source parameters for 1999 north anatolian fault zone aftershocks

Source Parameters for 1999 North Anatolian Fault Zone Aftershocks

RENGIN GOK,1 LAWRENCE HUTCHINGS,2 KEVIN MAYEDA,3 and DOGAN KALAFAT4

Abstract—We develop a data set of aftershock recordings of the 1999, M = 7.4 Izmit and M = 7.2 Duzce

(Turkey) earthquakes to study their source parameters. We combined seismograms from 44 stations maintained

by several sources (organizations) to obtain a unified data set of events (2.1 B Mw B 5.5). We calculate source

parameters of these small earthquakes by two methods that use different techniques to address the difficulty in

obtaining source spectra for small earthquakes subject to interference from site response. One method (program

NetMoment (NM), HUTCHINGS, 2004) uses spectra of direct S waves in a simultaneous inversion of local high-

frequency network data to estimate seismic moment, source corner frequency (fc), site attenuation (j) and whole-

path Q. This approach takes advantage of the source commonality in all recordings for a particular earthquake

by fitting a common Brune source spectrum to the data with a and individual j. The second approach (MAYEDA

et al., 2003) uses the coda method (CM) to obtain ‘‘nonmodel-based’’ source spectra and moment estimates from

selected broadband recording sites. We found that both methods do well for events that allow the comparison

with seismic moment estimates derived from waveform modeling. Also, source spectra obtained from the two

methods are very closely matched for most of the events they have in common. We use an F test to examine the

trade-off between k and fc picks identified by the direct S-wave method. About half of the events could be

constrained to have less than a 50% average uncertainty in fc and k. We used these source spectra solutions to

calculate energy and apparent stress and compare these to estimates from the selected ‘‘good quality’’ source

spectra from CM. Both studies have values mutually consistent and show a similar increase in apparent stress

with increasing moment. This result has added merit due to the independent approaches to calculate apparent

stress. We conclude that both methods are at least partially validated by our study, and they both have usefulness

for different circumstances of recording local small earthquakes. CM would work well in studies for which there

is a broad magnitude range of events and NM works well for local events recorded by band-limited recorders.

Key words: Source parameters, apparent stress, coda, attenuation, Izmit-Duzce, aftershocks, Marmara.

1. Introduction

A primary difficulty in determining the source spectra of small earthquakes is

accounting for the interference of site response, since this occurs over the same frequency

range. Site response is usually associated with soil sites, but rock sites may have a site

response of their own (CRANSWICK, 1988; STEIDL, 1996). Site response can result in

1 Lawrence Livermore National Laboratory, Atmospheric, Earth, and Energy Division, Livermore, CA

94551, USA.2 Lawrence Berkeley National Laboratory, Earth Sciences Division, Berkeley, CA 94720, USA.3 Berkeley Seismological Laboratory, University of California, Berkeley, CA 94702, USA.4 Kandilli Observatory and Earthquake Research Institute, Istanbul, Turkey.

Pure appl. geophys. � Birkhauser Verlag, Basel, 2009

DOI 10.1007/s00024-009-0461-x Pure and Applied Geophysics

amplification of seismic signals due to diminishing wave velocity in less competent soil

or rock, resonances due to trapped energy, focusing and defocusing due to refracted

energy, or diminution of signals due to attenuation. Resonance due to trapped energy

usually occurs at longer periods and can also result in amplification at frequencies as low

as 0.5 Hz (BAISE et al., 2002; BONILLA et al., 1997; JARPE and KASAMAYER, 1996), and can

bias moment calculations for small earthquakes. Often, small earthquake spectra are

dominated by noise at frequencies below 0.5 Hz.

Further, the apparent spectral fall-off of small earthquakes at high frequencies can

actually be the result of near site attenuation. HANKS (1982) noted that small earthquakes

below a threshold moment of about 1.5 9 1021 dyne-cm are band-limited in high

frequency with a constant corner frequency (fmax) near about 10 Hz, and their spectra

have the same shape as would be caused by a source spectral fall-off. Several authors also

observed fmax and note that it differs for different sites, indicating it is a site effect

(FRANKEL, 1982; ANDERSON and HOUGH, 1984; FRANKEL and WENNERBERG, 1989;

HUTCHINGS and WU, 1990). ABERCROMBIE (1997) found that apparent source corner

frequencies recorded at the surface on rock could be up to a factor of ten lower than those

recorded in boreholes for the same event, and she identified attenuation as the cause.

If one attempts to measure a source corner frequency (fc) for small earthquakes and

their source is at a higher frequency than fmax, then fmax can erroneously be misinterpreted

as fc.

We used two different techniques to address and overcome these issues. One method

uses spectra of direct S waves as an input to simultaneous inversion from local high-

frequency network data. This approach takes advantage of the source commonality in all

recordings for a particular earthquake by fitting a common Brune source spectrum to the

data with a simultaneous inversion (program NetMoment (NM); HUTCHINGS, 2004). The

second approach uses the coda method (CM) from local and regional broadband

recordings to obtain ‘‘nonmodel-based’’ source spectra and moment estimates (MAYEDA

et al., 2003).

Following the 1999 M = 7.4 Izmit and M = 7.2 Duzce, Turkey, earthquakes on the

North Anatolian Fault Zone, thousands of aftershocks were recorded by various seismic

networks supported by organizations from Turkey, Europe, Japan, and the United States.

