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Indian Plate Motion Revealed by GPS Observations: Preliminary Results

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In this study, we present a brief summary of the motion of the Indian plate and its interior deformation. An analysis of four GPS stations across the Indian subcontinent provides evidence of convergence towards the Eurasian plate at a velocity of about 50 mm/yr in the northeast direction. Our analysis shows that the internal deformation of the Indian plate is very low (~1±3 mm/yr) and the whole Indian plate interior behaves like a solid rigid plate. In addition, we observe that the Indian subcontinent is subsiding at a rate of ~3±1 mm/yr. Along the Himalayan arc, we find high velocity gradient which conforms to the rapid deformation along the plate boundary. Finally, we argue that the past earthquakes and possible future earthquakes along the plate interior depend either upon the internal lithospheric stress or on the stress from the plate boundary (i.e. Himalaya).
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203
Indian Plate Motion
Revealed by GPS
Observations:
Preliminary Results
Yogendra Sharma, Sumanta Pasari and Neha
Birla Institute of Technology and Science, Pilani,
Rajasthan, India
CONTENTS
15.1 Introduction ..................................................................................................203
15.2 GPS Overview .............................................................................................. 204
15.3 GPS Data Processing .................................................................................... 206
15.4 Time Series Analysis ....................................................................................208
15.5 Results and Discussion ................................................................................. 211
15.6 Summary ...................................................................................................... 213
References .............................................................................................................. 213
15.1 INTRODUCTION
The Indian plate is one of the most active tectonic plates in the world. This plate is
colliding with the Eurasian plate since 55 Ma [Yin, 2006]. Due to this persistent col-
lision, many types of tectonic hazards (e.g., earthquakes, volcanoes, landslides) have
occurre d along the plate bound ary as well as in the plate interior. This collision created
the world’s largest mountain range, the Himalayas, which has deformed many times
due to several large earthquakes, such as the 1905 Kangra earthquake (Mw = 7.8),
1934 Nepal-Bihar earthquake (Mw = 8.1), 1950 Assam earthquake (Mw = 8.4),
1991 Uttarkashi earthquake (Mw = 6.8), 1999 Chamoli earthquake (Mw = 6.8),
2005 Kashmir earthquake (Mw = 7.6) and the 2015 Gorkha earthquake (Mw = 7.8),
causing millions of deaths along this arc and its surrounding Indo-Gangetic plains
(Figure 15.2) [Ambraseys and Douglas, 2004; Avouac et al., 2015; Bilham, 2019;
Kaneda et al., 2008]. Apart from these interplate earthquakes, the Indian plate has
also experienced some devastating earthquakes at its interior part, such as the 1967
Koyna earthquake (Mw = 6.6), 1993 Latur earthquake (Mw = 6.2) and the 2001 Bhuj
earthquake (Mw = 7.7) (Figure 15.2) [Bilham et al., 2003]. While geodetic measure-
ments across the Indian plate suggest that the Indian continent behaves as a stable
15
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204 Mathematical Modeling and Computation of Real-Time Problems
shield, the appearance of notable events along the central part of India also intimates
minor deformation (
∼ ±32
mm/yr) within the Indian subcontinent [Bilham et al.,
1998; Gupta, 1993; Jade et al., 2004; Paul et al., 2001].
There have been several studies on Indian plate motion and its deformation
[Bilham et al., 1998; Jade et al., 2004, 2017; Paul et al., 2001]. For instance, Bilham
et al. (1997) suggested that 20 mm/yr of total convergence between the Indian
and Eurasian plate has been observed along the Himalaya [Bilham et al., 1997].
Similarly, the geological studies along the Main Himalayan Thrust (MHT) also sug-
gest that about 50 percent of the convergence is absorbed by the Himalayas [Lavé
and Avouac, 2000]. Lavé and Avouac (2000) have reported that the maximum
shortening along the Himalayas has concentrated well north of the surface trace of
MHT [Lavé and Avouac, 2000]. Using the observations from 50 GPS sites, Jade et
al. (2004) concluded that the peninsular India moves as a rigid plate, while about
∼ −10 20
mm/yr convergence occurs along the Himalayan arc [Jade et al., 2004].
