal variations of this parameter can be usedfor the analysis of seismic hazard [Kanamori, 1981;Sato and Masuda, 1981; Parolai et al., 2001], the mostsocially important parameter, obtained as a result of thestudies of a seismic process.
The first spectral determination of seismic momentwas made by K. Aki [Aki, 1966] for the Niigata earth-quake on June 16, 1964 (
å
= 7.5) according to therecords of surface
G
-waves. Later D. Brune proposed amodel of the source of an earthquake, according towhich, the spectrum of displacements of transverse
S
-wave in the far-field zone is connected with thesource parameters such as the seismic moment, thestretch, and the stress drop by a number of simple rela-tions [Brune, 1970; 1971]. Hanks and Wyss extendedthis model, using a spectra of teleseismic longitudinal
ê
-waves [Hanks and Wyss, 1972]. Thatcher and Hanks[Thatcher and Hanks, 1973] worked out in detail themethodology for the calculation of source parameters
on the basis of the spectra of transverse
S
-waves forregional earthquakes (
M
L
= 2.0–7.0). At present, themethod of determining the source parameters based onthe spectra of the displacement of the body and surfacewaves is extensively used for the study of the strong andweak earthquakes, recorded by the teleseismic, regional,and local networks of seismic stations, and also for labo-ratory studies [Riznichenko et al., 1976; Moskvina, 1978;
Daghestan
…, 1980
; Aref’ev, 1985; Aptekman et al.,1989; Zakharova et al., 1990; Trifunac, 1972; Kanamori,1981; Archuleta et al., 1982; Shapira and Hofstetter, 1993;Zobin and Havskov, 1995; Margaris and Hatzidimitriou,2002; and others].
This study aims to determine the source parametersof the earthquakes of the Baikal rift system, one of themost seismically active regions of Russia [
The Com-plete Set of Maps
…, 1999
]. In spite of the high seismicpotential of the region, the works regarding the deter-mination of the dynamic parameters of earthquakesources by spectral methods were practically not con-ducted in this region because of the absence of a digitaldata recording system. Two studies in this directionwere carried out by L.G. Danzig and E.A. Steimann forseparate regions of the Baikal rift system: the Barguzinand Northern Muya Troughs and their surroundings. Inthe first case, the data of highly sensitive seismic sta-tions with magnetic recording were used, and in thesecond case, the networks of local stations were used[Danzig, 1981; Kochetkov et al., 1985]. The highly sen-
Source Parameters of the Earthquakes of the Baikal Rift System
A. A. Dobrynina
Institute of the Earth’s Crust, Siberian Branch, Russian Academy of Sciences, ul. Lermontova 128, Irkutsk, 664033 Russia
Received September 1, 2008; in final form, February 9, 2009
Abstract
—The dynamic parameters of the earthquake source—the seismic moment, the moment magnitude,the source radius, the stress drop, and the amplitude of displacement—are determined by the amplitude Fourierspectra of the body shear waves (
S
-waves) for 62 earthquakes of the Baikal rift system with the energy class of
K
P
= 9.1–15.7. In the calculations I used the classical Brune model. The seismic moment of the earthquakesbeing investigated changes from
3.65
×
10
11
N m to
1.35
×
10
18
N m, and the radii of earthquake sources varyfrom 390 m to 1.84 km. The values of the drop in stress
Δσ
grow with an increase in the seismic moment up to
1.7
×
10
8
Pa. For the group of weak earthquakes (
Mw
= 1.7–3.3), extremely low values of the drop in stress
10
3
–
10
4
Pa are observed. The maximum amplitude of displacement in the source amounts to 5.95 m. The empiricalequations between the seismic moment and the other dynamic parameters of the source are determined. Theregional dependence of the seismic moment and energy class is obtained:
±
0.60 = 1.03
K
P
+ 3.17. Thecharacter of the relationship between the seismic moment and the corner frequency indicates that the classicalscaling law of the seismic spectrum for the earthquakes in question is not fulfilled. The obtained estimates ofthe dynamic parameters are in satisfactory agreement with the published data concerning the analogous param-eters of the other rift zones, which reflects the general regular patterns of the destruction of the lithosphere andthe seismicity in the extension zones of the lithosphere.
PACS numbers: 91.30.Px
DOI:
10.1134/S1069351309120064
M0log
1094
IZVESTIYA, PHYSICS OF THE SOLID EARTH
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DOBRYNINA
sitive digital instrumentation of the seismic stations ofthe region in 1998–2003 improved appreciably the con-ditions of the recording of seismic events in the Baikalrift system [Masalskii et al., 2007] and made it possibleto conduct the spectral analysis of the wave forms[Dobrynina, 2008].
1. THE STUDY AREA
The Baikal rift system is located in North Eurasiaand is the second largest continental rift system in theworld. It stretches along the edge of the Siberian plat-form, 1600 km from North Western Mongolia, throughthe mountain structures of East Siberia to South Yaku-tia, and consists of a linear system of uplifts and basins,limited by the faults of the predominantly faulting kine-matic type [Logatchev and Florensov, 1978]. In theneotectonic sense the Baikal rift system is confined to
the boundary of the North Eurasian and the Amur litho-spheric plates, the high contemporary mobility betweenwhich determines the seismic process taking placethere. It is characterized by a high level of seismicactivity. Since 1950, according to the data of the BaikalRegional Seismological Center of Geophysical Surveyof the Siberian Branch, of the Russian Academy of Sci-ences, 13 earthquakes with a magnitude of
Ms
≥
6.0
occurred there [http://www.seis-bykl.ru] (Fig. 1).According to historical evidence, events with a magni-tude of up to 8.2 are also confined to the region beinginvestigated [
New Catalog
…, 1977
]. The last strongevent occurred on August 27, 2008 in the South Baikalregion and according to the data of different seismolog-ical agencies it had a moment magnitude
Mw
from 6.1to 6.3 [http://www.isc.ac.uk]. The maximum quantities ofearthquakes are confined directly to the rift system (Fig.1). The number of weak and moderate events (with an
Fig. 1.
