Characterizing the noise affecting land-based gravity measurements for improved distinction of tectonic signals Michel Van Camp Collaboration with: T. Camelbeeck (ROB) A. Dassargues (U. Liège) O. de Viron (IPGP) O. Francis (U. Luxembourg) H.-G. Scherneck (Chalmers) M. Van Clooster (UCL) S.D.P. Williams (Nat. Oceanography Centre) etc…

1.Known seismic activity: (a) present-day seismicity; (b) large historical earthquakes; 2.Geology + paleoseismology ; 3.Continuous GPS measurements ; years of dedicated geodetic experiments: (a) CGPS across the Feldbiss fault zone (Roer graben); (b) Absolute gravity. How is the ground moving in Northwestern Europe ?  Available information : 30 m in 300,000 yr

Strain rate and seismic activity (Lower Rhine Embayment) Paleoseismology, geology and historical seismicity agree: Total moment release ~ N.m/yr 350 km of active faults with an average slip rate around 0.1 mm/yr during the Late Pleistocene.  Measuring such a deformation rate: hopeless with geodesy?

Glaciation Deglaciation Peripheral bulge (43 to 55 °N) GIA effects on the peripheral bulge predicted by models based on GPS measurements in Fennoscandia : -0.9 mm/year in Belgium (Milne et al., 2001)  Presently not well estimated by geodetic measurements But not hopeless!  Absolute gravity measurements can help Strain rate and Glacial Isostatic Adjustment around 50°N (peripheral zone) ???

Repeated Absolute Gravity measurements: profile (for details see Van Camp et al., JGR, 2011)

The Membach Geodynamic Station AG: since 1996: 190 data  ~1 /month SG: continuously since 1995

Instrumental noise of AG and SG  Using AG to remove the SG drift  Difference [SG-AG]  AG setup noise  AG and SG spectra: power law noise:  High freq. (> 1 cpd): aliased AG data + instrumental noise >> important for the measurement protocol  Low freq. (< 1 cpd): >> important for geodetic studies

Drift of the superconducting gravimeter : Obtained by taking the difference [SG-AG] Exponential Linear t in years Half-life = 6.3 years SG is drifting (~35 nm/s²/yr): SG drift given by [SG-AG] (the AG does not drift) 190 AG measurements to drops  ~ 1 to 8 days

Causes of the SG exponential drift Drift is downward (g increases  sphere goes down)  Correction of steps? No :Should compensate each other or form a random-walk signal  Room temperature? No: Stable, and when major transient changes occurred (Dt = 4-5°C), no influence on g  Barometer? No: +0.5 hPa/yr  -1.7 nm/s²/yr: negligible here  Tiltmeters and thermal levellers? No: Sensitive to temperature changes but no correlation with g ; tilt null position successfully checked in 2006: same as in  Leak in the SG sensing unit  Temperature control inside the SG  Stability of the magnetic field  The capacitance bridge  Gas adsorption or desorption on the sphere  Tests to investigate actual causes are difficult, due to the required time (> 10 years !) Probably a combination of them for details see Van Camp & Francis, J. Geod. 2007

Drift-free superconducting gravity and absolute gravity data 40 nm/s² or 4 µGal 1 year Micro-g LaCoste

AG “Setup” noise: difference between SG and AG On 190 AG points [ ]:  nm/s² - 1  ≤ 66 % ≤ 1  - 2  ≤ 97 % ≤ 2  - 3  ≤ 98.5 % ≤ 3   AG Instrumental setup noise is white (but distribution +/- normal...depends on tests) Slightly more AG data are lower than SG: poor alignment of the verticality or the test and ref. beams, …  “setup noise” ~ 15 nm/s² (16 nm/s² in Van Camp et al., JGR 2005: based on 112 AG data only : we can keep this more conservative estimate)  Causes: height measurement, alignment, clock, floor coupling… Histogram for details see Van Camp et al., JGR 2005

Spectra of SG and AG time series at Membach ~ f -2.5 : power law noise ~ f -1.2 : fractional Brownian noise 10 days1 day 100 days 27 µGal d to d 7 µGal d to d 5 µGal d to d High microseismic noise : aliasing 0.08 µgal daily or 7 µGal drop to drop (10 s) 5 µGal d to d ???

