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EARTH PHYSICS

SOURCE PARAMETERS FOR THE EARTHQUAKE SEQUENCE OCCURRED IN THE RAMNICU SARAT AREA (ROMANIA)

IN NOVEMBER – DECEMBER 2007

E. POPESCU1, C. NEAGOE1, M.ROGOZEA1, I.A. MOLDOVAN1, F. BORLEANU1, M. RADULIAN1

1National Institute for Earth Physics, P.O.Box MG-2, RO-077125 Bucharest-Magurele, Romania E-mail: [email protected]

Received July 21, 2009

We applied relative deconvolution methods (spectral ratios and empirical Green’s function) to estimate the source parameters for the earthquake sequence recorded in the Ramnicu Sarat area between 29 November and 3 December 2007. Basically, these methods are suitable for seismic sequences since they allow the retrieve of the source parameters by using data from pairs of earthquakes located close each other and recorded by common stations. Our analysis reveals distinct features compatible with previous investigations, such as the alignment of the aftershocks parallel to the Carpathians Arc bend in the Vrancea region (NE-SW). The focal mechanism shows a rupture plane in the same direction as well. The location of the main shock relative to the aftershocks indicates a unilateral rupture, from SW toward NE. The alignment of the aftershocks in the sequence of 2007 (N30oE) is approaching the alignments observed in the sequences of 1991 (N24oE) and 1997 (N37oE). The values of the source parameters are typical for the earthquakes in the Vrancea foredeep area.

Key words: earthquake sequence, spectral ratios, empirical Green’s function, source parameters, Ramnicu Sarat.

1. INTRODUCTION

Since the source properties can be obtained starting only from the effects recorded at Earth's surface, the correction factors for focus – site path and local structure response are fundamental to properly understand the rupture process in the source. The correction becomes increasingly difficult when higher frequencies are involved in the recordings because high frequencies are related to small-scale inhomogeneities, difficult or impossible to be controlled. For this reason, most of the source studies are limited to low frequencies and to a scale large enough so that we can ignore the detailed processes in the source and the structure inhomogeneities of small wavelength in the seismic wave path. Any extension in the upper frequency range represents a challenge for seismologists.

Rom. Journ. Phys., Vol. 56, Nos. 1–2, P. 265–278, Bucharest, 2011

E. Popescu et al. 2 266

Several techniques have been proposed to separate source, propagation and site effects in the recorded seismograms. Acceptable source and structure modeling are obtained if we limit ourselves to low frequencies, but the resolution is lower as well. From the standpoint of the civil engineers and for the purposes of seismic microzonation of the dense-populated areas, the contribution of high frequencies to ground motion is of major interest.

One possible way to consider higher frequencies is provided by the relative methods to constrain the source parameters: the spectral ratios method and the empirical Green’s function method. Basically, these methods allow the extraction of source parameters by using data from pairs of earthquakes located close each other and recorded by common stations. They are suitable for seismic sequences, characterized by cluster of events in space and time.

In the present paper, we shall apply relative methods to estimate the source parameters for the earthquake sequence recorded in the Ramnicu Sarat area between 29 November and 3 December 2007.

2. DESCRIPTION OF THE RAMNICU SARAT SEQUENCE

The Ramnicu Sarat (RS) seismic zone is located at the South-Eastern Carpathians arc bend in close connection with the Vrancea seismic region (Fig. 1). Hypothetically, the bursts of seismicity reported from time to time in the fore-arc area are induced by the intense seismic activity generated at intermediate depths [1]. In the last 25 years, a number of 7 sequences occurred in the RS region, all of them related to small-to-moderate size of the main shocks (M = 3.9 to M = 5.0).

Ukraine

Bulgaria

24o23o 25o22o21

o26o 27

o 28o 29o 30o

30o29o28o

27o26o25o24o

23o22o21o

49o

48o

47o

46o

45o

44o

43o 43o

44o

45o

46o

47o

48o

49o

Trotus faultBirlad

Ianca

Legend

faults

Cities

Epicentres of the earthquake sequence of 29 November-3 December 2007

Epicenter of the main shock

Gatati

Focsani

Buzau Tulcea

Bucuresti

Iasi

Ianca

Slobozia

Vrincioaia

Fig. 1. Epicentral distribution of the sequence of 29 November – 3 December, 2007. The positions of

Ramnicu Sarat source and Vrancea source are schematically drawn by empty and dashed ellipses, respectively. The sequence analyzed in the present study is located to the north of the RS crustal zone.

