- Email: [email protected]
Tectonic plate motions derived from LAGEOS
Earth and Planetary Science Letters, 103 (1991) 379 394 Elsevier Science Publishers B.V., Amsterdam
379
[XLeP]
Tectonic plate motions derived from LAGEOS R. Biancale, A. C a z e n a v e a n d K. D o m i n h CNES-GRGS, 18 Avenue E. Belin, 31055 Toulouse Cedex, France Received February 21, 1990; revision accepted October 29, 1990
ABSTRACT Five years of laser data (1984-1988) between the LAGEOS satellite and the ground station network have been analysed to recover tectonic motions affecting the stations. Precise orbit computations of the LAGEOS satellite have been carried out on a monthly basis. Then a global inversion over the five-year period has been performed to obtain solutions for absolute velocities in latitude and longitude of a selected subset of fourteen stations. Relative horizontal velocities have been derived between couples of stations located on different tectonic plates and compared to predictions of the NUVEL-1 geological model. For stations located far enough from plate boundaries, the agreement between the LAGEOS solution and the model is quite satisfactory. For some stations close to plate boundaries, the satellite solution shows discrepancies with the model as expected. This is the case in particular for Quincy (California), Simosato (Japan) and Arequipa (Peru). The relative motion between Quincy and Mt. Peak across the San Andreas Fault is found to be - 33 + 3 m m / y r , reducing the discrepancy with NUVEL-1 to only 12 ram/yr. The motion of Matera (Italy) agrees well with NUVEL-1 if the station is assumed on the African plate. Finally, no significant intraplate motions have been found over the five-year period.
1. Introduction
During the last decade, space geodesy has demonstrated its capability in measuring, at the cmlevel accuracy, station coordinates and baseline length between couples of stations. Secular changes in station coordinates have been also detected. Among the various potential applications of such measurements, tectonic plate kinematics is recognized as a goal of major importance. Global plate motions are determined by kinematic models based on geological data [1,2,3]. These models provide relative velocity between approx, twelve plates moving rigidly at the surface of a spherical earth. Three basic types of data are utilized: (1) spreading rates at mid-ocean ridges; (2) directions of relative motions from transformfault azimuths; and (3) earthquake slip vectors. Because spreading rates are based on magnetic anomalies averaged over the last 1-3 million years, geological models give plate motions averaged over this time-scale. The latest model by DeMets et al. [3] is the NUVEL-1 model. It gives the rotation vectors of ten plates relative to the Pacific plate assumed fixed. 0012-821X/91/$03.50
© 1991 - Elsevier Science Publishers B.V.
Space geodesy gives instantaneous plate motions since the current time scale over which geodetic data are analysed is a few years. Two space geodetic techniques are presently applied to monitor large-scale motions of the major tectonic plates as well as deformations at plate boundaries: (1) Very Long Baseline Interferometry (VLBI), and (2) Satellite Laser Ranging (SLR). VLBI utilizes couples of radio telescopes observing extragalactic radio sources. Time delays in receiving the signal at the two antennas depend, among others, on the Earth orientation in space and on the vector baseline between the two antennas. SLR comprises two components: a ground-based laser system sending a laser pulse to a satellite which is reflected back down to the l a s e r station, and a satellite equipped with an array of laser retroflectors. Laser data (i.e. station-satellite vector) are used to compute precise orbital elements of the satellite and station coordinates. If the station is slowly moving as a result of plate motions, the station velocity vector is also determined together with the above parameters. The best adapted laser satellite for global plate motion studies is LAGEOS. Launched in 1976 by
380
NASA into a circular orbit at 6000 km altitude, it is less perturbed by gravitational forces, in particular the Earth potential, and by atmospheric drag than low orbiting satellites like Starlette. Hence, its orbit and station position vectors can be accurately determined. Observed from more than a decade now by the international laser tracking network, LAGEOS has already been used to determine global plate motions over a few years time scale [4,5,6]. The remarkable agreement obtained statistically between SLR results and geological model predictions (e.g. [6]) constitutes a success for space geodetic methods. It confirms moreover the basic assumption of plate tectonic theory, i.e. plates move rigidly and accelerations in relative motion are negligible. The objectives in measuring instantaneous plate motion by space geodesy have been clearly defined [7]. They are as follows: (1) refine the instantaneous inter-plate motions by multiplying baselines crossing a variety of plate boundaries; (2) measure vector motions between