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Velocity and Attenuation Structure of the Tibetan Lithosphere Under the Hi-CLIMB Array
From the Modeling of Pn Attributes
ALI C. BAKIR1 and ROBERT L. NOWACK
1
Abstract—Using seismic data from regional earthquakes in
Tibet recorded by the Hi-CLIMB experiment, Pn attributes are
used to constrain the velocity gradient and attenuation structure of
the Tibetan lithosphere under the Hi-CLIMB array. Numerical
modeling is performed using the spectral-element method (SEM)
for laterally varying upper-mantle velocity and attenuation, and the
seismic attributes considered include the Pn travel-time, envelope
amplitude, and pulse frequency. The results from the SEM mod-
eling provide two alternative models for the upper-mantle beneath
the Hi-CLIMB array in Tibet. The first model is derived from the
3D velocity model of GRIFFIN et al. (Bull Seism Soc Am
101:1938–1947, 2011) with a constant upper-mantle velocity gra-
dient, and laterally varying upper mantle attenuation. The second
model has a laterally varying upper-mantle velocity gradient, and
constant upper-mantle attenuation. In both cases, the Qiangtang
terrane is distinguished from the Lhasa terrane by a change in
Moho depth and upper-mantle velocities. The lower upper-mantle
velocities, as well as higher Pn attenuation, suggest hotter tem-
peratures beneath the Qiangtang terrane as compared to the Lhasa
terrane. Although the fits to the Pn amplitude and pulse frequency
data are comparable between the two models, the first model with
the constant upper-mantle velocity gradient fits the travel times
somewhat better in relation to the data errors.
Key words: Tibet lithosphere, Pn waves, Seismic attributes.
1. Introduction
The Tibetan plateau is one of the most remark-
able topographic features on Earth with an average
elevation of about 5 km above sea level. The
Himalayan convergent zone where the continental
collision between Indian and Eurasian plates occurs
is located on the south and southwest of the Tibetan
Plateau (CHEN and MOLNAR, 1981). The collision of
the northward moving Indian continent with the
southern margin of Eurasia is associated with the
formation of the Himalayas, as well as the high
elevation and thickened crust of Tibet (MCNAMARA
et al., 1997).
In order to investigate the velocity and attenuation
structure beneath Tibet, spectral-element method
(SEM) modeling of Pn wave attributes, including the
travel time, the peak envelope amplitude, and the
instantaneous pulse frequency, is performed for
regional earthquakes recorded by the Hi-CLIMB
array. Regional earthquakes are chosen to be
approximately in-line with the Hi-CLIMB array, but
also provide some azimuthal coverage. The locations
of the events are shown in Figs. 1, 2.For the SEM modeling, the P-wave velocities are
derived from GRIFFIN et al. (2011) who used 3D ray
tracing for the modeling and obtained a 3D P-wave
velocity model along with a laterally variable Moho
which was similar to those found by TSENG et al.
(2009); NABELEK et al. (2009) and NOWACK et al.
(2010) using teleseismic waves. The Moho beneath
the Lhasa terrane of southern Tibet was found to be
over 73 km thick with a Pn speed of about 8.2 km/s.
The Qiangtang terrane to the north of the Bangong-
Nujiang suture (BNS) showed a thinner crust by up to
10 km and a Pn speed of 7.8–7.9 km/s. The upper-
mantle top velocities and upper-mantle velocity gra-
dients from GRIFFIN et al. (2011) are similar to those
found by PHILLIPS et al. (2007). The upper-mantle
velocity gradients from GRIFFIN et al. (2011) are also
similar to those found from a large regional model by
MYERS et al. (2010) for the Lhasa terrane, but the
upper-mantle velocity gradients from MYERS et al.
(2010) are lower in the northern Qiangtang terrane.
However, the large regional model of MYERS et al.
(2010) has different upper-mantle velocities from
those found by GRIFFIN et al. (2011), and from earlier
1 Department of Earth and Atmospheric Sciences, Purdue
University, West Lafayette, IN 47907, USA. E-mail: alicanba-
[email protected]; [email protected]
Pure Appl. Geophys.
� 2012 Springer Basel AG
DOI 10.1007/s00024-012-0482-8 Pure and Applied Geophysics
results of LIANG and SONG (2006) and PHILLIPS et al.
(2007) in Tibet.
From the 3D velocity model of GRIFFIN et al.
(2011), 2D slices were obtained and earth-flattened
for use in the 2D SEM modeling. The locations of the
2D slices are shown in Fig. 1. For the numerical
calculations, SPECFEM2D, a parallel 2D, viscoelas-
tic SEM code (KOMATITSCH and VILOTTE, 1998 and
KOMATITSCH et al., 2005) was used, and the SEM
results corrected for 3D geometric spreading as
described by BAKIR and NOWACK (2011). For the
seismic attribute modeling, one 2D slice along the
longitude of 84� (West Line) is used for the south
regional event L1E, a 2D slice along the longitude of
85� (Central Line) is considered for the south cluster
of events L1A, L1I, L1J, and L1K, and a 2D slice
along the longitude of 86� (East Line) is used for the
north event E3B (Fig. 1). All the 2D slices derived
from GRIFFIN et al. (2011) have a laterally varying
crust and upper mantle velocity structure.
We first show that the SEM modeling, not
including attenuation, does not fit the observed Pn
amplitude and pulse frequency attributes. The SEM
results from two models which include attenuation
are then compared with the observed data. The first
model derived from GRIFFIN et al. (2011) has a con-
stant upper mantle velocity gradient, but has variable
upper mantle attenuation. The second model has a
laterally varying upper-mantle velocity gradient and
constant upper-mantle attenuation. It is found that
both models can be used to fit the observed Pn
amplitude and pulse frequency attributes. However,
the model with a constant upper mantle gradient fits
the travel time data slightly better than the variable
velocity gradient case in relation to the data errors.
