Airborne Gravimetry

1. A Very Brief History and Motivation

2. Theory

3. Instruments

A Brief History of Airborne Gravimetry• Natural evolution of successes in 1st half of 20th century with ocean-bottom,

submarine, and shipboard gravimeters operating in dynamic environments

− airborne systems promised rapid, if not highly accurate, regional gravity maps for exploration reconnaissance and military geodetic applications

− 5-10 minute average, 10 mgal accuracy

• 1958: First fixed-wing airborne gravimetry test (Thompson and LaCoste 1960)

− high altitude, 6-9 km

• Special challenges

− trade accuracy for acquisition speed

− critical errors are functions of speedand speed-squared

− difficulty in accurate altitude & vertical acceleration determination

• Further tests by exploration concerns

− 10 mGal accuracy, 3 minute averages (Nettleton et al. 1960)

− LaCoste & Romberg, Austin, TX

− Gravity Meter Exploration Co., Houston, TX

First Airborne Gravity Test – Air Force Geophysics Lab1958

Instruction Manual LaCoste Romberg Model “S” Air-Sea Dynamic Gravity Meter, 2002; with permission

• The first LaCoste-Romberg Model “S” Air-Sea Gravimeter

• KC-135 jet tanker

− Doppler navigation system – elevation above mean sea level determined from the tracking data

− flights over an Askania camera tracking range at Edwards Air Force Base

First Successful Helicopter Airborne Gravimetry Test1965

• Further tests and development by exploration companies

− 5 mGal accuracy, hovering at 15 m altitude (Gumert 1998)

− Navy sponsored

• Carson Services, Inc. (Carson Helicopter)

− gimbal-suspended LaCoste and Romberg Sea gravimeter

− principally, Carson Services throughout the 1960s and 1970s

Rapid Development with Advent of GPS (1980s and 1990s)

• Naval Research Laboratory – John Brozena

• Academia (in collaboration with industry and government)

− University of Calgary (K.P. Schwarz)

− University FAF Munich (G. Hein)

− Swiss Federal Institute of Technology (E.E. Klingele)

− Lamont-Doherty Earth (Geological) Observatory (R. Bell)

• National Survey and Cadastre of Denmark (DKM) – Rene Forsberg

(Brozena 1984)

gravimeter system

GPS

P3-A Orion aircraft

Twin-Otter Aircraft

Olesen (2003)

• Industry …

…

Dedicated International Symposia & Workshops

• Gravity data until the early 1960s were obtained primarily by point measurements on land and along some ship tracks.

The Need for Global Gravity Data

− map of data archive of 1963 (Kaula 1963)

1990s – More Data, Still Many Gaps

• Greater uniformity, but only at relatively low resolution

− map of terrestrial 1°×°×°×°×1°°°° anomaly archive of 1990 (Rapp and Pavlis 1990)

Satellite Resolution vs Mission Duration and Integration Time

CHAMP: 10 s

GRACE: 5 s

GOCE: 5 - 10 s

Laser-interferometry GRACE follow-on: 1 - 10 s

*

Why Airborne Gravimetry?

• Satellite-derived gravitational models are limited in spatial resolution because of high inherent satellite speed

• Only airborne gravimetry yields higher resolution efficiently

mission duration

1 day 1 mo. 6 mo. 1 yr. 5 yr.

10,000

1,000

100

10

1

reso

lutio

n [k

m]

measurement integration

time*

10 s

5 s

1 s

(Jekeli 2004)

Gravity Resolution vs Accuracy Requirements in Geophysics

Satellite Gravimetry/GradiometrySatellite Gravimetry/Gradiometry Airborne Gravimetry/GradiometryAirborne Gravimetry/Gradiometry

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Geodetic Motivation

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River flooding

coastal flooding from hurricane (Sandy)

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• Moving-Base Gravimetry and Gradiometry are based on 3 fundamental lawsin physics

Fundamental Physical Laws

Issac Newton1643 - 1727

− Newton’s Second Law of Motion

− Newton’s Law of Gravitation

Albert Einstein1879 – 1955

− Einstein’s Equivalence Principle

• Laws are expressed in an inertial frame

• General Relativistic effects are not yet needed

− however, the interpretation of space in the theory of general relativity is used to distinguish between applied and gravitational forces

Newton’s Second Law of Motion

• In the presence of a gravitational field , this law must be modified:

