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…
How is the ground moving
in Northwestern Europe ?
Available information :
1.
2.
3.
4.
Known seismic activity:
(a) present-day seismicity;
(b) large historical earthquakes;
Geology + paleoseismology ;
Continuous GPS measurements ;
10 years of dedicated geodetic
experiments:
(a) CGPS across the Feldbiss fault
zone (Roer graben);
(b) Absolute gravity.
30 m
in 300,000 yr
Strain rate and seismic activity
(Lower Rhine Embayment)
Paleoseismology, geology and historical seismicity agree:
Total moment release ~1-2 1016 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?
Strain rate and Glacial Isostatic Adjustment around 50°N
(peripheral zone)
???
Glaciation
Deglaciation
Peripheral bulge
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
Repeated Absolute Gravity measurements:
profile
(for details see Van Camp et al., JGR, 2011)
The Membach Geodynamic Station
SG: continuously since 1995
AG: since 1996:
190 data  ~1 /month
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]
SG is drifting (~35 nm/s²/yr): SG drift given by [SG-AG]
(the AG does not drift)
190 AG measurements
2 000 to 20 000 drops
 ~ 1 to 8 days
Half-life = 6.3 years
Exponential
Linear
t in years
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 1995.
 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
Probably a combination of them
 Tests to investigate actual causes are difficult, due to the required time (> 10 years !)
for details see Van Camp & Francis, J. Geod. 2007
Drift-free superconducting gravity and
absolute gravity data
1 year
40 nm/s²
or 4 µGal
Maintenances @ Micro-g LaCoste
AG “Setup” noise:
difference between SG and AG
On 190 AG points [1996-2011]: s = 15 nm/s²
Histogram
- 1 s ≤ 66 % ≤ 1 s
- 2 s ≤ 97 % ≤ 2 s
- 3 s ≤ 98.5 % ≤ 3 s
 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…
for details see Van Camp et al., JGR 2005
Spectra of SG and AG time series at Membach
~ f -1.2 : fractional Brownian noise
???
~ f -2.5: power law noise
High microseismic noise :
aliasing
0.08 µgal daily or
7 µGal drop to drop (10 s)
100 days
10 days
1 day
27 µGal d to d
7 µGal d to d
5 µGal d to d
5 µGal d to d
AG noise at high frequencies (f > 1 cpd) at
industrial and coastal stations
PSD = 2 * s² * T [(nm/s²)²/Hz]
1.0E+009
1 µGal daily1.0E+008
or
4 µGal hourly or
75 µGal drop to drop
[(nm/s²)²/Hz]
1.0E+007
1.0E+006
0.08 Gal daily or
0.4 µGal hourly or
7 µGal drop to drop (10 s)
1.0E+005
1.0E+004
1.0E+003
Jülich quiet 1 / 10 s (drop to drop ~25 µGal)
Jülich quiet 1 / 5 s
Jülich noisy 1 / 10 s (drop to drop ~50-150 µGal)
Jülich noisy 1 / 5 s
Ostend 1 / 5 s
Ostend 1 / 10 s
POL 1 / 10 s (average of 200 PSDs)
1.0E+002
1.0E-005
1.0E-004
1.0E-003
Frequency [Hz]
1.0E-002
1.0E-001
More on the sampling rate:
the case of Jülich
Usually: 1 drop / 10 s, 100 drops (some users work with 150 or 200 drops):
Standard deviation :
s
Experimental st. dev. of the mean :
s/sqrt(N)
Also called: “Measurement precision”
One of the noisiest AG set we have ever recorded
(in the absence of earthquakes)
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
100 drops/set or 200 drops/set1 ?
1 drop/5 s or 1 drop/10 s ?
If white noise, s decreases as sqrt(N) : is the improvement just due to the number of drops (200 vs 100) ?