plates with poorly determined relative velocities; (3) determine the kinematics of deformation along plate margins; and (4) measure the non-rigid large scale behaviour of plates. For such a diversity of objectives, the various techniques of precise positioning developed by space geodesy have to be used. The SLR and VLB1 techniques are quite accurate but cost effective and limited to networks covering only portions of the global tectonic plate system. Doppler based techniques such as the Global Positioning System (GPS) and the DORIS system [8,9] allow more flexibility owing to easily deployable networks. They are most useful to study the objectives (2) and (3). DORIS should also deserve the objectives (1) and (4) via the dense large-scale network of - 5 0 fixed beacons in place for at least a decade. Involvement of space geodesy in measuring plate motion is still at its beginning. The first SLR solution was published by Christodoulis et al. [4]. It was based on 2-3 years of data on LAGEOS collected between 1979 and 1981, an epoch where the stations coverage was very poor. The recent solution by Smith et al. [6], the SL7.1 solution, uses a longer time span of data (up to 1988). The agreement observed between the SL7.1 solution and geologic models suggests that the numerous sources of errors affecting the SLR data
R. BIANCALE ET AL.
analyses have been handled correctly. We cannot be yet sure, however, that the remaining (although small) differences, of a few m m / y r , reveal real discrepancy between present day plate motions and million-year averaged motions. These differences may still result from errors affecting the geodetic solutions. Hence, independent analyses should be conducted by groups having the capabilities of precise orbit determination. Because the problem is important and challenging, because also new SLR data from the L A G E O S 2 (to be launched in 1991) will be available in the near future, we have initiated recently such an effort. We have analysed five years of LAGEOS data from 1984,0. Before this date, the coverage of observations collected by the global SLR network is too poor to obtain reliable solutions. Precise monthly orbital arcs of LAGEOS have been computed and horizontal absolute and relative station velocities have been determined over a five-year period. 2. The precise orbit computation software: the GIN and D Y N A M O systems The LAGEOS data have been analysed using the G I N - D Y N A M O software package developed at the Groupe de Recherche de Grod6sie Spatiale (GRGS) for precise orbit computation and geopotential models (GRIM) computation. G I N D Y N A M O performs a numerical integration of the satellite's equations of motion, using Cowell's method. It is based on a predictor-corrector type scheme with a fixed time step. The forces model includes: (a) the earth gravity field; (b) luni-solar and planetary gravitational perturbations; (c) direct and earth-reflected radiation pressure; (d) atmospheric drag and charged particules drag; and (e) solid and ocean tides. 2.1. Gravitational potential A spherical harmonic representation is used for the earth gravitational potential UGp: UG p _
GM r
1+
-{- Snm s i n m
(~m
cosm ),
n=2 m=0
)~)Pnm(Sin th)}
(1)
381
TECTONIC PLATE MOTIONS DERIVED FROM LAGEOS
where r, ~, 2~, are the spherical coordinates of the satellite in a terrestrial reference frame, a e and M are equatorial radius and mass of the earth. G is the gravitational constant. Cnm, Snm are normalised spherical harmonic coefficients. We used the C,m, Snm coefficients of the G E M - T 2 model, recently computed by the Geodynamics Branch of G o d d a r d Space Flight Center [10].
2.2. Luni-solar and planetary perturbations The gravitational attraction of the sun, moon and planets on the satellite derives from the potential Up:
0] m ' and r ' are mass and geocentric distance of the attracting body. d and 0 are distance and geocentric angle between satellite and attracting body. Gravitational perturbations of all planets except Uranus, Neptune, and Pluto are taken into account.
atmospheric density. O varies with season, altitude, local hour, solar and geomagnetic activity. Numerical tables have been proposed by several authors (e.g. [12,13]). ka is a free parameter adjusted to account for model errors. Charged particule drag is due to the relative displacement of electrons in the magnetosphere and the satellite. This perturbation has been considered by a number of authors as mainly responsible for the observed average decay of the semi-major axis of L A G E O S [14,15]. Recently, Rubincam [16,17] has proposed that Yarkovsky thermal drag is the major source of orbital decay of L A G E O S and accounts for at least 50% of the observed drag. Thermal drag depends on the L A G E O S spin axis position which evolution with time is not known. For this reason, we have not taken into account Yarkovsky thermal drag. Charged particule drag is modeled through a constant perturbing acceleration of - 3 × 10 -a2 ms -2. A constant term plus a linear drift are adjusted over monthly periods to absorb errors of the drag model.
