overview on earth gravity field theory - majid kadir
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Overview on Earth Gravity Field Theory: Background to Airborne Gravity Survey and Geoid DeterminationBy: Dato’ Abd. Majid A. KadirTRANSCRIPT
OVERVIEW ON
EARTH GRAVITY FIELD THEORY:BACKGROUND TO AIRBORNE GRAVITY SURVEY
AND GEOID DETERMINATION
By
Dato’ Abd. Majid A. Kadir
Info-Geomatik (M) Sdn. Bhd.
PNB PERDANA
KUALA LUMPUR
7-11 & 14-18 September 2015
LATIHAN MODUL III & IV:
KONTRAK JUPEM-T24/2014
1. Units
The gravity of the Earth, denoted g, refers to
the acceleration that the Earth imparts to objects on or near
its surface.
In SI units this acceleration is measured in metres per second
squared (in symbols, m/s2 or m·s−2)
The nominal "average" value at the Earth's surface, known
as standard gravity is, by definition, 9.80665 m·s−2
Normally Gal and mGal unit are used to define unit for gravity:
1 Gal = 10−2 m·s−2
1 mGal = 10−3 Gal = 10−5 m·s−2
2. Earth Gravity Potential and Gravity
Earth represented by Geoid
(EIGEN-CG01C) –
an equipotential surface that
coincide with the Mean Sea
Level (MSL) and denoted as
𝑾𝟎
Earth gravity potential (W) is the sum of:
1) Earth gravitational potential (V) due
to the attraction of the mass M of the
Earth, and
2) Earth centrifugal potential (𝑽𝒄) due
to the rotation of the Earth.
W (𝒙, 𝒚, 𝒛) = 𝑽(𝒙, 𝒚, 𝒛) + 𝑽𝒄 (𝒙, 𝒚)
Gravity 𝒈 is the gradient of the gravity
potential. The direction of the gravity
vector g is by definition the same direction
as the plumb line:
𝒈 = 𝒈𝒓𝒂𝒅 𝑾
𝑾𝟎
Equipotential surface which is
visible - The Geoid (𝑾𝟎) = the
particular equipotential surface
that coincide with the MSL.
The oceans are made of water: the
surface of a fluid in equilibrium
must follow an equipotential
Equipotential Surfaces and Gravity
Equipotential surfaces are
surfaces on which the
gravity potential (W) is
constant.
There are infinite number
of gravity equipotential
surfaces.
Practical use of
equipotential surfaces (eg.
levelling of surveying
equipments):
Definition of the
vertical =direction of
gravity=perpendicular
to equipotential
surfaces
Equipotential surfaces
=define the horizontal
Airborne
Gravity
Survey
Direction of gravity are perpendicular to equipotential
surfaces
The closer together the equipotential surfaces, the stronger
the gravity field (the larger the 𝒈) Gravity on an equipotential surface is not constant, but
varies.
Geodesy: The Concepts, 1982 The uneven surface of geoid:
an equipotential surface
To a second approximation the earth can be
considered as an equipotential ellipsoid
(Geodetic Reference System 1980, GRS80).
