1. Chalmers University of Technology
How a Superconducting gravimeter can support Absolute gravimetry: Eight years of investigations at Onsala Space Observatory
Hans-Georg Scherneck
Chalmers University of Technology
Göteborg, Sweden

2. Content About Chalmers and Onsala Space Observatory
Post-glacial land uplift – Glacial Isostatic Adjustment
Absolute gravimetry
with ancillaries: Superconducting stationary gravimeter and, occasionally, a seismometer
Multi-campaign data analysis
Main interest: rate of change of 𝑔 , and 𝑔 𝑢

3. Chalmers and Onsala
Chalmers is a university of technology in Göteborg (Gothenburg), Sweden
Department of Space, Earth and Environment Science (SEE), extended May 1, Concerning earth science,
Radar remote sensing (forestry and agriculture, sea ice and oil spill, ocean waves,…)
Optical remote sensing (volcanic gasses, air pollution)
Global Environmental Measurements and Modelling (tropo- strato- meso-sphere; ozone, CFC’s, radiation, mass transport,…; satellite atmosph. sounding and spectroscopy ….)
Onsala Space Observatory: Part of Sweden’s National Research Infrastructure
Short: OSO
Radio Astronomy and Astrophysics
Ground-based Aeronomy and Radiometry
Space Geodesy (VLBI, GNSS)
Gravimetry

4. Twin telescope inauguration May 18, 2017
King Carl XVI Gustaf at
25m radio telescope
inauguration 1976

5. Facilities at Onsala Space Observatory
OSO has:
20 m radio telescope (VLBI before VGOS)
25 m radio telescope (S to C band, eventually MEO and LEO satellite tracking)
OTT Twin telescopes (VGOS) since May 2017
GNSS tracking for IGS, SWEPOS network,… and a well-determined position and velocity in the ITRF.
GNSS tide gauge (and other, modern mareographs)
Water vapour radiometers (also: CO, O3)
and …

6. 25 m teleskop Seismometer GNSS-R- mareograf Tvillingteleskop
Gravimeter
20 m teleskop
GNSS
Radiometrar
Mareograf
LOFAR
25 m teleskop

7. Superconducting gravimeter
taken into operation
GWR #054, IGETS station OS, with a range of ancillary sensors for the near environment
Monuments for visiting Absolute Gravimeters
A broadband seismometer station of the SNSN network (Uppsala university)
The synergy between this threesome of techniques is the topic of this presentation
AG +SG + Seis = true

8. Superconducting gravimeter at OSO
Live page
with many links, incl. time series for ancillary sensors:
Invar rod ”anchor” 4 m depth, monitor monument height
thermometers in cabin and in monument at 3 depth levels
borehole pressure gauge, monitor ground water level
Just for fun:
biomass (visitors) at the gravimeter
(excursion for new-come department divisions)
and an earthquake

9. Purpose: Reference station for Nordic Geodetic Commission’s Working Group for Geodynamics
Why measuring gravity change?
GIA, Glacial Isostatic Adjustment, post-glacial land uplift still in progress
How?
with Absolute Gravimeters (micro-g FG5), coordinated project within the NKG
Are the results satisfactory?
well … not really. Perhaps marginally. Many more observations needed
Improvements?
difficult at the network stations; OSO clones are unrealistic. GNSS? – ok. SG? – rather not.

10. GNSS: BIFROST-project 3-d displacement rates
Continuous observations, 150 permanent stations, some already starting 1993
Observed Modelled Difference
Kierulf et al., J.Geophys.Res., doi: /2013JB010889, 2014

11. Do we need to know the slow surface gravity change?
Geoid change is important: tilt of level surfaces like in canals, transport pipes, big lakes; a contribution to sea level change. An obligation for Land Survey Agencies.
Up to 2000 km from a attractive source the sea level is dominated by Newtonian attraction; melting ice in Greenland will still yield a fall of sea level on Norway’s Atlantic coast even taking the water intake to the world ocean into account!
Thus, we should be able to distiguish between current, home-made change (from GIA) and from ”external” sources (present-day ice sheet melting).
Ground-truth in Fennoscandia’s GIA for space-borne observations (GRACE).
The answer seems: YES
The project has had its phases since the mid 1960’ies:
east-west profiles measured with LaCoste relative gravimeters
since using AG’s in a site network without emphasis on a specific lateral layout

