Displacement Of The Space Geodetic Observatory Arequipa Due To ...

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Fachbeiträge Kaniuth/Müller/Seemüller, Displacement of the space geodetic observatory Arequipa
zfv 4/2002 127. Jg.238
The space geodetic observatory at Arequipa (Peru) contributes to the maintenance of the International Terrestrial
Reference Frame by providing continuous time series of GPS
and SLR observations since many years. On June 23 and
July 07, 2001 two earthquakes of magnitude 8.4 and 7.6,
occurring at the boundary between the Nazca and South
American tectonic plates, have severely damaged Arequipa.
An analysis of six weeks of GPS data determines the coseismic displacements to 52.0 cm and 4.3 cm in SW-direction. The GPS observations allow also to assess significant
postseismic velocities of 1.8 mm/day and 1.0 mm/day respectively. The occurrence of two minor earthquakes in early
2002 gave rise for processing again three weeks of GPS observations. There is no evidence of further coseismic displacements but the results confirm a slowing down of the
last postseismic velocity. The observations acquired by the
global SLR network were processed continuously up to April
2002. Due to the sparse data distribution compared to GPS
as well as some lacks of observations at Arequipa itself, SLR
is not capable of monitoring details of the displacements
with the same resolution as GPS. Nevertheless, SLR confirms
the main features such as the total displacement due to the
two major earthquakes and the postseismic velocity after
July 07, 2001.
Die Satellitenbeobachtungsstation in Arequipa (Peru) trägt
seit vielen Jahren mit kontinuierlichen Zeitreihen von GPSund SLR-Beobachtungen zur Fortführung des Internationalen
Terrestrischen Referenzsystems bei. Zwei Erdbeben der Stärke
8.4 bzw. 7.6, die sich am 23. Juni bzw. 7. Juli 2001 an der Grenze zwischen der Nazca- und der Südamerika-Platte ereigneten, haben in Arequipa erhebliche Schäden verursacht. Eine
Analyse von sechs Wochen GPS-Messungen ergibt koseismische Verschiebungen von 52,0 cm und 4,3 cm in SW-Richtung.
Aus den GPS-Daten lassen sich auch signifikante postseismische Geschwindigkeiten von 1,8 mm/Tag und 1,0 mm/Tag ableiten. Zwei weitere, allerdings wesentlich schwächere Erdbeben Anfang 2002 waren Anlass für die Auswertung einer
weiteren Periode von GPS-Messungen. Die Ergebnisse zeigen
keine erneute koseismische Verschiebung, sondern bestätigen
das Abklingen der letzten postseismischen Bewegung. Die Beobachtungen des globalen SLR-Netzes sind kontinuierlich bis
April 2002 prozessiert worden. Allerdings kann SLR wegen der
vergleichsweise geringen Datenbelegung sowie des Fehlens
einiger Messungen in Arequipa selbst die Details der Bewegungen nicht mit der hohen Auflösung wie GPS nachweisen. Die
SLR-Ergebnisse bestätigen jedoch wesentliche Merkmale wie
die Gesamtverschiebung aufgrund der beiden großen Erdbeben und die postseismische Bewegung nach dem 7. Juli 2001.
Displacement of the space geodetic observatory Arequipa
due to recent earthquakes
Klaus Kaniuth, Horst Müller, Wolfgang Seemüller
1 Introduction
The space geodetic observatory at Arequipa (Peru) contributes continuous time series of Satellite Laser Ranging
(SLR) and Global Positioning System (GPS) observations
since 1981 and 1994 respectively. As such, Arequipa is
one of the most, if not the most important site in South
America as regards the realization and maintenance of
the International Terrestrial Reference Frame (ITRF). In
particular, the SLR station is the only permanent one on
the entire continent, and the system presently in operation belongs to the most well performing worldwide. The
observations collected by both the SLR and the GPS are
regularly processed at DGFI. The SLR data analysis is
done in the frame of the International Laser Ranging Service (ILRS) global network, and the GPS observations are
included in the permanent South American GPS network,
processed by DGFI on behalf of the International GPS
Service (IGS).