3 Earthquake sequence occurred in the Ramnicu Sarat area 267

The sequence of November 29 – December 3, 2007 complies with the general characteristics of the sequences in this seismogenic area, as we shall subsequently show.

To identify and locate the events all the available data recorded by the Romania seismic network carried out by the National Institute for Earth Physics of Bucharest are considered (short-period and broadband seismometers and digital accelerometers). Locations with acceptable accuracy are obtained for 41 events (Table 1).

Table 1 Catalog of the located events of the Ramnicu Sarat sequence. The third event is the main shock.

Nr. Year/month/day hh:mm:ss Lat (oN) Lon (oE) h (km) MD 1 2007/11/29 16:01:26.80 45.979 27.080 39 2.2 2 2007/11/29 18:03:26.41 45.658 27.244 10 2.1 3 2007/11/29 18:50:06.03 45.615 27.024 19 3.9 4 2007/11/29 18:54:36.38 45.729 27.060 31 2.4 5 2007/11/29 19:02:02.72 45.885 27.231 37 2.0 6 2007/11/29 19:32:52.57 46.032 27.338 30 2.2 7 2007/11/29 19:42:50.69 45.922 27.136 38 1.8 8 2007/11/29 19:42:50.43 45.945 27.193 35 1.8 9 2007/11/29 19:59:03.29 46.009 27.182 33 2.1

10 2007/11/29 20:09:18.05 46.018 27.181 31 2.1 11 2007/11/29 20:23:09.27 45.776 27.074 35 1.9 12 2007/11/29 20:33:53.91 45.993 27.186 33 2.1 13 2007/11/29 21:19:55.29 45.685 27.039 28 2.3 14 2007/11/30 02:04:35.96 45.935 27.140 31 1.8 15 2007/11/30 05:05:40.28 45.345 26.447 4 2.2 16 2007/11/30 05:24:01.08 46.008 27.205 30 2.0 17 2007/11/30 06:30:30.89 45.775 27.074 35 2.4 18 2007/11/30 06:38:29.33 45.858 27.088 41 2.0 19 2007/11/30 08:56:31.24 45.988 27.175 32 2.0 20 2007/11/30 09:21:20.92 45.636 27.037 17 2.3 21 2007/11/30 13:12:03.23 45.905 27.139 43 2.1 22 2007/11/30 13:17:44.51 45.925 27.145 40 2.0 23 2007/11/30 19:23:54.05 45.879 27.117 33 2.0 24 2007/12/01 03:13:44.46 45.683 27.110 27 2.6 25 2007/12/01 03:14:42.48 45.647 27.046 18 2.6 26 2007/12/01 07:55:07.19 45.581 27.060 7 2.7 27 2007/12/01 11:10:40.18 45.813 27.265 18 2.5 28 2007/12/01 18:23:01.34 45.566 27.032 10 2.7 29 2007/12/01 19:44:29.66 45.719 27.025 27 2.5 30 2007/12/01 21:31:47.74 45.883 27.154 33 2.3 31 2007/12/02 00:08:13.97 45.844 27.087 30 2.2 32 2007/12/02 11:02:28.04 45.917 27.115 29 2.4 33 2007/12/02 14:13:20.00 45.969 27.180 34 1.8 34 2007/12/02 16:45:11.08 45.555 27.003 10 2.0 35 2007/12/02 16:45:11.29 45.719 27.008 31 2.0 36 2007/12/02 16:51:00.33 46.034 27.218 32 2.0 37 2007/12/02 19:10:18.62 45.834 27.050 33 2.0 38 2007/12/02 19:17:55.04 45.638 26.971 27 2.3 39 2007/12/03 01:13:44.76 45.717 27.006 30 2.0 40 2007/12/03 07:16:50.71 45.744 27.017 33 2.0 41 2007/12/03 13:57:33.29 45.963 27.158 35 2.0


The station corrections are calibrated on a set of 50 crustal earthquakes produced in the RS region. The distribution of the epicenters is represented in Fig. 1 and Fig. 2. The epicenter distribution shows a NE-SW (approximately N30oE) elongation which is typical for the earthquake sequences observed in the RS area (Fig. 3).

