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Geophys. J. Int. (2007) 171, 390–398 doi: 10.1111/j.1365-246X.2007.03544.xG
JISei
smol
ogy
Evaluation of strength of heterogeneity in the lithosphere from peakamplitude analyses of teleseismic short-period vector P waves
Mungiya Kubanza, Takeshi Nishimura and Haruo SatoDepartment of Geophysics, Graduate School of Science, Tohoku University, Aramaki-aza Aoba 6-3, Aoba-ku, Sendai 980-8578, Japan.E-mail: [email protected]
Accepted 2007 July 2. Received 2007 June 28; in original form 2007 January 16
S U M M A R YWe quantitatively characterize the regional variations in the strength of heterogeneity in thelithosphere of the globe by analysing the observed seismogram envelopes of teleseismicP waves in the frequency band of 0.5–4 Hz. We apply a theoretical scattering model basedon the Markov approximation for a plane P wave propagating through the random mediumcharacterized by a Gaussian autocorrelation function. Since this model presumes the verti-cal incidence of an impulsive plane wavelet, we first analyse teleseismic P waves from deepearthquakes occurring along the western Pacific regions. We measure the ratios of peak inten-sity of transverse components to that of the sum of the three components, and determine thequantity of randomness ε2z/a, where ε, a and z are fractional fluctuation, correlation distanceand thickness of a heterogeneous structure, respectively. Although source time functions ofshallow earthquakes are too complex to directly apply the scattering model, a good correlationbetween the ratios of peak amplitude and the normalized transverse amplitude, which is thesquare root of the energy partition of the P-coda waves into the transverse component, enablesus to use the shallow earthquakes that occur widely around the world. As a result, the quantityε2z/a extends from 1.15 × 10−4 to 6.34 × 10−2 at 0.5–1 Hz, 2.02 × 10−3 to 1.89 × 10−1 at1–2 Hz and 1.49 × 10−4 to 1.89 × 10−1 at 2–4 Hz, which are in agreement with the results ofprevious studies using different methods. The spatial distribution of randomness almost agreeswith various tectonic settings and roughly correlates with lateral variations of Lg coda Q andshear wave velocity perturbations at 80 km depth, suggesting that lateral heterogeneity extendsfrom the shallow crust to uppermost mantle.
Key words: heterogeneity, lithosphere, peak amplitude, teleseismic P waves.
1 I N T RO D U C T I O N
Stochastic methods are often used for the characterization of seis-
mic wave propagation through randomly heterogeneous media. Peak
delay, duration and maximum amplitude of seismograms have been
considered as important parameters for the quantification of seismo-
grams and have been investigated in a number of studies. Generally,
peak delay is defined as a lag time between the onset of P or Sbody waves and the arrival time of its maximum amplitude, and the
envelope duration is defined by a lag time between the onset and
the time when the rms envelope decays to half of the maximum
amplitude. Atkinson & Boore (1995) showed that the envelope du-
ration generally depends on both source and path, and increases
with increasing travel distance. Using the Markov approximation,
which is a stochastic approximation applied to the parabolic wave
equation (e.g. Ishimaru 1978), Sato (1989) quantitatively explained
the envelope broadening of scalar wavelet by considering small-
angle scattering of waves around the forward direction caused by
the random heterogeneity of wave velocity. His model suggested
that the duration of seismogram is a good measure for representing
the heterogeneity of the lithosphere. Fehler et al. (2000) confirmed
the validity of the Markov approximation from a comparison of the
envelopes calculated by using that approximation and those from
waveforms of the 2-D finite difference simulation.
Maximum amplitude decay with traveltime distance increasing
has also been considered as one of the most important parameters
for the quantification of seismograms. The envelope broadening and
the maximum amplitude decay have been studied independently or
empirically, but Saito et al. (2005) recently provided a unified ex-
planation of those phenomena for high-frequency S-wave envelopes
based on wave scattering process. The observed duration and max-
imum amplitude are simulated simultaneously based on the theo-
retical envelope by using an appropriate statistical property of the
velocity heterogeneity and the attenuation of the lithosphere.
Characteristics of scattered seismic waves have been studied for
these several decades to investigate the spatial distributions of ran-
dom heterogeneity in the crust and upper mantle. Korn (1993) ap-
plied the energy flux model of the teleseismic P-wave envelopes
390 C© 2007 The Authors
Journal compilation C© 2007 RAS
Strength of heterogeneity in the lithosphere 391
to characterize the heterogeneity of the lithosphere and reported
the difference in Q-value between stable continents and tectoni-
cally active regions. Hock et al. (2004) interpreted the teleseismic Pcoda observed in northern and central Europe, and estimated litho-
spheric heterogeneity beneath the receivers by applying the energy–
flux model and the teleseismic fluctuation wavefield method. They
reported clear regional differences in scattering attenuation both
in size and in frequency dependence reflecting a spatial variation
of the scattering properties of the lithosphere. The largest scatter-
ing attenuation was found in the northern German basin and the
smallest scattering attenuation in the Baltic shield. Fredericksen &
Revenaugh (2004) used teleseismic P waves which are dominated
by energy scattered by small inhomogeneities in the receiver-side
lithosphere for investigating lateral variations of heterogeneity.