Nonetheless, in both cases the Qiangtang terrane is
3535
0
1
2
3
4
5
635
34
33
32
31
Ele
vatio
n (k
m)
E3B
L1E
L1A100 km
30
29
28
81 82 83 84 85 86 87
L1K L1IL1J
BNS
IYS
Qiangtang Terrane
Lhasa Terrane
Lat
itude
(de
g)
Longitude (deg)
West Line East LineCentral Line
Figure 1Elevation map showing selected stations of the Tibet component of the Hi-CLIMB array in Tibet (triangles) and the epicenters of the selected
local and regional earthquakes. The circles show the events used by GRIFFIN et al. (2011) to develop their velocity model where the open
circles are relocations. The dashed lines shows the locations of the 2D P-wave velocity slices obtained from the 3D velocity model of GRIFFIN
et al. (2011) with the East Line at 84�, the Central Line at 85�, and the West Line at 86� in longitude. The locations of the Bangong-Nujiang
suture (BNS) and the Indus-Yarlung suture (IYS) are shown by the dotted lines, and the Lhasa and Qiangtang terranes are also shown
A. C. Bakir, R. L. Nowack Pure Appl. Geophys.
distinguished from the Lhasa terrane by a change in
Moho depth and upper-mantle velocities. The lower
upper mantle velocities, as well as higher Pn atten-
uation, suggest hotter temperatures beneath the
Qiangtang terrane as compared to the Lhasa terrane
(NI and BARAZANGI, 1983; RAPINE et al., 1997;
TILMANN et al., 2003).
2. Regional Events
Broadband seismic stations of the Hi-CLIMB
array were used to record regional and teleseismic
earthquakes in Tibet (NABELEK et al., 2005). The
locations of the regional earthquakes used in this
study are reported from either the PDE or Engdahl
(EHB) catalogs (USGS, 2010 and ENGDAHL et al.,
1998; see GRIFFIN et al. (2011) for the specific loca-
tion information). Six regional events are utilized for
modeling of the seismic Pn attributes, one out-of-line
south event, L1E, one out-of-line north event, E3B,
and four in-line south events, L1A, L1I, L1J, and
L1K. The focal mechanism solutions of the selected
earthquakes are taken from BAUR (2007) for all events
except E3B which was obtained by T. L. Tseng
(personal communication). For each event, 2D
Focal Mechanism for E3B with Hi−CLIMB Stations
Focal Mechanisms for L1E with Hi−CLIMB Stations
Focal Mechanisms for South Events with Hi−CLIMB Stations
80 81 82 83 84 85 86 87 8827
28
29
30
31
32
33
34
35
36
Longitude (degrees)
2300
2100
1900
L1EL1E Revised
Lat
itude
(de
gree
s)
(a) (b)
Longitude (degrees)
Lat
itude
(de
gree
s)
80 81 82 83 84 85 86 87 8827
28
29
30
31
32
33
34
35
36
1650
1750
L1KL1A
L1I
L1J
80 81 82 83 84 85 86 87 8827
28
29
30
31
32
33
34
35
36
Lat
itude
(de
gree
s)
2500
2300
2100
1900
E3B TL-1
Longitude (degrees)
(c)
Figure 2a The original and revised focal mechanism for regional event L1E. b The focal mechanisms for the cluster of south regional events L1A, L1I,
L1J, and L1K. c The focal mechanism TL-1 for event E3B. The triangles show the Hi-CLIMB stations, where the black triangles along with
the solid lines show the orientation angles used for the specification of the moment tensor for the SEM modeling. The dashed lines show the
separation of ranges used to specify the moment tensor for the SEM modeling
Velocity and Attenuation Structure of the Tibetan Lithosphere
moment tensor slices are derived from the 3D
moment tensors for different azimuth angles from the
events to the Hi-CLIMB stations (Appendix 1). These
2D moment-tensor slices were used to specify the
source in the SEM modeling. Two, three, or four
station locations are selected for the azimuthal ori-
entation of the moment tensor depending on the range
of azimuths to the stations. Three reference stations
are chosen for L1E for the specification of the moment
tensor slices. Four reference stations are chosen for
E3B since it is the most out-of-line event. Two ref-
erence stations are found to be sufficient for the cluster
of events L1A, L1I, L1J, and L1K since they are the
most in-line with the Hi-CLIMB array. In Fig. 2, the
solid lines to black triangles show the azimuths used
to specify the moment tensor slices, with the dashed
lines separating the different azimuth ranges.
Event L1E is located to the southwest of the
Hi-CLIMB array and shown in Fig. 2a. The moment
magnitude (Mw) of the event L1E is 4.0 (GRIFFIN et al.
2011). The depth of the event L1E is 16.6 km below
sea level, and 5 km is added for the SEM calculation
to allow for the average topographic elevation above
sea level. The revised focal mechanism for this event
is used in order to avoid low amplitude Pg waves
which would have source take-off angles near nodal
and are not observed in the data. However, this
revision is within the uncertainties of the focal
mechanism derived by BAUR (2007) (J. Nabelek,
personal communication).
The four south events (L1A, L1I, L1J, and L1K)
shown in Fig. 2b are located to the southeast of the
Hi-CLIMB array and are the most in-line events with
the array. All these events have similar hypocenters,
as well as similar focal mechanisms. Therefore, they
are considered as a cluster of events, even though
L1K occurred 6 months earlier than the other three
events. The moment magnitudes (Mw) of these south
events vary between 4.0 and 5.0 (GRIFFIN et al.,
2011). The depths of the south cluster events vary
between 13.1 km to 20.3 km.
The event E3B is located to the northeast of the
Hi-CLIMB array and shown in Fig. 2c. The focal
mechanism of E3B as determined by T.L. Tseng
(personal communication) is labeled as E3B TL-1.
The moment magnitude (Mw) of this event is 4.0
(GRIFFIN et al., 2011). The depth of the event E3B was
found to be 19 km by T.L. Tseng (personal commu-
nication); however, modeling the cross over distance
of the travel-times suggested a somewhat shallower
focal depth as found by GRIFFIN et al. (2011).
2.1. SEM Modeling of Regional Events
with a Constant Upper Mantle Velocity Gradient
and No Attenuation
Seismic attributes for the six regional events are
first modeled using the SEM calculations with no
attenuation. The P-wave velocity slices for the SEM
modeling are shown in Fig. 3a–c and were derived
from the 3D velocity model of GRIFFIN et al. (2011).
The S-wave model is derived from the P-wave model
by assuming a Poisson solid, and the density of the
crust is specified as 2,700 kg/m3 and in the mantle it
is specified to be 3,200 kg/m3 for the SEM modeling.