12. NKG Absolute Gravimetry station network
AG-stations ~  Relative-g profiles

13. What needs to be investigated, and how?
From observations, the ratio 𝑔 𝑢 at as many field points as feasable
Is there a simple relation, 𝑔 =𝐶 𝑢 + 𝑔 0 , valid over long time, valid everywere ?
Predict 𝑔 and 𝑢 with a solid earth model and a loading history
add a self-constent ocean model (ice+ocean mass conservation; self-loading and self-attraction)
contemporary sea level change
take PREM, add and vary a viscosity profile

14. With the Sea-level equation and ICE-5G
Olsson et al., doi: /j.jog

15. g/u ratio from modelling
Olsson et al., doi: /j.jog
resolution ± 0.01 to 0.02 μgal/yr ( 0.1 to 0.2 nm/s2 )
required to investigate into regional variation of ratio.

16. Are the results satisfactory?
Answer depends upon what we need to know and whether the technique is fully exploited
Gravity change could be predicted from vertical uplift rates using
empirical relations
a geophysical model
The prediction could always be challenged
Nothing beats observable evidence
Gravity change relates to mass in motion, uplift rates to the surface in motion.
Where is the origin of the gravity effect? Concentrated in an asthenosphere? Wide-spread throughout the mantle?
How sophisticated does a model have to become? There have been overly simplistic models too.

17. Too simplistic Bouguer on a flat earth
dg = ( gamma + 2pi G rho ) dz
misses the finite extension not really negligible w.r.t. earth radius
Even a finite extent of a loading mass on a simple earth model (elastic litho, viscous mantle) shows:
Forbulge subsidence,
extent-dependent dg/dz (flexural rigidity => wavlength spectrum of compliance)

18. Slightly less simplistic just simple
δg = c ρm
δg = ρm f (λ)

19. Not a back-on-the-enevelope calculation, rather a Turcotte-Schubert exercise

22. 𝑔 𝑢 ratio depends on Lithosphere Load diameter thickness

23. An overlooked effect
Volume dilatation due to bending; attraction source moving down. ”No big deal” – Wrong!

25. Less simplistic
a repetition
heuristic approach to rotation to solve for secular polar motion
A model for a Spherically symmetric Rotating Visco-elastic self-Gravitating earth model (”SRVEG”)
spherical harmonics, Love-number approach (Love -> Pekeris -> Peltier -> …
Free viscous normal modes (instead of seismic)
Love number approach and visco-elastic free modes
shows a spectrum of relaxation times for the different modes
shows that the relation 𝑔 𝑢 depends on excitation wavelenghts
shows that 𝑔 𝑢 is not a constant
it varies in time (only slightly, and is difficult to measure back in time (land emergence depends on k’n – h’n )
it varies along the surface (measurable?). N.B.: Node lines for 𝑔 and 𝑢 are not co-inciding.

26. Vary viscosity profile Example: Olsson et al., 2014
In the figures,
Load Love numbers, gravity factor
𝛿′ 𝑛 =𝑛𝐻 𝑡− 𝑡 𝑢 +2 ℎ′ 𝑛 − 𝑛+1 𝑘′ 𝑛
and their infinit sums (Greens functions)
Vary viscosity profile Example: Olsson et al., 2014
𝑔 𝑢 is influenced by the
--- dominating spherical harmonic degree (”wavelength”) excited by the load (width and profile of the ice sheet).
--- upper/lower mante viscosity contrast
--- density of competent layer (asthenosphere, if there is one) or – in other words – the thickness of the lithosphere

27. GIA by GNSS – some after-thoughts
Continuous GNSS observations, 21+ years
150 stations
Use the S(N)RVESG model, vary its parameters and minimize the chi-square in fitting the obs.
Use different (de-)glaciation histories.
Unfortunately, ice models (Ice5g, Peltier et al.; Tarasov) are reconstructed using another SRVEG; any impact of lateral heterogeneity in earth structure and rheology is readily absorbed in the ice sheet; the historic thickness of ice sheets is a parameter that is difficult to come by. Even climate-dominated models need a GIA model to work. (At what height above (today’s) sea level was the snow line? What was the altitude of the terrain?)
Therefore, model inversions from precise observations regularly agree with the GIA model on which the ice model was based. Even in such basic aspects of viscosity contrasts and layer thicknesses: the same trade-off of litho-thick v upper mantle viscosity. GNSS as a test of internal consistency only?
How could ice models be disentangled from solid earth GIA models?
GIA on laterally homogeneous earth structure => spheroidal modes only; no curl! (you need a dense network though). Scherneck et al., 2010, tried at least.