The reference ellipsoid has the same
potential as the geoid U0 = W0
The reference ellipsoid encloses a mass
that is numerically equal to the mass of
the earth
The reference ellipsoid has its center at
the center of gravity of the earth
(geocentric)
Normal gravity at the surface of the ellipsoid
is given by the closed formula of Somigliana
(1929)
2222
22
0
sincos
sincos)(
ba
ba ba
𝜸𝟎 = 𝒏𝒐𝒓𝒎𝒂𝒍 𝒈𝒓𝒂𝒗𝒊𝒕𝒚 𝒐𝒏 𝒕𝒉𝒆 𝒆𝒍𝒍𝒊𝒑𝒔𝒐𝒊𝒅
𝜸𝒂 = 𝒏𝒐𝒓𝒎𝒂𝒍 𝒈𝒓𝒂𝒗𝒊𝒕𝒚 𝒂𝒕 𝒕𝒉𝒆 𝒆𝒒𝒖𝒂𝒕𝒐𝒓
𝜸𝒃 = 𝒏𝒐𝒓𝒎𝒂𝒍 𝒈𝒓𝒂𝒗𝒊𝒕𝒚 𝒂𝒕 𝒕𝒉𝒆 𝒑𝒐𝒍𝒆
b
a
𝑼𝟎
𝑾𝟎
3. NORMAL GRAVITY FIELD:
Airborne
Gravity
Survey
4. GEODETIC COORDINATE SYSTEM – GDM2000
b
a
𝑼𝟎
𝑾𝟎
𝝋
𝝀
𝒉
g(𝝋, 𝝀, 𝒉)
The equipotential
ellipsoid furnishes a
simple, consistent and
uniform reference
system for all purposes
of geodesy:
The ellipsoid as a
reference surface for
geometric use
(𝝋, 𝝀, 𝒉),
As a normal gravity
field at the earth’s
surface and in space
The small difference between the earth gravity potential W and the normal
gravity potential U is called the anomalous potential T at any location
(φ, 𝝀, 𝒉):
W(φ, 𝝀, 𝒉) = U(φ, 𝝀, 𝒉) + T(φ, 𝝀, 𝒉) or
T(φ, 𝝀, 𝒉) = W(φ, 𝝀, 𝒉) - U(φ, 𝝀, 𝒉) :anomalous potential
The geoid and reference ellipsoid are
defined as having the same potential values,
so that
𝑾𝟎(φ, 𝝀, 𝒉 = 𝑵) = 𝑼𝟎 (φ, 𝝀, 𝒉 = 𝟎)
Gravity anomaly is defined by
g = 𝒈𝒑 − γ𝒒
Where 𝒈𝒑 is the gravity on the geoid and γ𝒒 is the normal gravity on the
ellipsoid
5. GRAVITY ANOMALY
Gravity value at Sabah Air Hanger in Kota Kinabalu = 978,113 mGal:
g = 𝒈𝒑 − γ𝒒
g = 978,113 – 978,087 (GRS80) = + 26 mGal
2222
22
0
sincos
sincos)(
ba
ba ba
GRS80 Normal gravity
Free Air Gravity Anomaly around
Kota Kinabalu and offshore area
( + 40 to - 40 mGal)
Positive + g: 𝒈𝒑 > γ𝒒
Negative − g: 𝒈𝒑 < γ𝒒
6. Modern Definition of Gravity Anomaly
Classical Definition of Gravity Anomaly
In the classical geodetic practise, the height of the gravity
measurement was known only with respect to the geoid from
levelling but not with respect to the ellipsoid.
For this purpose the measured gravity has to be reduced
somehow down onto the geoid and the exact way to do so is the
harmonic downward continuation to the geoid and the “geodetic
boundary value problem” is solved for the geoid by means of
Stokes integral or similar formulas.
Thus the classical gravity anomaly depends on longitude and
latitude only (a two dimensional system- 2D) and is not a function
in space. Furthermore, the classical reduction of gravity to the
geoid and gravity anomaly computation pre-supposes gravity
measurement at the surface of the earth (terrain); not applicable
for gravity measurements above the terrain.
Modern Definition of Gravity Anomaly
The present day gravity measurement not only makes full use of
a three dimensional (3D) positioning system such as GPS but
also been carried out using airborne platform such as airborne
gravimetry, yielding gravity values in a three dimensional space
g(𝝋, 𝝀, 𝒉) above the terrain. Therefore, the classical approach of
gravity reduction to the geoid in a 2D system is no longer
relevance and the Molodensky’s theory seems more appropriate
to treat gravity reduction in 3D space.
