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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

=ρ+∆δ+ +++εRcdd 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

() ()

; , , ()XtYt Zt

sss

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 =ρ +∆δ+λ+ +++εcNdd 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 =ρ+∆δ+λ+ +++ε

cNdd d

a

j

a

j

a

j

aino

j

atrop

j

atide

jap

j

a

(15.4)

λφ =ρ +∆δ+λ+ +++ε

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 =ρ +∆δ+λ+ +++ε

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 =ρ +∆δ+λ+ +++ε

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

+++ε

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 scientic 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

BK-TandF-KULSHRESTHA_9780367517434-200153-Chp15.indd 206 30/09/20 8:10 PM

207Indian Plate Motion Revealed by GPS Observations

For further computation, let us dene 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 simplied 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 deciency 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 renement 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 signicant 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 inuence 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 prole 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 prole. 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% condence 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 insignicant 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 insignicant 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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