POTENTIAL METHODS2015-2016
Part 1
Gravimeters, Gradiometer
Carla BraitenbergTrieste University, DMG
Home page: http://www2.units.it/~braitenberg/e-mail: [email protected]
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Students• [email protected]• [email protected]• [email protected]• [email protected]• [email protected]• [email protected]• [email protected]• [email protected]• [email protected]• [email protected]• [email protected]• [email protected]
2(start 6.10.2015)2
Measuring techniques of GravMag fields
• Steps to consider if new data are needed:• Determine size of area to be studied.• Also size of expected signals.• Small size: high accuracy, high spatial resolution• Terrestrial measurements: best quality. Small
sampling distance. Time consuming.• Gravity: levelling and near topography
measurement
(6.10.2015)
Why is height measurement important?
• Remember: dz = 1 m -> 0.3 mgal signal• Microgravimetry: µgal -> 0.3 cm height
accuracy needed• GPS: very fast. Differential GPS. Precision of
some cm on z component.• On magnetic field: height less problematic.
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Where to obtain data?
• BGI: Bureau Gravimetrique International• Example Africa: see figure• Other sources:
– National geological surveys– Private data distribution centers
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BGI public data - Italy
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BGI public and private data N-Africa
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Aereal measurements• Independent on terrain• Regular spacing of measurements• Fast measurement• Continuous recording• To be corrected for vertical movements of
aircraft• Greater distance from source.• Practical: can microgravity measurements be
made?8
Shipborne measurements
• Horizontal ship movement slow with respect to vertical movement.
• Technique of averaging in time eliminates noise due to waves.
• Instruments can be installed routinely on vessels cruising for seismics. Measurements can be made automatically. Data analysis can be done later.
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Height for ship-borne observations
• Mean sea level and geoid differ little: height measurements unnecessary.
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Satellite measurements
• Greater distance from source• Spatial resolution is worse.• Global availability• Altimetric satellites:
– ERS, Topex, Jason, Envisat– Measure sea level height.– Sea level close to geoid – Gravity field can be derived.
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Altimetric measurements• Up to a few from coast good quality data claimed in
the newest release that will be published 2016. closer: lesser data due to footprint interference with coast.
• Degraded results over shallow seas: currents are important and sea surface deviates from geoid: dynamic topography of sea surface. But in the 20 years analysis of the altimetric field and comparison with independent measurements as ocean drifters and gravity measurements on ships, the ocean current models have been successively improved, so that the dynamic topography can be modelled and subtracted from the observations leading to a correct gravity field. 12
Fine 6 ott 2015
Geodetic satellites
• Geodetic satellites: deviation of orbit from predicted. Acceleration and gradiometer measurement on board.
13Start 8 ott 2015
Instrumentation:Relative gravity meters,
short introduction to absolute gravity meters, gradiometers, relative accuracies
Note: The gravity field measurements require a basis knowledge of the construction of the gravimeter, due to the inherent drift. We therefore discuss the gravimeter in greater detail. The magnetometer measurements do not present these problems and are therefore not treated here.
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1. gravity meters: What do they really measure?
- relative gravimeters:
linear and astatized systems
- absolute gravimeters
- gradiometers / torsion balance
- continuous recording of gravity changes at a site
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1.1 Relative gravimeters: linear and astatized systems
The principle of spring gravimeters:
ZLS-gravimeter (Burris gravimeter)
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Equilibrium for spring• Fg=mg Fk=(x-x0)k
– k=elastic constant of spring– x0= length of unloaded spring. Zero length spring x0=0.
• At equilibrium: Fg-Fk=0. The greater dx=x2-x1, the greater the resolution of the instrument.
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Fk
Fg1
Fg2
x
F
x0 x2 x1
Pendulum type instruments
• Increase sensitivity by introducing a rotational system.
• Consider torques.• Astatization: make system so it is near to
stable in any position. • Variation of gravity torque should be very
similar to torque exerted by spring in function of the rotation of beam.
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Astatized system –Consider the torque of spring and of gravity.The spring is a special zero-length spring.
a
rxxDM F )( 0
Equilibrium: Mg=Mf
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cosmgdM g
Torque of Spring:
Torque of gravity:
D= elastic constant of spring. Zero length spring:
DxrM F
Astatized system –Consider the torque of spring and of gravity.The spring is a special zero-length spring.
a
cos
sinsin
cos
sin
sin
cos
abD
ab
DM
ar
bx
F
Equilibrium: mgd cosα = D b a cosαNotice: if x0 ≠0 in the equation we have (x-x0) and
cannot eliminate sinβ in the Torque of the spring. 29
cosmgdM g
Torque of Spring:
Torque of gravity:
)( 0xxDFk
the acting torques
Left graph: corresponds to a beam suspended by a elastic spiral, for which the Elastic force is proportional to the rotation angle. Right graph: corresponds to the suspension of the spring as in the previous slide,for which the elastic force is proportional to the sine of the angle.
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From Torge (1989)
astatized system (cont.)To avoid total astatization we introduce an angle γ:
sin
)90sin(
:and90
b
x
)90sin(cossince
)cos(
)90sin(
Dba
DbaM FTorque of spring:
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astatized system (cont.)
We get: )cos(cos Dbamgd
The sensitivity follows from the differential of both sides (partial derivative respect to g and α:
)sincoscos(sin
sincos
Dba
mdgmdg
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Details (1): astatized system (cont.)
