Spectral determination of source parameters in the Marmara Region

Abstract

Ever since the 1999 Kocaeli earthquake, in which the Kandilli Observatory and Earthquake Research Institute (KOERI) was not able to correctly reflect the magnitude size in its preliminary report because of the saturation effect, a rapid and accurate determination of the earthquake becomes a very important issue. Therefore, in the framework of this study, an automatic determination of the moment magnitude was performed by using the displacement spectra of selected earthquakes in the Marmara Region. For this purpose, 39 three-component broadband stations from KOERI seismic network which recorded 174 earthquakes with magnitudes 2.5 ≤ M ≤ 5.0 in between 2006–2009 were used. Due to the importance of quality factor in determination of the moment magnitude with spectral analysis method, the quality factor was calculated for the whole region in the beginning. Source spectrum which was obtained by converting the velocity records to displacement spectra and moment magnitudes of earthquakes were determined by fitting this spectrum to classical Brune model. For this aim, an automatic procedure was utilized which based on minimizing the differences between observed and synthetic source spectra identified by the S waves. Besides moment magnitude and location parameters, some source parameters such as seismic moment, spectral level, corner frequency and stress drop were also calculated. Application of the method proves that determining the seismic moment from the source spectra is applicable not only for earthquakes with small magnitude but also moderate earthquakes as well.

1 Introduction

The Marmara Region is the most densely populated and fast-developing part of Turkey; 38.0° N to 42.0° N and 25.0° E to 33.0° E and its surroundings constitute one of the most active seismic regions in Turkey. This region has been unusually active during the last century with three destructive earthquakes namely the 1912 Ganos (M _S = 7.3), the 1999 Izmit (M _w = 7.4) and Düzce (M _w = 7.2) events. A question that must be addressed in any realistic assessment of the earthquake hazard in this populous area that includes Istanbul with 12 million inhabitants concerns the long-term seismicity of the region. To answer this question, Ambraseys and Jackson (2000), Ambraseys (2002) examined the long-term seismicity of the region in the years between 500 and 2000 for both instrumental and historical data. Based on comparisons of reported damage and how far away it was felt, the 1999 Izmit earthquake appears to be similar to an earthquake that damaged communities in 1719. Reports of shaking and descriptions of damage from the 1719 earthquake are remarkably similar to those observed in 1999 (Ambraseys and Finkel 1995; Ambraseys 2002). There were also two earthquakes in 1754 and one in 1766 that probably resulted from fault ruptures closer to Istanbul. These earthquakes were likely similar in size to the major events of the twentieth century. The robust measurement of earthquake parameters especially for the magnitude is still a very important issue for this region.

Following the disastrous 17 August 1999, M _w 7.4 Izmit and 12 November 1999, M _w 7.2 Düzce earthquakes, the seismic hazard in the Marmara Region has become a great concern. Recent studies (Atakan et al. 2002; Parsons 2004; Parsons et al. 2000; Erdik et al. 2004) display that the region has a great potential to produce M ≥ 7.0 earthquake within the next 30 years and may create very high damage. A better knowledge about the characteristics of an earthquake representing a major threat to the densely populated and heavily industrialized areas such as Istanbul city is a useful element at mitigating the seismic risk. Additionally, source parameters especially moment magnitude have a significant role in the estimation of attenuation relationships in the earthquake scenario studies, determination of the source parameter scaling relationships and prediction of the seismic hazard for the region. Meanwhile, there is an earthquake early warning system (EEW) in the Marmara Region run by Kandilli Observatory and Earthquake Research Institute (KOERI) that uses empirical formulas where moment magnitude is an important parameter in all of its algorithms. Since the accuracy and fastness of the moment magnitude parameter is also important for the early warning system, the proposed study will contribute to the automation and operation of the KOERI routine task.

There were not enough broadband stations for the determination of M _w in KOERI’s seismic network before and during the Kocaeli and Düzce earthquakes; most of the aftershocks of these earthquakes’ data sets consist of paper seismograms which do not enable us to identify consequently occurring aftershocks. This situation has mostly changed as the number of stations has been increased and the network configuration has been optimized with the establishment of modern digital broadband stations by KOERI. As a result, the number of events recorded in and around the Marmara Region has improved the accuracy of locations and magnitude determinations with a lower magnitude threshold of around 1.8. On the other hand, this allows real-time operation to accomplish a fast and accurate response in the case of a destructive earthquake which is expected to occur in the Marmara Region.