2.5. Solid and ocean tides 2.3. Direct and earth-reflected radiation pressure Direct radiation pressure acting on the satellite is given by:
siS
ffp=kpm c S
(3)
s / m is the area to mass ratio of the satellite, I is energy of incident photons, c is light velocity. S is the sun-satellite vector, kp is a parameter adjusted by the differential correction process to account for variations of the satellite reflective properties. Indirect radiation pressure due to Earth albedo and emitted I R flux are modeled according to the Stephens et al. model [11]. Crossing of the satellite into the earth and moon shadow is modeled through a regularizing function. 2.4. Atmospheric drag and charged particle drag Atmospheric drag on the satellite induces a force given by: 1
S
fro = - ~k o-~ CoPV~
(4)
Cd is the aerodynamic coefficient, ~ is the satellite velocity vector relative to the atmosphere, p is
The gravitational potential due to elastic deformation of the earth caused by the sun and moon is given by:
u, =
7k217
Pn(COS O)
(5)
0 is the geocentric angle between the perturbing body and the satellite, m ' and r ' are mass and geocentric distance of the perturbing body. We have assumed k 2 = 0 . 3 , except for five tidal components for which we applied Wahr's corrections according to the M E R I T standards [18]. Ocean tides potential is based on a spherical harmonic representation of the tidal model of Schwiderski [19]. Eleven ocean tides developed in spherical harmonics up to 20 are taken into account. Stations position are corrected for the solid earth tide and loading effect [20].
2.6. References system Numerical integration of the equations of motion is performed in the instantaneous celestial reference frame which is related to the J2000
382 reference frame by using the nutation model of Wahr [21] and precession model of Lieske et al. [22]. 2.7. Station coordinates and Earth rotation parameters
Earth rotation parameters (polar motion and UT1) are derived from a homogeneous series computed at the International Earth Rotation Service (IERS) for the period 1962-1987. This series utilizes, with an increasing weight through time, SLR and VLBI determinations of polar motion and UT1 [23]. This series has been completed for the years 1988 to 1990 by the series EOP (IERS)90-C-04 [24]. Necessary corrections have been applied to insure continuity between the two series. Coordinates of a selected station network have been computed by IERS to provide the BIH Terrestrial system (BTS) homogeneous with the earth rotation parameters series. Coordinates of the SLR stations provided by the BTS have been used. These are given at a fixed epoch. Position at any epoch t is derived using the absolute velocities of the global plate motion AMO-2 [2] in agreement with the M E R I T standards (1985).
3. SLR tracking data Five years of laser data on L A G E O S have been analysed. The period of analysis starts in January 1984 up to December 1988. Before 1984, the coverage of SLR observations is quite poor so that accurate L A G E O S orbit cannot be computed. Hence, we have not considered the data prior to 1984. About 50 laser stations have observed L A G E O S during the five-year period. Some stations however have observed over very short time spans (a few months) so that secular plate motions cannot be accurately determined at these stations. Although data of all stations have participated in the analysis, a subset of sixteen stations has been first selected for the purpose of plate velocities study. Figure 1 shows the geographical location of the sixteen laser stations, while Table 1 gives their geographical coordinates. Because of the large number of raw data within a satellite pass above a station (several thousands), it is usual to apply data compression techniques
R. B I A N C A L E E T A L .
and compute normal points. This procedure provides a reduced number of representative observations and eliminates aberrant data. We used L A G E O S normal points c o m p u t e d by the Deutsches Geodatisches Forschungsinstitut ( D G F I ) and kindly provided to us. L A G E O S normal points have been corrected for tropospheric refraction and spacecraft center of mass offset.