In this study, we combined seismograms recorded by 44 stations from these agencies to

obtain a unified data set of moment magnitudes. We estimate event source parameters,

apply and compare two independent methods for determining source spectra and examine

apparent stress versus moment scaling relations in the Marmara region. We used the

improved locations from GOK et al. (2004) to minimize any effect caused by event

mislocation in our NM inversion. We compared moments estimated from the CM with

those estimated from NM and compared results for those two studies to moments

obtained from 16 events for which waveform modeling was applied (ORGULU and AKTAR,

2001) and results from both CM and NM correlate well to the waveform-modeling

results. Source spectra obtained from the CM and NM are closely matched for most of the

events they have in common and are consistent with the Brune x-2 source model.

R. Gok et al. Pure appl. geophys.,

Finally, we calculated energy and compared apparent stress versus moment from both

techniques.

2. Data

We combined data recorded by six sources: (1) The United States Geological Survey

(USGS), Menlo Park, California (CELEBI et al., 2001); (2) broadband and strong motion

stations operated by the Kandilli Observatory and Earthquake Research Institute

(KOERI), Bogazici University, Istanbul, Turkey; (3) Lamont Doherty Earth Observatory

(LDEO), Columbia University, New York; (4) Earthquake Research Institute, Ministry of

Public Works and Reconstruction (ERD), Ankara, Turkey; (5) Geological Hazards Team

of USGS, Golden, Colorado; and (6) the Earthquake Hazards Team of USGS, Menlo

Park, California. We also obtained five broadband records from KOERI and one from

LDEO. The five KOERI stations are located at the eastern part of the fault, while the

LDEO station is located near the Karadere Fault (Fig. 1). Data at both locations were

recorded by CMG-40T type Guralp seismometers. This created a data set of 628

waveforms. The combined data set has been tested in other studies (e.g., AKINCI et al.,

2006).

We converted the USGS waveforms (http://geopubs.wr.usgs.gov/open-file/of01-163)

to Seismic Analysis Code (SAC) format. Seismograms from ERD, LDEO, USGS, and

part of KOERI had been instrument corrected. The strong motion instruments have a flat

response over a wide frequency range, and the broadband instruments are sensitive up to

40 s. The sampling rate is 100 sps at most of the stations. Finally, we stored waveforms in

our database to have the same format and units (acceleration-cm/s2).

Figure 1

Study area, events studied (red circles) and stations (black triangles). Note that the stations are mostly located on

the North Anatolian Fault. The short-period stations are mostly strong motion.

Source Parameters for 1999 North Anatolian Fault Zone

http://geopubs.wr.usgs.gov/open-file/of01-163

3. Event Locations

We obtained event locations from GOK et al. (2004) where they performed a

simultaneous inversion algorithm to solve the coupled velocity and location problem of

the Marmara earthquakes. Here, we briefly describe the method. They used KOERI and

other network catalog phase data to solve the coupled velocity and location problem. The

catalog phase picks provided the best distribution of ray paths with which to perform the

inversion. This should not be confused with the data set of waveforms discussed above.

To perform the inversion, they used a graded algorithm that starts with a 1-D grid and

refines it to a finer grid (10 km). The data selection for homogeneous ray-path

distribution was applied based on the minimum number of picks and the azimuthal gap

(85� gap and a minimum of 12 P-picks in the eastern section, 170� gap and minimum 8

P-picks in the western section). They first used the VELEST (KISSLING et al., 1994)

algorithm to invert for the reference 1-D velocity model. Using that reference model, a

coarse-grid (30-km grid spacing) 3-D P velocity inversion was applied using SIMUL-

PS14 (THURBER, 1993; HASLINGER, 1998) computer code. The resulting model from the

coarse grid used as an input model to the finer grid (10 km). They relocated all events

based on the final model.

After we obtained these new locations we associated them with available waveforms.

We confirmed the accuracy of association by applying theoretical P- and S-wave travel

time onsets. We eliminated events that considerably deviate from the theoretical arrival

times. After that strict elimination criterion, we selected 628 events recorded at 44

stations. Knowing that the location uncertainty can significantly affect corrections to

spectral shapes for local events, we identified another subset of 198 high-quality (HQ)

events based on their location quality; these had at least eight good quality P-wave arrival

times and a maximum azimuthal gap of 1908. We used this high-quality data set in the

direct S-wave approach.

4. Moment and Source Corner Frequency Estimates with Direct S-Wave Approach

For the first part of our source study, we conducted a simultaneous inversion for

moment, source corner frequency, and site-specific attenuation (j) with the program NM

(HUTCHINGS, 2004), using events with only high-quality (HQ) locations. We used a

10-second window of the direct S waves of the recorded seismograms. The simultaneous

inversion is based upon the assumption that corrected long-period spectral levels and the

source corner frequencies from a particular earthquake will have the same value at each

site; therefore, differences in spectra can be attributed to propagation path, individual site

attenuation, and site response. NM can invert for whole-path attenuation (Q) and site-

specific attenuation (j). However, this inversion may lead to a bias in corner frequency if

the whole-path Q differs at each site, which is likely true in the highly heterogeneous

Marmara region. Thus, we combined them as a site-specific attenuation effect and refer to


it as site-specific j. We do not estimate the amplification due to site response in this

study, which may cause some of the scatter in the results. A consideration when using

NM is that amplifications due to site response are usually pronounced over a narrow

frequency range and NM ‘‘averages through’’ these ‘‘bumps’’ in the spectra. If site

response is known, NM can remove it from the calculation (SCOGNAMIGLIO, 2004).

Another successful approach is to include only those sites that do not have site

amplifications (Hutchings et al., 2007). Spectral ratios between rock and soil sites show a

relative amplification of spectra at some frequencies. However, spectral ratios between

rock to other rock sites (and some firm soil sites) can have a flat spectra, indicating no

relative amplifications.

