Introduction to Geomatics Engineering

GEODESY « a branch of applied mathematics concerned with the determination of the

size and shape of the earth and the exact positions of points on its surface and

with the description of variations of its gravity field »

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Three pillars of Geodesy

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Geodynamical Geodesy Geodetic techniques are used

to study geodynamic processes, such as plate tectonic

motions, postglacial rebound (now called glacial

isostatic adjustment) or variations in Earth rotation and orientation.

Physical Geodesy: the observation and use of gravity

measurements (from ground, air and space) to

determine the figure of the Earth, notably the geoid,

which involves the formulation and solution of boundary-value problems

Geometrical/Mathematical Geodesy: computations,

usually on the reference ellipsoid, to yield accurate

positions from geodetic measurements, including map

projections, which involves aspects from differential

geometry.

Satellite/Space Geodesy: determination of the orbits of

satellites (hence inferring the gravity field) or for

determining positions on or near the Earth’s surface

from ranging measurements to navigation satellites.

Four branches of Geodesy

Geokinematics

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Global horizontal velocity vectors

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Station motion: Post glacial rebound

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Station motion: Solid Earth Tides

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Station motion: Tidal Ocean Loading

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International Terrestrial Reference Frame (ITRF)

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International Celestial Reference Frame (ICRF)

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Time Systems (Scales)

Siederal Time Scales Atomic Time Scales Dynamical Time Scales

GMST : Greenwich Mean Siederal Time

TAI : Temps Atomique International (Atomic time)

ET : Ephemeris Time

GAST : Greenwich Apparent Siederal Time

UTC : Universal Time Coordinated

TDT : Terrestrial DynamicalTime

LMST : Local MeanSiederal Time

GPST : GPS Time BDT : Barycentric Dynamical Time

LAST : Local Apparent Siederal Time

TCB : Barycentric Coordinate Time

UT1 : Universal Time 1 TCG : Geocentric CoordinateTime

TT : Terrestrial Time

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Siederal Time Scales

1 mean siederal day = 1 mean solar day – 3m 55.909s

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Atomic Time Scales

TAI – UT1 = 0s (The epoch of TAI agreed with the epoch of UT1 on 1st of January 1958)TAI – UT1 = 6.1s on 1st of January 1968TAI – UT1 = 16.4s on 1st of January 1978

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Earth rotation

• Why do we care?– Dynamical equations

expressed in a non-rotating frame (e.g. spacecraft tracking)

– Sensitive to mass transport in the earth (e.g. winds, ocean currents, etc)

– Sensitive to the deep internal structure of the earth

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Earth rotation

POLAR MOTION NUTATION

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Transformation schemebetween ITRF and ICRF

Pole of ICRS

TCP=CIP

R(t)Q(t)

W(t)

Pole of ITRS = Conventional Terrestrial Pole

CTP

„Top View“

CRS)t(Q)t(R)t(WTRS

W(t) ... Polar motion matrixR(t) ... Earth rotation matrixQ(t) ... Precession and Nutation Matrix

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Gravity field of the Earth and the Geoid

Combination Gravity Field Model EIGEN-CG01C (CHAMP-GRACE-TERR.)

GOCE global gravite ve jeoid belirleme uydusu (Mart 2009 , yükseklik: 250 km )

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Uydu İzleme

Uydu Altimetre

CHAMP (2000) GRACE (2002)

GOCE (2009)

max

0 0

)(sinsincos),,(N

n

n

m

nmnmnm

n

PmSmCr

R

r

GMrT

Gravity field of the Earth and the Geoid

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A-10FG-5 CG-5

Gravity field of the Earth and the Geoid

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Gravity field of the Earth and the Geoidg ≈ 9.8 m/s2 ≈ 980 Gal ≈ 980000 mGal

g = 9 8 0 7 2 4.6 7 3 1…. mGal

Yer basıklığı ve dönmesi (merkezkaç kuvveti)

Geniş su rezervuarları

Atmosferik basınç, okyanus topografyası, kutup hareketi

Dağlar, okyanus sırtları

Yer içerisindeki yoğunluk düzensizlikleri

Yer ve okyanus gelgitleri

Hidroloji, yer altı suları,

Kü

tle/

Yoğ

un

luk

Dü

zen

sizl

ikle

ri

Kü

tle

Değ

işim

leri

(za

ma

nsa

l değ

.)