4. Analysis A three-step analysis process has been applied. The time span of data has been divided into 30-day intervals forming the basic arcs of orbital analysis. The successive monthly arcs have been processed using the G I N software. Individual monthly solutions consist in initial orbital parameters (at the starting epoch of each arc), a constant parameter kp for the radiation pressure, a constant parameter k~ plus a linear drift for the drag acceleration. The intrinsic quality of each monthly arc is given by the RMS of the residuals between observations (tracking data) and theoretical stationsatellite vector. RMS of monthly arcs are typically around 10 cm. RMS for individual station observations are also estimated. The latter are useful indicators of the quality of the data and of the precision of the station itself. We will see in section 5 that the quality of the solution for the station velocity is directly related to the RMS of the station observations. If the RMS is high ( > 15 cm, on the average over the five-year period), the solution is unstable. If the RMS is low (~< 10 cm), the solution is quite stable whatever the boundary conditions. Figure 2 presents the temporal variations of the RMS for each of the sixteen stations of the selected network. The lowest RMS (~< 10 cm) are observed at Matera, Quincy, M o n u m e n t Peak, Wettzel, Graz, R G O and Greenbelt. Quite high RMS are reported for Potsdam, in particular beyond March 1985. In view of the poor quality of the laser data collected at Potsdam, we have eliminated the data of this station in the final solution. Other stations (see Fig. 2) have RMS oscillating between 10 and 20 cm. Arequipa has particularly high RMS. Some caution will be necessary when interpreting the results obtained at this station. Huahine presents also rather high RMS. Moreover, the data at Huahine cover a
9O
.
qS0
0 ~
~
j
-
7907
71og~ 7 ss -"Gos 711tZ~,.+ 0
"L
I
/ '," .
.... -
L
L"
[
-)
-L\/,
:ig. 1. Geographical location of the permanent stations of the global laser tracking network. Boundaries of major tectonic plates are shown.
-
7121
+
T210
%
r~
11 0
) )
)
q
384
R. BIANCALE ET AL.
TABLE 1 G e o g r a p h i c a l c o o r d i n a t e s of the laser stations Station
Potsdam McDonald Yarragadee Greenbelt Quincy M o n u m e n t Peak Huahine Mazatlan Maui Wet tzel Grasse Simosato Graz RGO Arequipa Matera
Number
1181 7086 7090 7105 7109 7110 7121 7122 7210 7834 7835 7838 7839 7840 7907 7939
Latitude
Longitude
(°)
(°)
52.19 30.51 - 28.88 38.83 39.79 32.72 - 16.63 23.20 20.58 48.95 43.56 33.40 46.88 50.68 - 16.36 40.46
13.07 255.98 115.35 283.17 239.06 243.58 208.96 253.54 203.74 12.88 6.92 135.94 15.49 0.34 288.51 16.70
short time interval (less than 3 years) with many gaps in 1985. Tests have shown that the velocity solution at Huahine is in error (quite large departures from model predictions). Such a result may be due to the too short time span of data used and low quality of SLR data over the period considered. We have thus decided to not solve for the Huahine velocity which has been fixed at its value of the initial model (AMO-2 model). In the second step of analysis, monthly normal equations are generated using the D Y N A M O software from the last iteration of the monthly-arc solutions. Computed partial derivatives concern: (1) orbital parameters; (2) station coordinates at origin epoch; (3) absolute velocities 0, ~ for each station; (4) corrections to the J2, J3 and J 4 earth potential zonal coefficients; (5) their time derivative J2, J.'~, J4; and (6) polar motion and UT1. In the final step, a global solution for the station coordinates and horizontal velocities over the five-year period are computed by cumulation of monthly normal equations, using a least square procedure and the inversion module of the DYN A M O software. Internal parameters (orbit parameters, drag and radiation pressure coefficient, etc.) are expressed as a function of external parameters. Zonal coefficients and their time derivatives are not solved. Earth rotation parameters (polar motion and UT1) can either be adjusted or fixed at their model values. The solution is stabi-
Plate
Eurasian North American Australian North American North American Pacific Pacific North American Pacific Eurasian Eurasian Eurasian Eurasian Eurasian South A m e r i c a n Eurasian
lized by fixing coordinates and horizontal velocity of one or two stations at their model values (BTS values for coordinates, AMO-2 model for velocity). Possible local displacements of the laser station over a given site are accounted for by entering constraints before inversion.