– Fg is a force associated with the gravitational accelerationdue to a field (or space curvature) generated by all masses in the universe, relative to the freely-falling frame (Earth’s mass and tidal effects due to moon, sun, etc.)

i gm +x = F Fɺɺ

• Time-rate of change of linear momentum equals applied force, F

– mi is the inertial massof the test body ( )constant i im m= → x = Fɺɺ

( )i

dm

dtx = Fɺ

miFx

− action forces, F, and gravitational forces, Fg, are fundamentally different

Newton’s Law of Gravitation

2

gg g

MmG m= =F n gℓ

• Gravitational force vector

– G = Newton’s gravitational constant

– g = gravitational acceleration due to M

– mg is the gravitational massof the test body

mg

n

M

ℓunit vectorattracting

mass

Equivalence Principle

• A. Einstein (1907): No experiment performed in a closed system can distinguish between an acceleratedreference frame or a reference frame at rest in a uniform gravitational field .

– consequence: inertial mass equals gravitational mass

i gm m m= =

• Equation of motion in the inertial framei

i i

m= +F

x gɺɺ specific force, or the acceleration resulting from an action force; e.g., thrust of a rocket

,i

i

m=F

a

i i i= +x a gɺɺ

• An accelerometer senses only a

⇒ a gravity meter is an accelerometer and senses only a

t0at rest on

launch pad

t1rocket ignites

t2fuel is gone

t3maximum

height

t4parachute deploys

t5at rest on

launch pad

time

Rocket: experiences no atmospheric dragengine has constant thrustlaunches vertically

g

0

Accelerometer axis: vertically up

What Does Accelerometer (or Gravimeter) on Rocket Sense?

• Accelerometry Methodto determine the unknown: gi i i= −g x aɺɺ

− Specific force, a : from accelerometer

− Kinematic acceleration, : by differentiating position from tracking system, like GPS (GNSS)

xɺɺ

• The method (like any other) requires two independent sensor systems

− Tracking system

− Accelerometer (gravimeter)

− Gravimetry accuracy depends equally on the precision of both systems

The Usual Approach to Determine g

− Advantage: g does not need to be modeled

− Disadvantage: positions are processed with two numerical differentiations

advanced numerical techniques → may be less serious than gravity modeling problem

The Challenge of Airborne Gravimetry

• Both systems measure large signals e.g., (> ±±±± 10000 mGal)

− signal-to-noiseratio may be very small, depending on system accuracies

• Desired gravity disturbance is orders of magnitude smaller

• e.g., INS/GPS system – data from University of Calgary, 1996

IMU accelerations

GPS accelerations(offset)

42 10⋅

[mG

al]

MathCad: example_airborne_INS-GPS.xmcd

[mG

al]

time [s]

Subtract and filter

Data Frame

1n

2n

3nh

λ φ

• Usually, north-east-down (NED)-frame, or n-frame

− moves with the vehicle –not used for coordinates of the vehicle

− used as reference for velocity and orientation of the vehicle; and, gravity

− conventional reference for terrestrial gravity

• Alternative: vertical along plumb line, n′-frame

− no “horizontal” gravity components

3n′3n

deflection of the vertical (DOV)

level

Body Frame

• Axes are defined by principal axes of the vehicle: forward (1), to-the-right (2), and through-the-floor (3)

3b

2b

1b G

• Gravity meter (G) measurements are made either:

− in the n-, n′′′′-frames –platform is stabilized using IMUs*

− in the b-frame – strapdown system; gyro data provide orientation

* inertial measurement units

Moving-Base Gravimetry – Strapdown Mechanization

ba – inertial accelerationsmeasured by accelerometers inbody frame

ixɺɺ – kinematic accelerationsobtained from GNSS-derived positions, x, in i-frame

( ) ( )( ) ( )

( ) ( )

sin cos sin sin cos

sin cos 0

cos cos cos sin sin

E E

E E

E E

ni

t t

t t

t t

φ λ ω φ λ ω φλ ω λ ω

φ λ ω φ λ ω φ

− + − + = − + + − + − + −

C – transformation obtained from GNSS-derived positions, φ, λ

− lever-arm effects are assumed to be applied

GNSStransformation from

inertial frame to n-frame

transformation from body frame to inertial frame

gyros

accelerometers

in i-frame

Gravitational Vector in n-frame

( )n n i i bi b= −C Cg x aɺɺ

Moving-Base Gravimetry – Stabilized Mechanization

GNSStransformation from

inertial frame to n-frametilt of platform

relative to n-frame

gyros

accelerometers:vertical plus2 horizontal

platform (p-) frame

Gravitational Vector in n-frame

n n i n pi p= −C Cg x aɺɺ

• Inertial accelerations, , from accelerometers inplatform framepa

adequate for benign dynamics

− two-axis damped platform– level (n′-frame) alignment using gyro-driven gimballed platform in the short term and mean zero outputof horizontal accelerometers in the long term