In KOERI, since the beginning of the 1990s, the most widely used magnitude scale to characterize the size of an earthquake was coda magnitude (M _C) which depends on duration of a signal on 1-s short-period seismograms. Therefore, KOERI’s seismic catalogue was mainly assigned by M _C magnitude till end of the year 2011. The analogue-type drum recorders’ noise level can change depending on their adjustments by different gains; this may lead to readers’ misjudgement about the duration of a signal and also improper estimation of a M _C scale. Furthermore, M _C tends to underestimate which magnitudes are greater than 4.0 and only should be used within the distance less than 350 km (Eaton 1992). As a result, to identify a simple relation between M _C and possible destruction on the buildings was impossible in most cases.

With the establishment of well-equipped broadband stations by KOERI, quantification of the size of earthquakes has been introduced to determine Richter’s local magnitude, M _L (1958) initially, and then extended by surface-wave magnitude, M _S to be able to use at larger distances. KOERI-NEMC (National Earthquake Monitoring Centre) currently uses ZSACWin Software (Yılmazer 2012) as its main seismic processing system since the year 2003. The system uses several magnitude scales such as Ms, M _C, M _L and M _w from moment tensor inversion (MTI) for magnitude determination depending on events’ size, depth and distance to the station. These magnitude scales constitute a great contribution for representing the size of an earthquake; their simplicity on application procedure just by using a single parameter (proportional to the maximum amplitude) and reliability for moderate-sized earthquakes carry out an advantage for quickly processing large number of events.

Nevertheless, these scales have conceptual limitations regarding their intrinsic definitions. Conventionally, M _S is determined by measuring periods at around 20 s where it is applicable for larger distances that cannot be applied in local networks. Moreover, it has been saturated for large magnitudes, caused by narrow frequency bandwidth in which the maximum amplitude is used. M _L also saturates for larger magnitudes at around 6.7 and above (Stein and Wysession 2003) since it is derived by short-period waves. Unlike these traditional amplitude-based magnitude scales such as M _L and M _S which have arbitrary natures caused by regional biases, moment magnitude M _w is the most widely accepted way to characterize the size of an earthquake which is directly derived from dislocation of the source model. This can be accomplished by MTI for fault mechanism solutions, or spectral M _w.

On the basis of KOERI’s newly available broadband data, several seismologists and researchers have been focused on the determination of M _w. In this content, Örgülü and Aktar (2001) analysed the regional moment tensor (RMT) inversion for Izmit earthquake aftershocks by using data from seven near-regional broadband stations. Pınar et al. (2003) added more studies about MTI of moderate-sized earthquakes in order to investigate implications of seismic hazard and active tectonics beneath the Marmara Sea. Recently, Yılmazer (2009) implemented Dreger’s time-domain moment tensor inverse code (2002) for automatic determination of M _w from MTI using local and/or regional distances where the magnitudes are greater than 4.0.

Nevertheless, most of the M _w determinations from MTI are only applicable for earthquakes with magnitudes greater than 4.0. These parameters are not always easy to determine and based on a semi-automatic basis in most cases; thus, they are cost-effective especially for big earthquakes. Thereby, M _w using displacement spectrum which is corrected for path and frequency-dependent attenuation effects appears to be an alternative way to provide an unbiased and unsaturated magnitude scale within a few seconds after the location parameters are estimated.

There have been a few studies for examining source spectra; Parolai et al. (2007) searched the source parameters for this same region applying spectral analysis method to the high frequency parts (f > 12 Hz) of the strong motion data. Another study within the framework of the source spectrum has been investigated by Gök et al. (2009). They applied two methods to overcome difficulty about obtaining source spectra for small earthquakes caused by site response; in order, one is S waves’ spectrum of local high frequency data to find seismic moment, corner frequency, site attenuation and Q and another one is that non-model-based source spectra. According to the study, they have found that the first method was applicable especially for local events recorded by band-limited recorders, and the second one is for broad magnitude range.

On the other hand, these approaches seem far from being applicable to provide source parameters of earthquakes immediately especially for large amount of dataset in an automatic basis. By this aim, CGS (converging grid search) method which has been initially developed and tested by Ottemöller and Havskov (2003) with earthquake data from Mexico, Norway and Deception Island was performed in the present paper. By the proposed study, the main objective is to determine a robust and reliable magnitude which can be used for real-time solutions. In this content, S wave displacement spectra using broadband seismograms were used to estimate M _w for the small- to moderate-sized local earthquakes.

Before going into the processing, due to the importance of quality factor in determination of the moment magnitude with spectral analysis method, the attenuation terms were calculated for the region. M _w magnitude was determined by fitting displacement spectrum to classical Brune’s ω ⁻² source model. For this aim, an automatic procedure was utilized which is based on minimizing the differences between observed and synthetic source spectra by using CGS approach. Besides moment magnitude and location parameters, some source parameters such as seismic moment, spectral level, corner frequency and stress drop were also calculated.