No !
s/21/2 = 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
1 drop/5s, 200/set
1 drop/5s, 100/set
Summary:
1 drop/10 s: 981110750.8 µGal; 100 drops/set  s = 25.9 µGal ; s/sqrt(N) = 3.7 µGal
1 drop/5 s : 981110745.3 µGal; 100 drops/set  s = 6.8 µGal ; s/sqrt(N) = 1.0 µGal
1 drop/5 s : 981110744.2 µGal; 200 drops/set  s = 5.8 µGal ; s/sqrt(N) = 0.8 µGal
6.8/sqrt(2) = 4.8…not
too bad: we have 5.8
Summary: reducing the aliasing :
Example: the Jülich site
1 µGal daily or
4 µGal hourly or
75 µGal drop to drop
0.08 Gal daily or
0.4 µGal hourly or
7 µGal drop to drop (10 s)
Not completely suppressed but much reduced using 1 drop/ 5 s
Summary: HF High noise : a problem ?
100 days
10 days
No, provided that :
- higher sampling rate and/or
No: at ~1 cpd
noise dominates:
- geophysical
longer measurement
time
1 day
HF noise not a problem, unless strong microseismic
and industrial noise: then better to take 1 drop /5 s
Low microseismic noise : small enough
to see the (white) instrumental noise ?
[Hz]
(for details see Van Camp et al., JGR, 2005)
Low frequency effects on repeated AG measurements (1/yr or 2/yr)
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
Slow
oscillations?
Caused by
hydrology?
How can we explain these oscillations?
AG noise at low frequencies: power law processes
Common for many type of geophysical signal
P(f)
k = -2  f-2 : random walk (Brownian)
????
First-order GaussMarkov
White noise
AG (f > 1 cpd) 105 (nm/s²)²/Hz
 10 nm/s² @ 20 min
k = -1  f-1 : flicker
f
Superconducting gravimeter
5 (nm/s²)²/Hz
0.2 nm/s² @ 100 s
 Effect on the estimated slope and the associated uncertainty !
Time (years) to measure a slope with an
uncertainty of 1 nm/s²/yr ( 0.5 mm/yr)
(for details see Van Camp et al., JGR, 2005)
Annual
Semi-annual
Flicker f -1
15
13
Fractional f -1.2
25
23
FOGM f -2+white
17
14
Does the power law process flatten at low frequency?
P(f)
k = -2  f-2 : random walk (Brownian)
First-order,
generalized
Gauss-Markov
White noise
k = -1  f-1 : flicker
f
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) ? (2s)
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, 2002-2007).
Gravity before/after correcting the loading & Newtonian effects
(Membach)
nm/s²
Worse
Scatter in the gravity residuals:
SG (raw):
15.6 nm/s²
SG – Load – Newton:
15.2 nm/s²
Better
Same problem (sometimes worse) in
nearly all GGP stations (Boy & Hinderer,
2006, Van Camp et al., 2010)
PSDsin the frequency domain
Hydrology at longer periods:
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)
1 cpy
1 cpy
1 cpy
Medicina (Italy)
Sutherland (South Africa)
Tigo (Chile)
 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
Van Camp et al., JGR 2010
Given the Generalized Gauss-Markov noise:
Time necessary (years) to be able to measure a slope with an uncertainty of 2
nm/s² /yr ( ~ 1 mm/yr) (2s),
based on SG & LaD time series:
3 to 17 years
Station
< 5 yr
< 10 yr
< 15 yr
> 15 yr
Medicina
Sutherland
Wettzell
Tigo
Time
(yr)
3.1
5.6
10.1
16.7
Not contradicted by the profile: after 11 years : 2s ≈ 1.5-4.0 nm/s² /yr
Future: GLDAS model since 1948, taking ground water unto account (coming…)
Repeated AG measurements
dg/dt resolved at the 1.7-3.9 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): 2s ~ 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 !
Perspectives
 Process the European GPS time series,
+ InSAR in the Roer Graben
Permanent GPS network
 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
Conclusions
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] (2s) 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.
Probably, discussing
gravimetry
That’s all