26.9 27.0 27.1 27.2 27.3 27.4Lon. E

45.5

45.6

45.7

45.8

45.9

46.0

46.1

Lat.

N

BRD

o

o

Fig. 2. Epicentres of the study sequence events. The solid line represents the large axis of the

associated ellipse distribution, oriented N28oE; red star is the main shock; the green cross is the foreshock; the blue cross is the first event generated after the main shock.

The BRD station is the closest station.

The aftershocks appear to be grouped around a direction oriented parallel to the Carpathian arc. This is in agreement with a clear and systematic feature of the seismic sequences recorded in the area of Ramnicu Sarat [1–4], respectively the migration of aftershock activity and the orientation of the rupture along a NE-SW direction (Fig. 3). The nodal plane NE-SW oriented in the fault plane solution for the main shock (Fig. 4) lays along the same direction and therefore it is considered as the rupture plane. The main shock is located toward the southwestern edge of the aftershock distribution suggesting a unilateral propagation toward north-east of the rupture. Somehow unexpectedly, the foreshock is located at the opposite side of the aftershock distribution.

The focal mechanism of the main shock is close to a strike-slip faulting. The number of available polarities (23) is relatively high and the solution is well enough constrained, as can be seen if we plot all the possible solutions with SEISAN algorithm [5]. The azimuth of the rupture plane dipping toward NW is N48oE. The P-axis location indicates compression on E-W direction, while the T-axis location indicates extension on N-S direction. The fault plane solution is compatible with the general features revealed for the area situated adjacently in front of the Carpathian Arc which is characterized by a complex field of transition from extension regime in the Moesian Platform to compression regime in the Vrancea subcrustal domain [6].


26.7 26.8 26.9 27.0 27.1 27.2 27.3 27.4 27.5

lon. ( E)

45.1

45.2

45.3

45.4

45.5

45.6

45.7

45.8

45.9

46.0

46.1

lat.

( N

)

1983

o

o

19861991

1997

2004

2005

Ramnicu Sarat

Buzau Ianca

2007

Vrincioaia

Focsani

Fig. 3. The epicentral distribution of the seismic sequences produced in the Ramnicu Sarat region in the last 25 years. For each sequence the epicenter of the associated main shock is represented by red stars. Triangles are cities. In all cases the main shocks are located at the SW edge of the aftershock

clusters, except the sequence on 10 September 2005. NN

T

P

T

P

T

P

T

P

T

P

T

P

T

P

T

P

T

P

T

P

T

P

T

P

T

P

T

P

T

P

T

P

T

P

T

P

N

ODB DPET C

GRE D

VRI DPLOR D

TUD D

GHR CVAR C

ISR DMLR D

TES D

CFR D

HARR CTLCR CVOIR DCVD CTIRR C

AR1 C

KIS D

MDB D

GZR C

BMR CBZS D

Fig. 4. The solution of the fault plan of the main shock of the Ramnicu Sarat 29 November 2007 sequence obtained from the polarities of the first P-wave arrivals. All the possible nodal planes

and principal axes are plotted [5].


3. DESCRIPTION OF THE RELATIVE METHODS TO RETRIEVE THE SOURCE PARAMETERS

To apply the relative methods to estimate the source parameters we use the database of waveforms recorded during the sequence by the Kinemetrics K2 digital stations of the Romania seismic network for the earthquakes in Table 1. Only the recordings with satisfactory signal-to-noise ratio are selected.

