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The earthquake spectral anomaly estimate by the MLH to mB relation and its possible application to earthquake prediction
Physics of the Earth and Planetary Interiors, 18 (1979) 326—329 © Elsevier ScientifIc Publishing Company, Amsterdam — Printed in The Netherlands
326
THE EARTHQUAKE SPECTRAL ANOMALY ESTIMATE BY THE MLH TO mB RELATION AND ITS POSSIBLE APPLICATION TO EARTHQUAKE PREDICTION A.A. GUSEV1, A.N. SEMENOV1 and L.G. SINELNIKOVA2 1lnstitute of Volcanology, F.E.S.C., U.S.S.R. Academy of Sciences, Petropavlovsk-Kamchatskii(U.S.S.R.) 2lnstitute of Physics of the Earth, U.S.S.R. Academy of Sciences, Moscow (U.S.S.R.)
(Accepted for publication August 8, 1978)
Gusev, A.A., Semenov, A.N. and Sinelnikova, L.G., 1979. The earthquake spectral anomaly estimate by the MLH to mB relation and its possible application to earthquake prediction. Phys. Earth Planet. Inter., 18: 326 —329. This paper presents a method of estimating a spectral anomaly based on the relation of medium- and shortperiod magnitudes. The method has been applied to the analysis of the temporal anomaly trend in the Kurile— Kamchatka zone in which four large earthquakes were developing. Moderately well-expressed anomalies with duration and lead time ofabout a year have been found in all four cases.
1. Introduction The paper discusses spectral anomalies of small earthquakes preceding a large earthquake. These anomalies were often noted previously before rock bursts (Buchheim, 1958) and earthquakes (Aki, 1972; S.A. Fedotov, pers. commun., 1970; Fedotov et al., 1972). An attempt has been made to study this phenomenon systematically. For this goal we have studied the relation between medium- and short-period magnitudes (MLH and mB) of earthquakes occurring in the zone in which future large earthquakes were developing several years before their occurrence.
classes of Fedotov KF68 (Fedotov, 1972) and Solovyev KS67 (Solovyev and Solovyeva, 1967) upon the mB magnitude is linear as the passbands of Benioff and Vegik® seismographs are close. Therefore, when it is necessary, in order to convert K values into mB one may use the formulae mB = 0.5 (KF6S 2.1) (Fedotov, 1972) and mB = 0.45 (KS67 0.2) obtained by the present authors from the earthquake catalogue data. If a standard mB(MLH) relation is known, one may —
—
II
K
Sb
——
2. Determination of ~mu value As is shown in Khalturin (1974), the average relation mB(MLJ~is nonlinear. Therefore, based on vanous published sources (Fedotov, 1972; Khalturin, 1974), the average nonlinear relation mB(MLH) has been constructed for the Kurile Islands and Kamchatka (Fig. 1). In this region the amplitude of short-period radiation can also be estimated from the value of the energy class K. The dependence of energy
9
I?
5
5
4
—
—
‘
.
Fig. I. The accepted average relation between the MLH magnitude (abscissa) and the mB magnitude, and the Fedotov’s KF68 and Solovyev’s KS67 energy classes (ordinate).
327
determine a deviation of the observed (or calculated from the K value) mB value from that expected from the mB(MLH) relation. This deviation (~mB)points to a relative excess or shortage of short-period radiation.
3. Relation of ~mB to spectral shape parameters In order to relate 5mB to spectral characteristics let us accept a schematic shape of the P-wave spectrum at the fixed epicentral distance (after Thatcher and Hanks, 1972). The shape is defined by the low-frequency level of spectral density flu, by corner-frequency f~and by exponent ‘y determining the slope of the high-frequency branch. Thus, the schematic spectrum will be:
1~o; =
~~.Lo(f/fcY’;
f~f~ f> fc
In order that SmB values are not to be affected by the focal depths, a correction should be made in respect of the fact that MLH values of earthquakes with a given ~ value begin to decrease sharply when the focal depth exceeds 30—40 km. To compensate for this decrease, a correction L~MLHis added to the observed MLH value prior to 6m~computation. This correction taken from Fig. 2, which is plotted using the results is obtained by Levshin and Grudeva (1974). Thus, if the MLH value and any of the m® KF6S or values are known for the earthquake, then ~mn is calculated in the following way: (l)MLH is corrected with respect to depth; (2) K is converted to mB; (3) various mB estimates are averaged; (4) the expected m~value is found from the mB(MLH) curve; and (5) = mB m~is determined. KS67
—
4. Empirical evidence on predictive ~m~variations
where f is the frequency.