Figure 4 shows the P-wave travel time of the
SEM calculations compared with the observed
P-wave travel time for the six regional events. The
uncertainties in the observed travel-times of ±0.3 s
from GRIFFIN et al. (2011) are also shown, along with
the rms residuals of the Pn phase for each event from
the SEM modeling. It was found that with only minor
adjustments of the velocities, the SEM calculations of
the travel times along the 2D velocity slices are able
to model the observed travel times to within the data
errors for these events.
Figure 5 shows the calculated P-wave peak
envelope amplitudes of the elastic SEM calculations
compared with the observed peak envelope ampli-
tudes for the six events. A description of how the
seismic attributes for both the observed and calcu-
lated data are estimated is given in Appendix 2
(MATHENEY and NOWACK, 1995). The rms difference
between the observed and calculated Pn log-ampli-
tudes are also shown, where the calculated Pn pulse
amplitudes are generally larger than the observed
pulse amplitudes. Without changes to the velocity
model the calculated amplitudes can be decreased by
incorporating attenuation into the modeling.
Figure 6 shows the instantaneous pulse frequen-
cies of the elastic SEM calculations compared with
the observed instantaneous and centroid pulse fre-
quencies (MATHENEY and NOWACK, 1995; Appendix
2). Differences between the observed instantaneous
A. C. Bakir, R. L. Nowack Pure Appl. Geophys.
and centroid pules frequencies are used to provide an
approximate estimate of the noise in the data, as well
as possible interference with later arrivals. Therefore,
both estimates are shown for the observed pulse
frequency data. However, since the calculated instan-
taneous and centroid frequencies are similar, only the
calculated instantaneous pulse frequencies are shown
to avoid clutter on the plots. The calculated pulse
frequencies for the Pn branch generally increase with
distance resulting from the upper mantle velocity
gradient, and can be decreased as a function of
distance by either increasing the attenuation or
lowering the velocity gradient in the upper-mantle.
However, for the velocity model derived from GRIFFIN
et al. (2011), both the calculated envelope amplitudes
and pulse frequencies are too high compared to the
observed data when attenuation is not included, and
therefore attenuation is required to match the
Distance (km)
0
Dep
th (
km)V
p (km/sec)
200 400 600 800 10000
50
100
150
200
250
5
5.5
6
6.5
7
7.5
8
8.5
Distance (km)
0
Dep
th (
km)
200 400 600 800 10000
50
100
150
200
250
5
5.5
6
6.5
7
7.5
8
8.5
Vp (km
/sec)
Distance (km)
0
Dep
th (
km)
200 400 600 800 10000
50
100
150
200
250
5
5.5
6
6.5
7
7.5
8
8.5
Distance (km)
0
Dep
th (
km)
200 400 600 800 10000
50
100
150
200
250
5
5.5
6
6.5
7
7.5
8
8.5
Vp (km
/sec)
Distance (km)
0
Dep
th (
km) V
p (km/sec)
200 400 600 800 10000
50
100
150
200
250
5
5.5
6
6.5
7
7.5
8
8.5
Distance (km)
0
Dep
th (
km)
200 400 600 800 10000
50
100
150
200
250
5
5.5
6
6.5
7
7.5
8
8.5
(a)
(b)
(c)
(d)
(e)
(f)
Event L1E VelocityConstant Upper Mantle Grad
Event L1E VelocityVariable Upper Mantle Grad
South Events Velocity Constant Upper Mantle Grad
South Events Velocity Variable Upper Mantle Grad
Event E3B Velocity Constant Upper Mantle Grad
Event E3B Velocity Variable Upper Mantle Grad
Vp (km
/sec)
Vp (km
/sec)
N
N
N
N
N
NS
S
S
S
S
S
Figure 3Subplots a, b, and c show the P-wave velocity slices with constant velocity gradient in the upper-mantle derived from the 3D model of GRIFFIN
et al. (2011) used for event L1E, the south cluster of events L1A, L1I, L1J, and L1K, and event E3B. Subplots d, e, and f show the P-wave
velocity slices with laterally variable velocity gradient in the upper-mantle used for event L1E, the south cluster of events L1A, L1I, L1J, and
L1K, and event E3B. Circles show the projected locations of the events along the profiles
Velocity and Attenuation Structure of the Tibetan Lithosphere
calculated amplitudes and pulse frequencies with the
observed Pn attributes.
2.2. SEM Modeling of Regional Events
with a Constant Upper Mantle Velocity Gradient
and Variable Attenuation in the Upper Mantle
For the modeling here, velocity models derived
from GRIFFIN et al. (2011) are again used, but now
including seismic attenuation. In Fig. 7, the calcu-
lated pulse amplitudes from the SEM modeling with
the laterally variable attenuation and a constant upper
mantle velocity gradient are compared with the
observed pulse amplitudes, and in Fig. 8 the calcu-
lated pulse frequencies are compared with the
observed instantaneous and centroid pulse frequen-
cies. For the results shown in Figs. 7, 8, an upper-
mantle QP-1 of 0.0038 in the Lhasa terrane to the
south and an upper-mantle QP-1 of 0.0077 (a QP
-1 of
0.0083 for E3B) in the Qiangtang terrane in the north
were obtained. It was also found that modeling with
constant upper mantle attenuation did not match the
amplitude data, particular for the larger distance
ranges of event L1E to the south and for event E3B
200 300 400 500 600 700
0
5
10Observed (Cross)SEM Synthetics (Circle)
T-x
/8 (
s)
Distance (km)
-5100
200 300 400 500 600 700
0
5
10
Observed (Cross)SEM Synthetics (Circle)
T-x
/8 (
s)
Distance (km)
-5100 200 300 400 500 600 700
0
5
10
Observed (Cross)SEM Synthetics (Circle)
T-x
/8 (
s)
Distance (km)
-5100
200 300 400 500 600 700
0
5
10Observed (Cross)SEM Synthetics (Circle)
T-x
/8 (
s)
Distance (km)
-5100 200 300 400 500 600 700
0
5
10
Observed (Cross)SEM Synthetics (Circle)
T-x
/8 (
s)
Distance (km)
-5100
200 300 400 500 600 700
0
5
10Observed (Cross)SEM Synthetics (Circle)
T-x
/8 (
s)
Distance (km)
-5100
Event L1E Travel Times Event L1A Travel Times
Event L1I Travel Times Event L1J Travel Times
Event L1K Travel Times Event E3B TL-1 Travel Times
average pick error
average pick error
average pick error
average pick error
average pick error average pick error
Pn-rms=.24 Pn-rms=.19
Pn-rms=.25 Pn-rms=.24
Pn-rms=.14 Pn-rms=.21
Pg
Pg
Pg
Pg
Pg
Pg
Pn
Pn
Pn
Pn
Pn
Pn
Figure 4Comparison between the calculated travel times of the six regional events from the SEM modeling with models of constant upper-mantle
velocity gradient and the observed travel times. Circles are the SEM calculated travel times and crosses are observed travel times. The average
pick errors from GRIFFIN et al. (2011) and the Pn rms residuals (Pn-rms) are also shown
