world gravity map - Le service Cartographie

COMMISSIO
ON FOR THE GE
EOLOGICAL MAP
P OF THE WORLD (CGMW)
COMMIS
SSION DE LA CAR
RTE GÉOLOGIQ
QUE DU MONDE (CCGM)
Notice
WORLD
W
GRAV
VITY MA
AP
CA
ARTE GRAVIM
G
METRIQ
QUE MONDIA
M
ALE
Scale 1 : 50 000 0
000 / Eche
elle 1 : 50 000
0 000
(Firstt edition – 2012)
M AP 1 / CARTEE 1
COM
MPLETE SPH
HERICAL BOU
UGUER ANOMALY
ANOM
MALIE DE BOU
UGUER SPHE
ERIQUE COM
MPLETE
M AP 2 / CARTEE 2
ISO
OSTATIC ANO
OMALY (AIR
RY-HEISKANEN)
ANO
OMALIE ISOS
STATIQUE (AIRY-HEISKANEN)
M AP 3 / CARTEE 3
FREE-AIR ANOMAALY ON THE EARTH’S SURFACE
ANOMALIIE A L’AIR LIBBRE SUR LA SURFACE
S
TE
ERRESTRE
Authors
S. BONVALLOT, G. BALLMINO, A. B RIAIS, M. KUHN, A. PEYREFITTE, N. VALES,
R. BIAN
NCALE, G. GABALDA, G
G. MOREAU
UX, F. REINQ
QUIN, M. SA
ARRAILH
BUR
REAU GRAVIMETR
R
RIQUE INTERNAT
N
TIONAL (B
BGI)
In c
collaboration with
CENTRE
E
NATIONAAL D’ETUDES SPATIALES (CNE
ES)
INSTITU
UT DE RECHERC
CHE POUR LE DEVELOPPEMENT (IRD)
INSTITUT
N
NATION
NAL DE L’INFOR
RMATION GEOGR
RAPHIQUE ET FORESTIERE (IG
GN)
INSTIT
TUT NATIONAL D
DES SCIENCES DE L’UNIVERS (INSU)
CURTIN U NIVERSITY (AUSTRALIA
U
)
INTERNATION
NAL ASSOCIATIO
ON OF GEODESY
Y (IAG) - INTER
RNATIONAL GRA
AVITY FIELD SER
RVICE (IGFS)
INTERNAT
TIONAL UNION O
OF GEODESY AN
ND GEOPHYSICS (IUGG)
INTERN
NATIONAL UNIO N OF GEOLOGIC
CAL SCIENCES (IUGS)
UNITED
D NATIONS, EDU
UCATIONAL, SC
CIENTIFIC AND CULTURAL ORGA
ANIZATION (UN ESCO)
Co-editeed by CGMW-B
BGI-CNES-IRD - Printed by IGN France
© CG
GMW-BGI-CNES-IRD
ISBN 978-2-2917310-08-3
Complete spherical Bouguer anomaly / Anomalie de Bouguer spherique complete
ISBN 978-2-2917310-09-0
Isostatic anomaly (Airy-Heiskanen) / Anomalie isostatique (Airy-Heiskanen)
ISBN 978-2-2917310-07-6
Free-air anomaly on the Earth’s surface / Anomalie à l’air libre sur la surface terrestre
Reference :
Bonvalot, S., Balmino, G., Briais, A., M. Kuhn, Peyrefitte, A., Vales, Biancale, R., Gabalda, G., Moreaux, G.,
Reinquin, F. Sarrailh, M. World Gravity Map, 1:50000000 map, Eds. : BGI-CGMW-CNES-IRD, Paris, 2012.