The relative methods (such as spectral ratios or empirical Green’s function deconvolution) belong to a class of techniques conceived to efficiently remove the undesired effects of path, site and instrument in order to constrain the source parameters [7–10]. The clue of such techniques is to analyze together pairs of events generated close each other and recorded by common stations. The conditions required are:

– to be located as close as possible – to have similar waveforms – to show similar focal mechanisms – to have differences among the magnitudes in a cluster of co-located events

of at least one unit In the case of the empirical Green’s function deconvolution, the smaller event

in a pair should approximate a Green’s function and therefore the pulse width should be significantly smaller than for the main event. This restriction is not compulsory in the spectral ratios technique which allows the simultaneous estimation of source parameters for the selected pair of events, as long as the instrument is broadband and the signal-to-noise ratio is sufficiently high in frequency band of interest.

For a source model with uniform rupture and high-frequency spectral decay of ω-2, the spectral ratio can be approximated by the theoretical function:

( )

( )

1/ 220

1/ 220

1 /( )

1 /

M Gc

G Mc

f fR f

f f

γ

γ

Ω + = Ω +

(1)

where Ω0M, Ω0G are low-frequency asymptotes of the amplitude spectra for the principal and Green’s function events, fcM, fcG are the corner frequencies, γ is the spectral decay at the high frequencies.

The function that best approximates the observed spectral ratio is obtained through a nonlinear regression procedure. The free parameters are: the ratio of the seismic moments (equal with the ratio of low-frequency levels) and the corner frequencies of the pair of events. As it is well known [11], the corner frequency is directly related to the size of the rupture area, according to the relation:

r = 0.28Vs/fc (2)

where r is the equivalent radius of the source and Vs is S waves velocity. With relation (2) we determine the radius of the source from the corner frequency


(rG sr – radius of the Green’s function from spectral ratios, rMsr the radius of the main event from spectral ratios).

We applied the spectral ratios and empirical Green’s function techniques to the events given in the Table 2. The seismograms (vertical component) for the ‘main’ and ‘empirical Green’s function’ earthquakes are presented in Fig. 5: the main shock of 29 November 18:50 and the aftershocks of 29 November 18:54, 1 December 03:14, 1 December 07:55.

Table 2 The earthquakes considered in the present study for application of relative methods.

The parameters for the main shock are represented by bold characters

Nr Data hh:mm lat (0N) lon (0E) h (km) MD P 2007/11/29 18:50:06.03 45.615 27.024 19 3.9 1 2007/11/29 18:54:36.38 45.729 27.060 31 2.4 2 2007/12/01 03:14:42.48 45.647 27.046 18 2.6 3 2007/12/01 07:55:07.19 45.581 27.060 7 2.7

-50000-40000-30000-20000-10000

01000020000300004000050000

Ampl

itude

[nm

/s]

0 10 20 30 40t [s]

-1800-1500-1200-900-600-300

0300600900

12001500

0 10 20 30 40

-2000-1600-1200

-800-400

0400800

120016002000

0 10 20 30 40

-2100-1800-1500-1200-900-600-300

0300600900

1200150018002100

0 10 20 30 40

main shock-29/11/2007, 18:50

empirical Green's function - 29/11/2007, 18:54

empirical Green's function- 01/12/2007, 3:14

empirical Green's function-01/12/2007, 7:55

Fig. 5. The waveforms of the main event of 29 November 18:50 and the associated empirical

Green’s functions of 29 November 18:54, of 1 December 03:14 and 1 December 07:55 as recorded at Vrincioaia station (VRI).


4. RESULTS

First, we applied the spectral ratios method to estimate the seismic moment and corner frequency for the selected events using the recordings at Vrincioaia station (for the station location see Figs. 1 and 3) alone because the waveforms for Greens’s events at other stations are too noisy. The spectra are computed for windows of P-wave train of 5 s for all events. The resulted spectral ratios are plotted in Fig. 6.

The seismic moment ratio (a) and the corner frequencies (fcM and fcG) for each pair are obtained by approximating the observed spectral ratio with the theoretical function (1). The resulted values are given in the Table 3. The corner frequency of the main event determined for the three pair ratios is quite stable (2.42–2.58 Hz). Because the method is relative, it does not allow simultaneous estimation of the absolute values of seismic moments for both earthquakes (but only their ratio). Choosing the seismic moment of the main event as reference (for the main shock we estimated seismic moment by using spectral methods), we estimate the absolute values of the seismic moments of the Green’s functions associated. The results are presented in Table 4. On the basis of the resulting corner frequency the source radius (rsr) is computed using equation (2).

