.

RIGIDITY OF NUBIA AND KINEMATICS OF THE EAR FROM COMBINED GPS AND DORIS SOLUTIONS: IMPLICATION TO AFREFSaria Elifuraha (esaria@purdue.edu), Calais Eric, (Purdue University, IN - USA), Altamimi Zuheir (ENSG, IGN, Paris, France), Willis Pascal (IPGP, IGN, Paris, France), Farah Hussein (RCMRD Nairobi, Kenya

Fernandes R.M.S. (University Beira Interior, IDL, CGUL, Covilhã, Portugal), D.Sarah Stamps (Purdue University, IN - USA),

CONCLUSION. This study provides the first continent-wide position/velocity solution for Africa, expressed in ITRF2008,

and is therefore a first contribution to the upcoming African Reference Frame (AFREF). Except for a few regions, the Afri-

can continent remains largely under-sampled by continuous space geodetic data. Efforts are in order to augment the geo-

detic infrastructure and openly share existing data sets so that the objectives of AFREF can be fully reached. In ad-dition

to the geophysical implications of this work, we argue that using a static frame for territories lo-cated on stable Nubia is

acceptable because of its low level of internal deformation. However, we also argue that deforming territories in northern

and eastern Africa should consider using a semi-dynamic (or prefer-ably dynamic) datum in order to avoid network distor-

tions that would be easily detected given the deforma-tion rates involved and the level of preci-sion currently achievable

by well-equipped surveyors. The kinematic model proposed here for East Africa can serve to define such a datum.

Close up on the East African Rift and the Somalian plate. A. Re-sidual velocities with respect to each plate

(only showing sites whose velocity uncertainties are less than 1.5~mm/yr). Residuals are small (less than

1~mm/yr) and show no systematic trend. Grey arrow at site ABPO in Madagascar shows ve-locity with re-

spect to So-malia, white arrow shows velocity with respect to Nubia. Site ABPO does not fit either plate.

B = Pre-dicted ve-locities with respect to Nubia for the Somalia, Victoria, and Rovuma plates.

0

1

2

Vel

oci

ty s

tan

dar

d d

evia

tio

n (m

m/y

r)

NJOR

BJSA B

0

1

2

Vel

oci

ty s

tan

dar

d d

evia

tio

n (m

m/y

r)

NS componentEW componentARMA

HNDI

KILW

A

2 4 6 8 10 12 14 16 18 20Time span (years)

2 4 6 8 10 12 14 16 18 20Time span (years)

UP component

0

1

2

Resi

dual

vel

ocity

(mm

/yr)

Time span (years)

NZG2 NJOR

EBBEELDS

wrt Nubiawrt Somaliawrt Victoriawrt Rovuma

2 4 6 8 10 12 14 16

Velocity uncertainties from CATREF solution as a function of observation time span after

applying 1.5 factor. The uncertainties decrease rapidly after 3 years of observation. A =

The EW and NS component, B = Vertical component.

Residual velocities

with respect to a rigid

plate model for the

sites used in the de�-

nition of Nubia, So-

malia, Victoria, and

Rovuma. Residual ve-

locities range be-

tween 0 and 1 mm/yr,

consistent with the

velocity uncertainties,

except for 4 sites on

the Victoria plate.

Figure shows the

Seismotectonic set-

ting, data used and

Best-�t model of the

EAR. Relative mo-

tions along plate or

block boundaries

are shown with dark

gray arrows, Open

arrow show the pre-

dicted velocity from

the model. Solid line

lines indicate in-

ferred plate bound-

ary trace. The Rela-

tive rotation poles

are shown with

black stars with 95%

con�dence error el-

lipse. VP = Victoria

Plate, RP = Rovuma

Plate, LP = Lwandle

Plate and AP = Ant-

arctic Plate.

INTRODUCTION: The African continent, in spite of its large extent and its on-land plate boundaries in northern and eastern Africa, still misses a

continent-wide and well-defined reference frame for both surveying and geophysical applications. As a result, our understanding of the kinematic

of its major plate boundaries remains limited. Here we analyzed 16 years of GPS and 17 years of DORIS data at continuously operating geodetic

sites distributed in Africa to describe the present-day kinematics of the Nubian plate and constrain relative motions across the East African Rift

(EAR). The resulting velocity field describes horizontal and vertical motions at more than 120 GPS and 9 DORIS sites. Velocities at sites located on

stable Nubia fit a single rigid plate motion model with a weighted root mean squares residual of 0.6 mm/yr. We find no detectable residual motion

within Nubia at a 95% confidence level, including in the seismically active southern Africa and Cameroon volcanic line (CVL). We confirm significant

motion (~1.5 mm/yr) in Morocco with respect to Nubia, consistent with earlier findings. We propose an updated angular velocity for the diver-

gence between Nubia and Somalia, which provides the kinematic boundary conditions to rifting in East Africa. We updated the present-day kine-

matics of the Somalian plate and propose, for the first time, a plate motion model for the East African Rift (Victoria and Rovuma microplates) that

is based on space geodetic data alone. Vertical velocities range from -2 to +2 mm/yr, close to their uncertainties, with no clear geographic pattern.