Diffusion :
CGMW, 77 rue Claude Bernard, 75005 Paris, France. [email protected] ; www.ccgm.org
IRD Editions, 44 Bd de Dunquerke, 13572 Marseille cedex 02, France. [email protected] ; www.editions.ird.fr
Contact :
BGI, Obs. Midi-Pyrénées, 14 av. Ed. Belin, 31400 Toulouse, France. [email protected] ; bgi.omp.obs-mip.fr
2 Worldd Gravityy Map
Expllanatory notees
The World
W
Gravity Maap (WGM) denootes a set of highh-resolution gravvity anomaly maps and digital grrids computed att global scale froom available refeerence
Earth’s gravity and eelevation modelss. The Release 1.0 (2012) incluudes a set of thhree anomaly ma
aps (surface freee-air, complete Bouguer and issostatic
malies) derived froom the EGM20088 Geopotential model
m
and the ETO
OPO1 Global Reelief model. The WGM
W
is the first set of global gravity anomaly maps that
anom
take into account a reaalistic Earth moddel and that consider the contributtion of most surfaace masses (atm
mosphere, land, ooceans, inland seeas, lakes, ice caps and
Based on rigoroous computationss that are consiistent with geodetic and geophyysical definitionss of gravity anom
malies, WGM prrovides
ice shhelves) (fig.1). B
homoogeneous informaation on the Eartth’s static gravityy field at regionall and global scales (also available in digital form)) for various geophysical applicattions in
educaation and researcch. Further releasses are expectedd to include moree surface data (fieeld, marine or airrborne surveys) tto improve the shhort wavelengthss of the
gravitty field (potential data providers arre invited to contact BGI).
Fig.. 1. Surface masses taken into accounnt in WGM Releasee 1.0 (2012) gravityy anomaly computaations
Defin
nition of gravity anomalies
The “gravity anomaly”” is defined as thhe difference betw
ween the gravitaational acceleratioon (i.e. gravitatio
on and rotation) ccaused by the Earth’s masses annd that
a
in thee Earth
generrated by a referennce mass distribuution. Its study iss of major importaance in geodesy and geophysics and concerns a wide variety of applications
sciencces. In geodesy,, gravity anomaliees are used to define
d
the figure of the Earth, parrticularly the geoid surface whichh is defined as thhe equipotential surface
s
that more
m closely reprresents mean seea level. In geopphysics, gravity aanomalies are ussed to investigate
e the mass-denssity distribution of
o the Earth’s inteerior to
providde constraints onn the geological structures
s
from subsurface,
s
crusttal to upper manttle depths. This approach
a
led to tthe concept of “ffree-air”, “Bougueer” and
“isostatic” gravity anoomalies describeed hereafter andd used extensiveely for decades in geophysical interpretation. R
Recently, new foormulations havee been
propoosed to compute gravity anomaliees based on both a realistic Earth model and rigoroous geodetic defiinitions. More dettails on these moodern views of annomaly
computation can be foound in Feathersstone and Dentithh (1997), Li and Götze (2001), Hackney
H
and Fea
atherstone (20033), Hinze et al. (22005), NGA (20008) and
Kuhn et al. (2009).
The Bouguer
B
gravity aanomaly at a giveen point P (on thee Earth’s surface)) is given by:
∆
wheree
is the observed gravityy at point P and
(1)
m the reference EEarth model.
is thee theoretical gravity computed from
As shhown in equation (1) and fig. 2, the theoretical ggravity corresponding to point P can
c be
deriveed from: the norm
mal gravity
determined oon the surface off the reference ellipsoid
(Somiigliana-Pizzetti foormula), a heigh
ht correction
(also called the free-air corrrection)
accouunting for the chaange in normal gravity
g
from the rreference ellipsooid to the point loocation
using the orthometricc height HP, and
d a topographic correction
accounting for
f the
gravityy attraction of thhe surface masses (topography aand bathymetry for instance) abbove or
below
w sea level. Thee topographic correction
, also called the
t complete Boouguer
correcction in geophysical applications, aims to model annd remove non-ggeological effectss and is
usuallly defined as the sum of two term
ms: the simple Boouguer correctionn (known as the Bullard
B
on (known as thhe Bullard C correction), both off which
B corrrection) and the terrain correctio
accouunt for the gravitaational attraction produced at poinnt P by, respectivvely, an infinite Boouguer
plate or shell of connstant thickness HP and density
ty c and by thhe irregularities of the
topog raphy/bathymetryy residuals to the
e Bouguer plate/sshell. Note that using
u
hP (instead of HP)
in thee free-air and Boouguer correction
ns will result in thhe computation of gravity disturbbances
is an atmospheriic correction term
m, given as a funcction of
(insteaad of gravity anoomalies).
elevattion with respect to sea level, accounting for the m
mass of the atmossphere.
m
geodetic surrfaces used in the computation of gravity
Fig. 22.: Schematic grapph showing the main
anomaalies. HP is the orthhometric height of P (normal to the ggeoid in P0). hP and NP are the ellipssoid and
geoid hheights, respectiveely (normal to the ellipsoid
e
in Q0). The
he lower part illustraates the principle of
o mass
compeensation at the crusst-mantle boundaryy used in the Airy-H
Heiskanen isostatic model.