AG noise at high frequencies (f > 1 cpd) at industrial and coastal stations PSD = 2 *  ² * T [(nm/s²)²/Hz] 0.08 Gal daily or 0.4 µGal hourly or 7 µGal drop to drop (10 s) 1 µGal daily or 4 µGal hourly or 75 µGal drop to drop Jülich noisy 1 / 5 s Jülich noisy 1 / 10 s (drop to drop ~ µGal) Jülich quiet 1 / 5 s Jülich quiet 1 / 10 s (drop to drop ~25 µGal) Ostend 1 / 10 s Ostend 1 / 5 s POL 1 / 10 s (average of 200 PSDs)

Usually: 1 drop / 10 s, 100 drops (some users work with 150 or 200 drops): More on the sampling rate: the case of Jülich One of the noisiest AG set we have ever recorded (in the absence of earthquakes) Standard deviation :  Experimental st. dev. of the mean :  /sqrt(N) Also called: “Measurement precision”

So, how to obtain valuable measurements at such a station? 1 drop / 10 s Increase sampling rate to reduce the aliasing effect: 1 drop/5 s, 200 drops/set

If white noise,  decreases as sqrt(N) : is the improvement just due to the number of drops (200 vs 100) ? No !  /2 1/2 = 25.9/1.4 = 18.3 µGal >< 5.8 µGal : we have much better! This is because we reduce the aliasing: The most important is increasing the sampling rate, not the number of data 100 drops/set or 200 drops/set1 ? 1 drop/5 s or 1 drop/10 s ? Summary: 1 drop/10 s: µGal; 100 drops/set   = 25.9 µGal ;  /sqrt(N) = 3.7 µGal 1 drop/5 s : µGal; 100 drops/set   = 6.8 µGal ;  /sqrt(N) = 1.0 µGal 1 drop/5 s : µGal; 200 drops/set   = 5.8 µGal ;  /sqrt(N) = 0.8 µGal 6.8/sqrt(2) = 4.8…not too bad: we have drop/5s, 200/set1 drop/5s, 100/set

Summary: reducing the aliasing : Example: the Jülich site 0.08 Gal daily or 0.4 µGal hourly or 7 µGal drop to drop (10 s) 1 µGal daily or 4 µGal hourly or 75 µGal drop to drop Not completely suppressed but much reduced using 1 drop/ 5 s

Summary: HF High noise : a problem ? 10 days No, provided that : - higher sampling rate and/or - longer measurement time Low microseismic noise : small enough to see the (white) instrumental noise ? 10 days1 day 100 days [Hz] No: at ~1 cpd geophysical noise dominates: HF noise not a problem, unless strong microseismic and industrial noise: then better to take 1 drop /5 s (for details see Van Camp et al., JGR, 2005)

Low frequency effects on repeated AG measurements (1/yr or 2/yr) Slow oscillations? Caused by hydrology? How can we explain these oscillations? 38.4  3.3 nm/s²/yr  ~19.4  1.6 mm/yr HF Noise not a problem, Rate similar to the expected ones in Fennoscandia or at plate boundaries

AG noise at low frequencies: power law processes Common for many type of geophysical signal  Effect on the estimated slope and the associated uncertainty !  = -2  f -2 : random walk (Brownian) First-order Gauss- Markov  = -1  f -1 : flicker f P(f) White noise AG (f > 1 cpd) 10 5 (nm/s²)²/Hz  min AnnualSemi-annual Flicker f Fractional f FOGM f -2 +white1714 Time (years) to measure a slope with an uncertainty of 1 nm/s²/yr (  0.5 mm/yr) Superconducting gravimeter 5 (nm/s²)²/Hz  s ???? (for details see Van Camp et al., JGR, 2005)