The height anomaly ζ(φ, 𝝀), the well known approximation of the
geoid undulation according to Molodensky’s theory, can be
defined by the distance from the Earth’s surface to the point
where the normal potential U has the same value as the
geopotential W at the Earth’s surface (Franz Barthelmes,
Scientific Technical Report STR09/02, Potsdam, 2013):
W(φ, 𝝀, 𝒉𝒕) = U(φ, 𝝀, 𝒉𝒕 − 𝜻)
Gravity anomaly at the surface of the earth:
g(𝝋, 𝝀, 𝒉) = g(𝝋, 𝝀, 𝒉) − γ(h − ζ, φ)
Normal gravity at (h – ζ) :
γ(h − ζ, φ) = 𝜸𝟎 +𝝏𝜸
𝝏𝒉𝒉 − ζ
γ(h − ζ, φ) = 𝜸𝟎 − 𝟎. 𝟑𝟎𝟖𝟔 𝒉 − 𝑵
Where 𝜸𝟎 is the normal gravity at the ellipsoid and height anomaly ζ is approximated by EGM geoid height 𝑵.𝝏𝜸
𝝏𝒉= -0.3086 mGal/m is the free air
gradient (upward)
γ(𝒉−ζ)
h
𝒈𝑻
γ𝟎
Terrain
Telluroid
Ellipsoid (𝑼𝟎)
ζ
𝝏𝜸
𝝏𝒉= −0.3086
H
N
𝒈𝟎
𝒈𝑻
γ𝟎
Terrain
Geoid (𝑾𝟎)
Ellipsoid (𝑼𝟎)
g𝒈𝒆𝒐𝒊𝒅 = 𝒈𝟎 − γ𝟎
g𝒈𝒆𝒐𝒊𝒅 = (𝒈𝑻+𝑭𝟏) − γ𝟎
γ(𝒉−ζ)
h
𝒈𝑻
γ𝟎
Terrain
Telluroid
Ellipsoid (𝑼𝟎)
ζ
g𝒕𝒆𝒓𝒓𝒂𝒊𝒏 = 𝒈𝑻 − γ(𝒉−ζ)
g𝒕𝒆𝒓𝒓𝒂𝒊𝒏 = 𝒈𝑻 − ( γ𝟎 + 𝑭𝟐)
Classical Definition Modern Definition
𝑭𝟏 = +𝟎. 𝟑𝟎𝟖𝟔 𝑯 𝐦𝐆𝐚𝐥/𝐦Free Air Reduction
𝑭𝟐 = −𝟎. 𝟑𝟎𝟖𝟔 (𝒉 − 𝑵) 𝐦𝐆𝐚𝐥/𝐦Normal gravity correction
𝝏𝜸
𝝏𝒉= +0.3086
𝝏𝜸
𝝏𝒉= −0.3086
h ≥ ht
𝒈
ht
W(h, λ, φ)
U(h − 𝒈, φ)
𝒈(𝝋, 𝝀, 𝒉)
7. Free Air Gravity Anomaly at
Aircraft Altitude
The generalised gravity
anomaly g according to
Molodensky’s theory is
the magnitude of the
gravity at a given point
(𝝋, 𝝀, 𝒉) minus the normal
gravity at the same
ellipsoidal latitude φ and
longitude 𝝀 but at the
ellipsoidal height (h−ζg )
where ζg is the
generalised height
anomaly, or in its
common form:
g(𝝋, 𝝀, 𝒉) = g(𝝋, 𝝀, 𝒉) − γ(φ, h − ζg)
W(φ, 𝝀, 𝒉) = U(φ, 𝝀, 𝒉 − 𝜻𝒈)
Since heights in
from airborne
gravimetry can be
many kilometres
(usually about than
2 km above the
terrain), it is usually
not sufficient to use
a constant free air
gradient (-0.3086
mGal/m), and the
more exact height
dependence for
normal gravity must
be used:
g(𝝋, 𝝀, 𝒉) = g(𝝋, 𝝀, 𝒉) − γ(φ, h − ζg)
𝒈(𝝋, 𝝀, 𝒉)
𝜸𝟎 +𝝏𝜸
𝝏𝒉𝒉 − 𝒈 +
𝝏𝟐𝜸
𝝏𝒉(𝒉 − 𝒈)𝟐
h
ζg
g(𝝋, 𝝀, 𝒉) = g(𝝋, 𝝀, 𝒉) − γ(φ, h − ζg)
Where normal gravity at altitude given by (Physical Geodesy,
Wellenhof and Moritz, 2005, page 298, equation 8-24):