A. C. Bakir, R. L. Nowack Pure Appl. Geophys.
located to the north in the Qiangtang terrane. QP-1
values of 0.0077–0.01 were used for the crust, but
these were less well constrained from the regional
event data used here and could also result from
unmodeled crustal velocity heterogeneities. For
variable upper-mantle attenuation, a smooth transi-
tion for the SEM modeling was created around the
ramp structure on the Moho near the Bangong-
Nujiang suture (BNS). From Figs. 7, 8, it can be
seen that the SEM modeling with variable upper-
mantle attenuation and a constant upper mantle
velocity gradient gives a better fit to the seismic
attributes than the elastic case for the velocity model
of GRIFFIN et al. (2011) in terms of the Pn rms
misfits. The mismatch in Pg amplitudes for events
L1A and L1I could result from uncertainties in the
focal mechanisms since the other two events of
the cluster have better matches, and all events of the
cluster match the Pn branch. The Pn rms misfits for
the instantaneous frequencies are now also compa-
rable with the observed instantaneous frequency and
observed centroid frequency misfits.
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1900 for Area4 2100 for Area32300 for Area22500 for Area1
Distance (km)
Pg
Event E3B TL-1 Envelope Amplitudes No Q
Pn
01 2 3 4
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1900 for Area3 2100 for Area22300 for Area1
Distance (km)
Pg
Event L1E Envelope Amplitudes No Q
Pn
0 1 2 3
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Distance (km)
Pg
Event L1A Envelope Amplitudes No Q
Pn
01 2
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Distance (km)
Pg
Event L1I Envelope Amplitudes No Q
Pn
01 2
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Distance (km)
Pg
Event L1J Envelope Amplitudes No Q
Pn
01 2
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Distance (km)
Pg
Event L1K Envelope Amplitudes No Q
Pn
01 2
Log
10(a
mpl
itude
)L
og10
(am
plitu
de)
Log
10(a
mpl
itude
)
Log
10(a
mpl
itude
)L
og10
(am
plitu
de)
Log
10(a
mpl
itude
)
Pn-rms=.57 Pn-rms=.66
Pn-rms=.76 Pn-rms=.57
Pn-rms=.47 Pn-rms=.39
Figure 5Comparison between the Pn amplitude attributes of the six regional events from SEM modeling with no attenuation from the SEM modeling
and the observed envelope amplitudes. The circles are the SEM calculated values and the crosses are observed envelope amplitudes. The
distance ranges for the specified orientation angles for the moment tensors used in the SEM modeling indicated by vertical dashed lines. For
event L1E, the revised moment tensor is used. The Pn rms of the log-amplitudes (Pn-rms) for each event is also shown
Velocity and Attenuation Structure of the Tibetan Lithosphere
2.3. SEM Modeling of Regional Events
with a Variable Velocity Gradient and Constant
Attenuation in the Upper Mantle
As discussed by BAKIR and NOWACK (2011), for
the distance ranges used here there can be trade-offs
between variable attenuation and velocity gradient
structures for the modeling of seismic attributes. To
further investigate the Pn amplitude and frequency
characteristics for this region, 2D models with
variable upper mantle velocity gradients are
constructed and used in the SEM calculations. These
models are shown in Fig. 3d–f for the different
events. For all events, the crustal structures are
chosen to be the same as in earlier calculations.
However, a single constant upper mantle QP-1 of
0.0038 is now used.
While the earlier P-wave velocity slices had an
upper mantle velocity gradient of 0.003 1/s for the
entire upper mantle before earth-flattening, the
velocity models here have an upper mantle velocity
Obs E3B TL-1 and SEM Pulse Freq No Q
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
Pg
Pn2
6Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1900 for Area4 2100 for Area3 2300 for Area2 2500 for Area1
100
1 2 3 4
200 300 400 500 600 7000
1
3
4
5
Distance (km)
Pg Pn2
6Obs L1E and SEM Pulse Freq No Q
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1900 for Area3 2100 for Area2 2300 for Area1
100
1 2 3
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
Pg Pn2
6Obs L1A and SEM Pulse Freq No Q
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1650 for Area2 1750 for Area1
100
1 2
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
Pg Pn2
6Obs L1I and SEM Pulse Freq No Q
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1650 for Area2 1750 for Area1
100
1 2
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
PgPn
2
6Obs L1J and SEM Pulse Freq No Q
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1650 for Area2 1750 for Area1
100
1 2
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
Pg Pn2
6Obs L1K and SEM Pulse Freq No Q
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1650 for Area2 1750 for Area1
100
1 2
Freq
uenc
y (H
z)
Pn-rms=.25IC-Pn-rms=.26
Pn-rms=.27IC-Pn-rms=.12
Pn-rms=.38IC-Pn-rms=.19
Pn-rms=.29IC-Pn-rms=.23
Pn-rms=.21IC-Pn-rms=.14
Pn-rms=.46IC-Pn-rms=.14
Figure 6Comparison between the calculated instantaneous pulse frequencies of the six regional events with no attenuation from the SEM modeling
with no attenuation and the observed instantaneous and pulse frequencies. The circles are the SEM calculations and the crosses and squares
are the observed instantaneous and centroid pulse frequencies. For event L1E, the modified moment tensor is used. The Pn rms between the
observed and calculated instantaneous pulse frequencies (Pn-rms) are also shown, along with the rms between the observed instantaneous and
centroid pulse frequencies (IC-Pn-rms) used to assess the errors in the data
A. C. Bakir, R. L. Nowack Pure Appl. Geophys.
gradient of 0.003 1/s in the Lhasa terrane to the south
and a velocity gradient of 0.001 1/s in the Qiangtang
terrane to the north (Fig. 1). This is similar to the
upper mantle velocity gradients found for this area
from the large regional model of MYERS et al. (2010).