On June 23 and July 07, 2001 two major earthquakes
occurred close to the Pacific coast of Peru, mutually
affecting the location of the Arequipa site. In order to
assess the coseismic insitu displacements as well as to
identify any postseismic signals, we have performed
dedicated analyses of GPS and SLR time series. The data
periods of several weeks and months respectively included
both earthquake epochs. The occurrence of two minor
earthquakes on January 30 and February 03, 2002 gave
rise to process another three weeks period of GPS observations covering the epochs of these events, while the SLR
analysis was continuously extended to mid April 2002.
After summarizing briefly the main characteristics of the
seismic events, we outline the data analyses performed,
and finally the obtained results are discussed in detail.
2 The Earthquakes
The first of the two major earthquakes with a magnitude
of 8.4 on the Richter scale occurred on June 23, 2001 at
20:33 UTC. The epicenter was localized at the boundary
between the Nazca and South American tectonic plate
(USGS 2001), about 200 km west of Arequipa at a depth
of 33 km. According to geological-geophysical models
these two plates are converging towards each other with
a rate of more than 7 cm/yr (Argus and Gordon 1991, De
Mets et al. 1994). The earthquake resulted from thrust
faulting along the plate boundary as the oceanic Nazca
plate is subsiding beneath the South American plate.
As a consequence of this earthquake, large structural
damages occurred in Arequipa and other places in
southern Peru. Fortunately, the anticipated large coastal
tsunamis did not occur, but more than 100 people were
killed. The earthquake was also strongly felt in northern
Chile, and the tide gauge in Arica recorded tsunamis
reaching peak to trough wave heights of up to 2.5 m.
Also several aftershocks were recorded, the strongest one
not exceeding a magnitude of 6.8 (USGS 2001).
Two weeks later another earthquake of magnitude 7.6
occurred, this time south west of Arequipa at a distance
of about 100 km. Table 1 summarizes the main characteristics of these two earthquakes, presumably leading to
significant displacements of the GPS and SLR systems at
Arequipa with respect to their previous positions. The
table includes also the same information regarding the
two minor earthquakes of early 2002.
3 Data Analysis
3.1 GPS
In order to assess the impact of the Peru earthquakes on
the position of the GPS station in Arequipa, we analyzed
an array of permanent GPS stations surrounding the
earthquake area. The selection criteria for the sites to be
included in the network were the continuous operation
with a minimum of data gaps during the first processed
period between June 17, 2001 and July 28, 2001 as well
as their distance to Arequipa. Table 2 lists the selected
stations; the 4-characters identifications are those used
by the IGS. The large distances between AREQ and the
other sites of between 1649 and 4007 km indicate the
rather sparse distribution of permanent GPS stations in
this area. Fortunately, the only data outages occurred on
one and a half days at CUIB. It should be noted that there
is no evidence of any earthquake effects on sites others
than AREQ itself. It should also be mentioned that the receiver at Arequipa ceased operating upon the first earthquake for about two hours. Thus, the position estimate
FachbeiträgeKaniuth/Müller/Seemüller, Displacement of the space geodetic observatory Arequipa
127. Jg. 4/2002 zfv 239
Date Time Magn. Depth Latitude Longitude Distance Azimuth
[UTC] Ms [km] [°] [°] [km] [°]
2001, June 23 20:33:15 8.4 33 –16.15 –73.40 208 279
2001, July 07 09:38:43 7.6 33 –17.38 –71.78 106 197
2002, Jan. 30 06:10:51 4.6 85 –13.92 –72.83 319 332
2002, Feb. 03 12:59:32 4.7 33 –15.65 –72.03 107 328
Table 1: Locations and magnitudes of the Peru earthquakes (USGS 2001, 2002), distances and directions from Arequipa
to epicenters
for AREQ on June 23, 2001 refers to the time period prior
to the seismic event.
During the second earthquake on July 07, 2001 the receiver proceeded tracking without loss of lock, and the 24
hours data file was split accordingly. Considering the observation rate of 30 seconds it seemed not worthwhile to
analyze the phase measurements around the earthquake
epoch in detail. The second processed period of GPS observations between January 22 and February 14, 2002
was centered around the epochs of the two minor earthquakes. During this entire period RIOP did not provide
any data at all, and no observations from CORD were
available during the last week.
In order to allow to relate the seismic effects to the
kinematic of Arequipa prior to the events, figure 1 displays the horizontal velocities of the seven sites included
in the analysis as predicted by the geophysical model
NNR NUVEL-1A (Argus and Gordon 1991, De Mets et al.