Nishimura (1996) pointed out that the amplitudes of transverse
component in long-period (about 20 s) P waves observed at sta-
tions on island arcs are much larger than those on stable continents.
Nishimura et al. (2002) further evaluated lateral heterogeneity in
the lithosphere by analysing the transverse amplitude of teleseismic
P wave. They showed that strong heterogeneity is recognized in and
around the tectonically active regions and estimated relative scat-
tering strength in depth assuming a single scattering process. Their
studies are restricted to the western Pacific region due to the limited
hypocentral distribution of deep earthquakes, because they needed a
simple source time function for evaluating the depth dependence of
scattering properties. Kubanza et al. (2006) systematically charac-
terized the medium heterogeneity of the lithosphere from the anal-
yses of transverse-component amplitudes of teleseismic P waves
from shallow earthquakes in short periods from 0.5 to 4 Hz. They
showed that the transverse-component amplitudes of teleseismic Pwaves are useful for detecting heterogeneity, but have not yet quanti-
tatively evaluated the medium heterogeneity by physical parameters
such as correlation distance or fractional fluctuations in the seismic
structure.
In the present study, we examine the characteristic features of
the envelopes of teleseismic P-wave seismograms and measure the
peak intensity of transverse component and that of the sum of three
components to quantitatively evaluate the heterogeneity of the litho-
sphere. We apply the theoretical scattering model (Sato 2006) that
establishes a relationship between the ratio of the peak intensity
and the randomness of the lithosphere. Since this kind of analy-
ses is valid when the seismic source time function is impulsive,
the target region is at first restricted at the western Pacific region
and middle of Eurasian continent, where deep seismic sources are
used for the analysis. We further examine the relation between peak
and averaged amplitudes in transverse component for shallow and
deep earthquakes, and quantify the strength of heterogeneity in the
lithosphere of the globe.
2 T H E O R E T I C A L M O D E L
The method is based on the measurement of the peak intensity of
vector wave envelopes predicted by seismic wave scattering due
to weak velocity inhomogeneities. The lithospheric heterogeneity
is modelled by uniform and isotropic random media statistically
characterized by the autocorrelation function of velocity fractional
fluctuation. When the wavelength is shorter than the correlation dis-
tance of random media, wave propagation is governed by a parabolic
wave equation. An ensemble average of the wave equation gives the
master equation for the two frequency mutual coherence function
(TFMCF), of which the Fourier transform gives the mean square
Figure 1. Plots of I Px0 and I P
y0 (thin solid line), I Pz0 (dashed line) and
I R0 (thick solid line) against reduced time t − z/V0 for the incidence of a
unit impulsive wavelet. The peak amplitudes of each component including
that of the sum of three components is analytically given. The time delay,
tM , is also analytically determined.
envelope of wavefield. This method is called the Markov approxi-
mation, which was developed for the studies of optical wave through
random refractive index or acoustic waves through random velocity
media (e.g. Ishimaru 1978); however, past studies developed are for
scalar waves. Recently, Sato (2006) developed a theoretical synthe-
sis of vector wave envelopes in randomly inhomogeneous elastic
media expressed by a Gaussian-type autocorrelation function as an
extension of the Markov approximation for scalar waves. It well
predicts not only the envelope broadening of a P wavelet in the
longitudinal component but also the excitation of amplitude in the
transverse component.
We define�
I x0P ,
�
I y0P and
�
I z0P as the mean square (MS) envelope
traces of x-, y- and z-component, respectively, for the vertical inci-
dence of a delta function-like plane P wavelet. The reference inten-
sity�
I 0R expresses the envelope of the sum of the three components.