Seismicity of the Baikal rift system in 1950–2003. The map of the earthquake sources is taken from the official site of theBaikal Regional Seismological Center of Geophysical Survey of the Siberian Branch, Russian Academy of Sciences[http://www.seis-bykl.ru/]. For the strongest events (
Ms
≥
6.0), the solutions of the focal mechanisms are shown, obtained from thepolarities of the first arrivals of the longitudinal waves [Solonenko et al., 1993; Mel’nikova and Radziminovich, 1998; Radziminov-ich and Mel’nikova, 2005], for the events, denoted by asterisks, the solution is obtained by the National Earthquake InformationCenter of the United States (NEIC) by the method of modeling of wave forms; for each event the date is shown (month/day/year).The map symbolsare as follows: (
1
) the stereogram of the focal mechanism (in the projection of the lower hemisphere), the emer-gences of axes of principal stresses are designated by points, the regions of compression waves are filled; (
2
) the state boundary;(
3
) large cities.
Energy class, K Magnitude,M
K
=13,
M
= 4.8–5.3
K
= 9–12
K
=14,
M
= 5.4–5.9
K
=15,
M
= 6.0–6.8
Ms
≥
6.0
1
2 3
April 4, 1950
Russia
ChinaMongolia
April 4, 1950August 29, 1959
June 27, 1957
March 21, 1999
August 21, 1994
November 10, 2005*
January 5, 1958
November 13, 1995
February 25, 1999
August 27, 2008*
60
°
56
°
52
°
48
°
100
°
104
°
108
°
112
°
116
°
120
°
Chita
IrkutskJanuary 18, 1967
September 14,1958
IZVESTIYA, PHYSICS OF THE SOLID EARTH
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SOURCE PARAMETERS OF THE EARTHQUAKES OF THE BAIKAL RIFT SYSTEM 1095
energy class of
ä
ê
≥
7
) is rather big: on the average,approximately three–four thousand earthquakes peryear [Masalskii et al., 2007]. The earthquake sources ofthe Baikal rift system are localized in the lower part ofthe Earth’s crust (at depths of 15–30 km) with the max-imum in the range of 15–20 km [Radziminovich et al.,2003]. The solutions of the focal mechanism of earth-quakes [Misharina and Solonenko, 1977; Mel’nikovaand Radziminovich, 1998; 2007] show the predomi-nance of normal fault displacements in accordance withthe kinematics of the seismoactive faults (Fig. 1). Theresults of structural-geological studies [Sherman andDneprovskii, 1989; San’kov et al., 1997], measure-ments by the method of GPS-geodesy [San’kov et al.,1999], and the calculations of the seismotectonic defor-mations [Mel’nikova and Radziminovich, 2007] indi-cate that at the center of the rift system the stretchingmode prevails. For the wings, the tendency of thestrengthening of the role of shear tectonic stresses ischaracteristic [Sherman and Dneprovskii, 1989].Oblique extension with respect to the axis of rift struc-tures is established for the northeastern wing of the riftsystem and a strike-slip with compression is revealedfor its southwestern wing [San’kov et al., 1997; 1999;Mel’nikova and Radziminovich, 2007].
2. MATERIALS AND METHODS
The Data
The numerical data used in the present work wereobtained by a permanent regional network of digitalseismic stations of the Baikal Regional SeismologicalCenter of Geophysical Survey of the Siberian Branch,Russian Academy of Sciences (international synopticcode BYKL [Masal’skii et al., 2007]). The networkconsists of 23 stations, of which 19 are located directlywithin the limits of the rift system (Fig. 2). The stationsare equipped with the digital seismic instrumentation ofthe “Baikal-10, 11” type, developed in the BaikalBranch of the Geophysical Service of the SiberianBranch, Russian Academy of Sciences. The equipmentset has three short-period seismometric channels ofincreased sensitivity (SM-3, SM-3KV seismometers),which record velocity from 0.01–0.1
μ
m/s up to 100–1000
μ
m/s; and three rough channels (OSP-2M seis-mometers) for recording acceleration from 50–500
μ
m/s
2
up to 100–250 cm/s
2
. The sampling rate is 100counts per second [Masalskii et al., 2007].