Banerjee et al. (2008) collected GPS data across the Indian subcontinent and sug-
gest that the whole of central India accommodates about
∼ −21
mm/yr convergence
[Banerjee et al., 2008]. Mahesh et al. (2012) have suggested that the Indian subcon-
tinent is deforming with a shallow rate (
<−12
mm/yr), and the whole plate interior
acts like a solid plate [Mahesh et al., 2012]. Similarly, Jade et al. (2017) have also
estimated the intraplate deformation rate of the Indian plate about
∼ −12
mm/yr
[Jade et al., 2017].
In the current study, we have used four years of GPS data from four continuous
International GNSS Service (IGS) stations (three from the Indian plate and one is
from the Eurasian plate) to estimate the present-day velocity eld of the Indian plate
in order to constrain the intraplate as well as the interplate crustal deformation of the
Indian subcontinent.
15.2 GPS OVERVIEW
Global Positioning System (GPS) is a space-based navigation system stabilized by
the US Department of Defense (DoD). GPS is composed of three main segments:
the space segment, the control segment and the user segment. The space segment
comprises 31 satellites placed in six different orbital planes at an inclination of
55
°
and elevation of 20,200 km above the Earth’s surface [Hofmann et al., 2012]. Each
satellite transmits the data at two different carrier frequencies of L1 = 1,575.42 MHz
and L2 = 1,227.69 MHz. The L1 band carries the navigation message, which consists
of the ephemerides information, predicted GPS satellite orbits, clock corrections,
ionospheric noise and satellite health status [French, 1996; Van, 2009]. The con-
trol segment contains one master control station (MCS), ve monitoring stations
and four ground antenna. The main jobs of this segment are tracing the satellite
orbit, determining clock corrections and formulation of the navigation data. The
user segment includes the GPS receivers that use the received information from the
satellites to calculate its position and time [Hofmann et al., 2012]. The clock read-
ing at the satellite antenna is compared with a clock reading at the receiver antenna.
This comparison provides the distance from receiver antenna to satellite (pseudor-
ange) and the time of traveling of the signal between satellite and receiver with the
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205Indian Plate Motion Revealed by GPS Observations
multiplication of speed of light [Hofmann et al., 2012; Van, 2009]. The pseudorange
can be displayed as
+∆δ+ ++Rcdd d
r
s
iontroptid
ep
(15.1)
Here,
()
()()()
() () ()
ρ=
−+ −+ 22 2
Xt XYtY Zt Z
r
ss
rsrsr (15.2)
is the geometric range between satellite and receiver antenna
are
the components of the geocentric position vector of the satellite at epoch t;
,,XYZ
rr r
are the three coordinates of the observing receiver;
c
is the speed of light;
∆δ
is the
offset between the receiver clock and satellite clock;
,d d
io
nt
ro
p
and
dtide
are the iono-
spheric delays, tropospheric delays and loading of tide effects, respectively; and
εp
represents the effect of multipath and receiver noise [French, 1996; Grewal et al.,
2007; Hofmann et al., 2012; Van, 2009].
On the other hand, the carrier phase is a measure of the phase difference between
the received carrier and signal generated by the GPS receiver. Positioning accuracy
from the carrier phase (ϕ) is many times better than the accuracy of code pseudor-
anges. The carrier phase equation can be represented as follows
λφ +∆δ+λ+ ++cNdd d
r
s
iontroptid
ep
(15.3)
Here,
N
is the ambiguity related to the receiver and satellite (number of fractional
phases), and
λ
is the carrier wavelength [French, 1996; Grewal et al., 2007; Hofmann
et al., 2012; Van, 2009]. There are many sources of error that could affect the accu-
racy of the GPS observations, namely the ionospheric/tropospheric delays, satel-
lite orbital errors, ocean tide loading effect, receiver and satellite clock biases and
multipath noises. To reduce these errors in the estimation of GPS coordinates and
relative velocity, the linear combination approach is used in the present analysis.