28. And now for the AG-SG-Seis synergetics
Multi-campaign analysis at the drop level
i.e. every drop measurement from all campaigns is reduced with the repective SG sample,
which requires a scale factor for the SG measurements, which are in Volt units.
Actually, the logic was the way around: AG campaigns have the additional purpose to calibrate the SG
and we found that
a slope must be estimated for every setup (drift of AG verticality)
when the tide signal is not perfectly symmetric (which it rarely is) during a project (=setup), slope and scale-factor estimates are severly co-variant.
Hence the idea to joinly analyse all campaigns
address the SG drift problem
wonder (hypothesize) whether the SG would provide a more complete ”correction” (reduction) of slow, time-variant g-excursions
and lead to a more robust estimate of a secular rate of change in g0.

29. And now for the AG-SG-Seis synergetics
AG standard analysis => project-mean reduced g
Reduce earth tides (a harmonic development with only a few wave groups – here with ocean loading):
Simple reductions for atmosphere and polar motion:
The final uncertainty for g per project is typically nm/s2
Schwiderski (1981) resolves Skagerak and Kattegat only poorly DC
Long Q1 O1 P1 K1 N2 M2 S2 K2 M3
Barometric Admittance Factor: 0.30
Polar Motion Coord: " " // uGal ± 0.05 uGal

30. The SG records all temporal variations
But: it has a drift B A C
A: Installation
B: Replacement of a failing circuit board (neck-pressure control)
C: A rough coldhead replacement

31. A comprehensive model for analysis of SG
SG data:
Subsampled to 1-h interval; 0-phase filter response is taken into account in analysis; likewise for the 1 Sps anti-aliasing filter.
Noise whitening the data using PEF’s (Burg’s MEM), iterated into self-consistency in post-processing of residuals.
A harmonic tide potential model with many wavegroups
Ancillary data:
Atmosphere (Atmacs; for every Atmacs channel an admittance coefficient is estimated).
Tide gauge series, stripped of tide harmonics.
ECCO1 (non-tidal ocean loading) and EARIN (hydrology), stripped of Sa tide.
Tide-delayed terms for the interaction of Kattegat sea level and barometric pressure (Wiener filters) in another post-processing step.
Polar motion (IERS) in-phase and cross-phase (the latter by Hilbert tr.)
Iterated outlier editing, residual ordinates that fall outside an n-sigma range, n determined from the quantile of the Normal distribution given the available data; typically NDATA = 64,000, n = 4, sigma = 6 nm/s2.
(That’s our so-called EXTENDED analysis)

32. Additional tricks
Monte Carlo test of robustness of estimated coefficients using the PEF forward noise model for spectral power.
Non-linear estimation of drift’s exponent parameter using Levenberg-Marquardt (according to H.P. Gavin)
RMS 5.6 nm/s2

33. AG – (SG – drift) = true
= 𝑔 𝑜 + 𝑔 𝑡− 𝑡 0 +𝑒𝑟𝑟
… if we accept that the SG drift consists of these few ”fundamental function” features
and if we manage to arrive at a multi-year drift range of less than 1 nm/s2 (0.1 nm/s2/yr),
then we meet the target (determining 𝑔 𝑢 ) from the SG’s side.
The AG’s are to blame for the remaining uncertainty / scatter, nm/s2
But there are other AG’s (Atomic Interferometry) …

34. Drift repeatability
Top 3 diagrams: Medians subtracted
Repeatability 2 nm/s2 / 7 years ?
0.3 nm/s2 / yr, not really reaching the goal (yet).
Waiting for Atmacs reprocessing,
need a consistent set of loading effects
presently has different radii distinguishing between
regional and local.