2 Methodology

2.1 Data preparation

As the analysis is based on broadband seismograms, the events (Table 1) were selected by the time period from January 2006 to December 2009 where the KOERI has been introduced by digital recording broadband seismograph networks since 2006. A database for the spectral analysis was formed from 39 broadband stations which are equipped with CMG-40T (30 s), CMG-3T (120 and 360 s) and CMG-3ESP (30 and 120 s) types of Güralp seismometers operated by KOERI using 24-bit digital recordings and decimation to 50 samples/s which covers the entire Marmara Region (Fig. 1).

Table 1 Estimated source parameters of events which are given with their mean values and standard deviations

Fig. 1

Overview map of regional topography, major fault lines, spatial distribution of calculated events and seismic stations in the Marmara Region. The black triangles indicate the broadband stations used in the study; the red circles display the relocated earthquakes between 2006 and 2009

Information regarding the size of an event (M _C) and distance range were taken from the KOERI’s catalogue. The compressed SAC-formatted waveform data was retrieved from website of KOERI (http://barbar.koeri.boun.edu.tr/sismo/zKDRS/) via internet. The artificial explosions were discriminated and removed from local small earthquakes prior to processing.

The data set of 174 earthquakes recorded by KOERI broadband network whose epicentral distances is within 26° E to 32° E and 39° N to 42° N and whose magnitude is ranging from 2.5 to 5.0 with the time period from 2006 to 2009 has been used to determine their seismic source parameters and scaling relations.

As the records were being converted to SEISAN format, further processing procedure such as location and estimation of the source parameters were performed by using the SEISAN (Havskov and Ottemöller 2012). Before the source parameters have been estimated, the first step was to determine accurate locations. The location uncertainty can significantly affect corrections to spectral shapes for local events. The fully automated phase picking may lead to erroneous locations that do not fit the theoretical P and S wave travel time onsets and to erroneous results in cases of changing seismic noise level or close together overlapping events. To overcome this, the selection of the events was carried out with the aim of obtaining reliable locations; phase arrivals were obtained manually and events that deviate from theoretical travel time onsets (root-mean-square values of the travel time residuals smaller than 0.9 s) and uncertain locations (smaller than 5P arrivals) were eliminated from the data set which allows to obtain 174 sufficient quality data set to do in the direct S wave approach.

The hypocentre locations of the selected earthquakes were calculated by using HYPOCENTER program taking into account the velocity model of Kalafat et al. (1987) and Kalafat et al. (1992). KOERI’s bulletin data was used in order to compare obtained hypocentral distances and magnitude results; therefore, selection of a 1-D crust model was carried out with the aim of avoiding possible variability in location parameters and to decrease possible hypocentral influences onto the magnitude results. For this purpose, the hypocentre locations of the selected earthquakes were accomplished by using a velocity model of the KOERI. Estimated location parameters are almost identical to those obtained from the bulletin data from KOERI. For used dataset, the average depth errors are 0.36 from KOERI’s preliminary results like the presented study as 0.32. Statistical distribution of obtained depth values was illustrated in Fig. 2.

Fig. 2

Histogram of the depth values against occurrence frequency (%) obtained by a KOERI and b the present study

2.2 Spectral model

The general model for the Fourier displacement spectrum A(f)  at frequency  f after removal of the instrument response is given by

$$ A(f)={M}_0\times 0.6\times 2.0\times S(f)\times D(f)\times G(R) $$

(1)

where M ₀  (Nm) is the seismic moment, the factor 0.6  accounts for average radiation pattern effect, the factor 2.0  is the effect of the free surface, S(f) is source spectrum of the S wave at the station, D(f) is the frequency-dependent attenuation function, R is hypocentral distance and G(R) represents the geometrical spreading factor, respectively.

Zero frequency intercepts ${}_0$ are utilized to calculate the seismic moment M ₀  following Brune (1970)

$$ {M}_0=\frac{\varOmega_0\times \kern0.5em 4\kern0.5em \times \pi \kern0.5em \times \rho \kern0.5em \times {v}_s^3}{G(R)\kern0.5em \times 2.0\kern0.5em \times \kern0.5em 0.6} $$

(2)

where M ₀  (Nm) is the seismic moment,  Ω ₀ is the flat level of the low-frequency asymptote (proportional to moment), the factor 0.6 accounts for average radiation pattern effect, the factor 2.0  is effect of the free surface, ρ  and ν _S represent the density (ρ = 2.7 g/cm³) and shear velocity (ν _S  = 3.5 km/s) at the source, respectively.