• Mechanizations

− Schuler-tuned inertial stabilized platform – alignment to n-frame based on inertial /GNSS navigation solution and gyro-driven platform stabilization

better for more dynamic environments

ideally, ; but note, n-frame differs from n′-frame by deflection of the verticalnp =C I

Two-Axis Stabilized Platform

− gryoscopemaintainsdirection in space, and commandstorque motor to correct deviation of platform orientation due to non-level vehicle

• Schematic for one axis

vehicle

accel gyro

gravity meter

motor

processor

• Schuler-tunedthree-axis stabilization: more accurate IMUs and n-frame stabilization (using navigation solution velocity in n-frame)

− horizontal accelerometer, through processor, ensures that gryoscopereference direction is precessedto account for Earth rotation and curvature

zero acceleration implies level orientation (without horizontal specific forces!)

corrects gyro drift, but is subject to accelerometer bias

ad hoc damping of platform by processor

Scalar Moving-Base Gravimetry

• Determine the magnitude of gravity – the plumb line component

− consistent with ground-based measurement (recall gravimeter is leveled)

centn n n= + ag g− gravity vector:

3ng g ′=

− since n′-frame is aligned to plumb line,

( )centn n i n b nn n

i b= − = − + −C C ag x a q aɺɺ− gravitation vector:

ellipsoid

hng

na

nq

along plumb line

deflection of the vertical(DOV)

3n

n n n= −g q a GNSS qn

n-frame mechanization does not account for the deflection of the vertical

n nq a≪− note: straight and level flight →→→→

− thus: , but note: 3ng g≠ng = g

− this holds in any frame! e.g., n n n′ ′ ′= −g q a

• One Option: n n ng = = −g q a

• Calgary group demonstrated good results (e.g., Glennie and Schwarz 1999); see also (Czompo and Ferguson 1995)

Unconstrained Scalar Gravimetry

• Requires comparable accuracy in all accelerometers and precision gyros if platform is arbitrary (e.g., strapdown)

centn n i n

i= +Cq x aɺɺ obtained exclusively from GNSS

n n bb= Ca a requires orientation of b-frame (relative to n-frame)

unconstrained in the sense that the frame for vectors is arbitrary (n-frame is used for illustration)

also known as strapdown inertial scalar gravimetry (SISG)

neglecting the DOV, qn′ = qn( ) ( )2 2' 23 3 1 2n n n ng g q a q q≡ ≈ − − −

Rotation-Invariant Scalar Gravimetry (RISG)

• Then ( ) ( )( ) ( )( ) ( )

2 223 1 2

2 221 1 2 2

2 221 2

n n n

n n n n

n n

a a a a

a q g q g

a q q

′ ′ ′

′ ′ ′ ′

′ ′

= − −

= − − − −

= − − 1 20n ng g′ ′= =since

• Platform orientation is not specifically needed for a2

− however, errors in qn, being squared, tend to bias the result (Olesen 2003)

( ) ( ) ( ) ( ) ( ) ( )( )2 2 2 2 2 221 2 3 1 2 3p p p n n na a a a a a a′ ′ ′= + + = + +

• Another option to get : based on total specific force from gravimeter and orthogonal accelerometers

g

• It can be shown that

( )n

n n n nie in

d

dt= + +Ω Ω

vq v

( )( ) ( )

( )

0 2 sin

2 sin 0 2 cos

2 cos 0

e

n nie in e e

e

λ ω φ φ

λ ω φ λ ω φ

φ λ ω φ

+ − + = − + − + +

Ω Ω

ɺ ɺ

ɺ ɺ

ɺ ɺ

• Define Earth-fixed velocity vector in the n-frame

( )( )cos

Nn n e

e E

D

v M h

v N h

v h

φλ φ + = = = +

−

Cv x

ɺ

ɺɺ

ɺ

sin cos sin sin cos

sin cos 0

cos cos cos sin sin

ne

φ λ φ λ φλ λ

φ λ φ λ φ

− − = − − − −

C

RISG Approach in More Detail (1)

