POTENTIAL METHODS Part 1 Gravimeters, Gradiometer Carla Braitenberg Trieste University, DMG Home page: 1

Students (start ) 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 ( )

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. 4

Where to obtain data? BGI: Bureau Gravimetrique International Example Africa: see figure Other sources: – National geological surveys – Private data distribution centers 5

BGI public data - Italy 6

BGI public and private data N-Africa 7

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. 9

Height for ship-borne observations Mean sea level and geoid differ little: height measurements unnecessary. 10

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. 11

Altimetric measurements Up to a few from coast good quality data claimed in the newest release that will be published 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. 13 Start 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. 14

Outline: 1.What influences the gravity field 2.The measurement of gravity: What do we want to measure? 3.The gravimeters: What do they really measure? 15

1. What influences the gravity field The gravity field is related to: the figure of the earth, elevation, underground mass distribution, mass redistribution below and above the earth‘s surface, and, thus, also to temporal changes of mass distribution, like: ground water level / soil moisture variations, glaciation / deglaciation, surface subsidence / elevation 16

Short- and long-term variations affect: the co-ordinates of reference points the gravity field and its derivatives. Since these effects are of anthropological origin as well as due to tectonic and climatic changes, gravity field analysis is part of the monitoring and evaluation of the human environment. But: What do we really measure and how do the signals look like? How to evaluate and to interpret the gravity signals? 17

1.The measurement of gravity: What do we want to measure? -gravitational law SI: gravity acceleration g measured in ms -2 1 µm s -2 = m s -2 and 1 nm s -2 = m s -2 Old: 1 Gal = m s -2 = cm s -2 1 mGal = m s -2 = 10 µm s -2 1 µGal = m s -2 = 10 nm s -2 G= m 3 kg -1 s -2 18

- height dependence: the vertical gradient of gravity -For the Earth the variation is, with h height (m) above geoid or ellipsoid (according to the reference system): ±0.01 mGal corresponds to ± 3 cm height difference 19

- mass dependence Conclusion: The Bouguer effect is about 1/3 of the height effect and has the opposite sign. or 112 µGal - Gravitational attraction of a plate Plate thickness of 1 m leads to (density : 2670 kg m -3 ) 20

Three different effects: (1)drift of gravimeter (2)elevation and / or mass changes (3)earth tides (1)Drift properties (or stability of gravimeter spring and electronics)  individual gravimeter, temperature stabilisation / outer temperature  handling of the gravimeter (transport conditions). (2)Repeated microgravity measurements are used in active regions like post- extraction areas and to determine gravity variations  due to mass and elevation changes;  separate elevation monitoring by GPS yields mass changes. Here, no topographic correction is needed because the same points are used in different campaigns. - time dependence 21

(3) Earth tides: maximum of the signal is about ± 1000 nm s -2 ≡ ± 1 µm s -2 The dedicated gravimeter records continuously at one site. The analysis of the time series allows the separation of different tidal waves of lunar and solar origin. Due to the stacking the resolution of the spectrum reaches values below 1 nm s -2. The time series contain information about the astronomical tides and the deformation of the earth, the ocean tidal attraction, deformation of the crust by ocean tidal loading, and ground water and soil moisture variations as well as air pressure and wind. Further: Such a gravimeter record contains long-period seismology as an ultra-broadband seismometer like surface waves and free oscillations of the earth. 22

conclusion: there are three different applications: (1)point data in gravity surveys (usually measured once) (2)point data in precise microgravity surveys (usually frequently repeated after some weeks or months, even years) (3)time series of gravity variations at one specific station (sample rates of 10 s, 1 min) 23

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 24

1.1Relative gravimeters: linear and astatized systems The principle of spring gravimeters: ZLS-gravimeter (Burris gravimeter) 25

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. 26 Fk Fg1 Fg2 x F x0 x2x1

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. 27

Astatized system –Consider the torque of spring and of gravity. The spring is a special zero-length spring. a Equilibrium: Mg=Mf 28 Torque of Spring: Torque of gravity: D= elastic constant of spring. Zero length spring:

Astatized system –Consider the torque of spring and of gravity. The spring is a special zero-length spring. a Equilibrium: mgd cosα = D b a cosα Notice: if x0 ≠0 in the equation we have (x-x0) and cannot eliminate sinβ in the Torque of the spring. 29 Torque of Spring: Torque of gravity:

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. 30 From Torge (1989)

astatized system (cont.) To avoid total astatization we introduce an angle γ: Torque of spring: 31

astatized system (cont.) We get: The sensitivity follows from the differential of both sides (partial derivative respect to g and α: 32

Details (1): astatized system (cont.) For equilibrium: 33

Details (2): astatized system (cont.) Total astatization, and no measurement possible. 34

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 gravimeters have to be nulled. This is done by moving the beam into null- position by turning the spindulum or using an automatic feedback system. 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. 35

The gravimeters: 36

Conclusions up to now: Different gravimeters with individual transfer functions and resolutions provide different data with different information content. 37

Under water gravimeter ROV-DOG Sasagawa et al., Sensor: Scintrex CG-3M. Precision: 5microGal Tilting system for remote leveling (0.02 nrad precision) Depth control: pressure meter Drift: mGal/day

39 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 gravimeters A mass is dropped in an evacuated tube and the time and distances are 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 40

JILA FG-5 absolute gravimeter From Torge (1989) Accuracy goes down to ± 2 µGal. 41

JILA absolute gravimeter From Torge (1989) Accuracy goes down to ± 2 µGal. 42

Absolute gravimeter Micro-g A10 43 Fine ()

Atom interferometric gravimeter 44 ( )

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 45

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, Performance: Target accuracy 0.5 microGal. Operates as absolute gravity measurement. Possible development to gradiometer Presently developped at: Humboldt University Berlin Onera and SYRTE, France China

Steady improvements of the accuracy of the gravimeters over 400 years: Development of the accuracy of gravimeters from the year 1600 on (after Torge, 1989); values of today: free fall: ± 2 µGal relative gravimeters ± 10 µGal ZLS <± 3µGal in recording mode: < ±.05 µGal averaging over 1 hr ZLS ? 48

Development of the number of terrestrial gravity values (after Torge, 1989) ?

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. 50

Scalar, vector, gradient tensor 51 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) 52

History of gradient tensor First field gradiometer measurements: about 1900 by R. v. Eötvös with the torsion balance Fischbach and Talmadge, 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 53

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 accelerometers Bell Geospace Inc.: Full tensor gradiometer (FTG) ARKeX Ltd: FTG Noise levels: 55

Principle of gradiometer Schematic diagram of the gravity gradient instrument. The sensitive axes of the accelerometers are indicated by arrows. Lee, NHP Billiton 56

Rotating gradiometer 57

Bell Geospace FTG 58

Cutting edge instrumental developments ARKeX Exploration Gradiometer: superconductive state at -269°C (4° above absolute zero) Target sensitivity for Tzz: 59

Thank you for your attention! 60