The receiver and satellite clock biases can be reduced using the double-difference
method [Hofmann et al., 2012]. To understand the double-difference method, let us
assume two receivers
, ,a b
and two satellites
,jk
. Two carrier phase observation
equations according to Eq. (15.3) can be written as:
λφ +∆δ+λ+ ++
cNdd d
a
j
a
j
a
j
aino
j
atrop
j
atide
jap
j
a
(15.4)
λφ +∆δ+λ+ ++


cNddd
b
j
b
j
b
j
bino
j
btrop
j
btide
jbp
j
b
(15.5)
First, we perform the single difference for satellite
j
and receivers
a
and
b
by sub-
tracting Eq. (15.4) from Eq. (15.5)
λφ +∆δ+λ+ ++


cNddd
ab
j
ab
j
ab
j
ab ino
j
ab trop
j
ab tide
j
ab p
j
ab
(15.6)
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206 Mathematical Modeling and Computation of Real-Time Problems
Similarly, the single difference for satellite
k
and receivers
a
and
b
is
λφ +∆δ+λ+ ++


cNdd d
ab
k
ab
k
ab
k
ab ino
k
ab trop
k
ab tide
k
ab
p
k
ab
(15.7)
To obtain double-difference, we have subtracted these single-difference equations
(Eqs. [15.6] and [15.7])
()
φ
=
λ
ρ+ +
λ
++
11


Nddd
ab
jk ab
jk ab
jk ab ino
jk ab trop
jk ab tide
jk ab p
jk (15.8)
The advantage of double difference is that the receiver clock biases are completely
eliminated and the ionospheric and tropospheric effects are reduced to a great extent
[French, 1996; Grewal et al., 2007; Hofmann et al., 2012; Van, 2009]. These cor-
rected GPS observations are now used to calculate the position and relative velocity
of the receiver.
15.3 GPS DATA PROCESSING
For the present study, we have accrued four years (
2015 2019
) of GPS data
from three IGS stations (IISC, HYDE and LCK4) from the Indian plate and one
IGS station (LHAZ) from the Eurasian plate along with four additional IGS sta-
tions (CHUM, KIT3, POL2 and URUM) from Scripps Orbit and Permanent Array
Center (SOPAC). GPS data is generally stored in RINEX (Receiver Independent
Exchange) format. The RINEX les are further used for data processing. For high
precision research work in geodesy, standard scientic GPS postprocessing software
(GAMIT/GLOBK, BERNESE and GIPSY) is utilized. In the present study, we have
used GAMIT/GLOBK postprocessing software to analyze the available GPS data.
GAMIT/GLOBK is available on the LINUX environment [Herring et al., 2010]. This
software is a GPS data processing software developed by the Massachusetts Institute
of Technology (MIT) for the estimation of three-dimensional relative positions of a
ground station. GAMIT uses GPS broadcast carrier phase and pseudorange observ-
ables (stored in RINEX le), also known as GPS readings, satellite ephemeris (stored
in navigation le) and satellite orbit data (stored in orbit le). Through the least-
squares estimation, it generates values of positions and other parameters (orbits,
Earth orientation, ambiguities and atmospheric delays) [Herring et al., 2010; Leberl,
1978]. We have derived the position of GPS station from Eq. (15.2). The linearized
form of the equation allows us to implement the least-squares algorithm. The simpli-
ed and linear form of Eq. (15.2) is given below
=+ dAx v
(15.9)
where
×[ 1]d n
= vector of observations
×[ ]An u
= design matrix
×[ 1]x u
= vector of unknowns (parameter)
[]
×1vn
= noise or residual vector
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207Indian Plate Motion Revealed by GPS Observations
For further computation, let us dene some additional parameters,
σ
0
2
= a priori variance
= covariance matrix
=σ
1
0
2
Q
d = the cofactor matrix of observations
=
 1
PQ
d
= the weight matrix
The least-squares adjustment provides a unique solution of Eq. (15.9)
=minimum.vPv
T
This adjustment principle provides following normal equation:
=APAx APd
TT
(15.10)
The solution of Eq. (15.10) is
()
=

,
1
xAPAAPd
TT
(15.11)
