Date post: | 20-Dec-2015 |
Category: |
Documents |
View: | 286 times |
Download: | 9 times |
An example of gravimetric geoid computation:
The Iberian Gravimetric Geoid of 2005
The figure of Earth in first approximation:the revolution ellipsoid
normal
Relationship between orthometric (H) and ellipsoidal (h) height:the undulation of the geoid (N)
H = h N
The figure of Earth in second approximation: the geoid undulation (N) measured over the ellipsoid
Ellipsoid
Geoid
Earthsurface
H
hNA
A
B
C
HA = hA NA
HB = hB NB
HBA = hBA NBA
NB
NBA = B – NA 0 HBA hBA
The leveling with GPS computing height differencesrequires the use of a geoid to calculate N
Calculating N for two paths of 100 km, it can be observed that the values of h H are related to the topography
N calculated in plane zone: path AB
N calculated in mountainous zone: path CD
• As conclusion, a geoid model is required to use GPS heights (h) for leveling.
• The geoid models available in the study area, have not enough precision to be used in the major part of the engineering problems.
• For this reason, it is necessary the computation of a new geoid for the Iberian area, which has the major precision possible.
Problem: the computation of an Iberian geoid
NECCESARY DATA
• Gravity data available from several international centers (usually, from internet links).
• Digital terrain models (DTM) that can be combined (and interpolated, if it is necessary) to get a high-resolution Iberian DTM.
• Validation data (GPS/leveling data) that can be supplied by several European centers.
Land and Marine Gravity Data
http://bgi.cnes.fr:8110/bgi_debut_a.html
Land and Marine Gravity Data
http://www.usgs.gov/
The gravity data needed for the computation canbe obtained from the above-mentioned centers
http://www.ngdc.noaa.gov/mgg/gdas/gd_designagrid.html
The elevation data needed for the computation canbe obtained from the above-mentioned centers
The short and long wavelength effects are removed from the gravity data by means of :
Thus, the interpolation of the gravity data randomly distributed over the study area to a regular grid, is facilitated (Corchete et al., 2005)
The term href corresponds to the elevations filtered with a long wavelength filter of 60 arc-minutes
n
0m
nmnmnm
n
2n
n
2GM msenKmcosJ)(cosP)1n(r
a
r
GMg
máx
EIGEN-CG01C Gravity Anomalies (nmax = 360)
The term gGM is calculated using a geopotential model
The short-wavelength contribution must be recovered after the interpolation by means of:
For it, the digital terrain model previously computed will be used (Corchete et al., 2005)
Obtained by interpolation
Obtained by interpolation
Determination of a geoid model (N)
N = NGM + Nb + NI
NGM : contribution of the geopotential model
Nb : contribution of the residual gravity
NI : indirect effect
n
0m
nmnmnm
n
2n
n
GM msenKmcosJ)(cosPr
a
r
GMN
máx
EIGEN-CG01C Geoid (nmax = 360)
NGM : contribution of the geopotential model
http://www.gfz-potsdam.de/pb1/op/grace/results/index_RESULTS.html
Nb : contribution of the residual gravity
g = gfree + c + g ,, g = 0.3086 NI
where:
d)(S g4
RN ),(b
f(x,y) and g are:
c: terrain correction(only considering the masses over the geoid)
]dxdy
)zh()yy()xx(
dz)hz([Kc
h
h23
2p
2p
2p
p
Ap
gh)hf(h2fh2
Kc 22
2/322 )yx(
1)y,x(f
A
dxdy)y,x(fg
Nb : contribution of the residual gravity(obtained after integration with the FFT 1D)
F1 = FFT 1D F1-1 = FFT 1D backward
where:
PQ222
2
1sins ,, s + s )ln6s - (3 - 10s + s 6 - 4-
s
1=)sS(
coscos)(2
1sin)(
2
1sin
2
1sin 22
PQ2
n
1
)S( cos)g(G4
R),(N 11
11 FFF
f(x,y) and g are:
NI : indirect effect
dxdy)yy()xx(
)y,x(h)y,x(h
6
K)y,x(h
KN
A2/3 2
p2
p
pp33
pp2
I
2/322 )yx(
1)y,x(f
A
dxdy)y,x(fg
332I gh
6
Khf
6
Kh
KN
MODEL VALIDATION
• The model validation is performed comparing its values with high-precision data.
• These data are the geoid undulations (N0) obtained by means of GPS/leveling.
• These data can be supplied by European centers for our study area: the Iberian Peninsula.
GPS/leveling process: calculation of the observed geoid undulations (N0)
N0 = hGPS - Hlev GPS satellite receiver
Leveling instrument
European Vertical Reference System
(EVRS)
http://crs.bkg.bund.de/evrs/
Organisms that can supply validation data
http://crs.bkg.bund.de/evrs/tabelle_neu.html
-10 -8 -6 -4 -2 0 2 4
36
38
40
42
44
Data of the European Vertical Network (EVRS) on Iberia
COMPARISON WITH OTHERS MODELS
• The official geoid used in Spain (Sevilla, 1997): the IBERian GEOid of 1995 (IBERGEO95).
• The European Geoid (Denker and Torge, 1998): the European Gravimetric Geoid 1997 (EGG97).
• The worldwide geoids EGM96 y EIGEN-CG01C.
IBERian GEOid 1995 (IBERGEO95)
European Gravimetric Geoid 1997 (EGG97)
EGM96 geoidEIGEN-CG01C Geoid
Worldwide geoid models
http://cddis.gsfc.nasa.gov/926/egm96/egm96.html
CONCLUSIONS
• The IGG2005 geoid model improves all previous geoid, being much more precise.
• The IGG2005 is a first step towards a centimetric precision geoid for the Iberian area.
• The centimetric precision in the geoid computation will be achieved, if more and more precise gravity data are available for the Iberian area.
REFERENCES
Corchete V., Chourak M. and Khattach D., 2005. The high-resolution gravimetric geoid of Iberia: IGG2005. Geophys. J. Int., 162, 676–684.
Denker, H., and W. Torge. The European Gravimetric Quasigeoid EGG97. International Association of Geodesy Syposia, Vol. 119, Geodesy on the Move. Springer-Verlag, Berlin-Heidelberg-New York, S. 249-254, 1998.
Sevilla, M. J. A new gravimetric geoid in the Iberian Peninsula. BGI Bull. D’Inf. Nº 77 (Toulouse) and IGeS Bull. Nº 4 (Milano), 163-180, 1995.
CONTACT
Prof. Dr. Víctor CorcheteDepartment of Applied Physics
Higher Polytechnic School - CITE II(A)UNIVERSITY OF ALMERIA
04120-ALMERIA. SPAINFAX: + 34 950 015477
e-mail: [email protected]