Since with regional recording (the epicentral dis-tances
Δ
≤
1000 km), the amplitude of the oscillations inthe transverse wave, as a rule, exceeds appreciably theamplitudes of the longitudinal waves [Kochetkov et al.,1985], the
S
-waves were used for calculating the spec-tra of displacements. From the catalog of earthquakes,prepared by the Baikal Regional Seismological Centerof Geophysical Survey of the Siberian Branch, RussianAcademy of Sciences [http://www.seis-bykl.ru],62 events were selected with energy classes of
K
P
=
9.1–15.7 (Fig. 2, table), which occurred in the limits ofthe Baikal rift system in 2003–2006. The epicentral dis-tances, depending on the energy class of the earth-quake, vary within a range of 70–1000 km. The selec-tion of data for spectral analysis was carried out takinginto account the following conditions: (1) the signal-to-noise ratio is no less than 5 : 1; (2) the clear arrival ofthe incident transverse wave (
Sg
phase) on the back-ground of the longitudinal wave; and (3) the number ofstations, used for determining the source parameters ofearthquake, must be no less than four (
N
≥
4
). For con-structing the spectrum of the transverse
Sg
-wave, therecording area was selected from the moment of itsarrival up to a decrease in the amplitude up to 1/3 of itsmaximum value. The spectra were calculated with theaid of the Fourier transform of the horizontal compo-nents of the records at each station. The spectra of dis-placement were obtained by the division of the spec-trum of velocities or acceleration by
2
π
f
or
(2
π
f
)
2
,respectively, where
f
is the frequency in Hz.
The Method
For calculating the seismic moment, the standardmodel of circular dislocation proposed by Brune wasapplied [Brune, 1970; 1971]. In accordance with it, thespectrum of displacements in the far-field zone can bedescribed by a constant amplitude (
Ω
0
) up to a certainfrequency (
f
c
), which is known as the corner frequency.It decreases as
f
–2
for frequencies, greater than the cor-ner frequency [Haskell, 1964; Aki, 1967 and others].Here the term “far-field zone” means a region forrecording seismic emissions, for which the “source–receiver” distance and the wavelength are considerablylarger than the maximum sizes of the earthquake’ssource. This means that the spectrum of displacementsin the far-field zone for the model with the asymptotesof
f
–2
can be written as follows:
(1)
The level of the spectral amplitude in the range oflow frequencies
Ω
0
(cm s) and the seismic moment
M
0
(dyne cm =
10
7
N m) are connected by the relation-ship [Haskell, 1964; Brune, 1970]:
(2)
where
ρ is the density, ρ = 2.7 g/cm3 [Riznichenko,1985], VS is the velocity of the transverse waves for theBaikal rift system VS = 3.55 × 105 cm/s [Golenetskii andNovomeiskaya, 1975] and Rθϕ is the directivity func-tion of the source emission, determined from the solu-tion of focal mechanism. It is known that the focalmechanism exerts considerable influence on the ampli-tudes of the seismic waves, recorded at a station, and itcan lead to a change of the seismic moment by severaltimes [Vidale, 1989]. In our case, in order to minimize
Ω f( ) Ω01
1 f / f C( )2+----------------------------.=
M0
4πρVS3Ω0
Rθϕ-----------------------,=
1096
IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 45 No. 12 2009
DOBRYNINA
Lake Baikal
The AngaraIrkutsk
2
6
1218
351
13
40
40
17
16
19
19
25
15
143323
21
20
5 4
563 3 26
26 30
60°
56°
52°
48°120°
116°112°108°104°100°
16
13–15
12
11
9–10
– 1
– 2
– 3 – 4
[1] [3]
[2]
River
Fig. 2. Epicenters of the earthquakes being investigated. For some events, the focal mechanism according to the data of the differentseismological agencies are shown: [1] Harvard University (the method of tensor of moment centroid) [http://www.seismology.har-vard.edu], [2] the National Earthquake Information Center of the United States (the method of modeling of wave forms)[http://earthquake. us gs. Govl], [3] the Institute of the Earth’s Crust, Siberian Branch, Russian Academy of Sciences (the methodof polarities of the first arrivals of longitudinal waves) [http://www.isc.ac.uk]. The map symbolsare as follows: (1) the energy classaccording to Rautian (KP); (2) the stereogram of focal mechanism as in the figure caption to Fig. 1; (3) the seismic stations; and (4)the state boundary.
the error in the determination of the seismic moment,for the events with a known individual solution of thefocal mechanism, their own coefficients of directivity ateach station were calculated [Aki and Richards, 1980].In the absence of the determination of the focal mecha-nism under the assumption of self-similarity of thestress-strain state [Mel’nikova, 2008] the average coef-ficient of directivity was calculated taking into accountthe focal mechanism of the earthquakes, localizednearby. In the absence of such events the average coef-ficient of directivity of emission for the transversewaves was taken: Rθϕ = 0.62 [Fletcher, 1982].
A radius of the source of an equivalent circular dis-location r (km) is connected with the corner frequencyfc (Hz) by the following relationship [Brune, 1970]:
(3)
The stress drop Δσ (dyne/cm2 = 0.1 Pa) is connectedwith the seismic moment and the source radius by therelationship [Brune, 1970; 1971]:
(4)
The amplitude of the displacement along the faultD (cm) is derived from the seismic moment (dyne cm)and the source radius (cm) by the equation:
(5)
r2.34VS
2π f C----------------.=
Δσ7M0
16r3----------.=
DM0
μS-------,=
IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 45 No. 12 2009
SOURCE PARAMETERS OF THE EARTHQUAKES OF THE BAIKAL RIFT SYSTEM 1097
IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 45 No. 12 2009
SOURCE PARAMETERS OF THE EARTHQUAKES OF THE BAIKAL RIFT SYSTEM 1099
where S = πr2 is the area of the circular dislocation andμ = 3.2 × 1011 dyne/cm2 is the shear Young’s modulus ofelasticity [Riznichenko, 1985].
