Jürgen
Neumeyer1), Franz Barthelmes1), Ludwig Combrinck2)
Olaf Dierks1), Piet Fourie3
1)GeoForschungZentrum
Potsdam, Division 1, Telegrafenberg, 14473 Potsdam, Germany
2) Hartebeesthoek
Radio Astronomy Observatory, Krugersdorp , South Africa
3)
South African Astronomical Observatory, Sutherland , South Africa
The
installed Superconducting Gravimeter (SG) and the environmental sensors
are continuously recording data since February 2000 (Neumeyer et al. 2001).
These data have been preprocessed and analyzed. In detail the noise at
the site, the tidal parameters, the vertical surface shift and the free
oscillation of the Earth after the Peru earthquake on June 23rd
2001 have been analyzed.
2.
Calibration of the two gravity sensors
From
both time series absolute and SG measurements the outliers and the linear
trend have been removed. For determination of the calibration coefficient
a linear least square fit has been performed between the Absolute Gravimeter
and the SG data.
In
a second estimation the method of Fourier coefficients has been used. This
method determines the amplitudes for selected frequencies from both data
sets. The calibration factor is determined by the amplitude ratio obtained
from Absolute Gravimeter and SG measurements at these frequencies. Both
methods deliver equivalent results within the required accuracy.
Fig.
2Calibration results of SG D037
As
the final calibration coefficient the mean between the parallel registrations
of theAbsolute Gravimeters FG5 (3),
JILAg5 (4) and the SG is used.The
calibration factors have been determined with an standard deviation of
0.2 percent.
In
a step response experiment (Van Camp et al., 1999) the time delay of both
sensors has been determinedto 8.7
seconds for G1l (lower
sensor)and to 7.9seconds
for G2u (upper sensor).
3.
Noise at the site SAGOS
The
investigation of weak gravity effects requires a low noise site. The quality
of the recorded gravity data depends on the noise at the site and the noise
of the instrument. The noise of the instrument is small in the inspected
frequency band.
For
estimation of the noise at the site the Noise Magnitude is used (Banka
and Crossley, 1999).
The Noise Magnitude [NM =10* log(PSD) in dB] is calculated by the Power
Spectral Density (PSD) of raw gravity data (1sec sampling rate) with a
length of one month (February 2001). In figure 1 the Power Spectral Density
(PSD,left axis) and the allocated
Noise Magnitude (NM, right axis) are diagrammed as function of the frequency.
Additionally the Noise Magnitude according to the ?New Low Noise Model?
is diagrammedas graph NLNM (gray).
A
comparison between the Noise Magnitude and the New Low Noise Model shows
that the Noise Magnitude characterizing the quality of the site is close
and even smaller as the New Low Noise Model values at frequencies below
1 mHz. This comparison shows that the site offers excellent conditions
for high precision gravity measurements and the detection of weak gravity
signals. In this frequency range the free oscillations of the Earth have
their modes too. Therefore they can be detected very well.
Fig
1 Noise
spectra at SAGOS site
Black:
Power Spectral Density (PSD) and Noise Magnitude (NM) of lower SG sensor
(G1l))
Grey:
New Low Noise Model (NLNM)
4.
Evaluation of gravity and environmental data
For
processing of the gravity and atmospheric pressure data the Earth Tide
Data Processing Package ETERNA 3.3 (Wenzel, 1996) has been used. The first
high precision tidal amplitudes, amplitude factors dand
phase leads khave
been determined for the Sutherland site and the South African region. The
tidal analysis has been performed on 18 month SG and atmospheric pressure
data. The amplitude factors and the phase leads are in good agreement for
both sensors of the SG. The standard deviation of the tidal analysis is ±0.7
nm/s².
Figure
3 shows the Wahr-Dehant model (white columns) and the measured tidal amplitudes
(black columns) for Sutherland. The tidal amplitudes are latitude dependent.