5. Results: global solution over the five-year period 5.1. Absolute motions
A global inversion has been carried over the 5-year period. Solutions for coordinates and absolute horizontal velocities d), ~ of the fourteen remaining stations have been computed. Several different solutions have been derived to evaluate the influence of boundary conditions: (1) Earth rotation parameters EPR (polar motion and UT1) fixed or adjusted at a 5-day interval; (2) one or two SLR station fixed (coordinates and horizontal velocity) at their model values. Table 2 displays the g; and ~ cos q5 values obtained in four different solutions: (a) EPR adjusted, coordinates and velocity of Greenbelt (7105) and R G O (7840) fixed at their model values; (b) EPR adjusted, coordinates and velocity of Greenbelt and Maui (7210) fixed at their model values; (c) EPR adjusted, coordinates and velocity of Maui fixed at their model values; and (d) same as (c) but EPR fixed.
TECTONIC PLATE MOTIONS DERIVED FROM LAGEOS
385
Also given in Table 2 are the values predicted by the geological models A M O - 2 and N U V E L - 1 ( N U V E L - 1 gives relative velocities with respect to the Pacific plate. To obtain absolute plate motions, we have assumed that the Pacific plate moves as in the A M O - 2 model. This is of course a simplification; but constructing an "absolute" N U V E L - 1 model using the " n o net rotation" cono
--
J oOeoooOoeoO
•
o°
--
•
cept as in A M O - 2 is b e y o n d the scope of this study). The reason for fixing either Greenbelt or Maui and R G O results from internal tests made in the course of the data analysis which have shown that the velocity estimated at these stations is stable and comparable to the model predictions. Results presented in Table 2 for cases (a) to (d)
•
1181 POTSOAM
°°°o
•o
--
°o°°e°°°°e°o°°°
e°oO°e°°°°°°°°Oo°°O
7086 MCDONALD
DoOOeooooeoOo
~ -- o Do eo eeooo • eloOOoOoooeO ° ° ° o ° ° o eOQO ooeoQeOo°oOOoOOOoO°OOoOo
7090 YARAGADEE
~oeOooeoooOeooOOooooooeoOeooO°oooe o oeoO°oeeoOoOOOOOooeOeoOO
7105 GREENBELT 7109 QUINCY
~ooO°O°eoO°°oOoooo°OooeoOOOoeOoeoeooeoO°°°oo°o°eOooOOooooeO
~°o°°°OoooOoooeOOooooOooO°Oo°OoooQoeooo°OOOoO°oOoOOOoooooe -o _
E
Oo°OoOoo°°oo o
°°o •
•
7110 Mt PEAK
7121 HUAHINE
oo o ° ° ° ° °
°°°eooeoOOOeO°OooeOOOOooeoeo ° o °ooOeoo oo°e oo Ooo
7122 MAZATLAN 7210
10 4oo°OOeooo oOooe°oOoOooOeeoOoOOOOoeo
e O o e ° ° o O o e o ° o ° ° ° ° ° o o°o
30 20 10 loOeOOoooOOo °ooOooooOOoOOoooO ° oOOoo • oooOoooooOOoooOoooOo 30 20 10 -
°oOe°oOOO°°ooOOOoo o o
30 20 10 ~ ° e ° ° 30 20 10
e°°°°
~ ° ° ° o ° o ° o °°
eo • Oo
e°°e°°°°°°°°e°lo°°oe°e°
oo ° ° e Oo°
go oo°o
• oo
•
MAUl 7834 WET[ZELL
oo°ooeoooooOo o
7835 GRASSE
eo°°°oo°°°°o °
7838 S~OSATO
eOlo°Oo • oo o°o°°oee°OooOooOoooOoOo
7839 GRAZ
30
784O
I°o°OOeooe°°Oooo°oooOoOOoOlOOoooooooooooooooooeeoooe°l°ooeoo
RGO
30
°°oeOo~oo°e°eoe°eooo°°
-
OooOO°OOoOOOo°oeoeoooo°oo° °oOOOOOoo
7939 MATERA
Jo°eOeeOeOe°eeeeoeeeeeeeeooe°°Oeeeeeoe°e°e°oeeeeeeeeOeoeeoeo I IllllllllllllllIlllIIIlll
1984
lllllllllllllllllllllllllllll
1985
1986
1987
~07 AREQUI~
llllll
1988
Fig. 2. RMS per station of monthly orbital arcs as a function of time.