For determining the spectral characteristics (thespectral amplitude Ω0 and the corner frequency fc) it isnecessary to consider the influence of external factorson the recording of the earthquake. In the general case,the spectrum of displacements, recorded at a seismicstation, can be represented in the form of the product ofthe source spectrum and a number of simple filters:
(6)
where Ω(f) is the source spectrum, I(f) is the amplitude-frequency characteristic of a recording device, G(f) isthe correction for attenuation of body waves as a resultof the geometric spreading, P(f) is the inelastic attenua-tion along the course of seismic wave propagation, andFS is the influence of free surface [Trifunac, 1972;Thatcher and Hanks, 1973; Aptekman et al., 1989; andothers]. The amplitude-frequency characteristics of therecording instruments are given by the Baikal Regional
S f( ) Ω f( )I f( )G f( )P f( )FS,=
Seismological Center of Geophysical Survey of theSiberian Branch, Russian Academy of Sciences. Thegeometric spreading and inelastic attenuation along theway of the propagation of the seismic wave path wascalculated by the formula [Douglas and Ryall, 1972]:
(7)
where Δ is the hypocentral distance, QS is the qualityfactor of a medium (for the transverse waves QS = 400[Gaiskii et al., 1977]). Following the works [Trifunac,1972; Thatcher and Hanks, 1973; and others] the factorof influence of the free surface is FS = 2.
The spectrum parameters, such as the amplitude inthe range of low frequencies (Ω0) and the corner fre-quency (fc), were determined via the comparison of thetheoretical and observed spectra, corrected for theamplitude-frequency characteristic of the instrument,the geometric spreading, and inelastic attenuation onthe “source–station” by formulas (6)–(7) (Fig. 3).
Notes: The sequential numbers of the earthquakes being investigated are given in column 1, the dates (month, day, year) and the time inthe source (hour, minute) are given in columns 2 and 3, respectively, and the energy class Kp is presented in column 4. The dates,the time in the earthquake source, and the energy class of the earthquakes in question are taken from the current catalog, presentedon the official site of the Baikal Regional Seismological Center of Geophysical Survey of the Siberian Branch, Russian Academy ofSciences [http://www.seis-bykl.ru]. The moment magnitude according to the data of Harvard University [1] and the National Seis-mological Information Center of the United States [2] are presented in column 5. The presence of the individual solution of thefocal mechanism for the earthquake is shown in column 6. The solutions of focal mechanisms are obtained in the international seis-mological agencies: [1] Harvard University [http://www.seismology.harvard.edii], [2] the National Seismological InformationCenter of the United States [http://earthquake.usgs.gov], [3] the Institute the Earth’s Crust, Siberian Branch, Russian Academy ofSciences (Irkutsk) [http://www.isc.ac.uk]. The values of seismic moment, obtained in the present work, are presented in column 7,the standard deviations of the logarithm of seismic moment according to [Archuleta et al., 1982] are presented in column 8, themoment magnitudes according to [Kanamori, 1977] are given in column 9; the radius of circular dislocation according to [Brune,1970] are presented in column 10; the root-mean-square deviations of the logarithm of the corner frequency according to [Archuletaet al., 1982] are given in column 11; the drops in the stress according to [Brune, 1970; 1971] are presented in column 12; the ampli-tude of displacement along the fault according to [Aki, 1966] is presented in column 13; the number of stations, used for determin-ing the source parameters is given in column 14.
1100
IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 45 No. 12 2009
DOBRYNINA
The mean seismic moment and the corner frequencyof the earthquake were determined from the values ofseismic moments and corner frequencies, obtained atdifferent stations, according to the formula [Archuletaet al., 1982]:
(8)
where N is a number of stations, ïi is the seismicmoment or the corner frequency, determined at the ithstation. According to the classical statistical approach,for the values in question the standard deviation of the
X0⟨ ⟩ anti1N---- Xilog
i 1=
N
∑ ,log=
logarithm σ[ ] was determined [Archuleta et al.,1982]:
(9)
The obtained mean values of seismic moments andcorner frequencies were used for determining theradius of circular dislocation, the value of the stressdrop and the amplitude of the displacement along thefault.
X( )log
σ Xlog( ) 1N 1–------------- Xi X⟨ ⟩log–log( )2
i 1=
N
∑1/2
.=
103
102
101
100
100 101 10210–1
Ω0 = 445.063 cm sKumoraΔ = 103 kmazimuth 343°
σ = 0.180
fc = 1.36 Hz
Dis
plac
emen
t, cm
s
103
102
104
100 101 10210–1
Ω0 = 34204.403 cm s
SeveromuiskΔ = 176 kmazimuth 41°
s = 7.492
fc = 1.88 Hz
103
102
101
104
100 101 10210–1
Ω0 = 3026.671 cm sCharaΔ = 461 kmazimuth 60°
σ = 0.155
fc = 0.89 Hz
101
100
10–1
10–3
100 101 10210–1
Ω0 = 8.407 cm s
NelyatyΔ = 302 kmazimuth 57°
σ = 0.001
fc = 1.26 Hz
Dis
plac
emen
t, cm
s
10–2
Frequency, Hz Frequency, Hz
105
1 2 3 4
Fig. 3. Spectra of displacements for the earthquake of November 10, 2006 (at 6.14 p.m.) recorded at different seismic stations. Themap symbolsare as follows: (1)–(3) the spectra, corrected for the amplitude-frequency characteristic of the instrument, for geomet-ric spreading, and inelastic attenuation on the “source–station” path according to formulas (6)–(7) with the implication of threemodels of quality: (l) a constant frequency-independent value Q = 400 for the Baikal rift system according to [Gaiskii et al., 1977];(2)–(3) frequency-dependent quality models, presented in the works [Zobin and Havskov, 1995; Margaris and Hatzidimitriou,2002], respectively; (4) the theoretical spectrum. For each station the following parameters are given: the hypocentral distance (Δ,km), the azimuth (degrees), and also the values of the spectral amplitude determined from spectrum 1 in the region of low frequen-cies (Ω0, cm s) and the corner frequency (fc, Hz). The standard deviation of the observed (1) and theoretical (4) spectra is shown inthe frames.
IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 45 No. 12 2009
SOURCE PARAMETERS OF THE EARTHQUAKES OF THE BAIKAL RIFT SYSTEM 1101
3. THE RESULTSThe results of determinations of source parameters
are presented in Table 1. The seismic moment of theearthquakes being investigated (KP = 9.1–15.7) changefrom 3.65 × 1011 N m to 1.35 × 1018 N m. The values ofthe standard deviation of the logarithms of å0 and thecorner frequency fc derived from relationship (9), onaverage, amount to 0.57 and 0.19 logarithmic units,respectively.
The Moment Magnitude
In Fig. 4, the values of the moment magnitudes Mw,calculated by me, are compared with the values of Mw,obtained by the method of the centroid moment tensorhttp://www.seismology.harvard.edu. The moment mag-nitude was obtained from the seismic moment å0 (Nm) by the formula of H. Kanamori [Kanamori, 1977]:
Mw = (10)
In spite of the use of different methods, satisfactoryagreement is observed between two determinationswithin the limits of magnitudes Mw = 5–6. The regres-sion equation is as follows:
Mw = 1.09 MwCMT – 0.47 (11)
(the correlation coefficient is equal to R = 0.9l; accord-ing to the estimate by the Student criterion, the correla-
23--- M0log 6.03.–
tion coefficient is significant with a probability of êα =0.95).
The Seismic Moment and the Energy Class
The relation of the seismic moment M0 (N m), cal-culated from the spectra of displacements of S-waves,and the energy class Kp, obtained from the amplitudesof displacement, takes the form:
+ 0.60 = 1.03KP + 3.17 (12)
(R = 0.93, êα = 0.95). Variations in the logarithm of the seis-mic moment ±0.60 include 68% of the obtained values.
The Seismic Moment and the Radius of the Source
The radii of earthquake sources, obtained accordingto the Brune formula [Brune, 1970; 1971], vary from390 m to 1.84 km for earthquakes with KP = 9.1–15.7,respectively. The dependence of the seismic momentå0 on the radius of the earthquake source r is shown inFig. 5a and the regression equation for the earthquakesbeing investigated takes the form:
± 0.90 = 8.85 + 15.16 (13)
(R = 0.77, êα = 0.95). Variations in the ± 0.90include 66% of the obtained values.
M0log
M0log rlog
M0log
Mom
ent m
agni
tude
Moment magnitude, [CMT]
Fig. 4. A comparison of the determinations of moment magnitudes, obtained in this study according to the data of the wave shapesof the regional BYKL network, and presented in the catalog of the CMT solutions of Harvard University [http://www.seismol-ogy.harvard.edu]. For each event, the standard deviation is shown. The encircled numerals correspond to the ordinal numbers ofearthquakes in the table.
6.5
6.0
5.5
5.0
4.5 5.0 5.5 6.0
59
78
36
87
83
8
48
44
1102
IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 45 No. 12 2009
DOBRYNINA
The Seismic Moment and the Drops in the Stress
The obtained values of the drops in the stress Δσaccording to Brune’s model [Brune, 1970; 1971] varywithin the limits from 1 × 103 to 1.7 × 108 Pa for eventswith KP = 9.1–15.7, respectively, which agrees with thedata, obtained by Danzig for the region of the Barguzintrough [Danzig, 1980] and by the other authors for anumber of rift zones [Shapira and Hofstetter, 1993;Zobin and Havskov, 1995; Margaris and Hatzidimi-triou, 2002 and others]. The linear regression analysisgives the following relationship between the seismicmoment M0 (N m) and the stress drop Δσ (Pa):
± 0.30 = 1.26 + 15.37 (14)
(R = 0.98, êα = 0.95). The ± 0.30 includes 82%of the obtained values.
The Seismic Moment and the Amplitudeof the Displacement
For the group of weak events (Mw = l.7–3.8), thetheoretical values of the amplitudes of displacement areobtained within the range of 10–3–10–1 cm. Actually,such slips in the Earth’s crust are imperceptible. Themaximum value of displacement (5.95 m) is deter-mined for the strongest of the events considered (onNovember 10, 2005, 19 : 29, Ms = 5.7). The amplitudeof displacement along the fault D (cm) as a function ofseismic moment å0 (N m) is shown in Fig. 5b. Theregression equation takes the form:
± 0.20 = 1.16 + 14.95 (15)
(R = 0.99, êα = 0.95). Variations in the ± 0.20
include 81% of the obtained values.