Prior to the inversion, we corrected the Fourier amplitude spectra of the recorded

seismograms for average radiation pattern and geometrical spreading. We then scaled the

spectra to calculate moment at the long-period asymptote. Following AKI and RICHARDS

(1980, p. 116), we corrected the spectra by:

X0 ðf Þi ¼

4pq1=2v q1=2

n b1=2v b5=2

n Ra

SSFSUðf Þ; ð1Þ

where U(f) is the recorded displacement spectra at the station, qv is density at the station

and qn is density at the source, bv is shear velocity at the station and bn is shear velocity at

the source. S and F are the free surface correction and focal mechanism correction,

respectively. Superscript s refers to values for S waves discussed in AKI and RICHARDS

(1980, section 3.2). We use the P-wave velocity to obtain density (q) values following

LAMA and VUTUKURI (1978). Ra is the geometrical spreading factor, where a = 1.0 for

distances less than 100 km and 0.5 greater distances (STREET and HERRMANN, 1975).

Before analyzing the data, we rotated the seismograms into radial and transverse

components. The focal mechanism radiation correction factor (F) was 0.47 for SV

arrivals and 0.52 for SH arrivals (PREJEAN et al., 2001). The free-surface correction factor

(S) was obtained from the one-dimensional velocity model.

To solve for our free parameters, we used a nonlinear least-squares best fit of the

BRUNE (1971) displacement spectral shape to the displacement spectra. We also allow a

site-specific attenuation operator. The corrected displacement spectra were fit to:

Xðf Þ ¼ M0 expð�pf jiÞ

1þ ffc

� �2� � ; ð2Þ

where M0 is the moment, f is frequency, fc is the source corner frequency, ji is the combined

site-specific and whole-path attenuation at station i. The best-fitting combination of free

parameters (M0, fc, ji) was found by iteration from a starting model using the Simplex

algorithm (NELDER and MEAD, 1965; CACECI and CACHERIS, 1984).

NM analyzes the data’s Signal-to-Noise Ratio (SNR) before performing the inversion

and uses only frequency ranges above a selected SNR in fitting the recorded spectra to the


Brune model. For this study, we chose an SNR of 10. Figure 2 shows an example spectra

fit simultaneously for source and individual station j. The different shapes in the

individual spectra are due to site-specific j. The solid line shows the modified Brune

model over the frequency band used. The seismic moment is calculated from the

projection of this fit to the low-frequency asymptote.

The fit to j and fc is dependent upon the long-period spectral level used in the

simultaneous inversion. A significant misfit between this level and the actual level of

a particular station can result in a bias. For example, if one site has a greater long-

period spectral level than the other stations but its site-specific high frequency is

forced to fit with the average moment, j will be higher and fc will be lower than if

spectra were fit individually. Therefore, in an effort to obtain unbiased values for jand fc, we normalized spectra to have the same long-period spectral level (averaging

all recordings for a particular event) before conducting the simultaneous inversion.

The adjustment did not significantly change moment calculations because the spectral

fit of the inversions is primarily the mean of the long-period values. This inherently

adds the assumption that at the longest periods, site response is not a factor and is

averaged out.

5. Uniqueness and Confidence Limits of Source Parameters

As ANDERSON and HOUGH (1984) pointed out, when exp (-ifj) operates on a

displacement spectrum, the apparent corner frequency can have the same shape and

fall-off as the source spectrum. Therefore, we examine the trade-off between source

corner frequency estimates and j by estimating confidence limits of these parameters.

In our study, we allow j to include the whole path and site attenuation. There is no

trade-off with Mo because it is estimated at frequencies that are not affected by either

fc or j. The uncertainty in moment is determined using a standard least-squares

estimate of the bias and variance for individual sites compared with independent

calculations.

We use the F test to estimate confidence limits of fc and j. We assume that the Brune

source model with j (equation 1) is correct for observed spectra, and deviations from a

perfect fit are due to noise. We further assume that the noise in the spectra has zero mean,

a lognormal random distribution, and a frequency-independent uncorrelated lognormal

variance. Some correlation in the observed spectral variations is caused by seismic-wave

Figure 2

An example of how we fit spectra simultaneously for source, site and path attenuation for event 99232000303

(Table 1). Corrected spectra from each station are fitted to Brune-spectra (gray lines). The frequency-range for

each individual fit is different for each station due to S/N ratio. The lower panel shows the velocity records of N-

S component with their theoretical arrival times at each station. The arrival times based upon IASPEI91 are

specific to the region. Approximate based upon IASPEI91 not specific for the region.

c


propagation, however this effect will actually lead to lower (improved) estimates of

confidence limits. An unbiased estimate of the true data variance is:

s21 ¼

1

N �M

XðXi � XcÞ2; ð3Þ

where Xi and Xc are observed and calculated spectra. N is the number of data samples,

which equals the number of frequency intervals df over the frequency range of the

inversion times the number of spectra used for all stations. M is the number of model

parameters, which in this study is 2. (N – M) is the degrees of freedom.

Next, we perturb the model parameters and calculate a new variance:

s22 ¼

1

N

XðXi � YcÞ2; ð4Þ

where M = 0 because no parameters are estimated and Yc is the new model

spectra.

We perturbed j values at each station by progressively adding or subtracting

dj = 0.002 to the site-specific solution for each station, and the source corner frequency

was progressively perturbed adding dfc = 0.1 Hz. We perturbed j to get j0, such that j -

0.05 < j0 < j ? 0.05, and we perturbed fc to obtain fc0, such that 0.2 < fc

0 < 20.0. The F

statistic is then used to find the perturbation of model parameters for the 98% confidence

limit.