To elucidate the predictive value of~mB,we have
It is obvious now that, when &2~is fixed, the spectral density ~2(f)for any frequency above f~ increases with a ~ decrease and a rise in corner-frequencyf~. One may assume as a first approximation that for the range nf magnitudes MLH = 4.0 6.0, log~2 0~5 linearly connected with MLH. On the other hand, the log spectral density within the 1-Hz band, log ~~(1)is linearly connected with mB. Since, as a rule,f~in the given8mB magnitude range is less than Hz, the deviaof the mB value from the0.5 average mB(MLH) tion points to either an anomalous value of cornercurve frequency f~or tc an anomalous intensity of high-frequency radiation defined by the “ value. It seems im~ possible to interrret the observed anomalous value in terms of only one of these two factors. Their influence cannot be separated at present.
investigated the areas in which four earthquakes with
MLH ~‘ 7.5, which occurred recently in the Kurile—
Kamchatka zone, had been developing. Their general location is seen in Fig. 3 (on the left). The initial
—
US.S.R.), from catalogues Kamchatka seismic net and from bulletinsofofthe “Petropavlovsk” seismic station. The use of MLH magnitudes determined by Petropavlovsk seismic station at epicentral distances of 3°—5° made it possible to increase notably the volume of available data. It is noteworthy that the periods in the L phase on the records of SK quakes in the
seismographs in all the correction cases have been in was the interval of 7—13 s. A constant of +0.6 added to the MLH value of the Petropavlovsk seismic station as it, like other Soviet Far-East seismic stations, gives anomalously low MLH values. In several cases MLV was determined instead of MLH.
AM LH 0.6
0.? ci
data were taken from N.E.I.C. and E.S.S.N. (joint seismic observation net of the U.S.S.R.) bulletins, from publications Zemletiyaseniya v S.S.S.R. (Earth-
40
50
‘1KM
Fig. 2. Diagram showing the focal depth correction MILH for theMLH value used in the ~mB computatiOn.
earthquakes The regions with within mB =which 3.9—6.0 epicenters and with were the taken focal of depth up to 60 km preceding the four large earthquakes of the zone are shown in Fig. 3 (on the right). For the first three events, namely 12/15/1971, 03/ 28/1973 and 08/11/1969 and for the fourth one 06/17/1973 data are given beginning from 1964 —
—
c~2_
328
_________
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f:
I ~‘
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~
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-
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--
..
/ I
HI
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1~.