)tancossin
tan
DbaDba
mdgmdg
)cos(
cos
g
md
DbaFor equilibrium:
)tan(tan
)cos(
)sin(tan
)cos(
sincoscossintan
)tancos)cos(
cos
sin)cos(
cos(tan
g
g
g
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Details (2): astatized system (cont.)
)tan(tan
1
0
)tan(tan
1
g
g
case
g
g
Total astatization, and no measurement possible.
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Characteristics of linear and astatized types:
- Linear gravimeters: linear relation between the torques of the spring force and the gravity force.
- Astatized gravimeters are non-linear, but more sensitive, because usually the beam movement due to the gravity force is bigger.
Consequences:
In order to avoid effects from non-linearity astatized gravimetershave to be nulled. This is done by moving the beam into null-position by turning the spindulum or using an automatic feedbacksystem. Since the gravity value measured is related to the spring we measure a relative gravity value. Thus, we can determine gravity differences between different locations.
Only if the absolute gravity value of one point is known we can convert our relative values to absolute ones.
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The gravimeters:
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Under water gravimeter ROV-DOG
Sasagawa et al., 2003.
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Sensor: Scintrex CG-3M. Precision: 5microGalTilting system for remote leveling (0.02 nrad precision)Depth control: pressure meterDrift: 0.3-0.8 mGal/day
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Deployment designed for up to 4500m depth.
Fine 8 ott 2015
(1) pendulums of different designs- so-called Sterneck-pendulum for ‘field measurements’;- reversion pendulum for operation in a laboratory under stable cond. Today: no use anymore
(2) free-fall gravimetersA mass is dropped in an evacuated tube and the time and distancesare measured. - rise-and-fall principle- free-fall principle (most important: JILA absolute gravimeter by Faller et al.,
1983, and Niebauer et al., 1986) special features:- very short height difference of less than ½ meter- ellimination of seismicity by using a long-period seismometer as support
(super-spring) - accuracy is now better than 50 nms-2 - a transportable ‘field version’ is now available.
Absolute gravimeters
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JILA FG-5 absolute gravimeter
From Torge (1989)
Accuracy goes down to ± 2 µGal.
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JILA absolute gravimeter
From Torge (1989)
Accuracy goes down to ± 2 µGal.
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Absolute gravimeter Micro-g A10
43Fine ()
Atom interferometric gravimeter
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https://www.physik.hu-berlin.de/
( )
Atom Interferometry absolute gravimeter – short description
• Measurement principle: use dual aspect of matter consisting in particle and wave properties.
• Analogous to wave and matter duality of light• Interference effects of two packets of atoms is
measured
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procedure• A) cool atoms by trapping them with laser-
light• B) Impose movement on a part of the atoms
by light-atom interaction with selected frequency (Raman transition of atom). The atoms separate in distance in the order of 5 mm, between atoms that move and atoms that do not move
• C) Let the separated atoms fall in the gravitational field
• D) measure interference between the two packages of atoms 46
First field measurements Schmidt, 2011
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Performance: Target accuracy 0.5 microGal.Operates as absolute gravity measurement.Possible development to gradiometer
Presently developped at: Humboldt University BerlinOnera and SYRTE, FranceChina
Steady improvements of the accuracy of the gravimeters over 400 years:
Development of the accuracy of gravimetersfrom the year 1600 on(after Torge, 1989); values of today:
free fall: ± 2 µGal
relative gravimeters ± 10 µGalZLS <± 3µGal
in recording mode:< ± .05 µGalaveraging over 1 hr
ZLS ? ?
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Development of the number of terrestrial gravity values(after Torge, 1989)
?
2010
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Gravimeter gradiometry
With spring gravimeters:
determination of small gravity differences Δg to a precision of ± 0.1 µms-2 or even ± 10 nms-2.
Thus, precisions in the order of a few 10 *10-9 s-2
are achieved with standard techniques using a tripot.
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Scalar, vector, gradient tensor
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Li, 2010
Gradiometers
Task: Determination of vertical gradient to convert continuous data from SG to elevation changes in the salt mine Asse / Germany (Prof. Gerhard Jentzsch)
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History of gradient tensor
• First field gradiometer measurements: about 1900 by R. v. Eötvös with the torsion balance
Fischbach and Talmadge, 1992. Nature
• Observation based on the measurement of the difference of the gravitational force in two points.
• Vertical gradient: two measurements of gravity at different heights
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Introduction to Gradiometers• First gradiometer supplanted in 1930s by
modern gravimeter-> faster data acquisition• In 1970s renewed interest for military
applications: Bell Aerospace awarded contract for U.S. Navy.
• Principle of measurements of modern gradiometers involve differential observations of accelerometers.
(DiFrancesco et al., 2009)54
Lockhead Martin rotating Accelerometer
Output of high precision room-temperature accelerometers are continuously combined to obtain2 tensor components.
Commercialization: BHB Billiton: FALCON: partial tensor with 4
accelerometersBell Geospace Inc.: Full tensor gradiometer (FTG)ARKeX Ltd: FTGNoise levels:
Hz
E355
Principle of gradiometer
Schematic diagram of the gravity gradient instrument. The sensitive axes of the accelerometers are indicated by arrows.
Lee, NHP Billiton56
Rotating gradiometer
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Bell Geospace FTG
www.bellgeo.com 58
Cutting edge instrumental developments
• ARKeX Exploration Gradiometer: superconductive state at -269°C (4° above absolute zero)
• Target sensitivity for Tzz:Hz
E3
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Thank you for your attention!
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