Fð98; ðN �MÞ;NÞ ¼ s21r1

s22r1

; ð5Þ

where r1 is the true variance of the data from the true model parameters. This value is the

same for both cases. The F statistic is obtained from published tables. Therefore, to find

the actual 98% error ellipse, we develop a matrix of perturbed model parameters and find

the contour interval where:

Fð98; ðN �MÞ;NÞ ¼ s21

s22

: ð6Þ

Figure 3 is the ellipse of the confidence interval for the spectra shown in Figure 2.

This ellipse is typical for the data we identified as HQ. Table 1 lists the standard error

in the moment (std-Mo), the corner frequency picks (std-fc), and for all stations

combined (std- j). Columns 13 and 14 show the ratio of the corner frequency and jstandard errors to estimates as percentages. We identified 71 events (Table 1) that had

at least three stations in the solutions and had the average of the two ratios to be

less than or equal to 50%. The moment magnitude range of those selected events

is 2.0 < Mw < 5.6 (Table 1). The standard deviation of a lognormal distribution of

the moment calculation for individual stations compared to the simultaneous

inversion results has a factor of 2.7 (for all events when four or more stations are

used).


6. Moment and Source Spectra Estimates Using Coda Method

The second approach used in our study is the CM introduced by MAYEDA and WALTER

(1996) and MAYEDA et al. (2003). In this approach, the coda part of shear waves is used to

obtain stable, narrow-band amplitude estimates using the coda envelope. The technique

was first applied to events distributed throughout the western United States and later

applied to events located along the Dead Sea Fault. The coda study demonstrated that the

source parameters using coda waves provide more stable estimates than using direct waves.

Successful applications have been made in Italy (western, eastern, and central), Korea, the

European Arctic region, and South Africa. Despite their complexity of the velocity

structure, coda waves average over path and source variability. In one application of this

approach, the 1-D radially symmetric path assumptions were sufficient to describe the

regional scale complexity (EKEN et al., 2003). Here, we briefly discuss the CM and refer

readers to MAYEDA et al. (2003) for more detailed information on the calibration steps.

To measure the coda amplitudes at each narrow frequency band, ranging between

0.03 and 10 Hz, the coda envelopes are formed from each horizontal component. The

amplitudes are then averaged for additional stability. The smoothed version of each coda

envelope is described following MAYEDA et al. (2003) that used a simple functional form:

Ac fi; t; rð Þ ¼ Wo fið Þ � S fið Þ � T fið Þ � P r; fið Þ � H t � r

vðr; fiÞ

� �� t � r

vðr; fiÞ

� ��c r;fið Þ�

exp b r; fið Þ � t � r

vðr; fiÞ

� �� :

ð7Þ

where Wo(fi) is the S-wave source amplitude, S(fi) is the site response, T(fi) is the S-to-

coda transfer function resulting from scattering conversion, P(r, fi) includes the effects of

Figure 3

The 98% confidence ellipse of kappa (j) and fc for event 99239153941 (Table 1). j is centered at 0 for

individual stations and fc ranges from 1–20 Hz in grid search. The contour boundary is F-test values of those

near the 98% confidence.


Table 1

Source parameters and solution qualities of 71 high-quality events. Data from events with asterisk symbols are