Table 3 a Source parameters obtained for the event pair 2007/11/29, 18:50 – 2007/11/29, 18:54

Station a fcG (Hz)

fcM (Hz)

rGsr (m)

rM sr (m)

τ1/2 (s)

r Mrt (m)

VRI 1.84 5.10 2.44 194 405 0.09 1102

Table 3 b Source parameters obtained for the event pair 2007/11/29, 18:50 – 2007/12/01, 3:14

Station a fcG (Hz)

fcM (Hz)

rGsr (m)

rM sr (m)

τ1/2 (s)

r Mrt (m)

VRI 2.20 6.09 2.42 163 408 0.095 1164

Table 3 c Source parameters obtained for the event pair 2007/11/29, 18:50 – 2007/12/01, 07:55

Station a fcG (Hz)

fcM (Hz)

rGsr (m)

rM sr (m)

τ1/2 (s)

r Mrt (m)

VRI 1.63 4.54 2.58 198 348 0.1 1094

Applying the empirical Green’s function (EGF) deconvolution we obtain the Source Time Function (STF) for the main shock, as shown in Fig. 7. If the conditions required for a proper deconvolution are fulfilled, we should get similar STFs, independently of the selected EGF event. The average STF (after normalizing the amplitudes) and the associated errors are plotted in Fig. 8. Note the close similarity of the results. From the average STF, the average source duration (τ1/2) is estimated (Table 4), while individual durations are presented in Table 3.


-0.5 0.0 0.5 1.0 1.5log f [Hz]

-1

0

1

2

3

log

sr

0

1

2

3

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5

-1

0

1

2

3

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 Fig. 6. Spectral ratios (sr) in the case of pairs of the main earthquake of 29 November 2007 and

empirical Green’s functions of 29 November 2007 18:54, of 1 December 03:14 and of 1 December 2007 07:55.

Table 4 The source parameters of the main event (average values) and of the selected aftershocks

Nr Data (Hz)

(m)

(s)

MPa

(Nm)

P 2007/11/29 2.48 ± 0.09 387 ± 34 0.095 ± 0.005 9.0 7.40 × 1014

1 2007/11/29 5.10 194 - 2.5 4.02 × 1014

2 2007/12/01 6.09 163 - 4.0 3.36 × 1014

3 2007/12/01 4.54 198 - 2.6 4.54 × 1014


0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0t [s]

-2

-1

0

1

2

rela

tive

ampl

itude

τ =0.18s

-3

-2

-1

0

1

2

3

4

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

-1

0

1

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

=0.19sτ

τ = 0.20s

Fig. 7. Source time functions for the main shock obtained by

empirical Green’s function deconvolution.

The source duration (τ) or the rise time (τ1/2) provides an alternative way to estimate the radius of the source according to [12]:

r = (τ1/2v)/(1-v/αsinθ) (3)

where τ1/2 can be approximated by half of the pulse width, v is the rupture velocity in the source (we adopt the value v = 0.9 β, where β is the S – wave propagation


velocity at the depth of seismic source), α – propagation velocity of P waves and θ is the angle from the normal to the fault and the direction of emergence of the P waves in the focus (in our case we can take θ = 45o). The radius values obtained from EGF deconvolution (r Mrt ) are given in Table 3.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0t [s]

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

rela

tive

ampl

itude

τ = 0.19 s

Fig. 8. Average source time function for the main earthquake of 29 November 2007 resulted from

deconvolution with the three selected Green’s function events. The dashed lines represent the standard error. The individual source time functions deconvolved using the three

empirical Green’s functions are normalized before averaging.