3 The resulting completee Bouguer anom
maly thus reflects the disturbance between the obsserved gravity an
nd that computedd for a given reference Earth moddel at a
as:
same point P. It is alsoo defined from the free air anomaly ∆
∆
∆
(2)
Globaal computation of gravity anom
malies
In geeophysical appliccations, the gravvity anomalies are usually compputed at local or regional scales and various aapproximations are
a applied to achieve
a
computations in planaar or spherical geeometries. Here, the complete sppherical Bouguerr anomaly is dete
ermined over thee whole Earth byy computing in a single
step the gravity contribution of all mentioned
m
surfacee masses abovee or below the mean sea surfa
ace (fig.1). In thhe same way, thhe contribution of
o their
c
in spheerical geometry on
o the base of isostatic equilibrium
m (Airy-Heiskaneen model) to determine
compensation at the ccrustal-mantle booundary is also computed
the coorresponding isoostatic anomaly. A spherical harm
monic approach has been used to provide homo
ogeneous and aaccurate global computations
c
of gravity
correcctions and anom
malies up to deggree 10800 (1’xx1’ half-wavelenggth equivalent spatial
s
resolution). To achieve thhis level of acccuracy, new theooretical
developments were reequired in order too handle sphericaal harmonics to uultra high degreess (Balmino et al., 2011).
s
Bouguer gravity anomalyy at a given pointt P of the Earth's surface is given by:
The spherical
∆
∆
(3)
wheree
is thee observed gravity at point P,
is the normaal gravity computted at point Q on
n the Telluroid (thhe best analyticaal representation of the
Earth’s Surface) correesponding to P and
s the gravity attraaction for all surrface masses ass described below. Note that thee usual
denotes
Bouguuer plate effect iss implicitly replacced here by the efffect of a global sspherical shell at each point P.
The teerm
d by the surface masses below annd above sea levvel was thus computed in sphericaal geometry at 1’x1’ resolution using the
produced
ETOP
PO1 ice surface aand bedrock moddels provided by the National Oceeanic and Atmosppheric Administra
ation (NOAA) (Am
mante and Eakinss, 2009) and taking into
accouunt the continentts, oceans and the precise charaacteristics (bounddaries and densities) of major lakes, inland seass, polar ice capss and shelves annd land
areass below sea levell. The resulting global
g
gravity effeect computed froom the spherical harmonic synthe
esis/analysis of thhe (orthometric) elevation data given in
tabless 1 and 2 is show
wn in fig. 3. As done
d
for the surfaace masses, we also derived the spherical harmo
onic gravity coeffificients for the coompensation of all
a relief
components for the Aiiry-Heiskanen isoostatic model (see fig. 2) with a cconstant compenssation depth Tc (here
(
arbitrarily fiixed to 30km). We
W thus produced global
correcction grids (1'x1')) for both surfacee masses and isoostatic effects coomputed at the Earth’s
E
surface to
o produce the finaal maps of compplete spherical Boouguer
and issostatic anomaliees. To keep the innformation contaiined in the originaal data sets, all computations
c
werre made up to deegree and order 10800.
1
The gravity
g
informatioon given in all graavity anomaly maaps (Bouguer, is ostatic and surfaace free-air) is de
erived from the EEGM2008 geopotential model (Paavlis et
al., 20008) / DTU10 graavity field (Anderssen, 2010). The surface free-air ggravity anomaly was
w computed att the Earth’s surfaace in the contexxt of Molodensky theory
(Heiskanen and Morittz, 1967) and inccludes correctionns for the mass of the atmospheere. All gravity anomaly maps annd grids were coomputed at the Earth’s
E
er and isostatic annomaly maps is 2670
2
kg/m3.
surfacce (lower limit of the atmosphere) with a 1’x1’ resoolution. The refereence density useed for the Bougue
Fig.
