POTENTIAL METHODS2015-2016

Part 1

Gravimeters, Gradiometer

Carla BraitenbergTrieste University, DMG

Home page: http://www2.units.it/~braitenberg/e-mail: berg@units.it

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Students• elisa.vnt@gmail.com• suzy.vizintin@gmail.com• elisadb93@libero.it• gaiatravan@gmail.com• a.geniram@gmail.com• contear@hotmail.com• marellomichele@gmail.com• giuliaareggi92@gmail.com• turcofrancesco@hotmail.it• m.savy97@hotmail.it• minuetto93@gmail.com• fadel-raad@hotmail.com

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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