After the estimation of seismic moment and source radius we calculate the Brune’s stress drop using:

03

716B

Mr

σ∆ = (4)

Finally, we interpret the behavior of the acceleration spectra at high frequencies as a function of theoretical modeling. For a source of ω-2 type (Brune’s source), the acceleration spectrum is given by:

( )( )

20

23

2( , )( ) ( )4 1 / c

M fRS f A ff f

πθ φπρβ

= ⋅+

(5)

where R(θ,φ) is radiation pattern of the source, ρ is density, β is velocity of the S waves, M0 is seismic moment and A(f) is an attenuation function at high frequencies given by:


A(f) = 1/(1 + (f/fmax)m) (6)

where fmax is the maximum frequency of the acceleration spectrum and m is the rate of the spectral decay at high frequencies. In this case, S(f) is characterized by 4 parameters: a0 correlated with the high-frequency level of the acceleration spectrum (here with seismic moment), fc the corner frequency, fmax and m as defined above.

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0log f [Hz]

2

4

6

8lo

g A

2

3

4

5

6

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

2

3

4

5

6

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0

2

3

4

5

6

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 Fig. 9. The acceleration spectra and the best approximating theoretical functions

for the study earthquakes.


Table 5 The spectral parameters estimated from the acceleration spectra recorded by the Vrincioaia

(VRI) station for the study earthquakes

Nr. Ev. h (km)

MW a0 fc (Hz)

fmax (Hz)

m

1. 2007/11/29 19 3.9 6.60 2.51 7.52 2.65 2. 2007/11/29 31 2.4 4.84 4.32 10.15 2.88 3. 2007/12/01 18 2.6 4.34 4.08 15.32 2.50 4. 2007/12/01 7 2.7 4.87 4.67 11.45 2.80

The parameters are estimated by fitting the observed acceleration spectrum with the theoretical one. The best approximating functions are represented in Fig. 9 and the corresponding parameters are given in Table 5.

5. CONCLUSIONS

The analysis of the earthquake sequence occurred in the Ramnicu Sarat region in November – December 2007 reveals features compatible with the distinct features previously emphasized in this region. Thus, the distribution of the aftershocks is oriented parallel to the Carpathians Arc bend in the Vrancea region (NE-SW) which looks like a fundamental tectonic alignment. The focal mechanism shows a rupture plane in the same direction as well. The location of the main shock relative to the aftershocks indicates a unilateral rupture, from SW toward NE. The alignment of the aftershocks in the sequence of 2007 (N30oE) is approaching the alignments observed in the sequences of 1991 (N24oE) and 1997 (N37oE).

Different techniques (spectral ratios, empirical Green’s function deconvolution, acceleration spectral modeling) are applied in order to estimate the source parameters for the main shock and other three aftershocks. The relative techniques allow an efficient removal of the factors related to path effects, site effects and instrument response. To compute the source radius and stress drop, a source model of Brune’s type is assumed. The results obtained through alternative approaches are matching acceptably each others.

The source time functions of the main shock inferred using three empirical Green’s functions are close each others showing a quite stable estimation. The uni-pulse shape suggests a uniform rupture process.

REFERENCES

1. E. Popescu, M. Radulian, Tectonophysics, 338, 325–337 (2001). 2. E. Popescu, Ph.D. Thesis, September (2000). 3. E. Popescu, M. Popa, M. Radulian, Romanian Report in Physics, 55, No. 1, 163–181 (2003).


4. E. Popescu, B. Grecu, M. Popa, M. Rizescu, M. Radulian, Romanian Reports in Physics, 55, No. 3, 2003, p. 458–509 (2003).

5. J. Havskov, L. Ottemöller, SEISAN: The Earthquake Analysis Software, Version 7.2, University of Bergen, Norway, 256 p. (2001).

6. M. Radulian, N. Mândrescu, G. Panza, E. Popescu, A. Utale, Pure Appl. Geophys., 157, Nos. 1–2, 57–77 (2000).

7. C.S. Mueller, Geophys. Res. Lett., 12, 33–36 (1985). 8. J. Mori, A. Frankel, Bull. Seism. Soc. Am. 80, 278–285 (1990). 9. S.E. Hough, K. Jacob, R. Busby, Seismol. Res. Lett., 60, 95–99 (1989). 10. G.T. Lindley, Bull. Seism. Soc. Am., 84, 1051–1057 (1994). 11. J.N. Brune, J. Geophys. Res., 75, 4997–5009 (1970) 12. J. Boatwright, Bull. Seism. Soc. Am., 70, 1–28 (1980).

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