For the analysis of individual wave MS envelopes, theoretical inten-
sities without wandering effect (e.g. Sato 2006),�
I x0P ,
�
I y0P and
�
I z0P ,
are appropriate since the lapse time is measured from the P-wave
onset, that is, the wandering effect is removed. Fig. 1 shows�
I x0P
and�
I y0P (thin solid line),
�
I z0P (dashed line) and
�
I 0R (thick solid line)
against reduced time. The reference intensity�
I 0R shows a broadened
envelope having a maximum peak of 0.46 /tM = 0.52V0a/(ε2z2)
at reduced time about 0.67tM , where the characteristic time is
tM = √πε2z2/(2V0a). Parameters ε, z, V0 and a are fractional
fluctuation of P-wave velocity, thickness of a heterogeneous struc-
ture, average velocity of P wave in the lithosphere and correlation
distance, respectively. The peak height of�
I x0P is about 0.94V0/z
at reduced time about 1.63tM . There is a time lag of 0.96tM be-
tween the peak arrivals. If the excitation of transverse amplitude is
small, we may roughly estimate the peak height of�
I z0P to be about
0.52V0a/(ε2z2)−1.88V0/z. The ratio of the peak value of�
I x0P to that
C© 2007 The Authors, GJI, 171, 390–398
Journal compilation C© 2007 RAS
392 M. Kubanza, T. Nishimura and H. Sato
of�
I 0R is
I P,peakx0
I R,peak0
≈ 1.81ε2
az. (1)
These simulations can be summarized as follows (Sato 2006).
For the incidence of an impulsive plane P wavelet, each of longi-
tudinal and transverse component envelopes shows peak delay and
envelope broadening with travel distance increasing. The transverse
component has a smaller amplitude and a longer peak delay than the
longitudinal component; however, the transverse component ampli-
tude essentially reflects scattering and diffraction effects: the time
integral of the MS amplitude of transverse component linearly in-
creases with travel distance increasing and are proportional to the
ratio of the MS fractional fluctuation of P-wave velocity to the cor-
relation distance. These theoretical results imply that the partition
of energy to the transverse component in the teleseismic P-wave
envelope could be a good stochastic measure of medium hetero-
geneity of the crust and the uppermost mantle. The validity of the
Markov approximation was confirmed from a comparison with the
numerical simulations by using a finite difference method (Fehler
et al. 2000; Korn & Sato 2005). We should note that the formula-
tion shown above does not include P–S conversion scattering which
might exists in real data.
3 DATA A N D WAV E F O R M P RO C E S S I N G
We use the seismic waveform data of deep earthquakes that oc-
curred along the western Pacific regions. We apply the theoretical
model presented in previous section to these data. Incidence angles
for the P wave we analysed extend from 0◦ to 40◦, but no systematic
change is observed in the following analyses for different incidence
angle. Fig. 2 shows the geographical location of the IRIS GSN sta-
tions (triangles) and deep earthquakes (solid circles) contributed to
the analysis. These data are collected in the observational period
of 1987–2000 for deep earthquakes with focal depths greater than
300 km, magnitudes of more than 5 and less than or equal to 6, and
epicentral distance of 0–60◦. For each earthquake-station pair, the
signal-to-noise ratio has to be high enough so that the coda ampli-
tude level at the end of the time window is still several times above
the noise level before the onset of P wave. We verify this for each
Figure 2. Geographical distribution of IRIS GSN stations (triangles) and
deep earthquakes (solid circles) used in this study. Deep earthquakes located
at the western Pacific regions with focal depth greater than 300 km and
magnitude between 5 and 7, are collected in the observational period of
1987–2000. Open circles indicate shallow earthquakes of focal depth less
than 35 km and magnitude between 5 and 6 taken in the period of 1998–
2002, and used for estimation of normalized transverse amplitudes around
the world (Kubanza et al. 2006).
of the frequency bands of 0.5–1, 1–2 and 2–4 Hz by calculating the
signal-to-noise ratio. The signal amplitudes are calculated for 10 s
time window from P-wave onset and the noise amplitudes are taken
at least 5 s prior to the P-wave onset. Only traces with signal-to-
noise ratio greater than or equal to 10 are selected for this analysis.
Seismograms are also visually examined for strange later arrivals
and other irregularities. Some of later arrivals may be caused by
complex behaviour of the faulting process, but must appear within
a few seconds because we analyse the data of magnitudes less than
or equal to 6. However, later arrivals caused by unknown struc-
tural complexities along the ray path may not be excluded in this
analysis.
4 C H A R A C T E R I S T I C F E AT U R E S
O F S E I S M O G R A M E N V E L O P E S
We obtain the general features of seismogram envelopes by per-
forming the following procedures for each station. First, we band-
pass filter the observed three component seismograms for 0.5–1,
1–2 and 2–4 Hz ranges where high signal-to-noise ratio are ob-
tained. Then, we calculate the square of seismogram with following
expression,
ei (t) = u2i (t) + H [ui (t)]
2, (2)
where ui (t) is the original velocity signal of ith component and
H [ui (t)] is its Hilbert transform. We note that i (=1, 2, 3) express
the vertical, radial and transverse components. Subsequently, we
normalize the seismogram envelopes of each component using the
following formula:
Ei (t) = ei (t)
E0
, (3)
where
E0 = 1
T
∫ T
0
E0(t ′) dt ′ = 1
T
∫ T
0
3∑j
e j (t′) dt ′,
where T is the duration time used for the normalization. MS en-
velope, 〈Ei (t)〉, is calculated by stacking the all of the normalized
seismogram envelopes for each component at each station. We stack
4–23 seismograms at each station, among a half of which more than
10 seismograms are stacked, for obtaining the average envelopes
used in the following analyses. Finally, for each station, we calcu-
late the average envelope for a time window of 60 s (T = 60 s) that
starts 10 s before the P-wave onset.