35. Micro-G LaCoste FG5 ± 20 nm/s2 reproducability
There are other AG’s (Quantum Interferometry) …

36. In fact, we had a QIG (called GAIN) at Onsala in Feb. 2015.
Front row: GAIN group Christian Freier and Matthias Hauth from Humboldt Univ. Berlin
Behind: Manuel Schilling from IfE Leibniz Univ. Hannover using a Micro-g FG5X

38. SG calibration a range of variants to account for SG-drift and
excepting some AG campaigns from common instrument bias
Note: max – min < 2 std devs

39. GAIN and FG5X-220 at Onsala
a - FG5 drop frequency does not reach microseismic band => aliasing ?
b - SG is affected by microseismicity; there is a filter on the analog side => what time delay?
c - GAIN is superior:
* 1.5 s repeat,
* no inter-set pauses,
* efficient attenuation of
microseismicity a b c
From Freier et al., Journal of Physics: Conference Series 723 (2016) doi: / /723/1/012050

40. Contributions, scaled by SG tide analysis
Grey: SG tide residual
= Δg of yet unknown origin
Black: Sum of signals not included in standard AG reduction = Σ
OSO tide gauge
ECCO non-tidal ocean load
ERAI hydrology
(from EOST Strasbourg)
Solar annual tide Sa is removed here
From local air pressure
(should be: Atmacs from BKG)

41. AG – SG Multi-campaign Σ Predictions, project averages
Residual, set-means Σ

42. Some important numeric results from multi-campaign analysis
AG orientation offset S – N
nm/s2/yr Std.dev.
FG5-220 (Hannover)
FG5-233 (LM Gävle)
AG offset
FG5-233 – FG
SG calibration nm/s2/V Std.dev.
Scale factor
Some significant intra-project slopes
nm/s2/h Std.dev.%
FG :
FG :
FG :
FG :
… (36 of 68 within 1 std.dev.)
Secular rate of change, 𝑔
Analysis and drift nm/s2/yr Std.dev.
variant
O-sdr-ochy
O-sdr-expf
O-lsdr-expf
O-ndr-expf
O-ldr-expf
O-expf
O-sdr-dsyn
O-dsyn
O-dwwf
O-sdr-dwwf O
O-expf-ndr
expf-nozacc
12/ => 𝑢 = 7.7 mm/yr
Lidberg et al., 2010,
using 10 yrs of GNSS: ± 0.44 mm/yr
hmmm?
It’s not a forgotten Nodal tide!

43. Use for a seismometer … with the SG … with the AG
How
Using the Guralp 120 s at a station 800 m to the west of the gravimeter:
Apply Passcal Guralp response function × 𝑖𝜔 for acceleration
For use with SG, pass the signal through the numerical equivalent of the SG’s anti-aliasing filter (a Bessel filter of order 8, design parameter rad/s.
… for timing, using a teleseismic waveform from an antipodal source: Macquarie Island, , M6.3
Purpose
… with the SG
timing of the response delay, including the filter chain
… with the AG
timing (i.e. time-stamping) of drop sequence
reduction of excessive drop-noise (source of noise: excessive microseismicity, as in Feb. 2015)

44. Honing of the numerical Bessel filter
Cross-correlation of Seismogram (100 Sps) with SG (1 Sps)
using microseismic noise
Varying the design parameter and find the maximum => design parameter
=> an additional delay on the order of 10 ms:
Reason? - SG ADC? Its sensor?

45. Using an antipodal earthquake to determine the time lag in the entire SG signal chain

46. Cross-correlation of seismometer with AG
AG: 0.1 Sps
Seismogram: 10 Sps
Cross-correlation of seismometer with AG
Obs! Anti-correlation – the FG5 over-compensates microseismic vibrations
Once the time-stamp offset is determined
(delay and delay rate in each project)
AG drop noise and seismometer acceleration can be compared…

48. Conclusions Multi-campaign analysis Atom interferometric AG ”GAIN”
SG provides a compehensive reduction model for AG campaigns;
rate of change of g estimated at ± nm/s2/yr;
remaining problems partly due to varying FG5 instrument offsets, partly due to branches in SG drift;
conflation of different contributions with annual tide period.
Atom interferometric AG ”GAIN”
afforded calibration of SG in one experiment with the same precision as nine FG5 campaigns in seven years.
Seismometer helps
reduce microseismic noise in FG5 measurements;
time-stamp AG records more precisely;
determine delays in the SG signal chain.
The g found is much too high with respect to GIA from current earth models