This study provides the first continent-wide position/velocity solution for Africa, expressed in ITRF2008, a contribution to the upcoming African

Reference Frame (AFREF).

Velocity solution with respect to Nubia. For only site whose velocity uncertainties is less than

1.6~mm/yr. Stars show the Euler poles and their associated 1-sigma error ellipse for Somalia-

Nubia,Victoria-Nubia, and Rovuma-Nubia. The nubian fixed frame is defined with high quality and

longterm GPS-DORIS time series located on stable Nubia using 21 GPS sites GOUG, YKRO, RBAY,

SUTM, ZAMB, SUTH, NIAM, SHEB, PRE1, RECT, INHB, LLN-GETJI, GMAS, BJCO, ULDI, UMTA, SBOK,

TAMP, HNUS and DEAR plus one DORIS site HBKA. The WRMS for horizontal velocity fit is 0.6mm/yr

GOUG

YKRO

ZAMB

NIAM

SHEB

RECT

INHB

LLNG

ETJI

GMAS

BJCO

TAMP

SEY1MAHB

REUNREUAREUB

MALIMAL2

RCMN

ETDD

HIMO

NKLG

340˚ 60˚20˚ 40˚0˚

−40˚

−20˚

0˚

20˚

40˚

5 mm/yr

LP

Nubian Plate

RP

Somalian Plate

Somalia-Nubia Euler pole

VP

Arabian Plate

EurasianPlate

340˚ 0˚ 20˚ 40˚ 60˚

−40˚

−20˚

0˚

20˚

40˚

hela

asdb

AFREF

IGS

UNAVCO

TRIGNET

DORIS

Individual Investigators or Agencies

LP

Nubian Plate

RP

Somalian Plate

VP

Arabian Plate

EurasianPlate

daka

liba

hbka

arma

reua

mhba

djia

Distribution of the continuous GPS and DORIS sites used in this study. Sites are color-

coded as a function of their availability. AFREF = AFrican REference Frame database; IGS

= International GNSS Service data centers; UNAVCO = UNAVCO archive; TRIGNET =

South Africa Mapping Agency archive. Sites labeled “indivudual investigators or agen-

cies'' are generally not available online. Many other continuous GPS sites operate in

Africa whose data are not made public. VP: Victoria Plate, RP: Rovuma Plate, LP: Lwandle

Plate

A. Distribution of continuous GPS sites in Africa used in this study as a function of obser-

vation time span. Many sites are still “young”, with less than 5 years of continuous ob-

servations. B. Histogram showing the cumulative number of continuous GPS sites in

Africa from 1996 to 2012. Note the rapid increase since 2008.

Site distribution (GPS only) as a function of velocity uncertainties (A) and residual

velocity (B). Solid line shows category A sites (Stable geodetic monument), dashed

line shows other sites. Overall, category A sites perform significantly better than

others.

0

10

20

30

40

Nu

mb

er

of

site

s

0 1 2 3 4 5 6

Residual Velocity (mm/yr)

Category “A” sites

Other categories

B

0

20

40

60N

um

be

r o

f si

tes

0 2 4 6

Velocity uncertainties (mm/yr)

Category “A” sites

Other categories

A

0

5

10

15

20

Nu

mb

er

of

site

s

Observation time span (yrs)

A

0

20

40

60

80

100

120

Cu

mm

ula

tive

nu

mb

er o

f sit

es

Year since instalation

B

0 842 6 10 12 14 16 1996 2000 2004 2008 2012

We are currently using the substantial increases in the geologic, geophysical and geodetic data in Africa to im-

prove upon recent kinematic models of the East African Rift (EAR; Calais et al., 2006; Stamps et al., 2008). We use a

block modeling approach where observed velocities are described as the contribution of rigid block rotation and

strain accumulation on locked faults (Mc Caffrey, 2009). We also use earthquake slip vector directions along the

EAR structures (Delvaux et al., 2009), as well as transform fault azimuths and 2Ma average spreading rates along

the Southwest Indian ridge (Horner-Johnson et al., 2007, DeMets et al., 2010). We statistically test whether the

data is fit significantly better by models that split the EAR into three separate subplates (Victoria, Rovuma,

Lwandle.