• Thus, strictly from GNSS, the third component is

2 2

3 2 cosn N Ee E

v vq h v

M h N hω φ= − + + +

+ +ɺɺ

• Third component of , along plumb line,'n n n′ ′= −g q a

( )2 2

3 tilt DOV2 cosp N EE E

v vg a h v a q

M h N hω φ δ δ= − − + + + + −

+ +ɺɺ

Eötvösgδgravimeter

( ) ( ) ( )2 223 3 tilt 1 23

n n p p n npa a a a q qδ′ ′ ′ ′ = = − = − −

C a

• Inertial acceleration includes tilt error if platform is not level

RISG Approach in More Detail (2)

• Kinematic acceleration (from GNSS) includes neglect of DOV

( )3 3 DOV3

n n n nnq q qδ′ ′= = −C q

Eötvös Effect

• Approximations

− spherical:

2

Eötvös 2 cosE E

vg v

R hδ ω φ≈ +

+

− first-order ellipsoidal (Harlan 1968):

( )( ) ( )2

2 2 2Eötvös 1 1 cos 3 2sin 2 sin cos 1E

v h hg f v O f

a a aδ φ α ω α φ ≈ + − − − + + +

a = ellipsoid semi-major axis; αααα = azimuth; v = ground speed!

Loránd Eötvös1848 - 1919

• Exact in n-frame (note: vN,E at altitude!)

( )2 2

Eötvös 2 cos N EE E

v vg v

M h N hδ ω φ= + +

+ +

total velocity [km/hr]E

ötv

ös

Eff

ect

[mG

al]

heading = 45°, latitude = 45°MathCad: EotvosEffect.xmcd

Tilt Error (1)

α

1p

3p

2p

χν

• Better model for the tilt error (Olesen 2003)

− define orientation angles, ν, χ, α

cos sin cos sin

sin cos sin cos

1

np

α α χ α ν αα α χ α ν α

χ ν

− + ≈ − −

C

− assumeν, χ are small; α is arbitrary

− thus, approximate platform stabilization is required!

• One way to compute tilt error (p. 3.27)

− random errors in are squared and can cause bias (rectification error)1 2,n nq q

( ) ( )2 22tilt 3 1 2

p n na a a q qδ = − − − (neglecting DOV)

Tilt Error (2)

( )( )

1 1 2 31

2 1 2 32

cos sin cos sin

sin cos sin cos

n p p pn

n p p pn

q a a ag

q a a ag

α α χ α ν αα α χ α ν α

− + − += − − − −

,n n n pp= − Cg q a• From

• Third component of tiltp n p

pδ = − Ca a a

tilt 1 2p pa a aδ χ ν≈ − (first-order approximation)

Tilt angles are computedfrom accelerometers, GNSS, and azimuth

( )1 2 13

1cos sinn n p

pq q a

aχ α α= + −

( )1 2 23

1sin cosn n p

pq q a

aν α α= − +

• If 1 20n ng g= = (neglecting DOV is second-order effect on tilt error)

• In practice, tilt correction is subjected to appropriate filters; see (Olesen 2003)

DOV Error

( )DOV 3 1 23

n n n n nnq q q qδ ξ η′= − = − −C q

• DOV error

• Assume rms(DOV) = 10 arcsec, q1,2 = 104 mGal

( )DOVrms 0.7 mGalqδ =

( ) ( )1 2

1 0

0 1

1

nn

ξη ξ η

ξ η

′

− = − = −

C R R

• DOV components define the small angles between the n-and n′-frames

− ignore rotation about 3-axis DOV

ξ

north pole

geodetic meridian

astronomic meridian

η

geodetic zenith

neg. plumb line

horizon

east

• This error is correctable, e.g., using EGM2008deflection model

Scalar Gravimetry Equation

− tilt error depends on accuracy of platform accelerometers

− gravimeter measurement, f , includes various inherent instrument corrections

− accuracy in must be commensuratewith gravimeter accuracyhɺɺ

− where is normal gravity at the normal height of above the ellipsoidaQγ ′ aP′

− where f0 – g0 is the initial offset of the gravimeter reading from true gravity