which can be simplied to
=
 ,
1
xGg
(15.12)
where
=GAPA
T
=gAPd
T
The cofactor matrix
Qx
follows from
=
 1
xGAPd
T
by the covariance propagation
law as
()()
=
−−

11
Q
GAPQ GAP
xTdT
T
(15.13)
and further reduces to
()
==
 
1
1
Q
GAPA
xT (15.14)
by substituting
=
 1
Q P
d
. The daily solutions from GAMIT provide the location
coordinates for each station along with the Earth orientation and satellite orbit cor-
rections. Further, the estimated loosely constrained daily solutions have been uti-
lized to estimate the station position and plate motion using GLOBK [Herring et
al., 2010]. GLOBK suite takes results from GAMIT solution les (called h-les) and
daily solution of global IGS stations processed and archived at SOPAC and merges
them together with a Kalman Filter estimator to provide the GPS time series and
velocity for all the GPS stations [Herring et al., 2010]. However, GLOBK assumes
BK-TandF-KULSHRESTHA_9780367517434-200153-Chp15.indd 207 30/09/20 8:10 PM
208 Mathematical Modeling and Computation of Real-Time Problems
a linear model, which cannot correct any deciency of initial loosely constrained
solution (h-le). To further identify and remove any measurements or stations which
are outliers, we have used GG-MATLAB (GAMIT/GLOBK MATLAB) toolbox
[Herring et al., 2010]. Once all corrections and renement of data are made, we lter
the data through GLOBK to obtain the station velocity. Further, we discussed the
time series of each station with the seasonal component and velocity estimation for
all four stations.
15.4 TIME SERIES ANALYSIS
The nal estimated daily positions at each site were transformed into the Inter national
Terrestrial Reference Frame 2008 (ITRF08) for further analysis [Altamimi et al.,
2012]. Figure 15.1 represents the time series result in the north, east, and upward
direction of each station. The discontinuities or jumps that occur in the GPS position
time series are probably due to the multipath effect, antenna error or the seasonal
variation. The seasonal variation is found to be signicant in the vertical component
of displacement vectors, whereas minor impact can be observed in the north and east
components for all the stations (Figure 15.1). The modulation of seasonal variation
can be the combination of surface loading related to water variations, ionospheric-
tropospheric pressure, vapor loading during the winter season (Dam et al., 2001).
The seasonal effect can be decomposed into annual and semiannual components.
These components can be represented into the linear function of sine and cosine
period terms:
()
=+×+×
π
π
π
π
cos
2244
yt abtc
t
T
dsin
t
T
ecos
t
T
fsin
t
T
(15.15)
Here,
a
is the intercept (constant value),
b
is the secular rate,
c
and
d
are the ampli-
tude of annual (12 months) periodic perturbations (sine and cosine terms) and
e
and
f
are the amplitude of semiannual (six months) periodic disturbances (sine and cosine
terms). We used the GG-MATLAB toolbox to derive the seasonal variation from
the GPS time series using the MATLAB function called tsview. The amplitude of
the annual seasonal effect is lying in the range of 0.3 mm to 1.7 mm, 0.2 mm to
0.9 mm and 1.3 mm to 2.1 mm for the north, east and vertical component, respec-
tively, for all the four stations. The amplitude of the semi-annual seasonal effect is
usually lesser than the amplitude of annual seasonal effects (Blewitt and Lavallee,
2002). It has been noted that continuous observations for a longer time span (>2.5
years) reduce the inuence of seasonal variation in the estimation of station veloc-
ity (Blewitt and Lavallee, 2002). The coordinate time series and velocities derived
from GAMIT/GLOBK are shown in Figure 15.1 and Table 15.1, respectively, in the
ITRF08 reference frame.