4. RESULTS AND DISCUSSION
The results of determinations of seismic moment inthe Baikal region are presented in Fig. 6: the values ofå0, calculated by me, the data of Danzig, obtained fromthe spectra of S-waves, for the weak earthquakes of theBarguzin trough (the energy class äP = 5.0–9.0) [Dan-zig, 1981], the regression dependence of M0 and äP,established by Steimann for the events of the NorthMuya region (KP = 8.0–13.0) from the results of thespectral analysis of SV-waves [Kochetkov et al., 1985]:
± 0.6 = 0.47KP + 10.65 = 0.85å + 12.53, (16)
where å0 (N m) is the seismic moment and M is themagnitude. Figure 6 also depicts the regression rela-tionship of the seismic moment expressed in N m andof the energy class, obtained by Yu.V. Riznichenko onthe basis of global data [Riznichenko, 1985]:
± 0.6 = 0.9ä + 4.8 = 1.6å + 8.4. (17)
Good agreement is observed in the values of å0,determined in the present study and reconstructed from
M0log Δσlog
M0log
M0log Dlog
M0log
M0log
M0log
the dependence of Riznichenko. The results of Ste-imann in the range of low energy classes (KP = 8.0–11.0) exceed by more than an order of magnitude thedeterminations, obtained by the other researchers. Sucha divergence can be explained by the fact that in thework of Steimann (1) the spectra of SV-waves wereused and (2) the influence of low-velocity near-surfacelayer was taken into account. Furthermore, Steimannstudied the earthquakes of the local North Muya region,while the determinations presented in the present workwere carried out for events, localized throughout theentire rift system.
The results of the determinations of seismicmoments obtained by me were compared with the data,published for the other rift zones: for the rifts of theNorth Sea, the Dead Sea, and the Aegean Sea [Zobinand Havskov, 1995; Shapira and Hofstetter, 1993; Mar-garis and Hatzidimitriou, 2002]. In the work [Zobin andHavskov, 1995] the seismic moments of local earth-quakes (ML = 2.5–3.5) are obtained from the spectra oflongitudinal ê-waves; in the works [Shapira and Hof-stetter, 1993; Margaris and Hatzidimitriou, 2002], thevalues of å0 are calculated from the spectra of trans-verse S-waves for events with magnitudes of ML = 3.0–6.7 and ML = 4.9–6.3, respectively. For convenience, inthe comparison of the data of different regions, the localmagnitude ML was used. For the earthquakes of theBaikal rift system, the local magnitude is recalculatedfrom the energy class by the formula of T.G. Rautian[Rautian, 1960] and is equal to ML = 2.8–7.0. For therift of Aegean Sea, the values of local magnitudes areused from the Bulletin of the International Seismologi-cal Center (ISC); in the remaining cases, the values ofML were used, given in the works [Zobin and Havskov,1995; Shapira and Hofstetter, 1993]. The relationships“seismic moment–magnitude” for the regions indicatedare presented in Fig. 7.
The greatest data scattering is observed for weakevents (ML = 2.5–3.7.), which can partially beexplained by the use of the averaged coefficient ofdirectivity of seismic emission. In spite of this, as awhole, good agreement in the values of seismicmoment is noted for different rift zones: the relation-ship between the logarithm of seismic moment and thelocal magnitude for the Baikal rift system ( ±0.60 = 1.79ML + 7.63, R = 0.92, Pα = 0.95) includes 63%of all values. This makes it possible to state that thesource parameters of earthquakes in the rift systems arecharacterized by a particular generality, which reflectsthe common regular patterns of the destruction of thelithosphere and seismicity in the extension zones of thelithosphere.
Scaling Law of the Seismic Spectrum
The concept of scaling the seismic spectrum wasproposed for the first time by Aki [Aki, 1967]. It isbased on the assumption that all earthquakes have a
M0log
IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 45 No. 12 2009
SOURCE PARAMETERS OF THE EARTHQUAKES OF THE BAIKAL RIFT SYSTEM 1103
constant drop in stress, independently of the seismicmoment, in other words, the shape of the seismic spec-trum changes with the earthquake’s magnitude accord-ing to the following law:
(18)
where γ = 3. The comparison of seismic moments, cor-ner frequencies and the values of the drops in the stress
M0 f cγ– ,∝
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
Seis
mic
mom
ent,
N m
10–0.6 10–0.4 10–0.2 100 100.2 100.4
Source radius, km
Δσ = 0.001 MPa
Δσ = 0.01 MPa
Δσ = 1 MPa
1011
1012
1013
1014
1015
1016
1017
1018
1019
Seis
mic
mom
ent,
N m
10–3 10–2 10–1 100 102 103
Amplitude of displacement, cm101
(a)
(b)
Fig. 5. Relation of (a) the logarithm of seismic moment å0 and the logarithm of the source radius r, and (b) the logarithm of theslip value D. The straight lines of regression are shown by the dotted lines, the levels of a constant drop in the stress, obtained bythe Brune formula (4) [Brune, 1970; 1971], are shown by the fine lines.
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DOBRYNINA
for a wide range of magnitudes showed that the scalinglaw is not always fulfilled, and the relationship å0 ∝
depends on tectonic conditions, earthquake magni-tude, the character of realization of seismic energy (sin-gle earthquake, cluster, aftershock succession), etc. Inaccordance with the results of studies of a number of
authors on the basis of the relationship å0 ∝ it ispossible to separate three basic models of earthquake:(l) the classical model of Aki [Aki, 1967] with a con-stant drop in stress [Hanks, 1977; Abercrombie andLeary, 1993; and others]; (2) the model, for which thedrop in stress is a variant, γ ≠ 3 [Archuleta et al., 1982;Shapira and Hofstetter, 1993; Zobin and Havskov,1995; and others] and (3) the intermediate model, inwhich, for different intervals of the values of the seis-mic moment and geometric sizes of the source, their
own relationships å0 ∝ exist [Jin et al., 2000]. Therelationship of seismic moments å0(N m) and the radiiof sources r (km), inversely proportional to corner fre-quency fc (Hz), is presented in Fig. 5a for the earth-quakes being investigated. It is evident that the relation-ship of seismic moments and corner frequencies for theearthquakes in question does not satisfy the classicalscaling law of the seismic spectrum and, according toequation (13), the exponent γ = 8.85. On the other hand,
f cγ–
f cγ–
f cγ–
a fast increase in the value of the stress drop with anincrease in the seismic moment is also noted (Fig. 8).