However, again, their upper mantle top velocities
were different from those found from the more
detailed models for Tibet found by GRIFFIN et al.
(2011); LIANG and SONG (2006) and PHILLIPS et al.
(2007). Figure 9 shows the P-wave travel times of the
SEM calculations with both a constant and variable
velocity gradient upper mantle compared with the
observed travel times. It can be observed that the
P-wave travel times for the variable upper mantle
velocity gradient deviate from the observed travel
times over the distance ranges used here. In terms of
the Pn rms misfits for the travel times, the rms values
for the variable upper mantle velocity gradient case
are comparable but slightly larger than the data errors
as found by GRIFFIN et al. (2011). This is in contrast to
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1900 for Area4 2100 for Area32300 for Area22500 for Area1
Distance (km)
Pg
Event E3B TL-1 Envelope AmplitudesVar Atten/Const Grad
Pn
01 2 3 4
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1900 for Area3 2100 for Area22300 for Area1
Distance (km)
Pg
Event L1E Envelope AmplitudesVar Atten/Const Grad
Pn
0 1 2 3
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Distance (km)
Pg
Event L1A Envelope AmplitudesVar Atten/Const Grad
Pn
01 2
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Distance (km)
Pg
Event L1I Envelope AmplitudesVar Atten/Const Grad
Pn
01 2
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Distance (km)
Pg
Event L1J Envelope AmplitudesVar Atten/Const Grad
Pn
01 2
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Log
10(a
mpl
itude
)
Distance (km)
Pg
Event L1K Envelope AmplitudesVar Atten/Const Grad
Pn
01 2
Log
10(a
mpl
itude
)
Log
10(a
mpl
itude
)L
og10
(am
plitu
de)
Log
10(a
mpl
itude
)
Log
10(a
mpl
itude
)
Pn-rms=.17 Pn-rms=.23
Pn-rms=.26 Pn-rms=.21
Pn-rms=.17 Pn-rms=.27
Figure 7Comparison between the peak envelope amplitudes of the six regional events from SEM modeling with variable upper mantle attenuation and
constant upper mantle velocity gradient models and the observed envelope amplitudes. The circles are the SEM calculations and the crosses
are observe envelope amplitudes. The Pn rms of the log-amplitudes (Pn-rms) for each event is also shown
Velocity and Attenuation Structure of the Tibetan Lithosphere
the constant upper mantle gradient case which had
rms misfits slightly smaller than the data errors.
The calculated SEM Pn amplitude and pulse
frequency attributes with constant attenuation and
variable upper mantle velocity gradients are then
compared with the observed data. In Fig. 10 the
comparison of the constant attenuation and a variable
upper mantle velocity gradient SEM amplitudes with
the observed amplitudes is given, and in Fig. 11a
comparison of the SEM pulse frequencies with the
observed instantaneous and centroid pulse frequen-
cies is shown. The modeling results for the Pn
amplitude and pulse frequency attributes are similar
to those obtained for the variable attenuation and
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
Pg
Pn2
6
Obs Event E3B TL-1 and SEM Pulse Freq Var Atten/Const Grad
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1900 for Area4 2100 for Area3 2300 for Area2 2500 for Area1
100
1 2 3 4
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
Pg Pn2
6Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1650 for Area2 1750 for Area1
100
1 2
Obs Event L1A and SEM Pulse FreqVar Atten/Const Grad
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
PgPn2
6
Obs Event L1I and SEM Pulse FreqVar Atten/Const Grad
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1650 for Area2 1750 for Area1
100
1 2
PgPn
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
2
6
100
1 2
Obs Event L1J and SEM Pulse Freq Var Atten/Const Grad
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circles)1650 for Area2
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
PgPn2
6
Obs Event L1E and SEM Pulse Freq Var Atten/Const Grad
100
1 2 3
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
Pg Pn2
6
Obs Event L1K and SEM Pulse FreqVar Atten/Const Grad
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1650 for Area2 1750 for Area1
100
1 2
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1900 for Area3 2100 for Area2 2300 for Area1
Pn-rms=.21IC-Pn-rms=.26
Pn-rms=.15IC-Pn-rms=.12
Pn-rms=.14IC-Pn-rms=.19
Pn-rms=.19IC-Pn-rms=.23
Pn-rms=.16IC-Pn-rms=.14
Pn-rms=.11IC-Pn-rms=.14
Figure 8Comparison between the instantaneous pulse frequencies of the six regional events from SEM modeling with variable attenuation and a
constant upper mantle velocity gradient models and the observed instantaneous and centroid frequencies. The circles are the SEM calculations
and the crosses and squares are observed instantaneous and centroid frequencies. The Pn rms between the observed and calculated
instantaneous pulse frequencies (Pn-rms) are also shown, along with the rms between the observed instantaneous and centroid pulse
frequencies (IC-Pn-rms) used to assess the errors in the data
A. C. Bakir, R. L. Nowack Pure Appl. Geophys.
constant upper-mantle velocity gradient case in terms
of rms misfits. This suggests a trade-off in model
parameters between upper-mantle attenuation and
upper mantle velocity gradients using the Pn ampli-
tude and pulse frequency attributes for this distance
range, and these trade-offs were further explored
using the modeling of synthetic data by BAKIR and
NOWACK (2011). However, the travel time data fit
slightly better for the model with a constant upper
mantle velocity gradient.