Left panels in Fig. 3(a) shows examples of the observed aver-
age envelope traces 〈Ei (t)〉 at frequency band of 0.5–1, 1–2 and
2–4 Hz, respectively. Station WRAB in Australia, which is located
on stable continent is shown. Dashed, dotted and thin solid lines
represent the vertical, radial and transverse component, respectively,
and thick line represents the sum of the three components. The radial
and transverse components are rotated from two horizontal compo-
nents using backazimuth calculated from the locations of hypocentre
and station. The peak amplitudes are measured on the average en-
velope traces. Since transverse components often have very small
amplitude, we show the rms of average envelopes,√〈Ei (t)〉, for
indicating clear view in the right three panels. Fig. 3(b) shows the
MS and rms envelopes at station PMG in New Guinea, locating at
tectonically active region.
The following characteristics are recognized in the averaged en-
velope traces. For about 5 s from the onset of P wave, amplitude of
the vertical component is larger than those of the other components
C© 2007 The Authors, GJI, 171, 390–398
Journal compilation C© 2007 RAS
Strength of heterogeneity in the lithosphere 393
MS
Am
pli
tude
Time (s)
RM
S A
mpli
tude
Time (s)
0.00
0.01
0.02
0.00
0.01
0.02
0.00
0.01
0.02
5 10 15 20 25 30
0.00
0.05
0.10
0.15
0.00
0.05
0.10
0.15
0.00
0.05
0.10
0.15
5 10 15 20 25 30
1-2 Hz 1-2 Hz
2-4 Hz 2-4 Hz
0.5-1 Hz 0.5-1 Hz
Station: WRAB (a)
0.00
0.05
0.10
0.15
5 10 15 20 25 30
0.00
0.05
0.10
0.150.00
0.05
0.10
0.15
0.00
0.01
0.02
5 10 15 20 25 30
0.00
0.01
0.02
0.00
0.01
0.02
MS
Am
pli
tud
e
Time (s)
RM
S A
mp
litu
de
Time (s)
Station: PMG
1-2 Hz 1-2 Hz
2-4 Hz 2-4 Hz
0.5-1 Hz 0.5-1 Hz
(b)
Figure 3. (a) Seismogram envelopes and its root mean square for station WRAB in Australia, representative of stable continents at the frequency band of
0.5–1, 1–2 and 2–4 Hz. Dashed, dotted and thin solid lines indicate the vertical, radial and transverse components, respectively. Thick solid line indicates the
sum of the three components.(b). Same as Fig. 3(a) except for the station PMG in New Guinea, representative of tectonically active regions.
for all of the frequency bands. Amplitude of the radial component
is generally larger than that of the transverse component, especially
at the low frequency bands of 0.5–1 and 1–2 Hz. As frequency in-
creases, the amplitude of radial component often approaches that of
the transverse component. At several stations, their amplitudes are
almost the same at 2–4 Hz. The amplitude of the three components
converges to almost the same levels about 5 or 10 s after the P-onset.
Transverse component reaches the maximum amplitude several sec-
onds later than the time when the maximum amplitude is recorded
in the vertical component. Such a peak delay is observed at all of
the stations.
These characteristics are qualitatively well explained by the
oblique incidence of P wave to a random heterogeneous layer be-
neath stations. In the first 5 s, the direct P wave is dominant so
that vertical amplitudes expected to be larger than the other. Direct
P wave is recognized in the radial component but not in the trans-
verse component. Later coda consists of the waves scattered by ran-
dom heterogeneity, which makes the energy partition of the seismic
C© 2007 The Authors, GJI, 171, 390–398
Journal compilation C© 2007 RAS
394 M. Kubanza, T. Nishimura and H. Sato
energy equal to the three components. Peak delay recognized in the
transverse component is qualitatively well explained by the theory
of Sato (2006).
5 E S T I M AT I O N O F R A N D O M
H E T E RO G E N E I T Y B A S E D O N A
S C AT T E R I N G M O D E L
We quantitatively evaluate the scattering property using eq. (1). We
measure the ratios of peak intensities, 〈E3(t)〉peak/〈E0(t)〉peak, from
the observed stacked envelopes at 13 stations locating in the west-
ern Pacific regions and middle of Eurasian continent. 〈E3(t)〉peakand
〈E0(t)〉peak are the peak of average envelope of the transverse com-
ponent and that of the sum of the three components, respectively.