F 3. Spherical grravity attraction prooduced by surface masses considereed from the ETOPO
O1 Global Relief model in the computtation of Bouguer and
a isostatic anom
malies. It
corresponds to the ggravity contributionn (in mGal) of all land topography, oceean bathymetry, lakes, inland seas, icce caps and ice shhelves (fig.1 and tabbles 1 and 2) compputed in
sppherical geometry at the Earth’s surfface (base of the atmosphere).
a
Densiities used here aree 2670 kg/m3 (crust), 1027 kg/m3 (oceean water), 1000 kg/m
k 3 (lake and inlaand sea
water),
w
917 kg/m3 (icce).
Data sources
Graviity field data
The gravity
g
informatioon used in this reelease 1.0 is derived from the Eaarth Geopotential Model EGM2008 developed in sspherical harmonnics and releasedd up to
degreee 2160 (with som
me terms up to degree
d
and orderr 2190) by the Naational Geospatiaal-Intelligence Ag
gency (NGA) (Paavlis et al., 2008)). The EGM2008 model
includdes surface gravvity measurementts (from land, marine or airbornee surveys), satellite altimetry and
d satellite gravim
metry (GRACE mission)
m
measurements.
Updated information oon the Arctic gravvity field providedd by the Technicaal University of Denmark
D
(Andersen, 2010) and inccluded in the DT
TU10 global graviity field
more details and technical specifications on EGM22008 and DTU100 gravity fields).
modeel (1’x1’ resolutionn) has been incluuded (see referennced website for m
4 Elevation data
Elevation data (i.e. topography and bathymetry) is from the 1’x1’ ETOPO1 Global Relief model. Ice caps are derived from the ice surface and bedrock ETOPO1
models (see Amante and Eakins, 2009 and referenced website for more details and technical specifications).
Lakes and inland seas
Lake features were extracted from the ILEC World Lake Database (see referenced website for more details and technical specifications). The lake boundaries
were sampled through a polynomial interpolation of points from the SRTM Digital Elevation Model.
Land
Oceans
Closed seas
Lakes
Above sea level: all ; Below sea level: Chott Algeria-Tunisia,
Quattara, Death Valley, Netherlands (part), Turfan
All
Aral sea, Caspian sea, Dead sea
See details in table 2
Ice caps
Ice shelves
Greenland, Antarctica
Ross, Ronne Filchner, Larsen and Amery
ETOPO1
ETOPO1
ETOPO1
ILEC,
SRTM
ETOPO1
ETOPO1
Africa
Asia
Europe
North
America
South
America
Oceania
Nyasa (Malawi), Tanganyika, Victoria
Baikal, Balkach, Ladoga, Tiberiade*, Yssyk-Koul*
Constance*, Leman, Onego
Bear lake*, Erie, Huron, Michigan, Ontario, Salton
Sea*, Slaves*, Superior, Winnipeg
Maracaibo*, Salto Grande, Titicaca
Eyre
*Not
Table 1: Sources of elevation data taken into account
in ILEC Data Base
Table 2: List of lakes taken into account
Densities
Map information
Crustal rock density : 2670 kg/m3
Mantle rock density : 3270 kg/m3
Ocean water density : 1027 kg/m3
Fresh water density : 1000 kg/m3
Ice density : 917 kg/m3
Coverage area : global (-180° to 180° ; -90° to 90°)
Mercator map projection
WGS84 ellipsoid
Equatorial scale : 1/50,000,000
North & South poles (60° to 90°): Polar stereographic projection
Geodetic Reference System (GRS80)
e=9.7803267715 m.s-2
p =9.8321863685 m.s-2
a=6378137 m
b=6356752.3141 m
e2=0.00669438002290
f=0.00335281068118
Acknowledgments : This work has been supported by the Centre National d’Etudes Spatiales (CNES), the Institut de Recherche pour le Développement (IRD),
the Institut National des Sciences de l’Univers (INSU), the Institut National de l’Information Géographique et Forestière (IGN) and the Bureau de Recherches
Géologiques et Minières (BRGM). We thank the International Association of Geodesy (IAG) and the United Nations Educational, Scientific and Cultural
Organization (UNESCO) for their support. We thank the external and internal review committees for their constructive comments and A.-M. Cousin, N. Lestieu
from Obs. Midi-Pyrénées (Toulouse), C. Cardenas from CGMW (Paris) and the Secteur Cartographie of IRD (Bondy) for their technical assistance. All maps
have been generated at BGI using the Generic Mapping Tool (GMT) freeware (Wessel and Smith, 1991; 1998; http://gmt.soest.hawaii.edu). The maps are coedited by CGMW-BGI-CNES-IRD and printed by IGN France.