𝜸(𝒉 − 𝜻𝒈, 𝝋) = 𝜸𝟎 +𝝏𝜸
𝝏𝒉𝒉 − 𝒈 +
𝝏𝟐𝜸
𝝏𝒉(𝒉 − 𝒈)𝟐
Substitute 𝜸(𝒉 − 𝜻𝒈, 𝝋) into 𝜟𝒈 𝝋, 𝝀, 𝒉 equation, we have gravity
anomaly at altitude:
𝜟𝒈(𝝋, 𝝀, 𝒉) = 𝒈(𝝋, 𝝀, 𝒉) − 𝜸𝟎 −𝝏𝜸
𝝏𝒉𝒉 − 𝒈 −
𝝏𝟐𝜸
𝝏𝒉(𝒉 − 𝒈)𝟐
𝝏𝜸
𝝏𝒉,
𝝏𝟐𝜸
𝝏𝒉are the first and second order normal gravity gradient
Substituting the first and second derivatives 𝝏𝜸
𝝏𝒉,
𝝏𝟐𝜸
𝝏𝒉with the
above expressions for GRS80 and the height anomaly 𝒈 is
approximated by EGM geoid height (𝑵𝑬𝑮𝑴), the equation for the
free-air gravity anomaly at altitude, 𝜟𝒈(𝝋, 𝝀, 𝒉), can be written as
(Rene Forsberg, in Sciences of Geodesy, 2012):
𝝏𝜸
𝝏𝒉= − 𝟎. 𝟑𝟎𝟖𝟕𝟕 𝟏 − 𝟎. 𝟎𝟎𝟐𝟒𝟐 𝒔𝒊𝒏𝟐 𝝋 𝒉 − 𝑵𝑬𝑮𝑴
𝝏𝟐𝜸
𝝏𝒉= − 𝟎. 𝟕𝟓 𝒙 𝟏𝟎−𝟕
𝜟𝒈 𝝋, 𝝀, 𝒉 = 𝒈 𝝋, 𝝀, 𝒉 − 𝜸𝟎 + 𝟎. 𝟑𝟎𝟖𝟕𝟕 𝟏 − 𝟎. 𝟎𝟎𝟐𝟒𝟐 𝒔𝒊𝒏𝟐 𝝋 𝒉 − 𝑵𝑬𝑮𝑴
+𝟎. 𝟕𝟓 𝒙 𝟏𝟎−𝟕 (𝒉 − 𝑵𝑬𝑮𝑴)𝟐
The above free air anomalies refer to the aircraft altitude and
hence downward continuation to the terrain level has to be
carried out for quasi-geoid determination.
EGM is a geopotential model of the Earth consisting of spherical
harmonic coefficients complete to degree and order n (=360, 720…).
The spherical harmonic expression for geoid height as a function of latitude,
longitude and height is of form:
where GM, R and are earth parameters. For the EGM08/GOCE
combination models, this involves up to 4 million coefficients Cnm and Snm
derived from a large set of global satellite data (satellite altimetry missions and
satellite gravity missions) and regional (average) gravity data from all available
sources.:
Earth gravity model is used to compute reference values of the earth gravity field :
Gravity anomaly reference values 𝜟𝒈𝑬𝑮𝑴
Geoid heights reference values 𝑵𝑬𝑮𝑴
8. Earth Gravity Model (EGM)
sinsincos02
nm
n
m
nmnm
nN
n
PmSmCr
R
R
GMN
EGM2008
Geoid - 𝑵𝑬𝑮𝑴
EGM2008 Gravity
Anomaly, 𝜟𝒈𝑬𝑮𝑴
9. Downward Continuation of Airborne Gravity Data
Downward continuation is necessary to reduce the airborne data from
the flight level to the terrain; for the marine area, terrain will coincide
with the mean-sea-level. Since gravity data both exist on the terrain and
at altitude, and since the flights will be at different altitudes, the method
of least squares collocation is used.