In our analysis, x-component in eq. (1) corresponds to the trans-
verse component, and reference intensity function�
I 0R is expressed
by the envelope of the sum of the three componentsE0(t), that is,
〈E3(t)〉peak/〈E0(t)〉peak ≈ I Px0,peak/ I R
0,peak. The results show that the
ratios are ranging from 0.010 to 0.099 for 0.5–1 Hz, 0.011 to 0.339
for 1–2 Hz and 0.015 to 0.325 for 2–4 Hz. Fig. 4 shows spatial vari-
ations of square root of the observed ratios of peak intensity in the
western Pacific regions and middle of Eurasian continent. Overall
characteristics are quite similar to the spatial distributions recog-
nized in the normalized transverse amplitude estimated by Kubanza
et al. (2006) for stations in the same regions. Stations located on
Australian continent and those on mid-Eurasia including a station
in Thailand indicate small ratios, while stations on island arc and
close to the collision zone of India and Eurasia continents show large
ratios. In Fig. 5, the ratios of peak intensity are plotted for each fre-
quency band. The ratios of peak intensity are scattered especially
at the high frequency, however their averages for each frequency
band increases with increasing frequency: 0.040 at 0.5–1 Hz, 0.087
at 1–2 Hz and 0.141 at 2–4 Hz.
We estimate ε2/a from the ratios of peak intensity by tentatively
assuming the thickness of heterogeneity to be z = 100 km and plot
it in Fig. 5 (see right vertical axis). As Flatte & Wu (1988) esti-
mates the thickness to be about 200 km and crustal structure is
often considered to be major origins of the scattered waves, the
thickness of heterogeneity may be ranging from a few tens to a
few hundred kilometres. Hence, the estimated ε2/a has an accu-
racy by a factor of about 3. In the 0.5–1 Hz band, ε2/a is ranging
from 5.30 × 10−5 to 5.49 × 10−4 km−1 with an average of 2.23 ×10−4 km−1; at 1–2 Hz, ε2/a extends from 6.00 × 10−5 to 1.87 ×10−3 km−1 with an average of 4.86 × 10−4 km−1; at 2–4 Hz, ε2/avaries from 8.40 × 10−5 to 1.80 × 10−3 km−1 with an average of
7.81 × 10−4 km−1. These averages are plotted with their standard
deviation. Assuming a = 5 km for all frequency bands, we estimate
ε to be 2–4 per cent for the lithosphere in the stable continents. On
the other hand, stations on Japan and collision zones of Indian and
Eurasian continents show larger ε2/a for all of the frequency ranges.
As a result, ε ranges from 5 to 10 per cent for a = 5 km. More large
ε is calculated when we assume larger a (e.g. ε is 7–14 per cent for
a = 10 km).
6 G L O B A L D I S T R I B U T I O N O F
S T R E N G T H O F H E T E RO G E N E I T Y
I N T H E L I T H O S P H E R E
We have shown that the ratios of peak intensity between the trans-
verse component and the sum of the three components of teleseismic
1.00.80.60.40.2
1-2 Hz
0.5-1 Hz
2-4 Hz
(max=0.58)
(max=0.32)
(max=0.57)
peakpeak tEtE ><>< )(/)( 03
Figure 4. Spatial distribution of the square root of ratios of peak intensity√〈E3(t)〉peak/〈E0(t)〉peak at the frequency bands of 0.5–1, 1–2 and 2–4 Hz.
Symbol sizes of the ratios are normalized by the maximum value (indicated
at the right bottom of each panel) observed at each frequency band.
C© 2007 The Authors, GJI, 171, 390–398
Journal compilation C© 2007 RAS
Strength of heterogeneity in the lithosphere 395
0.0
0.1
0.2
0.3
0.4
0.5-1 1-2 2-4
Frequency band (Hz)
220.0
165.0
110.0
55.0
0.0
P, peakxI 0
ˆ 2
[x10-5 km-1]
R, peakI 0ˆ a
Figure 5. Relations of the ratios of peak intensity, I P,peakx0 / I R,peak
0 , and the
ratio of the fractional fluctuation to the correlation distance, ε2/a, for three
frequency bands. The averages (black circles) are plotted with an error bar at
each frequency band. Star, triangle and square symbols indicate the values of
ε2/a estimated by Aki (1973), Powell & Meltzer (1984) and by Scherbaum
& Sato (1991), respectively.