The long periodic waves MF. MM, SSA und SA are small at Sutherland latitude
of 32.38 deg South. The minimum of these waves are about at latitude 35
deg. Therefore seasonal effects (like the atmospheric pressure effect)
and the polar motion (like the separation of the annual part of the polar
motion from the annual tidal wave SA) can be investigated with small influence
of the annual and semiannual tidal waves. The diurnal waves (maximum amplitude
at latitude 0 deg)and semidiurnal
waves (maximum amplitude at latitude 45 deg) can be observed well.
Fig.
3 Tidal amplitudes for SAGOS
White
columns: Wahr-Dehant Model amplitudes
Black
columns: measured amplitudes
Figure
4 shows the determined tidal parameters. For comparison the Wahr-Dehant
model (white columns) and the observed amplitude factors (gray columns)
are pictured. The deviations from the model can be seen clear. One reason
for the deviations is the influence of the ocean loading. Therefore the
ocean loading correction has been calculated for the diurnal partial tides Q1,
O1, P1, K1 and the semidiurnal partial tides N2, M2, S2, K2
(Schwiderski model). The black columns show the ocean loading corrected
amplitude factors. One can see that the ocean loading corrected amplitude
factors come closer to the model values
for the semidiurnal waves N2, M2, S2, K2 and the diurnal waves
P1 and K1. For the diurnal waves Q1 and
O1 the ocean loading corrected amplitude factors depart form the model
values. The reason for this behavior is the ocean loading model as shown
by Ducarme et. al. 2002.
The
model phase is zero. Larger deviations from the model phase show the semidiurnal
waves 2N2, N2, M2, L2, S2, K2 and the diurnal wave S1. The ocean corrected
phase leads for the diurnal waves N2, M2, S2, K2 give a good improvement
close to zero (observed values near 5 deg phase lead). The ocean correctedphase
lead for the diurnal waves Q1, O1, P1, K1 become larger than the uncorrected
value.
The
strong deviation (d
and k)
of the S1 wave to the model my be caused by the influence of the daily
variations of the atmospheric pressure. Investigations for a better modeling
of the atmospheric pressure influence are necessary. Furthermore the discrepancies
between real measurements and the Earth tide and ocean models for the South
African region have to be investigated more in detail. These discrepancies
have to be abolished by improving the models and data correction for non-tidal
induced gravity effects.
Fig
4Earth tide parameters d
and k
for SAGOS
White
columns: Wahr-Dehant Model parameter d
Gray
columns: calculated parameters d
and k
Black
columns: Ocean loading
corrected parameters d
and k
Fig.5Ocean
loading effect at SAGOS for the main tidal waves
The
ocean loading effect to gravity has been calculated with the program LOAD97.Figure
5 shows the correction amplitudes and the phases for the main diurnal and
semidiurnal tidal waves. The most affected wave is M2 with an amplitude
of 57.5 nm/s2.
5.
Vertical surface shift caused by Earth tides and atmospheric pressure
Because of the elastic behaviour of the Earth the tides and changing loading on the Earth(e.g. mass redistributions in the atmosphere measured by the atmospheric pressure) cause vertical surface shift zc. This shift can be calculated by the following formula
With the elastic parameters of the Earth the Love number for elastic deformation h2 = 0.6137 and the Love number for deformation potential k2 = 0.3041, the gravimetric factor d2= 1.159 , the geocentric radius R= 6373830.451m determined with the tidal analysis and g = 9.79079 m/s2 determined by absolute gravity measurements the elastic deformation coefficient for SAGOS has been determined to Dvs =-1.32 mm/µgal according to the formula
The vertical shift for SAGOS can be calculated by multiplying Dvs with the measured gravity changes Dg corrected for the atmospheric pressure effect. (Neumeyer, 1995; Kroner and Jentzsch, 1999). The atmospheric pressure correction of the gravity data has been done with the atmospheric pressure admittance coefficient apc = -2.92 µgal/hPa calculated for
Fig.
6 Vertical surface shift caused by the Earth tides for Sutherland
SAGOS.
These determined gravity changes induced by atmospheric pressure changes
have been subtracted from the gravity data. Figure 6 shows the vertical
surface shift zc
at SAGOS for18 days in July 2001. The maximal vertical shift caused by
the Earth tides and mass redistribution in the atmosphere during the time
from March 27th 2000 to August 1st 2001 is 41.9 cm.