Downward
continuation and
gridding of
gravity data
using Least
Squares
Collocation
Gravity anomaly data
at flight altitude
Gridded gravity
anomaly data
at terrain level
Quasi-Geoid
computation
using Fast Fourier
Transform (FFT)
technique
1
2g
g
g
g
g
34
Block-wise least-
squares
collocation
(implemented
uaing gpcol1
module of
GRAVSOFT)
The downward continuation of airborne gravity, and the gridding of data, have
been performed using block-wise least-squares collocation, as implemented
in the gpcol1 module of GRAVSOFT. This module uses a planar logarithmic
covariance function, fitted to the reduced data.
Covariances Cxx and Csx are taken from a full, self-consistent spatial
covariance model, and D is the (diagonal) noise matrix.
s = ∆𝒈𝒕𝒆𝒓𝒓𝒂𝒊𝒏
x = ∆𝒈𝒂𝒊𝒓𝒄𝒓𝒂𝒇𝒕 𝒂𝒍𝒕𝒊𝒕𝒖𝒅𝒆
D = 𝒆𝒓𝒓𝒐𝒓 𝒎𝒂𝒕𝒓𝒊𝒙 𝒐𝒇 ∆𝒈𝒂𝒊𝒓𝒄𝒓𝒂𝒇𝒕 𝒂𝒍𝒕𝒊𝒕𝒖𝒅𝒆
Covariance between gravity anomaly at aircraft altitude (h2)and gravity on the terrain ( h1) is given by (JUPEM-T24/2014 Airborne Gravity Survey Interim Report):
))(log(),(4
1
2
21
221
i
iii
hhhhDsDggC
1][ DCCs xxsx
x
For stabilizing the downward continuation, it is essential to use remove-restore
methods. This means that the gravity field at aircraft altitude is split into three
term (remove step):
𝜟𝒈𝒓𝒆𝒔 = ∆𝒈𝒂𝒊𝒓𝒄𝒓𝒂𝒇𝒕 − 𝜟𝒈𝑬𝑮𝑴 − 𝜟𝒈𝑹𝑻𝑴
𝚫𝒈𝑬𝑮𝑴 due to spherical harmonic reference field (EGM08/GOCE),
𝚫𝒈𝑹𝑻𝑴 due to terrain,
𝚫𝒈𝒓𝒆𝒔 due to the residual field.
Only the residual terrain-corrected term 𝚫𝒈𝒓𝒆𝒔 is then processed in the collocation
downward process, with the EGM and the terrain terms Δg𝑅𝑇𝑀 rigorously
computed either at the airborne point locations (for the “remove” step) or on the
ground (for the “restore”).
The gravity anomalies at the ground level are then computed from (restore step):
∆𝒈𝒕𝒆𝒓𝒓𝒂𝒊𝒏= 𝜟𝒈𝑬𝑮𝑴 + 𝜟𝒈𝑹𝑻𝑴 + 𝜟𝒈𝒓𝒆𝒔
In the downward continuation process by least squares collocation
10. Geoid Determination
Sanso and Sideris: Geoid Determination: Theory and Methods, 2012
Geoid and Quasigeoid
Terrain
Telluroid
g𝒕𝒆𝒓𝒓𝒂𝒊𝒏
Ellipsoid
Quasigeoid
Geoid
Geoid
Defined in 1828 by Gauss as the “equipotential surface of the Earth’s gravity field
coinciding with the mean sea level of the oceans” (𝑾𝟎). The name “geoid” was
only given in 1873 by Listing (Geodesy, Torge, 2012).
Quasigeoid
The quasi-geoid and the classical geoid
can be viewed as “the geoid at the
topography level” and the
“geoid at sea-level”, respectively.
If the height anomalies ζ are plotted
above the reference ellipsoid,
then we get the quasigeoid.h
ζ
ζN
The relation between the classical geoid N and quasi-geoid
height anomaly ζ is given by the approximate formula:
where gB is the Bouguer anomaly and H the topographic
height.
This is readily implemented as a small correction (typically <10
cm) on a final gravimetric geoid computed from surface data.