1994) and as resulting from geodetic space technique observations. The two geodetic solutions represented in the
figure are:
 The latest realization of the International Terrestrial
Reference Frame, ITRF2000 (http://lareg.ensg.ign.fr/
ITRF/ITRF2000). ITRF2000 is a combination of global
network solutions based on different space techniques,
as well as regional GPS densifications. Besides GPS, in
particular Satellite Laser Ranging (SLR) and Very Long
Baseline Interferometry (VLBI) contribute. The ITRF
realization implies also no net rotation conditions and
includes data up to early 2000.
 The most recent solution of the permanent South
American GPS network computed by DGFI as IGS
Regional Network Associate Analysis Center (RNAAC):
this adjustment labeled DGFI01P02 includes observations from July 1996 on to end of July 2001. It is
based on ITRF2000 by referring the network to a few
highly accurate fiducial sites. A brief discussion of the
applied analysis strategy is given in (Seemüller et al.
2002). The advantage of this regional solution over
ITRF2000 should be the higher reliability of position
and velocity estimates due to the considerably increased data time spans of some rather lately or not
continuously operational sites. Regarding the present
analysis, this applies in particular to the stations
The tremendous discrepancies between the geophysical
model and the geodetic results showing up at AREQ and
SANT are due to the fact that NUVEL-1A is not modeling
deformations in plate boundary zones. Another, but yet
well known phenomenon is the slower convergence of
the Nazca plate towards South America compared to the
geophysical prediction (Angermann et al. 1999, Norabuena et al. 1998, Norabuena et al. 1999).
Both data sets covering 42 and 24 days respectively were
processed with the Bernese Software version 4.2 (Hugentobler et al. 2001), the main characteristic of which is the
analysis of between stations and between satellites
double difference phase observables. The satellite orbits,
satellite clock offsets and Earth orientation parameters
were fixed to the final IGS products, being a combination
of the results provided by several analysis centers and referring to the ITRF adopted at the observation epoch. The
selection of models and settings for the least squares adjustment was based on experiences gained in previous
analyses (Kaniuth et al. 1998, Kaniuth et al. 2002):
 The model by Saastamoinen (1973) and the mapping
function by Niell (1996) were applied for predicting
the tropospheric path delays; residual zenith delays
were estimated for two hours intervals.
 The minimum elevation angle was set to 10°, and no
elevation dependent weighting was applied in order to
fully exploit the low elevation data.
 The Quasi Ionosphere Free (QIF) strategy was applied
for fixing the initial L1 and L2 phase ambiguities.
 The periodic site displacements due to ocean tide loading were modeled according to the FES95.2 ocean tide
model (Le Provost et al. 1994).
Each day was preprocessed separately, saving the unconstrained normal equations for further combination. The
following two alternative strategies were applied for deriving the effects of the earthquakes on AREQ:
Fachbeiträge Kaniuth/Müller/Seemüller, Displacement of the space geodetic observatory Arequipa
zfv 4/2002 127. Jg.240
Fig: 1: Locations of the GPS stations included in the
analysis and their horizontal velocities according to
NNR NUVEL-1A, ITRF2000 and the latest DGFI solution
ID Location (Country) Dist. [km]
CORD Cordoba (Argentina) 1808
CUIB Cuiaba (Brasil) 1649
EISL Easter Island (Chile) 4007
GALA Galapagos (Ecuador) 2679
RIOP Riobamba (Ecuador) 1811
SANT Santiago (Chile) 1844
Table 2: Stations included in the analyzed GPS network
and distances to Arequipa
 Performing daily network adjustments solving for the
position of AREQ and tightly constraining the fiducial
sites, thus generating a time series of daily position estimates;
 performing common adjustments of all 42 or 24 days
respectively solving for the instantaneous displacements of AREQ and for the inter- and postseismic velocities as linear functions in time, again constraining
the fiducials.
Thus the reference frame was in both approaches realized
by the positions and velocities of the six fiducial stations,
either adopted from ITRF2000 or from the regional DGFI
solution. The constraining is achieved by either simply
fixing the fiducials, solving for similarity transformation
parameters between the free and the fiducial sets of positions and velocities, or applying individual weights to the
fiducial points. Among these alternatives, the latter one
seemed to be the most appropriate choice accounting
best for the accuracy differences between the fiducials.