used in Figures 2, 3 and 5b

YYJDYHHMM Mw Mo ± std fc ± std Std-j Eo Sta.# Distance

range

Azimuthal

range

%fc %j

*99229181443 3.9 21.85 ± 0.07 1.0 ± 0.05 0.015 9.14 4 78.-250. 37 4.8 44.7

99229202859 3.1 20.70 ± 0.00 1.6 ± 0.30 0.003 8.03 4 27.-153. 193 18.3 9.7

99230093058 3.6 21.49 ± 0.01 2.1 ± 0.35 0.009 9.22 3 39.-182. 62 16.7 43.0

99231154819 3.8 21.80 ± 0.14 1.0 ± 0.00 0.005 9.05 4 21.-158. 217 0.0 39.3

*99232000303 3.9 21.88 ± 0.29 2.2 ± 0.10 0.012 10.39 5 45.-215. 206 4.5 36.6

99232092856 4.7 23.08 ± 1.18 0.5 ± 0.00 0.009 10.70 3 24.-129. 219 0.0 64.6

99234042737 3.2 20.91 ± 0.16 3.4 ± 1.85 0.010 8.96 4 16.-172. 144 55.0 40.6

99234082303 3.3 21.03 ± 0.19 1.9 ± 0.05 0.006 8.81 3 114.-178. 43 2.6 37.0

99235214429 4.4 22.59 ± 0.71 2.3 ± 1.10 0.014 11.42 3 15.- 38. 273 47.1 49.3

99237034547 3.7 21.66 ± 0.04 1.7 ± 0.00 0.010 10.19 3 29.- 35. 329 0.0 52.2

99238173507 3.7 21.56 ± 0.18 2.9 ± 1.35 0.009 9.91 10 15.- 60. 211 47.0 36.4

99238233902 3.5 21.30 ± 0.50 2.3 ± 0.05 0.006 9.07 7 22.- 39. 211 2.2 45.6

99239143953 3.8 21.78 ± 0.17 1.6 ± 0.05 0.005 9.45 8 15.- 38. 259 3.2 45.1

*99239153941 3.9 21.97 ± 0.41 2.3 ± 0.70 0.008 10.00 8 26.- 66. 184 30.6 47.1

99240061734 3.4 21.18 ± 0.72 2.8 ± 0.65 0.006 9.11 9 13.- 36. 219 22.8 44.6

99240114938 3.4 21.08 ± 0.43 3.6 ± 0.10 0.007 9.06 8 14.- 26. 200 2.8 34.6

99241000218 3.5 21.33 ± 0.46 3.0 ± 0.10 0.007 9.33 7 14.- 35. 253 3.3 40.5

99241165436 3.5 21.35 ± 0.42 1.9 ± 0.00 0.007 8.82 5 15.- 30. 253 0.0 69.1

99242152437 3.4 21.17 ± 0.35 3.8 ± 0.45 0.011 9.58 3 16.- 28. 29 11.8 28.0

*99243081050 5.3 23.95 ± 0.68 1.5 ± 0.20 0.045 14.15 7 7.-105. 97 13.8 40.3

99243222834 4.9 23.42 ± 0.53 0.9 ± 0.05 0.008 11.89 8 45.-169. 11 5.3 18.6

99244005925 3.7 21.62 ± 0.40 1.4 ± 0.15 0.003 8.74 8 15.- 30. 247 11.0 38.3

99244084059 3.9 21.83 ± 0.36 1.0 ± 0.15 0.005 8.81 6 15.- 19. 169 14.5 35.6

99244164313 3.8 21.80 ± 0.00 1.4 ± 0.10 0.003 9.59 8 11.- 30. 306 7.0 19.7

99245142015 3.3 21.00 ± 0.42 2.9 ± 0.00 0.005 8.86 5 14.- 29. 307 0.0 35.2

99245162934 4.2 22.34 ± 0.06 2.1 ± 0.00 0.012 10.81 5 15.- 58. 246 0.0 35.0

99245183851 3.7 21.56 ± 0.10 2.5 ± 0.00 0.005 9.41 9 15.- 34. 253 0.0 41.9

99246072604 3.4 21.22 ± 0.32 2.1 ± 0.00 0.014 8.60 8 20.- 36. 235 0.0 49.5

99246110717 3.3 20.94 ± 0.21 4.1 ± 0.65 0.012 8.82 3 17.- 33. 17 15.8 59.6

99246111947 4 22.01 ± 0.30 1.0 ± 0.05 0.045 8.83 7 20.- 30. 179 5.2 80.3

99246142234 3.6 21.39 ± 0.23 2.4 ± 0.00 0.008 8.89 9 17.- 35. 257 0.0 79.7

99248195248 4.3 22.54 ± 0.26 1.9 ± 0.15 0.020 11.20 11 14.- 72. 291 7.7 50.3

99249025507 3.5 21.25 ± 0.07 3.0 ± 0.25 0.022 9.26 8 15.-193. 296 8.4 73.0

99249063326 4.1 22.23 ± 0.12 2.5 ± 0.15 0.015 11.24 12 8.-209. 286 6.0 41.3

99249185359 4.2 22.29 ± 0.03 2.8 ± 0.05 0.016 10.73 7 26.- 65. 182 1.8 56.4

99249193739 3.8 21.78 ± 0.39 1.7 ± 0.25 0.023 9.92 6 9.- 53. 18 15.0 64.4

99251131043 3.5 21.36 ± 0.12 2.6 ± 0.00 0.019 9.14 7 24.-221. 213 0.0 68.6

99252004306 4.2 22.31 ± 0.13 3.1 ± 0.35 0.017 11.18 15 16.-297. 204 11.3 47.6

99252010220 3.5 21.35 ± 0.04 3.2 ± 0.60 0.012 9.53 9 13.-189. 269 18.6 33.4

99252013208 4.3 22.55 ± 0.45 1.2 ± 0.05 0.012 10.79 8 35.-155. 242 4.1 46.5

99252054124 3.6 21.52 ± 0.11 3.6 ± 1.80 0.016 9.61 9 25.-212. 196 50.2 41.5

99253082938 3.6 21.39 ± 0.27 2.8 ± 0.20 0.018 9.38 6 13.- 88. 344 7.1 86.1

99257213137 3.8 21.79 ± 0.11 1.5 ± 0.00 0.013 9.16 7 18.-155. 208 0.0 57.0

*99258093333 3.9 21.94 ± 0.26 1.6 ± 0.20 0.011 9.50 10 29.-266. 321 12.6 30.8

99259005646 3.5 21.27 ± 0.25 3.0 ± 0.05 0.007 9.25 8 17.- 55. 288 1.6 25.4

99259175845 3.4 21.22 ± 0.19 1.6 ± 0.05 0.014 8.82 8 32.-250. 278 3.0 36.5

99260195006 4.4 22.62 ± 0.08 2.9 ± 0.50 0.014 12.18 13 21.- 74. 188 17.3 46.6


geometrical spreading and attenuation (both scattering and absorption), H is the

Heaviside step function, v(r, fi) is the peak velocity of the S-wave arrival, c(r, fi) and

b(r,fi) control the coda envelope shape, and t is the time in seconds from the origin time.

The synthetic envelopes were estimated by fitting distance and frequency-dependent

velocity and coda shape parameters (equation 7) of observed coda envelopes. The coda

amplitude measurements (Ac) are obtained by fitting synthetic to the observed envelopes.

The log amplitude shift of observed envelope from the synthetic at unity is the raw coda

amplitude value at each frequency. The raw amplitudes are then path-corrected using 1-D

formulations. For the geometrical spreading correction, we modified and extended the

STREET et al. (1975) formulation. Assuming that the distance-dependence has the same

form for both coda and direct amplitudes (MAYEDA et al., 2003), we correct for the

geometrical spreading and the Q effect. The new formulation, which is called the

extended Street and Herrmann (ESH) approach, corrects for the geometrical spreading,

and its results are more stable than those derived from using the Brune-like corrections

(PHILLIPS, personal communication; MORASCA et al., 2007). Instead of critical distance, we

define a distance range where the transition changes smoothly. The spreading function is

a product of individual transition terms. This new spreading function is preferred because

it uses all the stations simultaneously to find the best fit to the path correction models.