Following Herrmann and Kijko (1983), the geometrical spreading for shear (S and L _g) waves is given by

$$ G(R)=\left\{\begin{array}{c}\hfill {R}^{-1}\kern8.5em \mathrm{for}\kern0.5em R\le 100\ \mathrm{km}\hfill \\ {}\hfill {\left(100\times R\right)}^{-1/2}\kern3.25em \mathrm{for}\kern0.5em R\ge 100\ \mathrm{km}\hfill \end{array}\ \right. $$

(3)

This form of G(R) assumes as body waves for R ≤ 100 km and surface waves for  R ≥ 100 km are dominant.

The exponential term constitutes the diminution factor D(f) in Eq. (1) models frequency-dependent function that modify the spectral shape can be given by

$$ D(f)= \exp \left[\frac{-\pi Tf}{Q(f)}\right]N(f) $$

(4)

where  f is the frequency, Tf is the travel time from the origin time to the start of the spectral window, inelastic attenuation Q(f) is assumed to be frequency-dependent quality factor, given in the simple form of Aki (1980),  Q(f) = Q ₀ f ^α .

The quantity expressed by N(f)  is the frequency-dependent attenuation function, which controls the shape of spectra especially for small earthquakes at high frequencies given by Singh et al. (1982)

$$ N(f)= \exp \kern0.5em \left(-\pi kf\right) $$

(5)

where κ  is the near-surface attenuation parameter which is determined from records at short hypocentral distances, where path attenuation is not important. For frequencies below the corner frequency, κ  can be determined from the slope of displacement spectrum, which when it is corrected for attenuation is expected to be flat if it is ignored by the frequency dependency of site amplification (Ottemöller and Sargeant 2010).

However, the number of studies on  κ term which differs at each site is very restricted and there is not enough information for site specific attenuation effect for the study area. In order to compensate for any unknown biases and scatters in the results by ignoring a correction of site response, the studied data was restricted to the vertical component which means that correction for site amplification is not required. Furthermore, it has not been observed misfit on the spectral shape caused by no correction was made for κ for small earthquakes, in many cases.

After removal of the propagation effects, the obtained ground displacement spectrum was modelled using ω ² model to fit using non-linear least squares:

$$ S(f)\frac{{}_0}{\left[1+{\left(\frac{f}{f_c}\right)}^2\right]} $$

(6)

where f _c   (Hz) is the corner frequency.

The fault dimension was described by the radius of equivalent circular fault (α), by assuming a circular rupture with rupture velocity of 2.6 km/s (0.8  ν _s ) is calculated using the most common Brune model.

$$ \alpha =0.37\kern0.5em {v}_s/{f}_c $$

(7)

Following Eshelby (1957), the static stress drop in bars through its relation to M ₀ and α can be estimated as follows:

$$ \varDelta \sigma =\frac{7}{16}\ {M}_0\ \frac{1}{\alpha^3} $$

(8)

where Δσ represents the stress drop.

Given the seismic moment calculated from Eq. (2), then M _w was estimated using the Hanks and Kanamori’s (1979) relationship and via

$$ {M}_{\mathrm{w}}=\frac{2}{3\ }\ { \log}_{10}\ \left({M}_0\right)-10.7 $$

(9)

where  M _w is moment magnitude.

2.3 Correction for path attenuation

The observed spectrum can be considered as the product of source and attenuation (in Eq. 1); hence, the correction for attenuation is particularly influential for getting the correct frequency and also source parameters. This is possible in case of having a good knowledge of attenuation for studied region. Nevertheless, the number of studies for investigating S wave attenuation for the Marmara Region is limited. Horasan et al. (1998) have found that the attenuation mechanism for coda waves Q _C is similar to that of direct S waves (Q _S) for a lapse time 50 s (Q _C = 411.07f ^{1.08 ± 0.03} and Q _S = 501.07f ^{1.09 ± 0.05}) for the Marmara Region (39.257°–41.154° N, 27.312°–30.747° E). Horasan and Güney (2004) have examined frequency-dependent attenuation for S waves for five distinct regions of the crust within the Marmara Sea by the method which is based on decreasing S wave to coda wave amplitude ratio with distance for earthquakes between 15 and 70 km with duration magnitudes between 2.4 and 3.9. The frequency dependency of average Q _S values at frequencies for five regions was identified as  405f ^{1.03 ± 0.06}. The estimated Q _S values for five regions is ranging from 13f ^{1.22 ± 0.05} to  943f ^{0.83 ± 0.04}.