386
R. B1ANCALE ET AL.
show a good general consistency: differences in and X cos 4' from one solution to another for a given station can be larger than associated standard errors but of the same order of magnitude as the differences between the AMO-2 and NUVEL-1 models. Results for McDonald (7086), Greenbelt (7105), Yarragadee (7090) and Maui (7210) are rather stable and in good agreement with the geological models. For the European stations (7840, 7835, 7839 and 7939) solutions (a), (b), and (c) indicate an absolute motion in latitude significantly larger than both the AMO-2 and NUVEL-1 models, while solution (d) (earth rotation parameters fixed) gives a better agreement with the model predictions. For Wettzel, the L A G E O S solution gives a slower motion in latitude than models. For stations located close to plate boundaries, the four solutions depart significantly from model values. This is particularly clear for Arequipa (7907) for which the AMO-2 and NUVEL-1 models predict a negative value for X cos 4' whereas L A G E O S results give a value of the order of - 30 m m / y r . We think however that the results for Arequipa lack reliability in view of the large RMS reported during the five years of analysis (see Fig. 2).
An important discrepancy in latitude between observed and predicted motion is noticed at Mt. Peak (7110) and Simosato (7838). The results for Simosato are nevertheless rather unstable from one solution to another, which is again probably linked to the low quality of the data. A smaller discrepancy is observed for Quincy (7109) although departure from global plate motions is expected at this station. Among the four solutions presented in Table 2, we believe that solutions (c) and (d) are the most reliable since they show globally less deviation from the geological models than the others. It is also reasonable to assume that the motion of Maul is well described by the geological models. The differences observed in absolute motions between solution (c) and (d) which differ only by adjusting the earth rotation parameters, result from systematic effects associated with the different reference frame used.
5.2. Relative motions
Relative velocities between couples of stations have been computed by estimating the temporal
TABLE 2 Absolute velocities ,~ and X cos ~ in m m / y r derived from the LAGEOS solution over the five-year period for the fourteen SLR stations selected
7086 7090 7105 7109 7110 7122 7210 7834 7835 7838 7840 7907 7839 7939
AMO-2
NUVEL-1
(a)
(b)
(c)
(d)
~, x cos ,~
~, Xcos ,t,
~, ~ cos,
~, ~ cos ,¢,
~, x cos ~,
~, ~ cos ,t,
10, 13 61, 43 2, 17 -16, -14 28, - 4 8 -11, -11 37, 68 16,20 17, 20 15,24 18, 17 10, - 7 16,21 16,21
3, 17 60, 37 2, 19 -10. -18 28, 48 -4, -15 37, 68 11,19 12, 19 -17,13 14, 17 12, - 1 1 10,20 10,20
- 4 +1, 16+2 62 _+1, 46 _+1 8 _+1, 16+1 - 2 1 _+1, -18_+1 9 -+1, - 3 6 + 1 6.5-+1, -6_+1 5 +2,23+2 24 _+1,23-+1 2 +2,7-+2 30 -+1,20_+1 20 +1,34-+1 30 _+2,22+2 35 _+1,25-+1
-2_+1, -19_+2 67 ± 1, 48 _+1 3_+1, - 1 2 + 1 -14+1, -16+1 15-+1, - 3 4 - + 1 -3+l, 7_+1 -8_+1,19_+1 13-+1, 21_+1 1-+1, - 4 + 2 17+1, 18_+1 10_+1,27_+2 22_+1,20+2 26+1,20-+1
10+1, - 2 2 + 2 59 _+1, 42 + 1 -25_+1, -23_+1 6+1, 39+1 -10_+1, -11_+1 26+1, 67+1 3-+1,20_+2 24+1, 15_+1 -6_+1,4_+2 15+1,35+1 28_+1,17_+2 34_+1,20_+1
- 7 + 1 , -13_+2 69 + 1, 48 _+1 20+1, 16+1 9_+1, 33_+1 -7+1, -4+1 6_+2,21-+2 26-+1, 18-+1 6-+2,9-+2 30-+1, 16+1 18+1,39_+1 31_+1,18_+2 36+1,22+_1
Solution (a) corresponds to EPR adjusted, 7805 and 7840 fixed (coordinates and velocities). Solution (b) is similar to solution (a) but with 7805 and 7210 fixed. Solution (c) is similar to solution (a) but with only 7210 fixed. Solution (d) corresponds to EPR fixed and 7210 fixed. Also given the values (in m m / y r ) predicted by the AMO-2 and NUVEL-I models (see text for explanations).