References
Amante, C., Eakins, B.W., 2009. ETOPO1: 1 arc-minute global relief model: procedures, data sources and analysis. NOAA Tech. Mem. NESDIS NGDC24, Boulder(Co).
Andersen, O., 2010. The DTU10 Global Gravity field and mean sea surface – improvements in the Arctic. 2nd IGFS meeting, Fairbanks, Alaska, Sept. 2010.
Balmino, G., Vales, N., Bonvalot, S. and Briais, A., 2011. Spherical harmonic modeling to ultra-high degree of Bouguer and isostatic anomalies. Journal of Geodesy (Published
online 10 december 2011). DOI 10.1007/s00190-011-0533-4.
Featherstone, W.E., Dentith, M.C., 1997. A geodetic approach to gravity data reduction for geophysics. Computers & Geosc. Vol. 23, No. 10, pp. 1063-1070, 1997.
Hackney R.I., Featherstone WE. Geodetic versus geophysical perspectives of the 'gravity anomaly'. Geophysical Journal Int.,154 (1): 35-43 Jul 2003.
Heiskanen, W.A., and Moritz, H., 1967. Physical Geodesy. W.H. Freemann & Co., San Francisco and London, 364p.
Hinze, W. J., Aiken, C., Brozena, J. , Coakley, B. , Oater, D., Flanagan, G., Forsberg, R., Hildebrand, T., Keller, G. R., Kellogg, J., 2005, New standards for reducing gravity data:
The North American gravity database. Geophysics, 70, J25–J32.
Kuhn, M., Featherstone, W.E., Kirby, J.F., 2009. Complete spherical Bouguer gravity anomalies over Australia. Australian Journal of Earth Sciences, 56: 213-223.
Li, X., Götze, H.J. Ellipsoid, geoid, gravity, geodesy and geophysics. Geophysics,66 (6): 1660-1668, Dec. 2001.
NGA (2008) Gravity station data format and anomaly computations. Technical Report, Geospatial Sciences Division, St Louis (Mo).
Pavlis, N.K., Holmes S.A., Kenyon S.C., Factor J.K., 2008. An Earth Gravitational Model to degree 2160: EGM2008. General Assembly of the European Geosciences Union,
Vienna, Austria, April 13-18, 2008.
Wessel, P., and Smith, W. H. F., 1991. Free software helps map and display data, EOS Trans. Amer. Geophys. U., vol. 72 (41), pp. 441, 445-446, 1991.
Wessel, P., and Smith, W. H. F., 1998. New, improved version of Generic Mapping Tools released, EOS Trans. Amer. Geophys. U., vol. 79 (47), pp. 579, 1998.
Websites
http://bgi.omp.obs-mip.fr : BGI - Bureau Gravimétrique International
http://www.ccgm.org : CGMW - Commission for the Geological Map of the World
http://earth-info.nga.mil/GandG/wgs84/gravitymod/egm2008 : NGA - EGM 2008 Geopotential Model
http://www.space.dtu.dk/English/Research/Scientific_data_and_models : DTU National Space Institute - DTU10 Global marine gravity field
http://www.ngdc.noaa.gov/mgg/global : NOAA - ETOPO1 Global Relief model
http://wldb.ilec.or.jp : ILEC - World Lake Database
Citation for this map and corresponding digital products:
Bonvalot, S., Balmino, G., Briais, A., Kuhn, M., Peyrefitte, A., Vales N. et al., 2012. World Gravity Map. Bureau Gravimetrique International (BGI), map, CGMW-BGI-CNES-IRD Ed.,
Paris.
5 MAAP 1 / CARTTE 1
COMPLLETE SPHEERICAL BOUGUER
O
AN
NOMALY
ANOMALIIE DE BOUUGUER SPHHERIQUE COMPLETE
C
6 MAAP 2 / CARTTE 2
ISOSTTATIC ANOOMALY (AIRRY-HEISKA
ANEN)
ANOMAALIE ISOSTTATIQUE (A
AIRY-HEISKKANEN)
7 MAAP 3 / CARTTE 3
FREE-AIRR ANOMALLY ON THE EARTH’S SURFACE
S
ANOMALIE
N
A L’AIR LIBR
RE SUR LA SURFACE
E TERRESTR
TRE
8