3. Discussion and Conclusions
Pn wave attributes including travel times, enve-
lope amplitudes, and instantaneous frequencies, have
been modeled using regional earthquakes recorded by
the Hi-CLIMB array in Tibet. Three 2D P-wave
velocity slices with a constant upper-mantle velocity
gradient were initially used for the SEM modeling of
the seismic attributes. A 2D P-wave velocity slice for
the south event L1E (West Line), another 2D P-wave
200 300 400 500 600 700
0
5
10Observed (Cross)SEM Synthetics Constant Gradient (Circle)SEM Synthetics Variable Gradient (Triangle)
T-x
/8 (
sec)
Distance (km)
-5
Event L1E Travel TimesConstant/Variable Gradient
100 200 300 400 500 600 700
0
5
10Observed (Cross)SEM Synthetics Constant Gradient (Circle)SEM Synthetics Variable Gradient (Triangle)
T-x
/8 (
sec)
Distance (km)
-5
Event L1A Travel TimesConstant/Variable Gradient
100
200 300 400 500 600 700
0
5
10Observed (Cross)SEM Synthetics Constant Gradient (Circle)SEM Synthetics Variable Gradient (Triangle)
T-x
/8 (
sec)
Distance (km)
-5
Event L1I Travel TimesConstant/Variable Gradient
100 200 300 400 500 600 700
0
5
10Observed (Cross)SEM Synthetics Constant Gradient (Circle)SEM Synthetics Variable Gradient (Triangle)
T-x
/8 (
sec)
-5
Event L1J Travel TimesConstant/Variable Gradient
100
200 300 400 500 600 700
0
5
10Observed (Cross)SEM Synthetics Constant Gradient (Circle)SEM Synthetics Variable Gradient (Triangle)
T-x
/8 (
sec)
Distance (km)
-5
Event L1K Travel TimesConstant/Variable Gradient
100 200 300 400 500 600 700
0
5
10Observed (Cross)SEM Synthetics Constant Gradient (Circle)SEM Synthetics Variable Gradient (Triangle)
T-x
/8 (
sec)
Distance (km)
-5
Event E3B Travel TimesConstant/Variable Gradient
100
Distance (km)
average pick erroraverage pick error
average pick error average pick error
average pick error average pick error
Pn-rms=.24
Pg
Pg
Pg
Pg
Pg
Pg
Pn
Pn
Pn
Pn
Pn
Pn
Pn-rms=.19
Pn-rms=.25 Pn-rms=.24
Pn-rms=.14 Pn-rms=.21
Pn-Vgrad-rms=.38 Pn-Vgrad-rms=.25
Pn-Vgrad-rms=.40 Pn-Vgrad-rms=.33
Pn-Vgrad-rms=.31 Pn-Vgrad-rms=.25
Figure 9Comparison between the calculated travel times of the six regional events from SEM modeling compared and the observed travel times.
Circles are the constant velocity gradient SEM calculated travel times, triangles are the variable velocity gradient SEM calculated travel
times, and crosses are observed travel times. The average pick errors from GRIFFIN et al. (2011), the Pn rms residuals (Pn-rms) for the constant
upper mantle velocity case, and the Pn rms residuals (Pn-Vgrad-rms) for the variable upper mantle velocity case are also shown
Velocity and Attenuation Structure of the Tibetan Lithosphere
velocity slice for the south cluster events L1A, L1I,
L1J, and L1K (Central Line), and a third slice for the
north event E3B (East Line) were obtained from the
3D velocity model derived by GRIFFIN et al. (2011).
The 2D velocity slices were then modified to have a
variable upper-mantle velocity gradient.
First, SEM calculations without attenuation were
performed for each event with a constant upper
mantle velocity gradient structure. The calculated
P-wave travel times match well the observed data.
However, the Pn amplitude and the instantaneous
pulse frequency attributes do not show a good fit with
the observed data, and for the velocity slices derived
from the 3D model of GRIFFIN et al. (2011) upper-
mantle attenuation is required.
Models with laterally varying upper-mantle
attenuation are then used in the SEM calculations.
Comparing the rms misfits, the Pn amplitude and
pulse frequency attributes fit the observed data much
better than for the elastic case. For a further
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Distance (km)
Pg
Event L1A Envelope AmplitudesConst Atten/Var Grad
Pn
0 1 2
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Distance (km)
Pg
Event L1I Envelope AmplitudesConst Atten/Var Grad
Pn
0 1 2
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Distance (km)
Pg
Event L1J Envelope AmplitudesConst Atten/Var Grad
Pn
0 1 2
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1650 for Area2 1750 for Area1
Distance (km)
Pg
Event L1K Envelope AmplitudesConst Atten/Var Grad
Pn
0 1 2
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1900 for Area4 2100 for Area32300 for Area22500 for Area1
Distance (km)
Pg
Event E3B TL-1 Envelope AmplitudesConst Atten/Var Grad
Pn
01 2 3 4
100 200 300 400 500 600 700
1
2
3
4
5
6Observed (Cross)SEM (Circle)1900 for Area3 2100 for Area22300 for Area1
Distance (km)
Pg
Event L1E Envelope AmplitudesConst Atten/Var Grad
Pn
0 1 2 3
Log
10(a
mpl
itude
)
Log
10(a
mpl
itude
)L
og10
(am
plitu
de)
Log
10(a
mpl
itude
)L
og10
(am
plitu
de)
Log
10(a
mpl
itude
)
Pn-rms=.19 Pn-rms=.27
Pn-rms=.23 Pn-rms=.21
Pn-rms=.16 Pn-rms=.25
Figure 10Comparison between the peak envelope amplitudes of the six regional events from SEM modeling with constant attenuation and a variable
upper mantle velocity gradient models and the observed envelope amplitudes. The circles are the SEM calculations and the crosses are
observed envelope amplitudes. The Pn rms of the log-amplitudes (Pn-rms) for each event is also shown