SO

RO

LW

SO−LWSO

VI

RO

LW

−20˚ −10˚ 0˚ 10˚ 20˚ 30˚ 40˚ 50˚ 60˚

−40˚

−30˚

−20˚

−10˚

0˚

10˚

20˚

30˚

Observed

Model

This work5 mm/yr

Stamps et al.,2008

Rotation poles:GPS velocities w.r.t. Nubia:

NUBIA

SOMALIA

ANTARCTICA

LWANDLE

ROVUMA

VICTORIA

VI

5 mm/yr

Nubian Plate

A B30 40 50 60

10

0

-10

-20

-30

30 40 50 60

10

0

-10

-20

-30

Nubian Plate

Somalian Plate Somalian Plate

LP

RP

VP

LP

RP

VP

5 m

m/y

r

Stamps et al. 2008 Calais et al. 2006 This Study

ABPO

10˚ 20˚ 30˚ 40˚ 50˚

−60˚

−50˚

−40˚

−30˚

−20˚

GEODVEL

0.02

0.04

0.06

0.08

0.10

0.12

rate

(deg

/My)

−0.03 0.00 0.03

east−west (deg)

0.02

0.04

0.06

0.08

0.10

0.12

rate

(deg

/My)

−0.03 0.00 0.03

north−east (deg)

MORVELITRF08HJ07

ST08

SA12SO12

NUBIA

ANTARCTICA

LWANDLE

SO, this work

LW, this workRO, this work

SO, this work

LW, this workRO, this work

SO, GPS only

SO, GPS only

GEODVELITRF08

ST08

MORVEL

HJ07

GEODVELITRF08

ST08

MORVEL

HJ07

95% confidence ellipses

Comparison between Somalia-Nubia angular velocity estimates. Angular velocities and 95% confidence limits in three perpendicular planes are shown: left panel = poles of rotation, bottom right panel = west-east profile, top right panel = south-north profile. HJ07 = Horner-Johnson et al., 2007; ST08 = Stamps et al., 2008; MORVEL = DeMets et al., 2010; GEOD-VEL = Argus et al., 2011; SA12 = Saria et al., submitted; SO12 = this work. Recent estimates agree well with each other, in-cluding the GPS-only GEODVEL estimate and the geological MORVEL estimate. The same holds for our own results except for an angular rate significantly lower than previous estimates, marginally consistent only with GEODVEL. We are currently investigating the cause of this discrepancy. Note that the Rovuma and Lwandle plate estimates (left panels) are signifi-cantly different from Somalia, but indistinguishable from each other.

CA

TREF

vel

oci

ty in

mm

/yr

CATS velocity in mm/yr

GLO

BK v

eloc

ity

in m

m/y

r

GLOBK velocity in mm/yr

CATR

EF v

eloc

ity in

mm

/yr

ASMA

ULUBA B C

100 20 30 40CATS velocity in mm/yr

100 20 30 40 100 20 30 40

ASMA

ULUB

10

0

20

30

40

−2.5

−2.0

−1.5

−1.0

−0.5

0.0

0.5

1.0

Spec

tral

indi

ces

Nor

th−

Sout

h

−2.5 −2.0 −1.5 −1.0 −0.5 0.0 0.5Spectral indices East−West

0−4 years4−6 years6−16 years

CATS uncertainty, mm/yr

GLO

BK u

ncer

tain

yy, m

m/y

r

GLOBK uncertainty, mm/yr

CATR

EF u

ncer

tain

ty, m

m/y

r

ROBE

A B C

20 4 6 8CATS uncertainty, mm/yr

10 2 3 4 10 2 3 4

NURK

MSKU

CA

TREF

vel

oci

ty in

mm

/yr

2

0

4

6

8

ROBE

NURK

MSKU1

0

2

3

4

1

0

2

3

4

Scatter of the spectral indices of the colored

noise for horizontal components of the GPS

time series. The black star indicates the cen-

troid of the scatter. It closely matches a

spectral index of 1 for both components, in-

dicative of flicker noise.

Comparison of GLOBK, CATREF and CATS softwares velocity field. A. CATREF velocities as a function of CATS velocities.