In areas where H = 0, i.e. over marine areas, the
quasigeoid coincides with the geoid ( = N).
Hg
N B
11. Practical Approach in Geoid Determination
Remove-Compute-Restore (RCR)Technique
Remove Step
The methodology for geoid construction is based on remove-compute -
restore (RCR) technique. The surface gravity anomaly g𝒕𝒆𝒓𝒓𝒂𝒊𝒏 is split into
three parts.
where
1) g𝑬𝑮𝑴 is the reference gravity anomaly of the EGM08/GOCE global field.
2) g𝑹𝑻𝑴 is the gravity anomaly generated by the Residual Terrain Model, RTM, i.e.
the high-frequency part of the topography.
3) g𝒓𝒆𝒔 is the gravity anomaly residual, i.e. corresponding to the un-modelled part
of the residual gravity field.
g𝒕𝒆𝒓𝒓𝒂𝒊𝒏 = g𝑬𝑮𝑴 + g𝑹𝑻𝑴 + g𝒓𝒆𝒔
g𝒓𝒆𝒔 = g𝒕𝒆𝒓𝒓𝒂𝒊𝒏 − g𝑬𝑮𝑴 − g𝑹𝑻𝑴
Compute Step
𝑟𝑒𝑠
is computed from Δg𝑟𝑒𝑠 using Stoke’s integration (Wellenhof and Moritz,
2005), extending in principle all around the earth
dg)S( g 4
R = resres )( 1
The function S is Stokes’ function
)2
+2
( 3 - 5 - 1 + 2
6 -
)2
(
1 = )S( 2
sinsinlogcoscossin
sin
The basic method of the gravimetric geoid computations will be spherical
FFT (Fast Fourier Transform Technique) with modified kernels on a
dense grid. The computations will closely follow the principles already
applied in the MyGeoid_2003 and MAGIC_2014 geoid. The software
package GRAVSOFT will be the base of all computations.
h
Terrain
Telluroid
Ellipsoid
ζ
GeoidN
Δ𝒈𝒓𝒆𝒔
Δ𝒈𝒓𝒆𝒔
Δ𝒈𝒓𝒆𝒔
Δ𝒈𝒓𝒆𝒔
Δ𝒈𝒓𝒆𝒔
Restore Step:
After residual height anomaly 𝒓𝒆𝒔 has been computed from 𝜟𝒈𝒓𝒆𝒔, the
contribution from EGM and RTM are added back to get total height anomalies:
= 𝒓𝒆𝒔 + 𝑬𝑮𝑴 + 𝑹𝑻𝑴
The relation between N and is given by the approximative formula (Wellenhof and
Moritz, 2005)
Hg
N B
where Bg is the Bouguer anomaly and H the topographic height. This is readily
implemented as a small correction (typically <10 cm) on a final gravimetric geoid
computed from surface data. In areas where H = 0, i.e. over marine areas, the
quasigeoid coincides with the geoid ( = N).
The outcome of the remove-compute-restore technique is a gravimetric
geoid, referring to a global datum; to adapt the geoid to fit the local vertical
datum, and to minimize possible long-wavelength geoid errors, a fitting of
the geoid to GPS/Tide Gauge control is needed as the final geoid
determination step.
The software package GRAVSOFT, developed by Rene Forsberg group
at KMS and later at DTU in Denmark over many years, and used widely in
many organizations around the world, will be the base of all computations.
Marine Geoid derived from airborne
Free Air Gravity Anomaly
(MAGIC_Phase II_2014) )(CI = 0.5 m)
Marine Free Air Gravity
Anomaly
from Airborne Gravity Survey
(MAGIC_Phase II_2014) )
(CI = 5 mGal)
g = g𝑬𝑮𝑴 + g𝒓𝒆𝒔
𝑵 = 𝑵𝒓𝒆𝒔 + 𝑵𝑬𝑮𝑴
Over marine areas, g𝑹𝑻𝑴 = 0
and quasigeoid coincide with
the geoid, ζ = N.