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209Indian Plate Motion Revealed by GPS Observations
FIGURE 15.1 Time series plot of coordinates of all the continuous IGS stations (a) LCK4,
(b) HYDE, (c) IISC and (d) LHAZ). The data gaps in the time series plot of all stations are
may be due to signal obstructions or electricity failure. First two plots for all the stations
show the linear trend along the northern and eastern direction, respectively, and the third
plot for the station represents the vertical displacement factor in the data. The blue dots are
daily position of each GPS station in the north, east and the upward direction along with their
uncertainties (light black bar).
BK-TandF-KULSHRESTHA_9780367517434-200153-Chp15.indd 209 30/09/20 8:10 PM
210 Mathematical Modeling and Computation of Real-Time Problems
FIGURE 15.1 (Continued)
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211Indian Plate Motion Revealed by GPS Observations
15.5 RESULTS AND DISCUSSION
The GPS processing results show that all GPS sites move with a velocity of about
∼ −16 42
mm/yr in the east direction and
∼ −35 45
mm/yr in the north direction
(Figure 15.2 and Table 15.1). We have calculated the arc-normal velocities (i.e., per-
pendicular to the Himalayan arc) of all the four stations to evaluate the internal and
plate boundary deformation of the Indian plate (Figure 15.3). We have observed that
HYDE station moves northward with a rate of
1.5
mm/yr relative to the IISC site
(Figure 15.3). Similarly, LCK4 station converges towards the Eurasian plate with
a velocity of
1.2
mm/yr relative to the HYDE site (Figure 15.3). These relative
surface velocities provide
∼ −13
mm/yr horizontal deformation rate of India (south
to the Himalaya). This result is consistent to the previous studies [e.g., Banerjee
et al., 2008; Jade et al., 2004, 2014; Paul et al., 2001]. In addition, we have also
observed that whole peninsular India is subsiding with a rate of
∼ ±31
mm/yr. To
derive the interplate deformation of the Indian plate, we have estimated the horizon-
tal velocity (
∼ ±48 1.5
mm/yr) of LHAZ station. Comparing the arc-normal velocity
of LHAZ with the other three stations (IISC, HYDE and LCK4), we have found that
the internal deformation rate between India and Tibet turns out to be about
∼ ±15 1
mm/yr. This deformation is mostly (about 50% of total deformation) concentrated
along the Himalayan arc (north to the MHT) [Banerjee et al., 2008; Jade et al., 2014;
Paul et al., 2001].
Low deformation rates (
∼ −13
mm/yr) along the plate interior show rigidness of
the Indian subcontinent (Figure 15.3). These low rates insinuate the rare occurrence
of earthquakes in the stable Indian plate. However, the central and southern parts of
India have been struck by a few hazardous events in the past, implying the steady
deformation of the Indian plate. In connection to this unusual phenomenon, Banerjee
et al. (2008) suggested that the motion of the Indian plate could be separated into the
TABLE 15.1
GPS Velocities (in mm/yr) of All Four Stations Along with the IGS Reference
Stations in the ITRF08.
