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AIRBORNE
GRAVIMETRY
M. Assumpció Termens

M. Assumpció Termens, 2017-05-09, Enginyeria en Geoinformació i Geomàtica
agenda
• background
• problem statement
• NA approach
• INS/GNSS gravimetry: geodesy as usual
• future
2

background
3

gravimetry – what is it?
4
• geophysical method to measure the
gravity field of the Earth.

gravimetry – what is it?
5
• geophysical method to measure the
gravity field of the Earth.
• helps the understanding of mass
transport phenomena within our planet, in
the oceans and atmosphere

6
geodetic motivation
• sea-level rise
• river flooding
• coastal flooding from hurricane
• ...

gravimetry - applications
• precise terrestrial reference frame
• local geoid determination
7

8
• volcano monitoring
• glaciers melting monitoring
• plate boundaries
• deformation measurements
• eartquake tectonic studies

9
• volcano monitoring
• glaciers melting monitoring
• plate boundaries
• deformation measurements
• eartquake tectonic studies
• Natural resources (i.e. Mineral exploration)

gravimetry – measurement methods
10
GLOBAL REGIONAL LOCAL
CHAMP (> 600 km)
GRACE (> 270 km)
GOCE (> 70 km) terrestrial
10 km100 km1000 km 1 km

11
Kinematic gravimetry
(> 1 km)
CHAMP (> 600 km)
GRACE (> 270 km)
10 km100 km1000 km 1 km

12
Airborne gravity is the only
technique that can
adequately connect existing
terrestrial data to existing
ship and altimetry data in
the oceans and fill coverage
gaps.
Airborne data will not
replace existing data, but
will be used as a baseline for
correcting that data to be
consistent across the
country.

13
airborne gravimetry

14
airborne gravimetry

problem statement
15

kinematic gravimetry (KG) - concept
1950’s: placing gravimeters
onboard vehicles
16
rapid and high-resolution
surveys in oceans, polar
regions, high mountains,
tropical forests...

17
The first LaCoste-Romberg
Model “S” Air-Sea
Gravimeter.
1958 - Air force Geophysics Lab

18
LaCoste-Romberg Model “S”

19
LaCoste-Romberg TAGS-6

20
BGM-3 Gravimeter - Bell Aerospace

21
Sea Gravimeter KSS31. Bodenseewerk Geosystem GmbH

22
Chekan-A Gravimeter

23
1965 - Carson Services, Inc.

onboard vehicles
1960’s: INS was introduced
as as surveying instrument
24
positioning limited by the
unknown anomalous
gravity field

onboard vehicles
25
positioning limited by the
unknown anomalous
gravity field
gravity field will be recovered from INS
measurements if accurate kinematic
positions and velocities are known and
the system errors are kept small

26
INS used for airborne gravimetry

onboard vehicles
1980’s: GPS represented
the opportunity to measure a
with adequate accuracy and
precision
27

28
Rampant Lion project

onboard vehicles
1980’s: GPS represented
the opportunity to measure a
with adequate accuracy and
precision
29
gravity computation is easy,
in principle ...

... but, gravity computation is hard
30
• very dynamic environtment:
• noise-to-signal ratios > 1000
• largest contributions to noise:
• high frequency noise (vibration)
• noise amplification when computing
accelerations
GNSS INS
meas. principle dist. from time delays inertial accel.
system operation reliance on space segment autonomous
output variables position, time position, orientation
long-wave. errors low high
short-wave. errors high low
data rate low (1Hz) high (≥ 25Hz)
instrument cost low high
INS/GNSS
limiting factors

airborne gravimetry - operational constraints
• navigation system used to position the aircraft
• aircraft speed: compromise between low vibrations (high
speed) and high spatial resolution (low speed)
• flight altitude: the signal to noise ratio improve with a lower
altitude
• use of an autopilot: to provide both smoother flight path and
the maintenance of a reference altitude
• weather condition: low turbulence is essential if high
frequency aircraft accelerations are to be avoided
• design of the aircraft
• design of the survey
31