In order to investigate the effect of attenuation on the spectral parameters (Ω ₀ and  f _c), quality factors for shear waves were investigated by using multiple station method under the assumption of the constant quality factor values characterized by reflecting the whole region. The principle for computation is based on the rate of decay of coda wave amplitude ratio to S wave in time and distance. By this aim, the standard coda Q method whereby a coda window is band-pass filtered, an envelope fitted and the coda Q at the corresponding frequency computed. The average values are estimated and a Q versus f curve is fitted to the estimated values. The methodology and its algorithm which have been applied within the study are described in detail by Havskov et al. (1989).

To examine the effect of attenuation for the area, coda Q for shear waves were calculated by using series of 179 events recorded by 39 vertical components of broadband seismograms. The epicentral distances of earthquakes were between 10 and 300 km and M _C magnitudes were between 2.5 and 5.0. The data was selected under the statement of the signal spectrum should be at least two times the noise spectrum. Coda window is Butterworth band-pass filtered for centre frequencies of 1, 2, 4, 8 and 16 Hz, an envelope fitted and the coda Q at the corresponding frequency calculated. The ${Q}_{\mathrm{C}}$ values are calculated as a function of frequency (1–16 Hz), and then Q _S are determined as a function of the ratio. In Q-fit procedure, the computation was used by the exponent of the geometrical spreading parameter factor as 1.0. The average values were computed, and Q versus  f curve is least squared to the calculated values.

The frequency-dependent Q _S values reflecting the whole region was computed by following Aki’s usual exponential law of the form

$$ {Q}_{\mathrm{S}}={Q}_0{f}^{\alpha } $$

(10)

where Q ₀  the value at 1 Hz and α is the frequency-dependency coefficient (Aki 1980). The average frequency-dependent Q value was computed as ${Q}_{\mathrm{S}}(f)=81{f}^{\mathrm{0.900.02}}$, and the surface projections of ellipsoids (coda volumes) were computed for the average event-station distances 123 km for the region for explaining the S wave attenuation with an average lapse time of 57 s. The results presented in this article were generally consistent with those of Horasan and Güney (2004). New measured path-averaged Q values of Q _S(f) = 81f ^0.90 taken into account by inverting for Q have been used for the entire region.

3 Methodology to estimate source parameters and the M _w magnitude

3.1 Application procedure

Source parameters and moment magnitudes of earthquakes were determined by applying ω ⁻² spectral fitting procedure to classical Brune’s (1970) model. In order to obtain source parameters and the moment magnitude, an automatic routine named as AUTOSIG which was developed by Havskov and Ottemöller (2012) was applied using the SEISAN analysis software. The algorithm involves (1) calculating the S wave displacement spectra for vertical components at a given station, (2) estimating corner frequency and seismic moment using CGS method and (3) computing M _w from M ₀ using Eq. (9). Due to the horizontal components more affected by soil amplifications at shallow depths, the vertical component seismograms were used for the computations. This methodology was tested by using different options (which parameters include geometrical spreading and attenuation) and event data base (which is consisting of different region and stations). As the main goal was to test and develop a methodology for a reliable magnitude determination after a few seconds for the real-time solutions, the method and all calculations presented here were applied in an automatic procedure.

In the present method, an initial model fits for each earthquake by minimizing the norm of the log difference between the observed displacement spectrum and shear-wave spectrum. The computation was applied by using named an error function E of the form by

$$ E={\left[{\displaystyle \sum_i}{\left[{\alpha}_{i,\mathrm{obs}}-{\alpha}_{i,\mathrm{synth}}\right]}^n\right]}^{1/n} $$

(11)

where n is the norm, α _i,obs is observed spectrum and α _i,synth is the synthetic spectrum.

While applying the CGS method, noise is an important criterion due to the fact that following ω ⁻² model along the whole frequency range was the main issue. Site effect, complexity of the source along the propagation path, earthquake size, and distance from the station and earth noise are some causes for deviation. To overcome this problem, signal to noise ratio was taken as much as higher than the noise level along the entire bandwidth (some details concerning the subject are discussed by Chun et al. (1989).

The average amplitude of the prevent noise (3 s preceding the first P wave onset) was computed by subtracting it from the whole signal and cutting the record at the end of the selected time window. The computation was undertaken as the signal spectrum is at least 2.5 times the noise spectrum. When the average amplitude ratio of signal to noise was smaller than 2.5, the data was discarded.

The selection of appropriate time window is another crucial factor to the CGS approach since it is affecting the seismic moment value. If the shear-wave time window would be taken too short, the moment magnitude will be underestimated. On the other hand, if the time window would be taken too long, the signal will include the surface waves. In the shallow crustal layers (such as the Marmara Region), the reverberating waves dominate in the late section of the records, displacement spectrum at low frequencies resulting in an overestimation of the seismic moment and moment magnitude. Another criterion for the selection of the time window is ensuring the P and S wave onsets and the accurate location estimation, since the window was computed based on location and origin time. Additional usage of the P wave may lead to an overestimate of the S wave spectrum at high frequencies. In the context of these conditions, the window length was therefore defined as a duration of 10 s, which starts 1 s before the S wave onset for all computations.