B. GLOBK velocities as a function of CATS velocities. C. GLOBK velocities as a function of CATS velocities. Only GPS sites

common to both solutions are shown. Gray circles show the NS component, open circles show the EW component.

A. Comparison of GLOBK and CATS velocity uncertainties. B. Comparison of CATREF and CATS velocity un-certainties. C. Comparison of CATREF and GLOBK velocity uncertainties. CATREF uncertainties have been scaled by 1.5, as explained in the text. Only GPS sites common to both solutions are shown.

0.0

0.5

1.0

1.5

2.0

2.5

Un

cert

ain

ties

(mm

/yr)

0 0.5 1.0 1.5 2.0 2.5 3.0Vertical velocity (mm/yr)

Ver

tica

l vel

oci

ties

& u

nce

rtai

nti

es (m

m/y

r)

Time span (years)

0

1

2

3

4 6 8 10 12 14 16 18

velocity (mm/yr)

uncertainty (mm/yr)A B

A. Vertical velocities (open circles) and their uncertainties (black circles) as a function of measurement time span. B. Vertical

velocities as a function of the corresponding uncertainty. We find no apparent correlation between observation time span

and vertical velocity, although sites with more than 12 years of continuous operations all have low vertical velocities, simi-

lar in magnitude to their uncertainty. We also find a weak correlation between vertical velocities and their uncertainties

REFERENCES1. Argus, D. F., R. G. Gordon, M. B. Heflin, C. Ma, R. J. Eanes, P. Willis, W. R. Peltier, S. E. Owen, The angular velocities of the plates and the velocity of Earth’s center from space geodesy, Geophys. J. Int. 180, 913-960 doi:10.1111/j.1365-246X.2009.04463.x (2010).2. Altamimi Z., X. Collilieux, Laurent Métivier, ITRF2008: an improved solution of the International Terrestrial Reference Frame, Journal of Geod-esy, 2010.3. Calais, E., C. J. Ebinger, C. Hartnady, and J. M. Nocquet (2006), Kinematics of the East African rift from GPS and earthquakeslip vector data, in The Afar Volcanic Province Within the East African Rift System, edited by L05304 G. Yirgu, C. J.Ebinger, and P. K. H. Maguire, Geol. Soc. Spec. Publ., 259, 922.4. Chu, D. & Gordon, R. 1999. Evidence for motion between Nubia and Somalia along theSouthwest Indian ridge. Nature, 398, 6466.5. DeMets C, R. G. Gordon and D. F. Argus (2010) Geologically current plate motions Geophys. J. Int. (2010) 181, 1–80 doi: 10.1111/j.1365-246X.2009.04491.x6. Dixon, T. H., A. Mao, and S. Stein (1996), How rigid is the stable interior of the North American Plate?, Geophys. Res. Lett., 23(21), 3035-3038.7. Fernandes R.M.S, Ambrosius, B.A.C., Noomen, R., Bastos, L., Combrinck, L., Miranda, J.M.& Spakman, W. 2004. Angular velocities of Nubia and Soma-lia from continuous GPS data: implications on present-day relative kinematics. Earth and Planetary Science Letters, 222, 197-208.8. Horner-Johnson, B. C., R. G. Gordon, and D. F. Argus (2007), Plate kinematic evidence for the existence of a distinct plate between the Nubian and Somalian plates along the Southwest Indian Ridge, J. Geophys. Res.,112, B05418, doi:10.1029/2006JB004519.9. Nocquet, J.M, P.Willis S. Garcia (2006), Plate kinematics of Nubia Somalia using a combined DORIS and GPS solution JGeodesy 80: 591607 DOI 10. 10 07/s00190-006-0078 10. Sella, G. F., Dixon, T.H. & Mao, A. 2002. REVEL : A model for recent plate velocities from Space Geodesy. J. Geophys. Res., doi: 107, 10.1029/ 2000 JB 00033.0.11. Stamps, D. S. et al. A kinematic model for the East African Rift. Geophys. Res. Letters 35, doi: 10. 1029/ 2007GL032781 (2008).12. Willis, P., Y.E. Bar-Sever, G. Tavernier (2005), DORIS as a potential part of a Global Geodetic Observing System, J. Geodyn., 40(4-5), 494-501, DOI: 10 .1016/j.jog.2005.06.01113.Willis, P., C. Boucher, H. Fagard, Z. Altamimi (2005), Applications geodesiques du systeme DORIS a l'Institut Geographique National, Geodetic appli-cations of the DORIS system at the French Institut Geographique National, C.R. Geoscience, 337(7), 653-662, DOI: 10.1016/j.crte.2005.03.002.