32
airborne gravity survey

33
airborne gravity survey

KG - mathematical models
34
INS navigation equations

stochastic processes
INS/GNSS gravimetry – traditional approach
35
apriori stochastic info from manufacturer’s,
tricky calibrations and field testing modelling

INS/GNSS-g – traditional approach
36
process noises:
where
dynamical system
State Space Approach (SSA)
• prediction, Kalman filtering and
smoothing
• generates and optimal estimates, but
not the best
• cannot use all the observational info.
• disadvantage trying to deal with space
correlations (i.e. crossover points)

INS/GPS-g – SSA methodology
37
STATE SPACE APPROACH
prediction + KF + smoothing
STOCHASTIC TIME SERIES
• stochastic differential equations
• state vector
• observations
Sander Geophysics
US Naval Research Lab
Geomatics Canada
KMS
AGMASCO
ITC Moscow
Intermap
Univ. of Calgary (UofC
Univ. Porto
• scalar: L&R + platform + DGPS
• scalar/vector: INS/GNNS

38
• state vector
• observations
• scalar: L&R + platform + DGPS
• scalar/vector: INS/GNNS
Kananaskis (UofC, 1995)
Skagerrak (AGMASCO, 1996)
Azores (AGMASCO, 1997)
Greenland (UofC-KMS, 1998)
Greenland, Baltic Sea, Great
Barrier Reef (KMS, 1999)
Alexandria (UofC, 2000)
Greenland (KMS, 2000)
Greenland, Crete, Corsica
(KMS, 2001)
Geophysical surveys
(Intermap, Sander Geophysics)

39
(KMS, 2001)
Geophysical surveys

40
(KMS, 2001)
Geophysical surveys

41
(KMS, 2001)
Geophysical surveys

42
(KMS, 2001)
Geophysical surveys

43
Greenland Aerogeophysical project 1991-92
• US Naval Research Lab
• NOAA
• Danish National Survey (now DTU-Space)
• NIMA (now NGA)

44
ArcGP
1992-2003

45
Arctic gravity project

46
Malaysia 2002-3

47
Rampant Lion project - Afghanistan 2006,2008

NA approach
48

INS/GNSS-g – Network Approach
49
Network Approach (NA)
• observation equations
• least-squares adjustment (LSA)
• the key to overcome SSA limitations is to look
as stochastic differential equations (SDE)
• discretisation
leads to a geodetic network new
approach
Geodesy
as usual

NA – network approach
• general advantages:
• parameters related by observations regardless of time
• networks can be static and/or dynamic
• covariance information can be computed selectively
• variance component estimation can be performed
• INS/GNSS gravimetry advantages:
• rigorous Earth gravity modelling
• better exploiting of external observational information
• more information for further geoid determination
• drawback:
• cannot be applied to real-time navigation
50

INS/GPS-g – approaches
PAST PRESENT FUTURE
51
NETWORK APPROACH
least-squares network adjustment
CLASSICAL NETWORKS
• static model, param. and obs.
NEW NETWORK APPROACH
• dynamic observation model
• static observation model
• time dependent parameters
(stochastic processes)
• time independent parameters
(random variable)
• independent observations
• state vector
• observations
STOCHASTIC
TIME SERIES
STATIC
NETWORKS
TIME DEPENDENT NETWORKS

INS/GNSS-g – NA approaches
CLASSICAL NET TIME DEPENDENT NET
52
Termens,A., Colomina,I. Network
approach versus state-space
approach for strapdown inertial
kinematic gravimetry. GGSM2004,
IAG Symposia Vol. 129, pp.
107-112
Termens,A. A Network Approach
for Strapdown Inertial Kinematic
Gravimetry. Ph.D.
Colomina,I., Blázquez,M. A unified
approach to static and dynamic
modelling in photogrammetry and
remote sensing. International
Archives of the Photogrammetry,
Remote Sensing and Spatial
Information Sciences 35(B1). pp.
178-183
GAL FP7-287193 project “Galileo
for Gravity”
GAL final review. Castelldefels,
2014-02-10.
2004
2012
2014
...