Considering its mentioned advantages over the ITRF
2000, the regional South American GPS network solution
by DGFI was adopted as reference frame for the final
Figure 2 displays the time evolution of the daily
position components of AREQ during the first analyzed
period. The figure is not only showing the instantaneous
displacements caused by the two major earthquakes but
demonstrates also the high consistency of the daily estimates, in particular of the horizontal position components. As expected both earthquakes of magnitude less
than 5 in early 2002 did not lead to any significant
coseismic effects on AREQ. However, the new position
estimates provide further information regarding the evolution of the postseismic velocity after July 07, 2001.
The results of the second approach, the common adjustment of all days of data, are summarized in table 3,
again for the solution based on applying individual
weights to the fiducials. The table gives the coseismic
displacements due to both major earthquakes and the
postseismic velocities in the horizontal as well as the
vertical components. The one sigma standard deviations
resulting from the adjustment are less than one mm for
the horizontal and vertical coseismic displacement components. In case of the postseismic velocities the standard
deviations of the estimates are less than 0.1 mm/day for
all three components.
3.2 SLR
The SLR data analysis comprised the processing of the
range measurements to Lageos-1 and Lageos-2 acquired
by the global laser tracking network during the period
FachbeiträgeKaniuth/Müller/Seemüller, Displacement of the space geodetic observatory Arequipa
127. Jg. 4/2002 zfv 241
Displacement North East Height Length Azimuth
Coseismic displacement [mm]
– June 23, 2001 –294 –428 –38 520 234°
– July 07, 2001 –30 –31 +7 43 225°
Postseismic velocity [mm/day]
– June 23, 2001 → July 07, 2001 –1.3 –1.3 0.4 1.8 223°
– July 07, 2001 → July 28, 2001 –0.6 –0.8 0.0 1.0 214°
– July 07, 2001 → Feb. 14, 2002 –0.2 –0.2 0.0 0.3 216°
Table 3: Displacements of the GPS station AREQ resulting from the common adjustment of the two data sets in the
reference frame realized by the fiducial stations
Fig. 2: Daily estimates of the AREQ position components
in the reference frame realized by the fiducial stations
January 01, 2001 to April 12, 2002. Each measurement
represents a normal point generated at the tracking site
from all observations performed during a two minutes
interval. We used DGFI’s Orbit and Geodetic parameter
estimation Software DOGS; a documentation can be
found under projects at http://www.dgfi.badw.de .
In a first step 67 weekly orbital arcs were processed
separately for both satellites. Compared to GPS the data
distribution is rather inhomogeneous. Therefore, the
number of involved stations varied between 18 and 28,
and each arc comprised between 89 and 197 satellite
passes with about 900 to 2200 normal points. Table 4
summarizes the data resources available during the
periods prior to the first major earthquake, between the
two events and after the second major shock. The reference frame definition, the force field and measurement
modeling followed the IERS conventions (Mc Carthy
1996). The a priori station coordinates were based on our
multi-years SLR solution (Angermann et al. 2001).
The set of adjustment parameters included six orbital
elements, weekly corrections to the empirical along track
acceleration and the solar radiation pressure as well as
daily Earth orientation parameters. In addition, depending on statistical tests, we solved for pass specific range
and time biases. Table 5 gives some information regarding the quality of the adjusted orbits. As can be seen the
root mean square (rms) fit between the Arequipa data
and the orbits is slightly worse than for the entire network. This is due to the fact that we did not exclude any
measurements at Arequipa. From these single satellite
arcs normal equations including station positions and
velocities as solve for parameters were generated. These
weekly normal equations were accumulated and solved
after adding datum information.
The datum of the SLR solution is realized by applying
six condition equations (Gerstl 1999) minimizing the
common rotation and rotation rate with respect to our
multi-years solution for eight globally distributed stations of high performance.
It is obvious from table 4 that the few observations at
Arequipa during the two strong earthquakes do not allow
to separate the coseismic displacements and the motion
between the shocks from each other. Therefore, our displacement estimate includes all three contributions. In
order to assess whether the postseismic motion after the
second major quake on July 07 is constant or is easing
off with time we solved for the velocities during two time
spans, the first one from the event to September 30, and
the second one from October 01 to April 12, 2002. Table 6
summarizes the obtained results.
The standard deviations of the displacement components given in table 6 are 4.5 mm on the average. In case
of the velocity estimates these are less than 0.1 mm/day.