Spherical FFT (Fast
Fourier Transform)
Technique
12. Applications of Earth Gravity Field
Seamless Land-to-Marine Geodetic Vertical Datum (MGVD)
In recent years there has been a growing awareness of the fragile ecosystems
that exists in our coastal zones and the requirement to manage our marine
spaces in a more structured and sustainable manner. Therefore, the challenge
is to provide seamless spatial data across the land/sea interface. A major
impediment is that we do not have a consistent height datum across the
land/sea interface.
Seamless Geoid
Representing a Seamless
Land-to-Sea Geodetic
Vertical Datum
Therefore, for the purposes of developing seabed
topographic database to support marine cadastre
activities at JUPEM, there is an urgent need to
develop a Marine Geodetic Vertical Datum
(MGVD). MGVD will be defined by a precise
marine geoid fitted to the National Geodetic
Vertical Datum (NGVD), a seamless vertical
reference surface for the whole area of Malaysian
waters.
UNCLOS: Article 76 Definition of the continental shelf
Marine gravity and magnetic data can assist in interpreting other geological
features and concepts mentioned in article 76 of the The United Nations
Convention on the Law of the Sea (UNCLOS), such as:
i) “Submerged prolongation of the land mass” (paragraph 3): In particular,
the style of anomaly pattern can be a useful indicator of the extent to
which the structures and rock types seen on the landmass continue
offshore.
ii) “Deep ocean floor with its ocean ridges” (paragraph 3)
iii) “Submarine elevation that are natural components of the continental
margins (paragraph 6)
The offshore prolongation of continental crust, one of the basic definition of
continental shelf, can often be demonstrated by the continuation of offshore
potential field anomaly pattern. Such extensions are usually apparent from
maps especially from airborne platform.
Airborne gravity and magnetic surveys has been completed for Sabah waters
and continental shelf in Phase I and II of MAGIC implementation (2014-2015).
Marine thematic maps consisting of Free Air Gravity Anomaly map,
Bouguer Gravity Anomaly map, Geoid Map and Magnetic Map can now be
produced for Sabah, as part of Malaysia Continental Map series by JUPEM.
Combined airborne
gravity data for Sabah
(yellow: 2002-2003,
magenta: 2014 and
black: 2015 campaigns)
Seabed Topography Data Acquisition Based On MGVD
During the implementation of MAGIC Phase I and II (2013-2014), seabed
topographic data has been acquired using hydrographic survey system for the
coastal zone of Tawau to Lahad Datu in Eastern Sabah. The seabed
topographic data has been integrated with land topographic data to form a
seamless land to sea topographic database. This can be achieved by reducing
the seabed topographic data to MSL by using the airborne marine gravimetric
geoid as shown in the following figure.
DH
N
hGPSK
Seabed (Terrain)
H = D+K-(hGPS-N)
Inst. Sea-Level
(Negative H indicate height of terrain below
sea level)
Example of Hydrographic Data Reduction to MSL
Using Airborne Gravimetric Geoid in Eastern Sabah
Determination of Synthetic Seafloor Topography
Another important application of marine gravity field information is the
development of synthetic seabed topography. For example, global seabed
topographic maps such as GEBCO has been produced based on gravity field
information derived from satellite altimetry missions (ERS-1, GEOSAT,
JASON, etc. with a resolution of about 200 km).
Airborne gravity data provides much higher resolution of a few km and
density than satellite altimetry derived gravity information; thus
airborne gravity data can be used in combination with sparse
measurements of seafloor depth to construct a uniform higher
resolution map of the seafloor topography.
These synthetic bathymetry maps do not have sufficient accuracy and
resolution to be used for assessing navigational hazards, but they are
useful for such diverse applications as locating obstructions/constrictions to
the major ocean currents and shallow seamounts where marine lives are
abundant. Detailed bathymetry also reveals plate boundaries and oceanic
plateaus.
Map showing seabed
topography based on
GEBCO dataset. Red line
indicates international
maritime boundaries of
East Malaysia
High Correlation Between
Airborne Free Air Gravity
Anomaly with Sea-bed
Topography in Terumbu Ubi,
Terumbu Laya and Pulau
Layang-Layanag areas