P waves can be useful to evaluate randomness of the lithospheric
structure. However, since the scattering model used requires the
seismic data having an impulsive source time function, we can-
not easily estimate the randomness of the lithospheric structure
at the region where deep earthquake data are not available. Shal-
low earthquakes are recorded at many stations around the world,
but complex fault motions and contamination of reflection and
refraction phases from the ground/water surface and heterogene-
ity often prevent us from correctly reading the peak amplitude. In
this section, therefore, we evaluate the randomness of the structure
around the world by using the normalized transverse amplitudes
〈A〉, which is defined as the square root of the energy partition of
the P-coda waves into the transverse component (Kubanza et al.2006):
〈A〉 =⟨√√√√∫ TA
0
e3(t)dt
/ 3∑i=1
∫ TA
0
ei (t)dt
⟩,
where bracket 〈 〉 represents the average of all events recorded at each
station. We use a time window of TA = 20 s in the present study. It is
noted that the normalized transverse amplitude generally increases
with time window length since the energy of scattered waves comes
to be almost equally partitioned into the three components as lapse
time increases.
Fig. 6 compares the square root of ratios of peak intensity with
the normalized transverse amplitudes at the stations located on the
western Pacific regions and middle of Eurasian continent, where
deep earthquake data are available (the same data used in Sec-
tion 5). It is clearly seen that the ratios of peak intensity linearly
increase with the normalized transverse amplitude at all of the fre-
quency bands. Correlation coefficients are quite high: 0.94 at 0.5–
1 Hz band, 0.88 at 1–2 Hz band and 0.97 at 2–4 Hz band. Therefore,
we can relate the ratios of peak intensity with the normalized
<A
>
0.5-1 Hz
1-2 Hz
2-4 Hz
r = 0.97
r = 0.94
r = 0.88
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0
0.2
0.4
0.6
0.0 0.2 0.4 0.6
<A
>
<A
>
peakpeak tEtE ><>< )(/)( 03
Figure 6. Comparison between the square root of the ratios of peak inten-
sity and the normalized transverse amplitudes. The data are obtained from
seismograms of deep earthquakes recorded at stations in the western Pacific
regions. Thin lines are linear regressions at each frequency band. Correlation
coefficients of each regression line are 0.94, 0.88 and 0.97 at 0.5–1, 1–2 and
2–4 Hz frequency band, respectively.
C© 2007 The Authors, GJI, 171, 390–398
Journal compilation C© 2007 RAS
396 M. Kubanza, T. Nishimura and H. Sato
transverse amplitudes:
〈A〉 = 1.08√
〈E3(t)〉peak/〈E0(t)〉peak + 0.07 for 0.5−1 Hz
〈A〉 = 0.65√
〈E3(t)〉peak/〈E0(t)〉peak + 0.15 for 1−2 Hz
〈A〉 = 0.65√
〈E3(t)〉peak/〈E0(t)〉peak + 0.15 for 2−4 Hz.
(4)
We should note that the normalized transverse amplitudes in
eq. (4) are estimated from the P waves for 20 s, hence different
regression lines are necessary for the cases using shorter or longer
time windows. Kubanza et al. (2006) showed that the normalized
transverse amplitudes obtained from deep earthquakes are nearly
equal to those estimated from shallow earthquakes (see Fig. 3 of
Kubanza et al. (2006)). This result strongly suggests that the empir-
ical relations indicated in eq. (4) can be used for shallow earthquake
data. That is, we can systematically estimate the quantity of ran-
domness of the lithosphere, ε2z/a, at almost all of the world only
by measuring the normalized transverse amplitude of shallow earth-
quakes.
Fig. 7 shows the global distribution of the randomness ε2z/a of
the lithosphere estimated from the normalized transverse amplitudes
of shallow earthquakes evaluated by Kubanza et al. (2006). Colour
scales at the bottom of each panel indicate amplitude of ε2z/a.
This spatial distribution of randomness almost agrees with various
tectonic settings. Small randomness are dominant at stations on
stable continents such as Australia, mid-Eurasia, Africa and eastern
North America, most of which shows ε2z/a of 0.000–0.016 at 0.5–
1 Hz, 0.000–0.025 at 1–2 Hz and 0.000–0.050 at 2–4 Hz. On the
other hand, large randomness of more than 0.024 at 0.5–1 Hz and
more than 0.075 at 1–2 and 2–4 Hz are found at tectonically active
regions such as the Arabia–Eurasia and the India–Eurasia collision
zones, the island arcs in the western Pacific regions, the east African
rift system and the transform fault and subduction zones along the
western coast of the American continents. The randomness of ε2z/aat several stations, however, does not reflect the tectonic settings
characterized by the seismicity (stations of Category B in Kubanza
et al. 2006).