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~
U a~
329 and 1970, respectively, since the zones of preparation of the two Kurile earthquakes overlapped each other, The boundaries of the aftershock zones outlining the epicentral areas of the large earthquakes are also given in Fig. 3. The temporal variation of~mBvalues for the four regions is plotted in Fig. 3 (center). Single data points are denoted by crosses. Smooth curves were drawn along the centers of gravity of four successive points. As it seemed inexpedient to assign high weight to the aftershock swarms, ~ values of swarm earthquakes were averaged and their center of gravity, denoted by a black point, was used equally with the other data points. The plots considered show that a more or less evident negative ~mB anomaly is observed before the large earthquake in all the four cases. In the first case it is most clearly seen, being of a “bay-like” shape. The anomaly duration is of about a year, it begins 1.5—0.5 year before the large earthquake. Only one “false” anomaly (in the fourth plot) has an amplitude compatible with that which had preceded the earthquake. One may infer that the large (MLH ~ 7.5) earthquakes of the Kurile—Kamchatka zone are preceded
by moderately well-expressed anomalies in spectra of earthquakes occurring in the zones of preparation of large events. The anomaly duration is 0.5—1 year and the lead time is 1.5—0.5 year. The anomaly is characterized by a relative slackening of the short-period radiation. This can be caused by either a relative
decrease of the corner-frequency or a decrease of the source roughness. References Aki, K., 1972. Recent results on the mechanism of earthquakes with implications for prediction and control program. Tectonophysics, 14(3/4): 227—243. Buchheim, W., 1958. Geophysikalische Methoden zur Erforschung des Spannungstandes des Gebirges im Steinkohlen und Kalisalz Bergbau. Internationale Gebirgsdrucktagung Leipzig, Akademie-Verlag, Berlin. Fedotov, S.A., 1972. Energy Classification of the Kurile— Kamchatka Earthquakes and the Problem of Magnitudes. Nauka, Moscow, 116 pp. (in Russian). Fedotov, S.A., Gusev, A.A. and Boldyrev, S.A., 1972. Progress of earthquake prediction in Kamchatka. Tectonophysics, 14(3/4): 279—286. Khalturin, V.1., 1974. Correlations between expected and observed magnitude estimates. In: Magnituda I energeticheskaya klassifikatsiya zemletryasenii, Vol. 1, Nauka, Moscow, pp. 145—153 (in Russian). Levshin, A.L. and Grudeva, N.P., 1974. Some problems of theory of magnitudes. In: Magnituda I energeticheskaya klassifikatsiya zemletryasenii. Vol. 2, Nauka, Moscow, pp. 203—207 (in Russian), Solovyev, S.L. and Solovyeva, O.N., 1967. Correlation between the energy class and magnitude for the Kurile earthquakes. Akad. Nauk U.S.S.R., Fiz. Zemli, No. 2, pp. 13—22 (inIzv. Russian). Thatcher, W. and Hanks, T.C., 1973. Source parameters of of southern California earthquakes. J. Geophys. Res., 78: 8547—8576.
326
THE EARTHQUAKE SPECTRAL ANOMALY ESTIMATE BY THE MLH TO mB RELATION AND ITS POSSIBLE APPLICATION TO EARTHQUAKE PREDICTION A.A. GUSEV1, A.N. SEMENOV1 and L.G. SINELNIKOVA2 1lnstitute of Volcanology, F.E.S.C., U.S.S.R. Academy of Sciences, Petropavlovsk-Kamchatskii(U.S.S.R.) 2lnstitute of Physics of the Earth, U.S.S.R. Academy of Sciences, Moscow (U.S.S.R.)
(Accepted for publication August 8, 1978)
Gusev, A.A., Semenov, A.N. and Sinelnikova, L.G., 1979. The earthquake spectral anomaly estimate by the MLH to mB relation and its possible application to earthquake prediction. Phys. Earth Planet. Inter., 18: 326 —329. This paper presents a method of estimating a spectral anomaly based on the relation of medium- and shortperiod magnitudes. The method has been applied to the analysis of the temporal anomaly trend in the Kurile— Kamchatka zone in which four large earthquakes were developing. Moderately well-expressed anomalies with duration and lead time ofabout a year have been found in all four cases.
1. Introduction The paper discusses spectral anomalies of small earthquakes preceding a large earthquake. These anomalies were often noted previously before rock bursts (Buchheim, 1958) and earthquakes (Aki, 1972; S.A. Fedotov, pers. commun., 1970; Fedotov et al., 1972). An attempt has been made to study this phenomenon systematically. For this goal we have studied the relation between medium- and short-period magnitudes (MLH and mB) of earthquakes occurring in the zone in which future large earthquakes were developing several years before their occurrence.
