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