7 D I S C U S S I O N S A N D C O N C L U S I O N S
We compare the scattering properties estimated from the peak ra-
tios of transverse component to the sum of three components with
the results in the previous studies. For the lithosphere in the stable
continents, Aki (1973) estimated ε2/a of the lithospheric hetero-
geneity to be 1.60 × 10−4 km−1 at about 0.5 Hz, analysing the cor-
relation between log-amplitude and phase fluctuation of teleseismic
P waves arriving with near vertical incidence at LASA in Montana.
Ritter et al. (1998) reported ε2 ≈ 0.0009–0.005 and a ≈ 1–16 km
of lithosphere with a thickness of 70 km for the frequency of 0.3–
3 Hz by analysing differences in frequency-dependent intensities
of the mean wave and the fluctuation part of teleseismic P waves
observed in Massif Central, France. From their results, we estimate
ε2/a = 5.6 × 10−5–5 × 10−3 km−1. Hock et al. (2004) reported
ε2 ≈ 0.0009–0.005 and a ≈ 1–7 km for the lithosphere in northern
and central Europe, and their results indicate that ε2/a are rang-
ing from 1 × 10−4 to 2 × 10−3 km−1. Scherbaum & Sato (1991)
estimated the ratio ε2/a ≈ 5.40 × 10−4 km−1 from the envelope
analysis of S waves at 2–16 Hz in Kanto, Japan. Powell & Meltzer
(1984) analysed traveltime fluctuations of teleseismic P waves of
dominant frequency near 1 Hz observed in southern California, and
obtained a = 25 km and ε2 = 0.001, which gives ε2/a = 4 ×
0.5-1 Hz
1-2 Hz
2-4 Hz
0.000 0.100 0.200
0.000 0.100 0.200
0.000 0.032 0.064
2 /a z
2 /a z
2 /a z
Figure 7. Spatial distribution of the randomness of the lithosphere on the
globe at frequency bands of 0.5–1, 1–2 and 2–4 Hz. The scale bars indicate
the variation of strength of heterogeneity for each frequency band.
10−5 km−1, for the heterogeneous structure with a thickness of
at least 119 km. Our estimation of ε2/a at island arcs and tec-
tonically active regions are ranging from 4.27 × 10−4 to 1.87 ×10−3 km−1 and ε2/a for stable continent from 5.30 × 10−5 to
3.63 × 10−4 km−1, which are almost consistent with these previ-
ous studies although the methods for estimation of ε2/a are not the
same.
The series of studies by Mitchell (1995), Mitchell et al. (1997,
1998), DE Souza & Mitchell (1998), Baqer & Mitchell (1998) have
provided new insights on the relation of seismic wave attenuation to
the tectonic history of continents for various regions of the world by
using Lg coda Q tomography. In Fig. 8, we characterize the strength
of heterogeneity of the lithosphere on the basis of Lg coda Q val-
ues taken from the studies of Mitchell and his colleagues for five
different continents (Eurasia, Australia, Africa, North and South
America). The data are scattered, but we notice that the stations
having large ε2z/a always show small Lg coda Q (region III in
C© 2007 The Authors, GJI, 171, 390–398
Journal compilation C© 2007 RAS
Strength of heterogeneity in the lithosphere 397
1-2 Hz
200
400
600
800
1000
Lg c
oda
Q
0.00 0.05 0.10 0.15 0.20
I
II III
1
2
2 /a z
Figure 8. Relation between the randomness of the lithosphere at 1–2 Hz
band and Lg coda Q values taken from the studies of Mitchell’s group. The
encircled numbers indicate tentative boundaries of categories I, II and III:
Category I indicates the region with small ε2z/a and large Lg coda Q, II
with small ε2z/a and small Lg coda Q, and III with large ε2z/a and small
Lg coda Q.
Fig. 8). These stations are generally located at tectonically ac-
tive regions. The stations having large Lg coda Q always indicate
small ε2z/a (region I), which are located on stable continents. We
also find stations having small ε2z/a and small Lg coda Q (re-
gion II). These are located at eastern China, Russia, Mongolia,
California (USA), Arizona (USA), Tennessee (USA), Indiana
(USA), Argentina, Kenya, Namibia and Australia, but no simple
relation to tectonic settings has yet been found.
Fig. 9 compares the randomness of the lithosphere with the shear
wave velocity perturbations at 80 km depth reported by Gung &
Romanowicz (2004). Although the correlation coefficient between
the two parameters is weak, –0.52, a negative trend as shown by
the regression line is visible such as fast velocity anomaly corre-
sponds mainly to small randomness while low velocity anomaly
corresponds to large randomness. These characteristics suggest that
lateral heterogeneity generating transverse amplitudes at least ex-
tends from shallow crust to deeper portions in the uppermost mantle.