classes of Fedotov KF68 (Fedotov, 1972) and Solovyev KS67 (Solovyev and Solovyeva, 1967) upon the mB magnitude is linear as the passbands of Benioff and Vegik® seismographs are close. Therefore, when it is necessary, in order to convert K values into mB one may use the formulae mB = 0.5 (KF6S 2.1) (Fedotov, 1972) and mB = 0.45 (KS67 0.2) obtained by the present authors from the earthquake catalogue data. If a standard mB(MLH) relation is known, one may —
—
II
K
Sb
——
2. Determination of ~mu value As is shown in Khalturin (1974), the average relation mB(MLJ~is nonlinear. Therefore, based on vanous published sources (Fedotov, 1972; Khalturin, 1974), the average nonlinear relation mB(MLH) has been constructed for the Kurile Islands and Kamchatka (Fig. 1). In this region the amplitude of short-period radiation can also be estimated from the value of the energy class K. The dependence of energy
9
I?
5
5
4
—
—
‘
.
Fig. I. The accepted average relation between the MLH magnitude (abscissa) and the mB magnitude, and the Fedotov’s KF68 and Solovyev’s KS67 energy classes (ordinate).
327
determine a deviation of the observed (or calculated from the K value) mB value from that expected from the mB(MLH) relation. This deviation (~mB)points to a relative excess or shortage of short-period radiation.
3. Relation of ~mB to spectral shape parameters In order to relate 5mB to spectral characteristics let us accept a schematic shape of the P-wave spectrum at the fixed epicentral distance (after Thatcher and Hanks, 1972). The shape is defined by the low-frequency level of spectral density flu, by corner-frequency f~and by exponent ‘y determining the slope of the high-frequency branch. Thus, the schematic spectrum will be:
1~o; =
~~.Lo(f/fcY’;
f~f~ f> fc
In order that SmB values are not to be affected by the focal depths, a correction should be made in respect of the fact that MLH values of earthquakes with a given ~ value begin to decrease sharply when the focal depth exceeds 30—40 km. To compensate for this decrease, a correction L~MLHis added to the observed MLH value prior to 6m~computation. This correction taken from Fig. 2, which is plotted using the results is obtained by Levshin and Grudeva (1974). Thus, if the MLH value and any of the m® KF6S or values are known for the earthquake, then ~mn is calculated in the following way: (l)MLH is corrected with respect to depth; (2) K is converted to mB; (3) various mB estimates are averaged; (4) the expected m~value is found from the mB(MLH) curve; and (5) = mB m~is determined. KS67
—
4. Empirical evidence on predictive ~m~variations
where f is the frequency.
To elucidate the predictive value of~mB,we have
It is obvious now that, when &2~is fixed, the spectral density ~2(f)for any frequency above f~ increases with a ~ decrease and a rise in corner-frequencyf~. One may assume as a first approximation that for the range nf magnitudes MLH = 4.0 6.0, log~2 0~5 linearly connected with MLH. On the other hand, the log spectral density within the 1-Hz band, log ~~(1)is linearly connected with mB. Since, as a rule,f~in the given8mB magnitude range is less than Hz, the deviaof the mB value from the0.5 average mB(MLH) tion points to either an anomalous value of cornercurve frequency f~or tc an anomalous intensity of high-frequency radiation defined by the “ value. It seems im~ possible to interrret the observed anomalous value in terms of only one of these two factors. Their influence cannot be separated at present.
investigated the areas in which four earthquakes with
MLH ~‘ 7.5, which occurred recently in the Kurile—
Kamchatka zone, had been developing. Their general location is seen in Fig. 3 (on the left). The initial
—
US.S.R.), from catalogues Kamchatka seismic net and from bulletinsofofthe “Petropavlovsk” seismic station. The use of MLH magnitudes determined by Petropavlovsk seismic station at epicentral distances of 3°—5° made it possible to increase notably the volume of available data. It is noteworthy that the periods in the L phase on the records of SK quakes in the
seismographs in all the correction cases have been in was the interval of 7—13 s. A constant of +0.6 added to the MLH value of the Petropavlovsk seismic station as it, like other Soviet Far-East seismic stations, gives anomalously low MLH values. In several cases MLV was determined instead of MLH.