INS/GNSS-g – NA approaches
CLASSICAL NET TIME DEPENDENT NET
53
Termens,A., Colomina,I. Network
approach versus state-space
approach for strapdown inertial
kinematic gravimetry. GGSM2004,
IAG Symposia Vol. 129, pp.
107-112
Termens,A. A Network Approach
for Strapdown Inertial Kinematic
Gravimetry. Ph.D.
Colomina,I., Blázquez,M. A unified
approach to static and dynamic
modelling in photogrammetry and
remote sensing. International
Archives of the Photogrammetry,
Remote Sensing and Spatial
Information Sciences 35(B1). pp.
178-183
GAL FP7-287193 project “Galileo
for Gravity”
2004
2012
2014
...
GeoTeX
GENA

INS/GNSS gravimetry:
geodesy as usual
54

ICC GeoTeX package (1988 - )
• adopts a simple adjustment oriented point of view
• main data types: observations, parameters and sensors.
• Functional model
• FORTRAN-90 dynamic memory 32-bit implementation
55

GeoTeX functional model implementation
56
discretization
deriva1:
midpoint or
leap-frog
stochastic process Hz(INS)
Hz(cal)
Hz(g)
interpolation
intp: nearest point
RW process

INS/GNSS-g GeoTeX models
57
gravity
GNSS
INS
equations

GeoTeX WIB – INS angular rate vector model
58
Euler angles differential equations:
equivalent equations in terms of quaternions:
GeoTeX/ACX functional model

GeoTeX gravity parameters
59
DG-P
G-P
GRAVITY-P
G-P
DG-P

GeoTeX models – INS/GNSS gravimetry
60
38 observations 9 parameters
AB AB-O AB-P AOFF-O AOFF-P CUPT
CUPTX DG-O DG-OBS DG-OBS-GG DG-P
DGUPT-GG FB-DGE FB-DGN FB-GG G-O
G-OBS G-P GDT-DGE GDT1-DGE GDT-DGN
GDT1-DGN GDT-GG
GRAVITY GRAVITY-P
GUPT-DGE GUPT-DGN
GUPT-GG GUPTN-DGE GUPTN-DGN OB OB-O
OB-P Q-NORM Q-O Q-P RE-O RE-P VEL
VE-O VE-P VUPT VUPTX WIB XOVER-DGE
XOVER-DGN XOVER-GG

INS/GNSS-g – implementation issues
61
Cfg.1 Cfg.2 Cfg.3
IMU
Hz (IMU)
Hz (GPS)
T (s)
LN200
200
10
12 000
LTN101
50
1
12 000
LN200
200
5
14 400
N(imu)
N(gps)
N(aux)
45 599 982
360 003
720 000
11 399 982
36 003
180 000
54 719 982
216 003
N*(eq)
N(eq)
N(par)
45 959 985
46 679 985
45 600 000
11 435 985
11 615 985
11 400 000
54 935 985
54 935 985
54 720 000
Rb*
Rb
0.007 83
0.023 14
0.003 15
0.018 59
0.003 93
0.003 93
Rb =
N(eq) – N(par)
N(eq)

• large band-bordered matrix
• sparse matrix techniques
• fill-in reduction techniques
• memory-to-disk paging
• reducing parameters
• small redundancy
• increasing AUX obs.
62
ctra_LN200_v2a2x

• large band-bordered matrix
• sparse matrix techniques
• fill-in reduction techniques
• memory-to-disk paging
• reducing parameters
• small redundancy
• increasing AUX obs.
63
ctra_LN200_v2a2x
GDT GDT-p & XOVER

future
64

65
Kinematic gravimetry
(> 1 km)
CHAMP (> 600 km)
GRACE (> 270 km)
10 km100 km1000 km 1 km

66
alternative survey platforms ?

67
airborne gravimetry

68
alternative survey platforms ?

69
global gravity … long-wavelength help aerogravity

70
satellite gravity: GOCE

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