TECTONIC PLATE MOTIONS DERIVED FROM LAGEOS
387
change in the spherical distance r between two stations 1 and 2: 1 = sin r { [sin 4', cos <
+10
cos( ,l -
- c o s 4', sin 4'2]4, + [sin 4'2 cos 4'/'1 cos(X, - X2) - cos 4'2 sin 4', ] 42
+ c o s < cos4'2
(6)
with: COS
r =
COS 4'1 COS 4'2 C O S ( ~ I - - ~ 2 ) -10
+ sin 4'1 sin 4'2
+10
(7) NUVEL-1(cm/yr)
Table 3 presents relative velocities in m m / y r between couples of stations located on different plates as well as associated uncertainty. Only results for solutions (c) and (d) are given in Table 3. Standard errors have been computed using the covariance matrix of the global solution. Also given in Table 3 relative velocities from the NUVEL-1 model as well as from the SL7.1 solution [6] and DGFI89L03 solution [5].
5.2.1. Interplate motions North American-Eurasian plates. Relative motion between Greenbelt (7105) and McDonald (7086), on one hand, and European stations, on the other hand, appear systematically lower than NUVEL-1 predictions, except for Wettzel. A mean relative motion of - 13 m m / y r is reported for solution (c) and of 16-17 m m / y r for solution (d). The lowest relative motion concerns Graz (7839) and Matera (7939). Although Matera is located close to the boundary between Eurasian and African plates, we have nominally assumed this station on the Eurasian plate. It is clear from the L A G E O S solutions that its relative motion with the North American plate would be in much better agreement with the NUVEL-1 model if this station belongs to the African plate (14 m m / y r ) . Such a conclusion has also been drawn by Smith et al. [5]. We notice also from Table 3 that relative motion between Graz (7839) and all other stations is always very similar to that of Matera (7939). Graz which is classically affected to the Eurasian plate
Fig. 3. LAGEOS solution over the five-year period (solution c) for the relative horizontal velocity (in c m / y r ) between couples of stations located in stable tectonic regions as a function of the NUVEL-1 model predictions. The straight line corresponds to a perfect agreement between LAGEOS solution and model.
seems to move very much like Matera. Results for Wettzel (7834) appear in closer agreement with NUVEL-1 than all other European stations. Then if we exclude Matera and Graz the average relative motion between N O A M and E U R A raises to - 2 0 23 m m / y r , now in perfect agreement with NUVEL-1.
Pacific plate to North American and Eurasian plates. Mr. Peak (7110) is located close to the San Andreas Fault System so that its motion is not representative of the Pacific plate. Thus relative motion between North American and Pacific plates is only given by the relative velocity between Maui (7210) and Greenbelt (7105) and McDonald (7086). Results of both solutions (c) and (d) are very comparable to the NUVEL-1 predictions (but recall that the motion of Maui is constrained). A similar conclusion can be drawn for the motion of Maui relative to RGO, Wettzel and Grasse (solution c). Australian plate to Eurasian, Pacific and North American plates. Relative motion between Yarragadee (7090) and stations located on the North American, Pacific and Eurasian plates (7105, 7210, 7840, 7834, 7835, 7839) are globally in good agreement with NUVEL-1. The rate between Yarraga-