3.2 Data processing

The preliminary selections of the waveforms have been obtained by the signal which is noise corrected and spike extracted. For the analysis, crustal shallow earthquakes (depths < 30 km) at short to intermediate distances from the source were used. P and S arrival times were manually picked in order to ensure the time windows and to prevent wrong determination of the radiation pattern. Trends from the chosen signal windows were removed, and a 10 % cosine tapering window was applied at both ends of the signal. After taking all data into account the transfer function of the seismometer system, baseline corrections were performed to remove any long-period trends. The time series were band passed with corner frequencies at 0.05 and 25 Hz from velocity seismograms. Next, the velocity input time series were integrated and FFT algorithm was applied to obtain displacement spectrum of the signal. The spectrum was not smoothed.

The displacement spectrum was obtained by removing all known path effects including average inelastic attenuation and geometrical spreading parameters. Following Eq. (4), the displacement spectrum was corrected for inelastic attenuation functions and constitute the diminution factor which affects the shape of the spectrum. The average value of inelastic attenuation of Q _S(f) = 81f ^0.90  was taken into account by inverting for Q and has been used for the entire Marmara Region.

The near-surface amplification effects that control the shape of the spectra above the upper corner frequency (f > 10 Hz) were modelled with the quality factor kappa (κ), but there was not enough knowledge about the factor κ which varies regionally over a large distance range. To minimize these effects, the smaller events in the sequence (M _L < 2.5) were not included in the analysis. In this content, the method was applied only on vertical component data, caused by the shear window is relatively less affected by crustal and near-surface amplification effects, which represents the calculated spectra are to be trusted (Ottemöller and Sargeant 2010).

The corrected spectra were scaled to compute moment at the long-period asymptote corresponding to the spectral plateau. Using the spectral amplitude for 0 Hz (Ω ₀), M ₀ and f _c which control the shape of the spectra were derived from the projection of the fit to the Brune’s model. The fitting combination of these parameters was obtained by following the CGS technique by iteration from a starting model described in the previous section. The best fitting iteration of these parameters was obtained after a few seconds. The noise spectrum was also plotted within the same figure in order to suggest comparison between signals to noise ratio before performing the inversion. Consequently, in the case of weak events, which have the low signal to noise ratio (SNR) were excluded from the computations.

Following Eqs. (7) and (8), the source dimension over a circular fault area using the shear-wave spectrum and the average stress drop with respect to the seismic moment value were being estimated, respectively. As a final step, the M _w was calculated out of the seismic moment following empirical relation proposed by Hanks and Kanamori (1979).

4 Results and discussion

The source parameters for 174 events of moment magnitude have been estimated varying from 2.5 to 5.0 from the S wave displacement spectra by using CGS method as have been listed in Table 1. The estimated source parameters consist of seismic moment, corner frequency, stress drop, source radius and moment magnitude have been computed for each station separately and then were averaged to give the mean values of each event. The error in the source parameter was estimated by computing the standard deviation. Figure 3 demonstrates a graphical representation of adopted and observed displacement spectra for event #136 which was given in Table 1 recorded at GEMT, ADVT, CTYL and SILT stations. The blue line presents the original displacement spectrum; the red line indicates the synthetic spectrum resulted from the automatic procedure; the grey line at the bottom signs the noise spectrum taken from the signal before the first P phase arrival. Based on visual inspection of waveform similarity, observed displacement spectra were very well adapted to the ω ⁻² source model for many stations and events, which also confirms that the model parameters were appropriate for the region. Although the spectra were not corrected for frequency-dependent site effects, it has been seen that they still carry in good agreement with a nearly ω ⁻² fall at higher frequencies and results were reasonable for events with M _w ≥ 2.5. The key issue was to establish database with a big enough S/N (SNR > 2.5) ratio. In order that the initial P wave onset may disappear for the smaller events especially at larger distances, it is absolutely essential that the signal must be noise corrected before the processing.

Fig. 3

Plot examples of displacement source spectra obtained from 4 stations for event #136 (see Table 1). The blue line presents the original displacement spectra; the red line indicates the synthetic spectra resulted from the automatic procedure; the grey line at the bottom signs the noise spectra. Top, in order: date of occurrence, origin time, the mean values of the  M _w. Left, bottom: station name, moment magnitude of the present station and geometrical distance for each station

The overall range for number of stations per event is varying from 1 to 23, and there is no significant inconsistency among the stations. The mean values of the estimated source parameters for 174 earthquakes corresponding to each station point out that these average values display good agreement with those computed for each station separately as being observed in the majority of the events. The method can automatically compute the spectra even for only a single station which also points out the advantage of the method. Majority of the standard deviations among the stations are less than 0.2; the average standard deviation was found as 0.12 magnitude units, in case of estimations by single station were excluded. Only the event #105 (event number is displayed in Table 1) has a higher deviation by 0.6; for this event, RKY station can be responsible for such deviation that has the smallest magnitude size (Mw = 2.0) among the processed stations.