VV
en
, ,
and
U
Represent the Station Velocity in East,
North, and Upward Direction Along with Their Respective Uncertainties
(
σσe
,
σσn
, and
σσu
)
Site
Name Longitude (°) Latitude (°)
Ve
(mm/yr)
σσe
(mm/yr)
Vn
(mm/yr)
σσn
(mm/yr)
U
(mm/yr)
σσu
(mm/yr)
LCK4 80.9556 26.9121 36.12 0.24 34.81 0.06 4.36 0.24
HYDE 78.5509 17.4173 39.97 0.07 34.68 0.06 1.05 0.25
IISC 77.5709 13.0212 42.94 0.07 34.38 0.05 2.53 0.24
LHAZ 91.104 29.6573 45.27 0.05 15.47 0.05 0.76 0.21
CHUM 74.7511 42.9985 27.42 0.06 2.47 0.06 2.23 0.21
KIT3 66.8855 39.1348 27.56 0.06 4.41 0.06 1.21 0.24
POL2 74.6943 42.6798 27.21 0.04 4.61 0.04 2.23 0.15
URUM 87.6007 43.8079 29.6 0.07 1.81 0.08 1.35 0.26
BK-TandF-KULSHRESTHA_9780367517434-200153-Chp15.indd 211 30/09/20 8:10 PM
212 Mathematical Modeling and Computation of Real-Time Problems
FIGURE 15.3 Arc-normal velocity prole of the studied GPS stations. The velocity differ-
ence of all stations in the normal direction has evaluated by xing the IISC station situated on
the stable Indian plate. All the velocities are projected in the NE 40° SW prole. The dotted
black line indicates the MHT.
FIGURE 15.2 Surface velocity led along the Indian subcontinent in the ITRF08. Blue
arrows indicate the horizontal velocity of the four GPS stations. Small black circles are the
95% condence error ellipses of GPS velocities. The blue star represents past large earth-
quakes with their respective magnitude (in bracket) along the plate interior as well as along
the Himalaya. The solid black line indicates the Narmada-Son lineament. The red line rep-
resents the Main Himalayan Thrust (MHT). The black rectangle in the inset gure indicates
the boundary of the main gure.
BK-TandF-KULSHRESTHA_9780367517434-200153-Chp15.indd 212 30/09/20 8:10 PM
213Indian Plate Motion Revealed by GPS Observations
motion of two plates: southern Indian plate and northern Indian plate detached by
the Narmada-Son lineament. In this setting, although the model ts the observations
data, the relative motion of two plates shows a statistically insignicant change in
the surface velocities [Banerjee et al., 2008]. However, Mahesh et al. (2012) tested
the same hypothesis based on their GPS measurements and reported that the Indian
plate could not be segmented into two or more plates [Mahesh et al. 2012]. Hence,
due to the insignicant internal deformation of the stable Indian plate, the present
study suggests that tectonic stress could be the main cause of the frictional failure
of the plate interior [Zoback et al., 2002]. This means that, the occurrence of past
intraplate earthquakes within India may be considered as produced either by the
perturbations of the stress of lithospheric in the interior plate or by the compressive
plate boundary stress from the Himalayan arc [Banerjee et al., 2008; Sharma et al.,
2018, 2020].
15.6 SUMMARY
We accrue GPS data from four continuous IGS stations; three of them are estab-
lished along the Indian plate (HYDE, LCK4 and IISC), and one is installed on the
Eurasian plate (LHAZ). We utilize GAMIT/GLOBK post-processing software to
analyze these GPS data. We obtain estimated velocities of these four stations in the
north, east and the upward direction. The horizontal velocities of the Indian-plate
stations lie between 50 and 55 mm/yr in the northeast direction, whereas the verti-
cal velocities of these sites lie between 1.05 and –4.36 mm/yr. In addition, the
surface velocity of LHAZ station (
±48 1.5
mm/yr) shows oblique motion towards
east direction along with minor subsidence rate (0.76 mm/yr). Using these veloci-
ties, we interpret the minor internal deformation of the Indian plate (1–3 mm/yr)
as well as the large deformation along the plate boundary
∼±(151
mm/yr). The
increased deformation rates along the plate boundary suggest higher seismic hazard
along the Himalayas. In contrast to that, the lower displacement rates along the plate
interior support the rigidness hypothesis of the Indian plate [Banerjee et al., 2008;
Mahesh et al., 2012]. However, due to lithospheric stress or stress generated from the
Himalayas, the possibilities of a large earthquake in the future along the plate inte-
rior are undeniable [Zoback et al., 2002]. As a future work, re-analysis based on the
dense GPS coverage along the Indian subcontinent could provide more constraints
on the heterogeneity of the crustal deformation and associated seismic hazard esti-
mation in the study region.
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