The drop in stress characterizes the ratio of theamplitude of the displacement at the earthquake sourceto its size:
(19)
In Aki’s model, the drop in stress does not depend onthe value of the seismic moment (Δσ = const); i.e., thesize of source and the value of slip must be related bylinear dependence [Aki, 1967]. The relationship of thevalue of the dislocation and the radius of the source forthe events being investigated takes the form:
= 6.85 + 0.17, (20)
where D is the amplitude of the displacement along thefault in cm and r is the source radius in km (R = 0.68,Pα = 0.95). This means that a nonlinear (power) depen-dence exists between the amplitude of displacementand the source radius for the earthquakes in question.Nonlinear coupling between the amplitude of slip andthe geometric size of the fault (the length and the width)is also established by V.V. Ruzhich and S.I. Shermanwith the statistical processing of the results of the fieldobservations of the fault of the Baikal rift system, inEastern Siberia, Mongolia, and other regions [Ruzhichand Sherman, 1978]. Such a character of dependence
Δσ Dr----.∝
D( )log r( )log
1019
1018
1017
1016
1015
1014
1013
1012
1011
1010
1094 6 8 10 12 14 16
Energy class
Seis
mic
mom
ent,
N m
1
2
3
4
5
Fig. 6. Relation of the logarithm of the seismic moment å0 and energy class äê for the earthquakes of the Baikal rift system. Themap symbolsare as follows: (1) the data, obtained in the present work, (2)–(3) the results of L.G. Danzig and E.A. Steimann, respec-tively [Danzig, 1981; Kochetkov et al., 1985], (4) the correlation dependence of Riznichenko [Riznichenko, 1985], (5) the straightline of regression, obtained in this work.
IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 45 No. 12 2009
SOURCE PARAMETERS OF THE EARTHQUAKES OF THE BAIKAL RIFT SYSTEM 1105
can be explained by the relative change in the elasticproperties of a medium for earthquakes of differentmagnitudes. This means that with an increase in theearthquake’s magnitude, a medium behaves no longeras a brittle, but as a viscoelastic (elasto-plastic) body,for which the ratio of the slip amplitude to the faultlength vary nonlinearly. The stronger the earthquake,the lower the viscosity of a medium and the more rap-idly the amplitude of the displacement increases withan increase in the fault sizes. Thus, for describing theearthquakes in question, the theoretical model of Akifor a uniform source with a constant drop in the stressis not suitable.
For the group of weak earthquakes (Mw = 1.7–3.3),extremely low values of the drop in stress 103–104 Paare observed. The low values of the drops in stress canbe caused, first, by the low values of the seismicmoment and, second, by the low values of corner fre-quencies. As it has been noted above, the seismicmoment depends on the directivity function of seismicradiation but, since the absolute value of the coefficientRθϕ changes within the range from 0 to 1, its variationsnevertheless cannot explain the extremely low values ofthe obtained drops in the stress. The underestimating ofthe spectral amplitude and corner frequency could alsooccur as a result of the utilization of a constant value ofthe quality factor (QS = 400) instead of the frequency-
dependent quality function Q(f), used in the works[Zobin and Havskov, 1995; Margaris and Hatzidimi-triou, 2002]. This is connected with the fact that up tonow, works regarding the frequency-dependent modelof the attenuation of seismic waves for the Baikal riftsystem have not been carried out. I used the values ofQ(f) presented in the works [Zobin and Havskov, 1995;Margaris and Hatzidimitriou, 2002] in order to make anapproximate estimate of a change in the spectrum levelfor different models in terms of quality. The spectra ofthe earthquake of November 10, 2006, at 6.14 p.m. atdifferent seismic stations, corrected for inelastic atten-uation, taking into account three models of quality, arecompared in Fig. 3: (1) a constant frequency-indepen-dent quality, obtained by V.N. Gaiskii with co-authorsfor the central region of the Baikal rift system of earth-quakes [Gaiskii et al., 1977]; (2) a frequency-dependentquality model for the rift of the North Sea Q = 121f 0.89
[Zobin and Havskov, 1995]; and (3) a frequency-depen-dent quality model for the rifts of the Aegean Sea Q =88f 0.90 [Margaris and Hatzidimitriou, 2002]. As can beseen from Fig. 3, the use of the frequency-dependentmodels leads to an increase in the level of the spectralamplitude in the range of low frequencies, on average,by a factor of 3–4, and to a decrease of the spectrumlevel by a factor of 0.06–0.11 for the high-frequencyrange, which corresponds to an increase of the seismic
1020
1019
1018
1017
1016
1015
1014
1013
1012
10112 3 4 5 6 7
Magnitude
Seis
mic
mom
ent,
N m
log(M0) = 1.65ML + 8.87
log(M0) = 1.75ML + 7.63
log(M0) = 1.31ML + 9.96
1
2
3
4
5
6
7
Fig. 7. Comparison of the relations of the logarithm of the seismic moment and local magnitude ( –ML) for some rift zonesof the world. The map symbolsare as follows: (1) the Baikal rift system (this work), (2) the North Sea rift [Zobin and Havskov,1995], (3) the Dead Sea rift [Shapira and Hofstetter, 1993]), (4) the Aegean Sea rift [Margaris and Hatzidimitriou, 2002], (5)–(7)the straight lines of regression of the logarithm of seismic moment and local magnitude for the Baikal rift system, the rifts of theDead and Aegean Seas, respectively. For each straight line in Fig. 7 the regression equation is shown.