Once the source parameters were estimated automatically, applying the same procedure manually to the same waveforms provides an additional comparison on the results. This was performed by approximating two straight lines to the Brune’s model, where the shear-wave spectral plateau for 0 Hz is flat and decay proportionally for frequencies larger than corner frequency being assumed. After the same fitting combination was applied, source parameters and the moment magnitude were computed for each station separately; they were averaged to give the mean value for the same earthquake. The estimations of source parameters modelled from 12 stations for event #136 (the event number is displayed in the Table 1) were examined (Table 2). Comparisons of automatically obtained source parameters are spatially almost the same with an alignment corresponding to manual results (Fig. 4). Based on this, the station values of source parameters were found to be almost equal and no significant scattering among the stations was observed. These results were important because the application process was based on equivalent assumptions in each method and therefore also justify the reliability of the method used.

Table 2 Source parameters of automated and manually determined by displacement spectra

Fig. 4

Comparison of the automated versus manually obtained M _w results from 12 stations for event #136. These values were plotted, respectively, to the M _w values at the reference results in which manually computed with their associated standard deviations

Apart from the corrections based on the same methodology, the M _w results for several earthquakes with magnitude ranging from 3.2 to 5.0 have been compared against M _w from MTI solutions (see Table 3). Reference seismic moment tensor solutions have been estimated from Yılmazer (2009) using MTI for the long-period waveform modelling of Dreger and Helmberger (1993) and Dreger (2002). Real-time waveform inversions for moment tensor and displacement spectrum are conventionally used methods for estimating moment magnitude computed by waveform analysis. It may not seem to be convenient using comparison between the two distinct methods, but it must be taken into account that there were no more M _w magnitude solutions using displacement spectra available from other sources; hence, M _w from MTI solutions thereby have to be used for the verification purposes. Moreover, these comparisons are necessary to carry out the important examination not only for variability of different magnitude results, but also for further information to understand the earthquake source process. Of the M _w from MTI solutions, there were no earthquakes of magnitude exceeding of M _w > 5.0 within the study period; the comparison has to be limited by just 19 events. As a spatial distribution of estimations from two methods was shown in Fig. 5, M _w from MTI does not differ significantly from estimates determined from the spectrum. The general manner of the spectral M _w for small (M ≤ 4.0) events appears to be underestimated than the M _w from the Green’s function results. This can be caused by different magnitude scales which are using different crustal conditions such as scattering mechanism, attenuation and path effects, and corrections are possible responsible factors for the variance. It should be noted that from the MTI point of view, since the model particularly lies on the basis of long-period motions from large events, it is not easy to find M _w from MTI correction for smaller events; hence, the estimations for the magnitude interval larger than M _w ≥ 4.0 should be considered more reliable than the smaller events. This may explain the spectral M _w were underestimated for smaller events, so differences for smaller events M _w ≤ 4.0 may be considered not significant.

Table 3 Events used to compare spectral M _w and M _w from MTI methodology

Fig. 5

Comparison of the spectral M _w results (M _w spec) versus M _w results from the MTI methodology (M _w MTI) for 19 events. These values were plotted, respectively, to the M _w values at the reference results which were taken from MTI solutions with their associated standard deviations

The estimated M _W values have been compared with previously determined M _C results which were taken from KOERI’s catalogue. It has been observed that amount of the earthquakes at a given magnitude range (2.4 to 5.2) display totally different from each other; in fact, such difference still carries out its independent character within the whole examined magnitude range (Fig. 6). While the number of earthquakes with magnitude M _W ≤ 2.8 appears to increase, M _C increases for the magnitude range between 2.8 ≤ M _C ≤ 3.6, while their extrapolations display more consistency after the magnitude size of M _W greater than 4.4. Such a phenomenon is difficult to explain, but this can probably be explained by analogue-type drum recorders’ noise level which can change depending on their adjustments by different gains; this may lead to readers’ misjudgement about the duration of a signal and also improper estimation of a M _C scale. To reveal a relation between M _W and M _C, a least-squared method has been applied for fitting a linear line (Fig. 7). A relation of the form was found as