Such vertical extension of the heterogeneity is also suggested by the
results of Nishimura et al. (2002) in which large scattering coeffi-
cients are found at deeper portions exceeding 100 km beneath the
island arcs.
We considered several simplified assumptions in the application
of the theoretical model to the observed data: uniform and isotropic
randomness with a Gaussian ACF for the lithospheric heterogeneity,
vertical incidence of teleseismic P waves to the lithospheric layer, no
large angle scattering and no conversion scattering between P and
S waves. The resultant randomness parameter ratio ε2z/a increases
with frequency increasing, which suggests a power-law spectrum
for randomness, although the ratio is scattered at high frequency. So
far we have theoretical vector envelopes only for a Gaussian ACF,
however, we need to introduce von Karman type ACF to explain
such a frequency dependence (Saito et al. 2002). The theoretical
model qualitatively explains characteristics of observed vector en-
1-2 Hz
-6
-4
-2
0
2
4
6
dV
(%)
0.00 0.05 0.10 0.15 0.20
r = - 0.52
2 /a z
Figure 9. Relation between ε2z/a of the lithosphere at 1–2 Hz band and
shear wave velocity perturbation determined by Gung & Romanowicz
(2004). Thin line indicates a regression line showing a negative trend with a
weak correlation coefficient of –0.52.
velopes; however, this theoretical model fails to explain the conver-
gence of longitudinal and transverse amplitudes each other, which
can be explained with the introduction of large angle scattering and
PS conversion scattering. Also the ground-free surface effects and
layered structure, which are often determined by receiver function
analyses, have been neglected, hence, we need to develop a model,
which take into account the above mentioned effects. We may be able
to estimate the heterogeneity by comparing the observed normalize
transverse amplitude with Sato (2006)’s model. However, numeri-
cal calculation is necessary for evaluating the normalized transverse
amplitude, and later coda is not well modelled by the Markov ap-
proximation in which the forward scattering becomes a dominant
process. Hence, the present study used empirical relations in eq. (4)
for estimating the heterogeneity from shallow earthquake data.
We have examined the P-wave seismogram envelopes of teleseis-
mic events recorded at stations located along the western Pacific
region and middle of Eurasian continent where deep earthquakes
having a simple source time function are available. The observed
envelopes are qualitatively well explained by the theoretical predic-
tion of the scattering wave model of Sato (2006) using the Markov
approximation. Some amounts of the seismic energy are distributed
in the transverse components and peak intensity of transverse com-
ponents appears later than that of vertical component. Applying
a theoretical scattering model of plane P wavelet propagation in
random medium (Sato 2006), we have quantitatively evaluated the
heterogeneity in the lithosphere from the ratios of peak intensity
of the transverse component and the sum of the three component
in the western Pacific region and middle of Eurasian continent. We
further estimate the heterogeneity on the globe using the empirical
relationship between the ratios of peak intensity and the normal-
ized transverse amplitudes from shallow earthquakes estimated by
Kubanza et al. (2006). The results show that the quantity of random-
ness ε2z/a extends from 1.15 × 10−4 to 6.34 × 10−2 at 0.5–1 Hz,
2.02 × 10−3 to 1.89 × 10−1 at 1–2 Hz and 1.49 × 10−4 to 1.89 ×
C© 2007 The Authors, GJI, 171, 390–398
Journal compilation C© 2007 RAS
398 M. Kubanza, T. Nishimura and H. Sato
10−1 at 2–4 Hz, which are in good agreement with the results of pre-
vious studies using different methods. The spatial distribution of the
quantity of randomness of the lithosphere roughly agrees with var-
ious tectonic settings. Small quantity of randomness are observed
at stations on inactive regions such as stable continents while large
quantity are found at tectonically active regions such island arcs,
collision zones, transform faults and subduction zones. We com-
pare the quantity of randomness of the lithosphere we obtained with
Lg coda Q and shear wave velocity perturbations at 80 km depth.
These spatial distributions are roughly correlated with each other,
suggesting that lateral heterogeneity extends from shallow crust to
upper mantle.
The consistency of the spatial distribution of the quantity of ran-
domness of the lithosphere on the globe evaluated by using the
Markov approximation model and that of the normalized transverse
amplitudes has proved that the partition of energy into the trans-
verse component could be used for evaluating the strength of het-
erogeneity in the lithosphere. These analyses as well as tomography
technique, Q estimation using more densely distributed stations will
help us to understand the lithospheric structure of the globe.
A C K N O W L E D G M E N T S
The manuscript was significantly improved by careful comments by
Prof Michael Korn, Dr Ulrich Wegler and an anonymous reviewer.
We like to thank all members of the Data Management Center of
IRIS for making the seismic data available through the internet.
MK is supported by MEXT under the Grant-in-aid from Japanese
Government scholarship.
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