Does the power law process flatten at low frequency?  = -2  f -2 : random walk (Brownian) First-order, generalized Gauss-Markov  = -1  f -1 : flicker f P(f) White noise Does it flatten? How long does it take? Time (years) to measure a slope with an uncertainty of 2 nm/s²/yr (  1 mm/yr) ? (2  )  hydrology What is the cause of such a power-law noise?  hydrology

Correcting gravity (SG) using modelled water storage effects - Gravity changes predicted from the LaDworld-Gascoyne Land Water-Energy Balances model (1° x 1°, monthly) (Milly & Shmakin, ). Gravity before/after correcting the loading & Newtonian effects (Membach) nm/s² Worse Better Scatter in the gravity residuals: SG (raw): 15.6 nm/s² SG – Load – Newton:15.2 nm/s² Same problem (sometimes worse) in nearly all GGP stations (Boy & Hinderer, 2006, Van Camp et al., 2010)

PSDs LaD & SG in the time domain:  But LaD & SG similar in frequency domain : Power spectrum densities of SGs and LaD: black: SG (in the best case, since 1995) red : LaD (since 1980) Toward a flattening at periods > 1 year, for both SG and LaD  Hydrology follows a ”Generalized Gauss-Markov” behavior, which is included in the gravity signal 1 cpy Hydrology at longer periods: in the frequency domain Medicina (Italy) Sutherland (South Africa) Tigo (Chile) Van Camp et al., JGR cpy

Given the Generalized Gauss-Markov noise: StationTime (yr) Medicina3.1 Sutherland5.6 Wettzell10.1 Tigo16.7 Time necessary (years) to be able to measure a slope with an uncertainty of 2 nm/s² /yr (  ~ 1 mm/yr) (2  ), based on SG & LaD time series: 3 to 17 years < 5 yr < 10 yr < 15 yr > 15 yr Not contradicted by the profile: after 11 years : 2  ≈ nm/s² /yr Future: GLDAS model since 1948, taking ground water unto account (coming…)

Repeated AG measurements dg/dt resolved at the nm/s²/yr (95% confidence interval) after 11 years

Stability of repeated AG measurements  Gravity rate of change as a function of the length of the time series (Membach): 2  ~ 1 nm/s²/yr or 0.5 mm/yr after ~10 years

PSDs Hydrology: how to mitigate this? What you can do: 1)Like Jülich, Membach, Wettzell, Strasbourg...: Try to correct for local and large-scale effects (but I’m not so optimistic, not applicable everywhere) 2) Be patient : wait till hydrological signal averages zero. But how long ???  Investigating long superconducting gravimeter time series and predictions from LaD hydrological model (Milly & Schmakin): “HOW LONG”  < 15 years  Unless significant climate change, hydrology should not mask the GIA effect on the peripheral bulge.  Long AG time series may also be useful to investigate slow environmental changes !

Permanent GPS network Perspectives  Process the European GPS time series, + InSAR in the Roer Graben  Use the Absolute Gravity data as a constrain for the vertical component (see Teferle et al., GJI, 2009)  Necessity to improve GIA model to investigate other tectonic processes  Necessity to work on the (dg/dt)/(dz/dt) ratio

AG : Setup noise ~1.5 µGal; dominates the error budget of one AG value; When microseismic noise is low, instrumental (white) noise dominates, specific to each instrument; When the microseismic noise is high: clear aliasing effect : “easy” to reduce by increasing sampling rate... even in noisy stations such as Jülich (industrial) or Oostende (coastal), if measurements taken carefully; Uncertainty on the trend depends on the noise structure; If 2 measurements/yr: 2 nm/s²r [  1 mm/yr] (2  ) after 3-15 years if Generalized Gauss-Markov noise (flattens at low freq.). SG : Drift : for C021 exponential model to be preferred for records longer than 10 years (to be investigated for other SGs); SG great to monitor gravity between AG measurements; SG great as long period seismometer. Conclusions

That’s all Probably, discussing gravimetry