Table 1

contd.

YYJDYHHMM Mw Mo ± std fc ± std Std-j Eo Sta.# Distance

range

Azimuthal

range

%fc %j

99261004825 4.9 23.38 ± 0.85 0.9 ± 0.00 0.015 12.06 6 38.-108. 22 0.0 31.3

99262202636 4.7 23.09 ± 0.38 3.4 ± 1.05 0.041 13.00 10 16.- 66. 293 31.0 50.8

99263212800 4.9 23.47 ± 0.20 2.3 ± 1.10 0.020 13.03 14 29.-237. 230 47.8 39.0

99266202407 3.3 20.98 ± 0.11 3.1 ± 0.15 0.018 8.91 6 12.-160. 250 4.9 73.5

99267134452 4.3 22.53 ± 0.08 3.3 ± 0.50 0.027 11.89 8 33.- 65. 199 15.3 35.8

99269033442 3.3 21.06 ± 0.08 1.9 ± 0.05 0.023 8.61 3 15.- 70. 165 2.6 77.4

99270154123 3.5 21.34 ± 0.07 2.1 ± 0.50 0.023 9.31 3 8.- 9. 149 24.1 57.2

*99272001307 5.5 24.29 ± 0.34 1.8 ± 0.00 0.037 14.65 7 22.- 91. 28 0.0 47.8

99276223518 2.6 19.97 ± 0.24 5.9 ± 0.40 0.019 7.83 6 18.-172. 245 6.8 73.7

99280005514 2.8 20.26 ± 0.13 14.2 ± 2.85 0.027 9.52 3 24.- 99. 232 20.0 55.8

99282213247 3.8 21.75 ± 0.25 1.8 ± 0.15 0.016 9.32 11 24.-237. 172 8.3 53.3

99293230820 5.1 23.73 ± 0.84 0.6 ± 0.00 0.016 12.22 14 26.-147. 224 0.0 52.0

99296024951 3.5 21.26 ± 0.56 1.8 ± 0.00 0.020 8.93 5 10.- 11. 1 0.0 61.3

99299182406 3.2 20.85 ± 0.55 1.9 ± 0.05 0.023 8.52 3 19.- 19. 0 2.7 60.7

*99315144126 5.6 24.39 ± 0.84 0.5 ± 0.00 0.023 13.32 9 40.-221. 181 0.0 68.5

99317025307 3.7 21.62 ± 0.42 2.1 ± 0.20 0.016 10.10 11 33.-247. 196 9.4 49.5

99322214947 2.9 20.42 ± 0.10 4.7 ± 0.00 0.023 8.42 3 83.-131. 83 0.0 92.7

72193701 2.9 20.35 ± 0.01 7.1 ± 2.60 0.018 8.37 3 43.-121. 130 36.6 62.7

85191911 2.5 19.79 ± 0.01 3.6 ± 0.10 0.006 7.05 3 51.-198. 17 2.8 31.1

91150126 2.1 19.26 ± 0.09 8.6 ± 2.20 0.007 6.86 3 52.-146. 285 25.4 26.7

121212506 2.2 19.28 ± 0.02 8.3 ± 5.85 0.005 7.09 3 52.-102. 153 70.2 25.7

188001531 4.3 22.49 ± 0.61 0.9 ± 0.00 0.003 10.60 4 34.-142. 143 0.0 24.7

334134610 3.1 20.69 ± 0.08 1.8 ± 0.00 0.007 8.17 3 86.-159. 78 0.0 47.2


To apply the CM to our study we used five broadband stations, which recorded 230

events in the Marmara region (shown in Fig. 1). We did not use the elimination criteria

based on the location quality, since we had used only broadband data and that criterion

would have left us with very few events. The CM also seems be less sensitive to location

accuracy than the direct S waves. The inter-station scatter is always lower than direct

waves that are an indication of this less decreased sensitivity. After estimating the coda

amplitudes for each station, we corrected for path using the ESH technique. Figure 4

shows the inter-station scatter after the ESH correction (red). The inter-station standard

deviation for MRMB and YLVB stations is 0.064 at 1.5–2.0 Hz. The new spreading

correction produces less scatter in the inter-station amplitudes than the one critical-

distance model (0.16) (black), especially at higher frequencies. The path-corrected coda

amplitudes are now dimensionless and station-dependent because they are a composite of

site effect and the S-wave-to-coda transfer function. Independent estimates of spectral

amplitudes for a number of events are essential to determine the combined effect of

these variables at each station, which can then be applied to each distance-corrected

measurement.

For this study, we used waveform-modeled Mw estimates published by ORGULU and

AKTAR (2001) as well as unpublished estimates from their research (ORGULU et al., 2003).

Figure 5a shows the moment rate spectra obtained from four different events calculated

Figure 4

Path corrected coda amplitudes at YLVB and CTTB. The inter-station scatter is lower with ESH than the Brune-

like correction at 1.5–2.0 Hz. Blue is the raw amplitude correlation; black is Brune-like correction and red is

ESH.


at individual stations. They match each other remarkably well. We calculate an average

source spectrum for each event and obtain the final moment and energy from those

values. Figure 5b shows the source spectra derived from NM and coda for the events

Figure 5

(a) Coda source spectra at individual stations for four different events. Note the similarity of spectra at different

stations. (b) NM source spectra (solid black) for the well located HQ event solutions compared to the solution

for CM (red dotted) for the same event.


modeled by both approaches, and both provide reasonable agreement. Although some

differences are apparent, they seem to lay within areas of the coda source spectra that do

not match a Brune source spectral shape.