Yer’

in ş

ekli

ve d

ön

üşü

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Yer’in Şekli

Fiziksel Yüzey (Topografya)

(Dağlar, Ovalar, Vadiler vb.)

Matematiksel Yüzey (Model)(JEOİT)

Elipsoit, Küre, Düzlem

+8,000 m (Everest),

−11,000 m (Mariana Çukuru)

Gravity field of the Earth and the Geoid

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dgSR

N )(4

Gravity field of the Earth and the Geoid

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Gravite – Yükseklik

Elipsoit Yük.

h

W0 : JeoitFiz Yük.

H

Jeoit Yük.

N

g

Q

P

PQQP gdHCCC

dgSR

N )(4

Ort.Deniz Sev.

Gravite Vektörü

JeoitFiziksel Yeryüzü Elipsoit

Gravity field of the Earth and the Geoid

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GRS80-WGS84

CLARKE 1866

GEOID

Earth Mass

Center

Approximately

236 meters

Local vs. Global

Reference Ellipsoid

Datum

• A datum defines the

position of the ellipsoid

relative to the center of

the earth 23

Datum

Ellipsoid vs. Geoid

Ellipsoid

– Simple Mathematical Definition– Described by Two Parameters– Cannot Be 'Sensed' by Instruments

Geoid

– Complicated Physical Definition– Described by Infinite Number of

Parameters– Can Be 'Sensed' by Instruments

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Space/satellite Geodesy

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Sensitivity of the space geodetic techniques to geodetic parameters

Parameter Type VLBI GPS/GLON.

DORIS/PRARE

SLR LLR Alti-metry

Quasar Coord. (ICRF) X

Nutation X (X) X

Polar Motion

XUT1

XLength of Day (LOD)

X X X X

Coord.+Veloc.(ITRF) X X X X X (X)

Geocenter X X X XGravity Field X X X (X) X

Orbits X X X X XLEO Orbits X X X X

Ionosphere X X X XTroposphere X X X X

Time/Freq.; Clocks X X (X)

(X)

ICR

FITR

F

Earth R

otatio

nG

ravity Field

Atm

osp

here

X

X X X X

Markus Rothacher, 9-13 Ocak 2006. The Global Geodetic Observing System and the IVS Service, Fourth

IVS General Meeting, Concepcion, Şili. 26

Very Long Baseline Interferometry

x

y

z TRF

b

b b

b

cos cos

cos sin

sin

x

y

z CRF

k

k k

k

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VLBI observes quasars at radiowavelengths of which frequencies are at S and X bands

This research has made use of the United States Naval Observatory(USNO) Radio Reference Frame Image Database (RRFID).

S-band X-band

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Global Navigation and Satellite Systems

( ) ( ) ( )S

R R r S t R S

S S

R trop ion R

L x t x t c t t

N

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Satellite/Lunar Laser Ranging (SLR/LLR)

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Satellite Altimetry

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International Association of Geodesy IAG

http://www.iag-aig.org/

• International Gravimetric Bureau

• Time Section of the International Bureau of Weights and Measures

• International Altimetry Service

• International Center for Earth Tides

• ICGEM (International Centre for Global Earth Models)

• International DEM Service

• International Doris Service

• International Earth Rotation and Reference Systems Service

• International Geoid Service

• International Gravity Field Service

• International GNSS Service

• International Laser Ranging Service

• International VLBI Service

• Permanent Service for Mean Sea Level32

Thanks for your attention !

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