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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…

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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

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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?

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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) ???

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

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

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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

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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

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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

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

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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

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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 ???

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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)

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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”

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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

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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

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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

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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)

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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

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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)

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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

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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)

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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

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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…)

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

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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

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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 !

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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

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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

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That’s all Probably, discussing gravimetry

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