4 Conclusion
The horizontal motions of the Arequipa site as resulting
from the GPS and SLR data analyses are displayed in figure 3. As concerns GPS, the coseismic displacements due
to both major earthquakes as well as the released postseismic velocities are shown. In case of SLR the figure
gives the total difference between the positions prior to
the June 23 shock and after the July 07 event. In addition, the creeping motion after July 07 is shown.
Comparing the results, one should consider that the
GPS estimates are based on continuous series of observations during the processed periods, resulting in a total of
4.8 million double difference phase measurements,
whereas the SLR solution suffers from some lacks of observations at Arequipa itself. Thus, although the agreement between both techniques is not perfect, SLR confirms the main features and the appearing differences are
within the confidence margins. One should also consider
that the monumentation of both systems at Arequipa is
quite different. Whereas the GPS antenna is mounted on
Fachbeiträge Kaniuth/Müller/Seemüller, Displacement of the space geodetic observatory Arequipa
zfv 4/2002 127. Jg.242
Period Lageos-1 Lageos-2
2001/2002 SP NP SP NP
Jan. 01 – June 23 52 550 69 747
June 24 – July 06 2 8 2 30
July 07 – Sept. 30 49 515 36 348
Oct. 01 – April 12 35 285 35 295
Table 4: Number of available satellite passes (SP) and
normal points (NP) at Arequipa
Satellite All Stations Arequipa
Lageos-1 9.8 11.0
Lageos-2 9.7 12.9
Table 5: Root mean square orbital fit [mm]
Displacement North East Height Length Azimuth
Total displacement [mm]
– June 23, 2001 → July 07, 2001 –334 –487 –13 590 236°
Velocity [mm/day]
- July 07, 2001 → Sept. 30, 2001 –0.1 –0.3 0 0.3 252°
- Oct. 01, 2001 → April 12, 2002 –0.1 –0.1 0.1 0.1 218°
Table 6: Total displacement of the SLR station Arequipa due to both major earthquakes and postseismic velocities
the roof of an office building of the Smithsonian Astronomical Observatory, the Transportable Laser Ranging
System (TLRS) is housed in a container placed on a concrete pad. Thus, both set-ups might have experienced
slightly different shock effects.
An attempt to solve in the GPS adjustment for nonlinear postseismic motions indicated indeed that the
velocities given in table 3 are averages during the specified periods but might not completely match the real site
motion in detail. In particular, the motion after the
June 23 earthquake of 1.8 mm/day may be superimposed
by small additional episodic displacements because about
30 aftershocks of magnitudes stronger than 5.0 occurred
during the first days after the main shock.
As concerns the postseismic motion after the July 07
earthquake, both GPS and SLR confirm that the initial
velocity of 1.0 mm/day during the first weeks was slowing down and eased off completely after a few months.
As regards the vertical component, the coseismic subsidence of about 38 mm on June 23 was partly compensated by subsequent uplift.
Trying to assess the implications of the earthquakes at
the Arequipa site on the International Terrestrial Reference Frame (ITRF) we refer mainly to the GPS results. The
following corrections to the ITRF should enable users to
meet the earthquake effects to a large extent:
 Application of leaps to the previous ITRF cartesian
coordinates [mm]:
June 24, 2001
∆X = –445 ∆Y = –23 ∆Z = –270
July 07, 2001
∆X = –474 ∆Y = –30 ∆Z = –300
 Application of average velocities [mm/day]:
After June 23, 2001
VX = –1.3 VY = –0.4 VZ = –1.3 until July 06
After July 07, 2001
VX = –0.5 VY = –0.1 VZ = –0.4 for about
two months.
The GPS observations from Cuiaba were provided by the
Instituto Brasileiro de Geografia e Estatistica (IBGE), Rio
de Janeiro.
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Anschrift der Autoren
Dipl.-Ing. Klaus Kaniuth
Dipl.-Ing. Horst Müller
Dipl.-Ing. Wolfgang Seemüller
Deutsches Geodätisches Forschungsinstitut (DGFI)
Marstallplatz 8
D-80539 München
FachbeiträgeKaniuth/Müller/Seemüller, Displacement of the space geodetic observatory Arequipa
127. Jg. 4/2002 zfv 243
Fig. 3: Coseismic displacements and postseismic motions
of Arequipa resulting from GPS and SLR analyses

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