The long-period waveform modeling results were used to test and calibrate (for CM

only) the long-period spectral level. Figure 6 compares the waveform-modeled Mw to the

coda- and NM-derived Mw estimates. The scatter in coda and NM estimates are both low

compared with the waveform-modeled Mw. NetMoment magnitudes are slightly higher

than both CM-Mw and waveform-modeled-Mw while Mw > 4.0.

7. Radiated Seismic Energy and Scaling

Calculations of apparent stress allow us to determine whether results from each

approach are within the range of expected values over this magnitude range (i.e., are the

results basically realistic?) and whether they are consistent with results from other studies

that have better constraints on source parameters (i.e., do other studies validate these

approaches?). In addition, apparent stress calculations can help us analyze the

contribution that these results make to research on energy scaling. The energy radiated

Figure 6

Pairwise comparison of moment magnitudes (Mw) calculated by the three different procedures: CM, NM and

waveform modeling (WM). The blue circles are CM (y axis) versus WM Mw’s (x axis) (16 events). The black

diamonds are NM (x axis) versus WM Mw’s (y axis) (10 events). The reverse red triangles are CM (y axis)

versus NM (x axis) (56 events). The solid black line is the 1-to-1 line.


from a seismic source can be estimated from the energy flux by integrating the squared

velocity seismogram in the time or frequency domains (KANAMORI et al., 1993). The

radiated S-wave energy is the integral of energy flux around the sphere. If we assume an

x2 model (equation (2) without the exponent for (j), the solution for S waves becomes:

ES ¼1

10p2qb5

� �Z1

0

w2 M�ðwÞ

��2

dw ¼ 4p

5qb5

� �Z1

0

f 2 M�ð f Þ

��2

df ¼ p2f 3c M2

0

5qb5: ð8Þ

In this equation, we assumed that q = 2700 kg/m3 and b = 3500 m/s, which are the

values commonly used in most local estimates of energy. Figure 7 shows a plot of our

energy estimates versus moment along with values from other studies. Apparent stress

estimates are consistent with other studies over the same moment range. Apparent stress

is the fraction of the effective applied stress that is tied to the energy in the seismic waves

(WALTER et al., 2006).

The energy from the coda source spectra is calculated similarly except that we used

the integrated real spectra. First, we extrapolated the low frequency to f = 0 Hz;

for higher frequencies above our last amplitude measurement (8.0 Hz), we assumed an

x2 fall-off. The P-wave contribution is 7% of the total radiated elastic wave energy

where E is,

ES ¼1

4p2qb5

Z1

0

w:M�ðwÞ

��2

dw: ð9Þ

In equation (9), we assumed that q and b are the same as in equation (8). We

calculated the energy for events. We extrapolated the coda source spectra to low

frequency at the flat part of the moment rate spectra and high frequency assuming an

omega-squared fall-off (MAYEDA and WALTER, 1996). We included spectra in which the

high and low frequency extrapolation contributed less than 30% of the total energy along

with the rest of the Marmara data (162 events). We see similar scaling when we limit our

coda measurements to less extrapolated energy versus the NM spectra of HQ events with

corner frequency j errors less than 50% (71 events).

Figures 7a, b and c show the grouped events according to their total energy estimate

from the coda source spectra and NM. We plotted results for the selected HQ events (71

from NM and 162 from CM) together with ABERCROMBIE (1995) and western U.S. events

calculated with the CM (Fig. 7b). The scaled energy, e ¼ E/M0, is the apparent stress

(e.g., WALTER et al., 2006) divided by rigidity. The y axis in Figure 7c is then effectively

the log of the apparent stress, therefore Figure 7c can be interpreted as a plot of the log

apparent stress versus log moment for the CM and NM results (assuming the rigidity to

be constant). The scaling shows an increase with increasing moment with the slope of

0.41 for NM results and 0.31 for CM. As would be expected from measurements of direct

waves, NM-derived data have more scatter than those derived from the CM. In fact, the

NM energy estimates are unrealistic for events larger then the Mw > 4.2, exhibiting


corner frequencies for larger events that are too high. That might also be the reason for

the higher slope for NM results. However, the coda magnitudes match well with those

from the waveform-modeled estimates (Fig. 5a). MAYEDA (2005) found the slope to

be * 0.13 for the Izmit aftershocks with CM using Mw C 4.0 events.

8. Summary and Conclusions

In this study, we developed a unique data set of aftershock recordings from the

1999 M = 7.4 Izmit and M = 7.2 Duzce, Turkey, earthquakes. We combined seismo-

grams recorded by 44 stations to obtain a unified data set of events. The aftershocks

log Moment (N-m)

log

En

erg

y (J

)

log Moment (N-m)

log

En

erg

y/M

om

ent

log Moment (N-m)

log

En

erg

y (J

)

(a) (b)

(c)Coda Method ( <= 30% of energy extrapolated)

NetMoment (High Quality, lower fc error)

Coda Method (all events)

NetMoment (all events)

Western US events with coda method ( Mayeda et al., 2005)

Abercrombie et al., (1995)

Figure 7

a) Energy estimates versus moment for all events in this study and selected high quality (HQ) events. Yellow

diamonds are HQ-located events (198) for NM and yellow triangles are all coda events (182). Events with lower

error have less scatter for NM, direct S wave inversion, b) Energy versus moment of high quality selected events

(71 for NM and 162 for CM) along with values from various studies, c) NM and CM scaling relations of log

apparent stress versus log moment. The best-fit least-squares lines are solid blue and red for CM and NM,

respectively. The slope for CM is 0.31 and 0.41 for NM. The dotted line is constant scaling (-4.3 in log). The

scaling term clearly increases with increasing event size.


studied primarily have magnitudes Mw < 4.0. In validating the data quality of aftershocks

recorded by various networks, we did not find significant inconsistencies among data sets,

even though different institutions operated the networks. We used two techniques to

calculate the source parameters for the aftershocks.