M0log
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DOBRYNINA
moment and the stress drop by a factor of 3–4. Thevalue of the corner frequency for the event in questionchanges insignificantly, by 0.12–0.5 Hz, which leads toan increase of the stress drop by a factor of 1.2–2. Thus,the absence in the calculations of the individual direc-tivity function of the seismic radiation for weak earth-quakes and the frequency dependence of the attenua-tion of the seismic waves does not completely explainthe obtained extremely low values of the drop in stress.However, it is known that considerable influence on therecording of a weak earthquake is exerted not only bythe attenuation effects on the way of the propagation ofthe seismic wave, but also by the local characteristics ofthe Earth’s crust directly near the seismic station (site-effect), which are not known for the majority of stationsof the Baikal rift system. For these reasons, the conclu-sion about the extremely low values of the drops instress for the weak earthquakes of the Baikal rift systemcannot be considered to be completely proven. At thesame time, the low values of the drops in the stress,obtained by me, agree with the data about the drops inthe stress for a number of microearthquakes (of magni-tude å = 0.7–2.5) in other regions of the world [Bruneet al., 1991; Zobin and Havskov, 1995; Jin et al., 2000;and others]. In the opinion of Brune [Brune et al.,1991], this phenomenon can be explained by the non-uniform release of stresses on the fault or by the slidingwith a very low velocity along the already existingfault. In any case, this question for the Baikal rift sys-
tem requires a special study, based on a larger quantityof data on weak earthquakes, with the simultaneousdetermination of the attenuation of seismic waves andthe amplitude-frequency characteristics of the Earth’scrust under the seismic stations.
CONCLUSIONS
Based on the spectral analysis of seismograms, thedynamic parameters of the sources of the regionalearthquakes of the Baikal rift system were obtainedwithin 2003–2006: the seismic moment å0, themoment magnitude Mw, the source radius r, the value ofthe stress drop Δσ, and the amplitude of the displace-ment D. Altogether, 363 spectra of S-waves, for62 events with energy classes of KP = 9.1–15.7 at epi-central distances of 70–1000 km, were analyzed.
The results of studies of the dynamic parameters ofthe earthquake sources of the Baikal rift system andtheir comparison with the data for the rift zones and theother seismically active regions allowed me to make thefollowing main conclusions:
(1). Good data consistency on the dynamic parame-ters of earthquakes for the different rift zones makes itpossible to speak about the existence of general regularpatterns of the destruction of the lithosphere and seis-micity in the extension zones of the lithosphere.
(2). The obtained relationship between the seismicmoment and the corner frequency indicates that the
103
102
101
100
10–1
10–2
10–3
the
stre
ss d
rop,
106 P
a
1011 1012 1013 1014 1015 1016 1017 1018 1019
Seismic moment, N m
Fig. 8. A comparison of the values of the logarithm of the stress drop Δσ and the logarithm of the seismic moment M0 for the Baikalrift system. The straight line of regression is shown by the dotted line.
IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 45 No. 12 2009
SOURCE PARAMETERS OF THE EARTHQUAKES OF THE BAIKAL RIFT SYSTEM 1107
scaling law of the seismic spectrum of Aki has not beenfulfilled for the earthquakes of the Baikal rift system.
(3). For the group of weak earthquakes (Mw = 1.7–3.3), extremely low values of the stress drop (103–104 Pa)are observed, which can be explained by the specific fea-tures of the destruction process in the source [Brune et al.,1991]. At the same time, this question requires a moredetailed study.
On the whole, the obtained results give fundamentallynew information on the earthquake sources of the Baikalrift system. A number of empirical equations are derived,which connect the basic parameters of the earthquakesource, such as the magnitude, the energy class, the seis-mic moment, the source radius, the slip amplitude, and thevalue of the stress drop. These equations can be used forthe quick evaluation of the dynamic characteristics ofearthquake sources of the Baikal rift system. In this case itis necessary to emphasize that the obtained equations can-not be extrapolated for events beyond the energy classrange of KP = 9.1–15.7.
ACKNOWLEDGMENTS
I am grateful to V.I. Mel’nikova for the formulationof the problem of the present study and for his criticalremarks, to the Baikal Regional Seismological Center ofGeophysical Survey of the Siberian Branch, RussianAcademy of Sciences and personally to N.A. Gileva andV.V. Chechel’nitsky for access to the digital records ofearthquakes and information on the characteristics of seis-mic stations and the regional format of digital records, toN.N. Drennova for his consultations, and to V.A. San’kovand S.I. Sherman for their useful advice and support on thepresent paper. I thank the anonymous reviewer for hisvaluable constructive comments, which contributed to theimprovement of this paper.
The catalogs and the digital records of earthquakes,obtained by the Baikal Regional Seismological Centerof Geophysical Survey of the Siberian Branch, RussianAcademy of Sciences, were used in the present work.
This work was supported by Program No. 16.8 ofthe Presidium of the Russian Academy of Sciences.
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