A. C. Bakir, R. L. Nowack Pure Appl. Geophys.
investigation of the Pn amplitude and pulse fre-
quency attributes of these events, a variable P-wave
upper mantle velocity gradient is then constructed,
but with a constant upper-mantle attenuation struc-
ture. Although the travel times for the variable upper
mantle gradient case deviate from the observed travel
times at larger offsets, they are still comparable to the
data errors. Nonetheless, the fit to the travel times for
the case with a constant upper mantle gradient is
somewhat better and within the data errors. However,
the rms misfits for the Pn amplitude and pulse fre-
quency attributes are found to be similar to those for
the constant upper mantle velocity gradient and var-
iable attenuation SEM results. Nonetheless, from the
3D velocity model of GRIFFIN et al. (2011) the upper
mantle P-wave velocities of the Qiangtang terrane are
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
PgPn2
6
Obs Event L1A and SEM Pulse FreqConst Atten/Var Grad
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1650 for Area2 1750 for Area1
100
1 2
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
PgPn2
6
Obs Event L1I and SEM Pulse FreqConst Atten/Var Grad
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1650 for Area2 1750 for Area1
100
1 2
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
PgPn2
6
Obs Event L1J and SEM Pulse FreqConst Atten/Var Grad
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1650 for Area2 1750 for Area1
100
1 2
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
PgPn2
6
Obs Event L1K and SEM Pulse FreqConst Atten/Var Grad
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1650 for Area2 1750 for Area1
100
1 2
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
Pg
Pn2
6
Obs Event E3B TL-1 and SEM Pulse FreqConst Atten/Var Grad
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1900 for Area4 2100 for Area3 2300 for Area2 2500 for Area1
100
1 2 3 4
200 300 400 500 600 7000
1
3
4
5
Freq
uenc
y (H
z)
Distance (km)
PgPn2
6
Obs Event L1E and SEM Pulse Freq Const Atten/Var Grad
100
1 2 3
Observed Inst Freq (Cross)Observed Centroid Freq (Square)SEM Inst Freq (Circle)1900 for Area3 2100 for Area2 2300 for Area1
Pn-rms=.24IC-Pn-rms=.26
Pn-rms=.21IC-Pn-rms=.12
Pn-rms=.14IC-Pn-rms=.19
Pn-rms=.14IC-Pn-rms=.23
Pn-rms=.21IC-Pn-rms=.14
Pn-rms=.13IC-Pn-rms=.14
Figure 11Comparison between the instantaneous pulse frequencies of the six regional events from SEM modeling with constant attenuation and a
variable upper mantle velocity gradient model and the observed instantaneous and centroid frequencies. The circles are the SEM calculations
and the crosses and squares are observed instantaneous and centroid frequencies. The Pn rms between the observed and calculated
instantaneous pulse frequencies (Pn-rms) are also shown, along with the rms between the observed instantaneous and centroid pulse
frequencies (IC-Pn-rms) used to assess the errors in the data
Velocity and Attenuation Structure of the Tibetan Lithosphere
lower than those of the Lhasa terrane, and this is
consistent with earlier studies of Pn propagation in
Tibet (e.g. LIANG et al., 2004; LIANG and SONG 2006;
SUN and TOKSOZ, 2006; and HEARN et al., 2004).
TILMANN et al. (2003) suggested this could be due to a
warmer mantle in north central Tibet.
The SEM modeling of the Pn amplitude and pulse
frequency attributes for the constant upper mantle
velocity gradient model derived from GRIFFIN et al.
(2011) suggests a variable upper mantle structure in
which the Qiangtang terrane has higher Pn attenua-
tion than the Lhasa terrane. A variable upper mantle
attenuation structure with lower Qp values to the
north is consistent with the inefficient Sn propagation
at higher frequencies beneath northern Tibet as
inferred by BARAZANGI and NI (1982), NI and
BARAZANGI (1983), MCNAMARA et al. (1995), RAPINE
et al. (1997), and BARRON and PRIESTLEY (2009). This
is also consistent with the Pn attenuation values from
XIE (2007) who found a Q0 of 183 ± 33 at 1 Hz and
g values of 0.3 ± 0.1 for paths that heavily sample
northern Tibet, and a Q0 between 250 and 270 and gvalues between 0.0 and 0.1 for paths that sample a
mixture of northern and southern Tibet. The attenu-
ation values found in this study are comparable, but
represent the individual Lhasa and Qiangtang terranes
and also are for the region of Tibet beneath the
Hi-CLIMB array about 5� in longitude to the west of
the paths studied by XIE (2007). Although the upper
mantle Qp values here are frequency independent, the
Pn pulse frequencies investigated had a limited fre-
quency range between about 1 and 2 Hz.
The variable upper mantle velocity gradient SEM
models with a constant attenuation structure in the
upper mantle can also provide a good fit to the
observed Pn amplitude and pulse frequency attributes.
The existence of such an upper mantle structure with
laterally varying velocity gradient in the region,
however, is in contrast with the first model investi-
gated here with a constant upper mantle velocity
gradient, and also in contrast with that of XIE (2007)
who assumed a simplified geometric spreading model
of D-1.3 beneath all of Tibet. Also, the model with a
constant upper mantle gradient fits the travel time data
somewhat better than the alternate model.
Possible explanations for lower Pn amplitudes, as
well as inefficient Sn propagation, beneath northern
Tibet might be widespread basaltic volcanism (NI and
BARAZANGI, 1983), a partial melting process (RAPINE
et al., 1997), a warmer mantle to the north (TILMANN
et al., 2003), and a weak or missing lithosphere
(BARRON and PRIESTLEY 2009). Temperature varia-
tions between central and northern Tibetan
lithosphere might be explained by a squeezed and
sheared upper mantle (HUANG et al., 2000), a steep
overturn of a down going slab (TILMANN et al., 2003),
or a detachment of the mantle lithosphere (CHEN and
TSENG, 2007; CHEN et al., 2010). The upper mantle of
the Qiangtang terrane can be distinguished from the
Lhasa terrane to the south by the shallow Moho,
lower Pn velocities, and lower Pn amplitudes, sug-
gesting hotter temperatures in the upper mantle
beneath the Qiangtang terrane as compared to the
Lhasa terrane.
3.1. Data and Resources
The spectral element method (SEM) was per-
formed using the SPECFEM2D code by KOMATITSCH
and VILOTTE (1998) and KOMATITSCH et al., (2005).
Acknowledgments
This work was supported by the U.S. National
Science Foundation grants EAR06-35611 (R.L.N.),
and the Air Force Research Laboratory contract
FA8718-08-C-002 (R.L.N and A.C.B.). We thank the
Editor and Reviewer for their constructive comments.