Fig. 6

Comparison of the M _w (present study) and M _C (KOERI) results versus occurrence frequency (%) for examined magnitude range (2.4 to 5.2)

Fig. 7

Comparison of the spectral M _w results (M _w) versus M _C results (M _C) taken by the KOERI’S catalogue. These values were plotted, respectively, to the M _w values at the reference results which were taken from M _C solutions with their associated standard deviations

$$ {M}_{\mathrm{W}}=0.974\times {M}_{\mathrm{C}}-0.26 $$

suggesting that M _C tends to overestimate than those of M _W results throughout the entire magnitude range of interest. However, suggested explanations cannot be ensured by the present data as their theoretical concepts are not analogous and more studies are needed to obtain convincing conclusions. It is recommended that more studies for revising M _C across the other magnitude scales should be studied, to be able to examine more reliable corrections.

Even though the analysis of earthquake parameters from displacement spectra and examination between the tectonic settings are beyond the scope of the proposed study, the M _w magnitude results of 174 events have been displayed consistently with results from source parameters. Within the magnitude range, the seismic moments are in range 12.8 × 10²⁰ to 16.6 × 10²⁰ dyn cm, stress drops on the fault are in range 0.017 to 647.600 bars and corner frequencies are 0.2 to 15 Hz, and the source sizes of the events amount to 0.0862 to 5.1042 km have been estimated. The standard deviation values of f _c and M ₀ with the majority of being less than 1 Hz and 0.50 dyn cm, respectively, confirms the accuracy of derived source parameters such as source radius, stress drop and moment magnitude and also provides information about the accuracy of their estimation.

For 174 events of moment magnitude 2.5 to 5.0, the source radius and the corner frequency correlate well with the seismic moment and the M _w magnitude, respectively. The corner frequency has been plotted against the moment magnitude value which infers the corner frequency was found to be decreasing with the increasing M _w magnitude as an expected manner (Fig. 8). The seismic moment has been plotted against the Brune’s source radius which displays a linear scaling between M ₀ and ɑ where the determined source radius value displays a tendency to increase with M ₀ (Fig. 9). For this case, the source radius varies from roughly 80 m to 3.0 km which is identical within the whole region and is consistent with those of Parolai et al. (2007) of approximately 100 m to 2.5 km.

Fig. 8

Relation between the average corner frequency f _c and the M _w magnitude. These values were plotted, respectively, to the ${f}_{\mathrm{c}}$ values at the reference results which were taken from M _w solutions with their associated standard deviations

Fig. 9

Relation between the average seismic moment and the source radius. These values were plotted, respectively, to the  M ₀ values at the reference results which were taken from ɑ solutions with their associated standard deviations

5 Conclusions

By the proposed study, the main focus was to attempt to establish an automatic determination of moment magnitude, which is based on o direct measures of physical quantities available for the real-time operation. In this content, in order to determine M _w from a S wave displacement spectrum, CGS approach has been used which follows to Brune’s ω ⁻² source model. This allows the spectra to be tested on 174 events with the hypocentral distances within 10–300 km over a magnitude range of 2.5 ≤ M _w ≤ 5.0. Unfortunately, the method could only be tested for moderate to small events since there were no earthquakes of magnitude exceeding of M > 5.0 within the study time period.

As general results, the estimated values against other methodologies have been compared and validated; agreements of the computed values were satisfactory, and there were no significant differences observed among the other methodologies. It was a good justification that observed displacement spectra were virtually well adapted to the ω ⁻² source model in the whole frequency range for many waveforms, and due to it, it also argues the model parameters were appropriate for the region. The proposed model has the significant merit that automatically obtained source parameters and are almost the same with corresponding manual results, which infer the reliability of the method since both process were based on equivalent assumptions. The M _w results obtained from displacement spectra were very similar to the MTI methodology. Application of the approach proved that there is a very low threshold for event size to determine the reliable M _w magnitude from the source spectra which is applicable not only for earthquakes with small magnitude but also moderate earthquakes as well. This allows a reliable practical method for all earthquakes with magnitudes greater than 2.5 and can be applied to earthquake activity for the routine processing. Reliable estimations are available only within a few seconds even in the occurrence of a moderate earthquake, though the location estimation is necessary.

The applied methodology is advisable which is easy to implement automatically and which also gives a robust measure of earthquake size. The most important one for the advisable factors is M _w can be determined by using a single-station record of a broadband seismograph. The proposed approach for determination of the source parameters and M _w could be extended to other regions of Turkey just by computing attenuation.

In the near future, it is recommended that automatic implementation of the method into the next version of currently used software package ZSACWin which has been used as a routine analysis tool for real-time processing since the year 2003 in KOERI will be carried out to further understanding the earthquake source process.