AM LH 0.6
0.? ci
data were taken from N.E.I.C. and E.S.S.N. (joint seismic observation net of the U.S.S.R.) bulletins, from publications Zemletiyaseniya v S.S.S.R. (Earth-
40
50
‘1KM
Fig. 2. Diagram showing the focal depth correction MILH for theMLH value used in the ~mB computatiOn.
earthquakes The regions with within mB =which 3.9—6.0 epicenters and with were the taken focal of depth up to 60 km preceding the four large earthquakes of the zone are shown in Fig. 3 (on the right). For the first three events, namely 12/15/1971, 03/ 28/1973 and 08/11/1969 and for the fourth one 06/17/1973 data are given beginning from 1964 —
—
c~2_
328
_________
0’
f:
I ~‘
/I-
11II
~
H
,.
I
-I
~
~ -~
/
-
r
--
..
/ I
HI
‘
1~.
*
I
~
U a~
329 and 1970, respectively, since the zones of preparation of the two Kurile earthquakes overlapped each other, The boundaries of the aftershock zones outlining the epicentral areas of the large earthquakes are also given in Fig. 3. The temporal variation of~mBvalues for the four regions is plotted in Fig. 3 (center). Single data points are denoted by crosses. Smooth curves were drawn along the centers of gravity of four successive points. As it seemed inexpedient to assign high weight to the aftershock swarms, ~ values of swarm earthquakes were averaged and their center of gravity, denoted by a black point, was used equally with the other data points. The plots considered show that a more or less evident negative ~mB anomaly is observed before the large earthquake in all the four cases. In the first case it is most clearly seen, being of a “bay-like” shape. The anomaly duration is of about a year, it begins 1.5—0.5 year before the large earthquake. Only one “false” anomaly (in the fourth plot) has an amplitude compatible with that which had preceded the earthquake. One may infer that the large (MLH ~ 7.5) earthquakes of the Kurile—Kamchatka zone are preceded
by moderately well-expressed anomalies in spectra of earthquakes occurring in the zones of preparation of large events. The anomaly duration is 0.5—1 year and the lead time is 1.5—0.5 year. The anomaly is characterized by a relative slackening of the short-period radiation. This can be caused by either a relative
decrease of the corner-frequency or a decrease of the source roughness. References Aki, K., 1972. Recent results on the mechanism of earthquakes with implications for prediction and control program. Tectonophysics, 14(3/4): 227—243. Buchheim, W., 1958. Geophysikalische Methoden zur Erforschung des Spannungstandes des Gebirges im Steinkohlen und Kalisalz Bergbau. Internationale Gebirgsdrucktagung Leipzig, Akademie-Verlag, Berlin. Fedotov, S.A., 1972. Energy Classification of the Kurile— Kamchatka Earthquakes and the Problem of Magnitudes. Nauka, Moscow, 116 pp. (in Russian). Fedotov, S.A., Gusev, A.A. and Boldyrev, S.A., 1972. Progress of earthquake prediction in Kamchatka. Tectonophysics, 14(3/4): 279—286. Khalturin, V.1., 1974. Correlations between expected and observed magnitude estimates. In: Magnituda I energeticheskaya klassifikatsiya zemletryasenii, Vol. 1, Nauka, Moscow, pp. 145—153 (in Russian). Levshin, A.L. and Grudeva, N.P., 1974. Some problems of theory of magnitudes. In: Magnituda I energeticheskaya klassifikatsiya zemletryasenii. Vol. 2, Nauka, Moscow, pp. 203—207 (in Russian), Solovyev, S.L. and Solovyeva, O.N., 1967. Correlation between the energy class and magnitude for the Kurile earthquakes. Akad. Nauk U.S.S.R., Fiz. Zemli, No. 2, pp. 13—22 (inIzv. Russian). Thatcher, W. and Hanks, T.C., 1973. Source parameters of of southern California earthquakes. J. Geophys. Res., 78: 8547—8576.