− where is the gravity meter reading3pf a= −

( )Eötvös tilt DOV 0 0a aP Qg f h g a q f g∆ δ δ δ γ′ ′= − + + − − − −ɺɺ

• Final equation for the gravity anomaly at altitude point, aP′

− exact and sufficiently approximate formulas exist for normal gravity at aQ′

• All gravimetersare single-axis accelerometers

− mechanical spring accelerometers (vertical spring, horizontal beam)

manual or automatic (force-rebalance) nulling

− vibrating string accelerometers

− electromagnetic spring (force-rebalance)

− torsion wire (horizontal beam, no nulling)

• Instrumentation overview of scalar airborne gravimetry

− LaCoste-Romberginstruments dominate the field

− many other instrument types in operation or being tested

Airborne Gravimeters

At University of Texas, Austin

*https://web.archive.org/web/20080527061634/http://www.agu.org/sci_soc/lacoste.htmlEarth in Space Vol. 8, No. 9, May 1996, pp. 12-13. © 1996 American Geophysical Union;see also (Harrison 1995).

“The gravity meters Lucien B. LaCoste invented revolutionized geodesy and gave scientists the ability to precisely measure variations in Earth's gravity from land, water, and space” J.C. Harrison (1996)*

Lucien J.B. LaCoste (1908-1995)

• Scientist

• Inventor

• Teacher

• Entrepreneur

( )0 sin sink b mgaβ α− =ℓ ℓ

− independent of α α α α →→→→ equilibrium at any beam positionfor a given g

− independent of →→→→ no change in spring length could accommodate a change in g

ℓ

LaCoste-Romberg Air-Sea Model S Gravimeter

finite sensitivity infinite sensitivity

g

• From (Valliant 1992):

− zero-length spring: 0 0=ℓkbd mga⇒ =

− law of sines: sin sindβ α=ℓ

• Beam is in equilibrium if torque(spring) = torque(mg)

d

ba

mg

ℓ

βα

damperO

A

exactly vertical

( )0k −ℓ ℓ

with damperg g∆+

measure beam velocity!

(Inherent) Cross-Coupling Effect

aθ

( )m g z+ ɺɺ

mxɺɺ

z

x

• Horizontal accelerations couple into the vertical movement of horizontal beam gravimeters that are not nulled

− total torque on beam due to external accelerations:

( )( )sin cosT ma x g zθ θ= + +ɺɺ ɺɺ

• There is no cross-coupling effect for

− force-rebalance gravimeters

− vertical-spring gravimeters

− it can be shown (LaCoste and Harrison 1961) that the cross-coupling error is

1 1

1cos

2xε θ ψ= ɺɺ

where are amplitudes of components of and , respectively, that have the sameperiod and phase difference,

xɺɺ θψ

1 1,x θɺɺ

21 11 , 0.1 m/s 90 mGalxθ ε= ° = ⇒ =ɺɺ− e.g.,

LaCoste-Romberg Model S Sensor and Platform

From: Instruction Manual, LaCoste and Romberg Model “S” Air-Sea Dynamic Gravimeter, 1998; with permission

Stabilized Platform

Outer Frame

Dampers

Interior Side View

view of top lid

Gyroscopes

Accelerometers

LaCoste/Romberg TAGS-6(Turn-key Airborne Gravity System)

http://www.microglacoste.com/tags-6.php

BGM-3 Gravimeter

Fugro WHOI Two BGM-3 gravimeters installed on the USCG ship Healyhttps://www.unols.org/sites/default/files/Gravimeter_Kinsey.pdf

• Bell Aerospace (now Lockheed Martin)

− Model XI pendulous force-rebalanceaccelerometer

− current needed to keep test mass in null position is proportional to acceleration

induction

(Seiff and Knight 1992); see also (Bell and Watts 1986)

Sea Gravimeter KSS31, Bodenseewerk GeosystemGmbH

− force rebalancefeedback system

− highly damped output, ~ 3 minute average

•http://www.bgr.bund.de/DE/Themen/MarineRohstoffforschung/Meeresforschung/Geraete/Gravimeter/gravimeter_inhalt.html•http://www.bgr.bund.de/EN/Themen/GG_Geophysik/Aerogeophysik/Aerogravimetrie/aerogravimetrie_node_en.html

• Gravity sensor based on Askania vertical-spring gravimeter

− sensor on a gyro-stabilized platform

− Federal Institute for Geosciences and Natural Resources (BGR)

− also used for fixed wing and helicopter gravimetry

capacitive transducer

tube

spring

damping unit

permanent magnet

threadHeyde, J. (2010)

(Krasnov et al. 2008)