Waveform inversion has proven to be a reliable method for estimating seismic

moment, and we assume that it provides a stable estimate with which to compare moment

estimates. Moment estimates from this study compared well with independent results

from moment tensor inversion. Coda waves have also proven to be a stable estimate of

moment, although they have been used primarily for larger events (Mw C 3.5) than we

examined in this study. We found that the NM-derived moment estimates have a log10

bias of 0.00021 and a variance of 0.0094 while the coda-derived moments have a bias of

0.00015 and a variance of 0.0085. We note that in equation (3), moment depends on

seismic velocity raised to the 4th power (we calculate density from the P-wave velocity).

A difference of 20% in velocity, for example, changes moment by a factor of

approximately 2.4. The CM (MAYEDA and WALTER, 1996) scales spectra from waveform

inversion result to obtain moment estimates for all spectra. We recommend a similar

approach for NM because it would identify and remove the bias from all moment

calculations.

We used an F test to examine the trade-off between j and the source corner frequency

picks (fc) identified by NM and found 71 events (of 198 examined) that we considered

high-quality solutions. These solutions had an average ratio of corner frequency

estimated error to calculated value pick to its standard error and the ratio of the average jstandard error to estimated value to be B 50%. These events generally were for

magnitude 4.0 > Mw > 3.0. Smaller events were generally recorded by too few stations to

constrain the solutions.

We compare source spectra between our Brune source models derived by NM

and coda ‘‘parameterless, empirical’’ models. Figure 7 shows source spectra obtained

from NM and coda for the six events they have in common. Here, we note that four

of the six solutions nearly overlay one another, which supports the Brune x-2 source

model.

We also calculated apparent stress and found that it increases with increasing

moment, which is consistent with findings in a number of studies that used different

techniques (KANAMORI et al., 1993; SINGH and ORDAZ, 1994; ABERCROMBIE, 1995; MAYEDA

and WALTER, 1996; IZUTANI and KANAMORI, 2001; PREJEAN and ELLSWORTH, 2001;

RICHARDSON and JORDAN, 2002; MORI et al., 2004). A recent study of MAYEDA et al. (2003)

using the coda-derived source spectra in different tectonic regions (e.g., Landers, Izmit,

Hector Mine, and Aquaba) shows that the scaled energy, e = Er /M0, increases with

increasing moment (ABERCROMBIE, 1995) for common magnitudes and continues to higher

magnitude with the same slope.

The debate regarding whether the relation between apparent stress drop and moment

is the same for small and large earthquakes (MAYEDA and WALTER, 1996) significantly

affects hazard estimates, since extrapolating stress drops of large earthquakes by using


the relation obtained from smaller size earthquakes may artificially result in higher stress

drop estimates for larger earthquakes and therefore, result in higher ground motion

estimates for earthquake hazard analyses (ATKINS and SILVA, 2003).

One question addressed in this paper is whether researchers can obtain reliable

source parameters from surface recordings of small earthquakes when site response

interferes with attempts to identify source parameters. We conclude that reliable

estimates are possible, provided that the data available are from a good azimuthal

distribution of stations. We also found that a bias can occur in moment estimates if

parameters are not calibrated against more stable solutions, such as full waveform

modeling. We compared source spectra from two independent techniques and found

that the Brune x-2 spectral shape is consistent with both approaches. Finally, we

validated that the CM and NM accurately estimate source parameters if certain

conditions are met. Obtaining an accurate estimate of source corner frequency and

long-period spectral levels of small earthquakes is important since they are used to

estimate moment and stress drop (BRUNE, 1970), scale summation of empirical

Green’s functions for strong motion synthesis (JOYNER and BOORE, 1982; IRIKURA,

1983, 1986; HUTCHINGS, 1994; PIOR, 2005), calculate relative source time functions

(LAY et al., 2004), deconvolve out the Brune source spectra of empirical Green’s

functions (HUTCHINGS et al., 2007), and examine seismicity (NADEAU and JOHNSON,

1998).

The purpose of this study has been to apply and compare two completely different

approaches, NM and CM, to obtain estimates of source parameters. Each method

presented in this manuscript has advantages and disadvantages. It is more common to use

CM for events recorded on a regional scale for a broad range of magnitudes. There is a

possibility that the path correction may introduce 2-D effects at high frequencies. CM

requires a long record length, which may not always be available in local aftershock

studies. NM does not seem to perform well for larger events (Mw > 4.2), possibly due to

the finite source effect. This study shows that the energy-moment scaling is not constant

in the Marmara region and the apparent stress increases with moment. The Marmara

region is expecting another large event in the not too distant future, and scaling is an

important component of seismic hazard studies.

Acknowledgments

We like to thank associate editor, Arthur Snoke for enhancing the paper with his

critical comments. We also express thanks to Eliza Richardson and the other anonymous

reviewer for their valuable contributions. This project was partially supported by the

Lawrence Livermore National Laboratory under the auspices of the U.S. Department of

Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-

07NA27344. This is LLNL contribution LLNL-JRNL-408432.


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