Appendix 1: Specification of the Moment Tensor
for 2D SEM Modeling
From AKI and RICHARDS (2002), Eqs. 4.96, 4.97),
the ray-theoretical far-field P-wave radiation pattern
incorporates the moment tensor using a term
c p_Mp q ð t � TP Þ cq where there are implied sums
over p and q from 1, 3, cp is the unit take-off vector at
the source, _Mp q ðtÞ is the time derivative of the
moment tensor which for a step source-time function
would be the moment tensor elements times a delta
function, and TP is the travel time. If the coordinate
system is specified with x1 - x3 in the plane of
A. C. Bakir, R. L. Nowack Pure Appl. Geophys.
incidence of the ray from the source, then the radiation
pattern term incorporating the moment tensor for the
far-field P-waves can be written in terms of a reduced
2 9 2 moment tensor as ð c1 c3 ÞM11 M13
M31 M33
� �
c1
c3
� �d ð t � TPÞ: The elements of this 2 9 2
moment tensor represent the strengths of the couples
and dipoles in the plane of incidence of the ray from
the source. We first make several 2D azimuthal
slices of the 3D moment tensor shown in Fig. 12a
along specific azimuths to the receivers and rotate
the moment tensor in the azimuthal directions noted
by the dashed lines. The dashed circles denote the
approximate take-off angles at the source for the Pg
and Pn waves from ray tracing using the velocity
model from GRIFFIN et al. (2011). The radiation
patterns determined from the reduced moment ten-
sor terms given above rotated along the different
azimuths are shown in Fig. 12b, and the radiation
pattern terms are consistent with the overall focal
mechanism pattern given in Fig. 12a.
We next compare the calculated P-wave ampli-
tudes for several azimuths using the reduced moment
tensor slices derived from the 3D moment tensor and
input into the 2D SEM modeling. It was found that to
be consistent with the amplitudes for the Pg and Pn
arrivals with take-off angles given by the dashed
circles given in Fig. 12a, and additional factor of
p - az in the azimuth was required for specification
in the 2D SEM code and related to how the moment
tensor is specified. The Pn and Pg amplitudes com-
puted from the SEM modeling are then shown in
Fig. 12c for several azimuths with respect to the 3D
focal mechanism in Fig. 12a. For these cases, the
SEM amplitudes of the Pg and Pn are consistent with
the radiation patterns of the 3D moment tensor.
Appendix 2: Calculation of Seismic Attributes
The amplitude and pulse frequency attributes are
obtained following the approach of MATHENEY and
Radiation Patterns for Different Azimuthal Angles
Take-off Angle (Degree)
Am
plitu
des 0.0
0.5
-0.5
-1.00 20 8040 60
Azimuthal Angles
30
210
60
240
90270
120
300
150
330
180
0E3B TL−1
2500
1900
2100
2300
Pg
Pn
100 200 300 400 500 600 7000
1
2
3
4
5
6
190 Degree210 Degree230 Degree250 Degree
SEM Envelope Amplitudes for Different Angles
Distance (km)
log1
0(E
nvel
ope
Am
plitu
de)
(a)
(b)
(c)
Pg
Pn
Azimuthal Angles190 Degree210 Degree230 Degree250 Degree
Figure 12a Shows the 3D focal mechanism for a particular double-couple moment tensor source with different azimuth angles given by dashed lines.
The regional Pg and Pn take-off angles in Tibet are shown by small circles. b Shows the amplitudes on the focal sphere from the reduced
moment tensor for the azimuthal angles given in a as a function of take-off angle derived from the 3D moment tensor. c Shows the SEM
envelope amplitudes for the azimuthal angles given in a. Different symbols represent different azimuthal angles
Velocity and Attenuation Structure of the Tibetan Lithosphere
NOWACK (1995). The data is first bandpass filtered
with a 0.5 to 5 Hz six-pole Butterworth filter to
reduce low and high frequency noise. The Hilbert
envelope is computed from the analytic signal
(BRACEWELL, 2000). An assessment is first made if the
Hilbert envelope sufficiently drops after the first
arrival P-wave pulse. If so, a cosine tapered box-car
is chosen to window out the first arriving P-wave
pulse. If not, then it is assumed that the P-wave pulse
is contaminated with later arrivals and the trace is not
included for further processing. Once the P-wave
pulse is windowed, the peak of the Hilbert envelope
is used to measure the pulse amplitude. Following
MATHENEY and NOWACK (1995) the instantaneous
frequency at the peak amplitude is utilized to estimate
the pulse frequency. Damping and weighting are used
to stabilize the instantaneous pulse frequencies,
although this is less important at the peak of the signal
envelope. In addition to the instantaneous pulse fre-
quency estimates, the centroid of the power spectrum
weighted by the squared envelope of the windowed
pulse is used to estimate the pulse frequency. For
noise free data, the averaged instantaneous pulse fre-
quency will approach that of the weighted centroid
pulse frequency (MATHENEY and NOWACK, 1995;
NOWACK and STACY, 2002), and the consistency of the
two values can be used to assess the reliability of the
observed pulse frequencies.
An example of a data trace from the Hi-CLIMB
array, and a windowed trace and envelope amplitude,
are shown in Fig. 13. For the pulse, the amplitude is
taken at the peak of the Hilbert envelope. The
instantaneous pulse frequency is also obtained at the
time where the peak of Hilbert envelope occurs. The
centroid pulse frequency is obtained from the
weighted centroid of the power spectrum of the
windowed seismic pulse. If the envelope does not
sufficiently drop after the first arriving pulse of the
original data, the trace is not included for further
amplitude and frequency analysis (MATHENEY and
NOWACK, 1995). Also, if the estimated instantaneous
and centroid frequencies are not consistent with each
other or with adjacent trace values with distance, then
the pulse is assumed to be contaminated with later
arrivals and not included for further processing. Both
the observed and the calculated data are analyzed
using the same processing steps, although only the
instantaneous frequency values are shown for the
calculated data.
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0 1 2 3 4 5 6 7 8 9
−2
−1
0
1
Time (s)
Hilbert Envelope
Window
Original Trace
Windowed Trace
Estimation of Hilbert Envelope AmplitudeAnd Instantaneous Pulse Frequency
Am
plitu
de
0.5
-0.5
-1.5
-2.5
Figure 13Example of the windowing of the Pn wave and the extraction of the
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(Received December 1, 2011, revised March 12, 2012, accepted March 14, 2012)
Velocity and Attenuation Structure of the Tibetan Lithosphere