Chekan-A Gravimeter

− cross-coupling effect minimized by double-beam reverted pendulums

(Hinze et al. 2013)

− evolutionary modifications: Chekan AM, “Shelf” (Krasn ov et al. 2014)

− gravity sensed by deflection of pendulum hinged on quartz torsion wire in viscous fluid

− pendulum deflection: 0.3–1.5 ″″″″/mGal; e.g., ±±±±1°°°° →→→→ ±±±±10 Gal total range (0.36″″″″/mGal)

• Air-Sea gravimeter; CSRI* Elektropribor, St. Petersburg, Russia

*Central Scientific & Research Institute

(Stelkens-Kobsch 2005)

Installation in test aircraft

http

://w

ww

.gra

vio

nic.

com

/gra

vim

etry

.htm

l

Relative gravimeter Chekan in a cabin of AU

Airborne Gravimetry on Airship Platform

− test flight January 2014

− reported in IAG Commission 2 Travaux 2015

Airship AU-30

(http://rosaerosystems.com/airships/obj17)

http://eongeosciences.com/wp-content/uploads/2015/01/GT_2A.pdf(Canadian Micro Gravity)

Airborne Gravimeter GT -2A

√√√√√√√√

− vertical accelerometer of axial design with a test mass on spring suspension

• Gravimeter system designed by Gravimetric Technologies (Russia)

− photoelectric position pickup

− moving-coil force feedback transducer

− three-axis gyro-stabilized platform

− large dynamic range

(Gabell et al. 2004)

Sander Geophysics Ltd. AirGrav System• “Purpose-built” airborne gravimeter designed for airborne environment, not modified sea gravimeter

− Schuler-tuned (three axis) inertially stabilized platform

− three-accelerometer system; vertical accelerometer used as gravimeter

− demonstrated success in vectorgravimetry

− advertize gravimetry on topography-drapedprofiles

− Honeywell inertial navigation grade accelerometers(Annecchione et al. 2006, Sinkiewicz et al. 1997)

http://www.sgl.com/news/Sander%20Geophysics%20-%20Antarctica.pdf

− comparison tests over Canadian Rockies between AirGrav and GT-1A(Studinger et al. 2008)

Annecchione, M.A., Keating, P., Chouteau, M. (2006): Validating airborne vector gravimetry data for resource exploration. Geophysics, 71(6), 171-180.Bell, R.E., Watts, A.B. (1986): Evaluation of the BGM-3 sea gravity meter system onboard RJV Conrad. Geophysics, 5l(7):1480-1493.Brozena, J.M. (1984): A preliminary analysis of the NRL airborne gravimetry system. Geophysics, 49(7):1060-1069.Czompo, J., Ferguson, S.T. (1995): Design considerations for a new scalar gravity meter for airborne surveys. In: K.P Schwarz et al. (eds.), Airborne

Gravimetry, IAG Symposium G4, IUGG XXI General Assembly, 2-14 July 1995, Boulder, Colorado.Gabell, A., Tuckett, H., Olson, D. (2004): The GT-1A mobile gravimeter. In: R.J.;L. Lane (ed.), Airborne Gravity 2004 – Abstracts from the ASEG-

PESA Airborne Gravity 2004 Workshop: Geoscience Australia Record2004/18, 55-61.Glennie, C., Schwartz, K.P. (1999): A comparison and analysis of airborne gravimetry results from two strapdown inertial DGPS systems. Journal of

Geodesy, 73(6):311-321.Gumert, W.R. (1998): An historical review of airborne gravity. The Leading Edge, 17(1):113-116.Harlan, R.B. (1968): Eötvös corrections for airborne gravimetry. Journal of Geophysical Research, 73(14): 4675-4679. Harrison, J.C. (1995): Lucien J.B. LaCoste (1908-1995). EOS, Transactions of the American Geophysical Union, 76(50).Heyde, I. (2010): Aerogravity Survey of the German Bight (North Sea). In: Gravity, Geod and Earth Observation,S.P. Mertikas (ed.), IAG Symposia

135, pp.37-46, Springer-Verlag, Berlin. Hinze, W.J., von Frese, R.R.B., Saad, A.H. (2013): Gravity and Magnetic Exploration. Cambridge University Press, Cambridge.Jekeli, C. (2004): High-Resolution Gravity Mapping: The Next Generation of Sensors. In: R.S.J. Sparks (ed.), The State of the Planet: Frontiers and

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