For separation of the atmospheric pressure influence to the vertical surface shift the Greens function method which calculatesthe attraction and deformation term separately has to be used (Sun, 1995;Neumeyer et al. 1998). With the deformation term the surface shift induced by atmospheric pressure changes can be calculated. For the Potsdam site this effect is about 2.3 cm (Neumeyer et al.,2001)
These
vertical surface shift is derived from gravity measurements only. The gravity
signal includes height and mass changes. It is impossible to separate mass
and height changes with the gravity measurements. Therefore GPS measurements
have been used to calculate the height changes for SAGOS..
Initial
results to determine vertical displacement due to tidal forces using GPS
were obtained using the GAMIT (King and Bock, 1999) software package. Additional
scripts were developed to allow processing of 24 hour GPS data files using
a stepped, sliding window technique. The scripts allow seamless processing
over the start and end of the individual 24 hour GPS data files. Alternative
processing strategies were used, varying the length of the window, the
step size as well as GPS station geometry and station position constrains.No
earth-tide and ocean-tide modeling were used during the processing and
GPS stations were constrained horizontally but not vertically. ITRF2000
coordinates and velocities were used. The best results were obtained using
a four hour window, which is stepped by 30 minutes, followed by a running
average procedure to smoothen the results. This results in 48 four hour
sessions per day.
Fig.
7Vertical surface shift calculated
from gravity (black line) and GPS (dashed line)
Only
two GPS stations (separated by about 1000 km), the IGS stations HRAO (located
at Hartebeesthoek Radio Astronomy Observatory near Pretoria)) and SUTH
(located at Sutherland) were finally used. Another station towards the
south (SIMO) located at Simonstown marginally degraded solutions and was
therefore not included. This station (SIMO) will be included once a new
station has been installed at Windhoek, Namibia, which is towards the north
of Sutherland. The degrading effect is probably due to poor network geometry.Including
both SIMO and the Windhoek station will improve the network geometry considerably.
Improved network geometry in combination with further development of the
processing scripts is expected to yield improved results.
The
first result of this calculation is shown in Figure 7. The black line shows
the vertical surface shift derived from gravity measurements and the dashed
line shows the first result from the GPS measurements. There is in some
parts already a good agreement of both curves.
6. Analysis
of the free oscillation modes after the Peru earthquake on June 23rd
2001
The
Earthquake near the coast of Peru (latitude 16.14S, longitude 73.312 W,
depth 33 km,) on June 23rd 2001 at 20:33:14.14 with a
magnitude of 8.4 has been recorded by the mode channel of the Superconducting
Gravimeter at SAGOS site.
Fig
7Spheroidal free oscillation modes
after the Peru earthquake on June 23rd 2001
The
data of this Earthquake have been analyzed for detection of the free oscillation
modes of the Earth. For this purpose a data set of 96 hours after the Earthquake
has been corrected for atmospheric pressure. After low pass filtering (corner
frequency of the filter 6 mHz) of the data the mode spectrum has been calculated
by using a Hanning window (Fig. 7). Above the spectrum the different spheroidal
modes are listed. Their model frequencies are at the horizontal grid lines.
The
spectrum shows the model modes up to the frequency of 0S10. Especially
the long periodic modes 0S3, 2S1 and 0S2 are very well marked after this
Earthquake and less disturbed because of the low noise site. Compared to
the results of Van Camp (1999) 2S1 and 0S2 are clear detected.
7.Acknowledgment
We
thank very much Jacques Hinderer, Martine Amalvict and Bernard Luck ?Ecole
et Observatoire desSciences de la
Terre? Strasbourg ,France for carrying
out absolute gravity measurements at SAGOS with the Absolute Gravimeter
FG5 in February 2001.
We
thank very much Jaakko Makinen ?
Finnish Geodetic Institute? Masala, Finland
for carrying out absolute gravity measurements at SAGOS with the Absolute
Gravimeter JILAg5 in March
2001.
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