388
R. BIANCALE ET AL.
TABLE 3 Relative horizontal velocities (in m m / y r ) determined in the global LAGEOS solutions (c) and (d) over the 5-yr period for all couples of laser stations except those belonging to the same plate. Also given the values predicted by the NUVEL-1 model, as well as the values of the SL7.1 and DGFI89L03 solutions. The two model values for Matera correspond to the Eurasian and African plates respectively NUVEL-1 N O A M - EUR A 7105-7840 7105-7839 7105-7939 7105-7834 7105-7835 7086-7840 7086-7839 7086-7939 7086-7834 7086-7835 7109-7840 7109-7839 7109-7939 7109-7834 7109-7835 7122-7840 7122-7839 7122-7939 7122-7834 7122-7835
22 22 23/16 21 23 22 22 22/14 21 22 20 19 20/11 19 20 22 21 22/15 21 22
SL7.1 18±2 19±2 11±2 14±4 21±4 23±3 23±3 16±3 19±3 26±5 12±3 9±2 3±2 8±2 12±5 16±2 16±3 9±2 12±3 19±4
NOAM- PCFC 7105-7110 7105-7210 7086-7110 7086-7210 7109-7110 7109-7210 7122-7110 7122-7210
15 14 35 3l - 45 7 47 43
25±2 26±2 -26±1 6±2 34±2 ~±2
NOAM-SOAM 7105-7907 7086-7907 7109-7907 7122-7907
-5 - 8 - 8 - 9
-5±2 2±2 10±2 5±2
NOAM- A UST 7105-7090 7086-7090 7109-7090 7122-7090
16±2 -
87 67 80 54
-75±3 -65±3 -74±3 -48±3
NOAM- EURA(Japan) 7105-7838 -5 7086-7838 - 9 7109-7838 - 9 7122-7838 -10
-7±3 -3±3 -7±3 0±3
-
DGF189L03 14±2 6±2 9±2 10±2 6±2 7±2 21±2 14±2 17±2 -
23±2 3±2 28±2 49±2
33±1 50±2
-3±2 --2±2 3±1
-79±2 -50±2 -48±2
2±2 10±2 -
(c)
(d)
17±6 11±6 11±6 23±6 17±7 16±4 10±5 9±4 27±5 18+6 19±3 13±4 10±4 35±4 21±6 13±3 8±4 7±3 24±4 15±6
19±6 14±6 10±6 25±6 21±7 21±4 14±5 11±4 28±5 24±6 21±3 13±4 9±4 37±4 24±6 15±3 9±4 6±3 26±4 18±6
15±5 18±5 22±1 32±3 -33±1 3±2 33±2 52±2
13±5 21±5 18±1 29±2 -34±1 7±2 33±2 51±2
-7±5 9±3 6±2 7±2
-8±5 5±3 -2±2 0±2
-94±2 -75±2 -90±2 -55±2
--92±2 -81±2 -92±2 --57±2
-15±7 --12+5 -8±4 -5±4
-7±6 -10±5 -3±4 0±4
TECTONIC PLATE MOTIONS DERIVED FROM LAGEOS
TABLE
389
3 (continued) NUVEL-I
SL7.1
DGFI89L03
(c)
(d)
E URA - P C F C 7840-7110
9
10_+2
7839-7110
5
6 _+ 2
15_+2
9+3
- 1 _+ 4
1 +4
-3-+4
7939-7110
8
1 +2
7834-7110
1
4,+ 2
7835-7110
0
7840-7210
- 24
- 30 ± 3
7839-7210
- 37
- 4 6 ,+ 3
- 46 _+ 5
- 48 + 5
7939-7210
-37/-46
-51_+3
-39+2
-53_+6
-53+6
7834-7210
-41
-43+3
-3l_+2
-28_+5
-17_+5
7835-7210
- 27
- 35 _+ 5
EURA
7+ 1
9_+3
1 _+ 4 10 -+ 2
22 _+ 4
13+5 - 22 + 2
21 _+ 4
13_+6
13_+6
28 _+ 4
- 26 ,+ 4
27 _+ 7
- 27 + 6
SOAM
7840-7907
18
6 _+ 3
7839-7907
21
11 ,+ 4
7939-7907
24/22
7834-7907 7835-7907
10 ,+ 2
- 5+ 3
6 ,+ 3
-
- 9+ 6
7 _+ 6
5 ,+ 3
4 ,+ 2
- 8 _+ 6
6 ,+ 6
20
4 _+ 3
1 _+ 2
- 14 ,+ 4
2 _+ 4
22
14 ,+ 4
- 8 _+ 6
8 _+ 6
7840-7090
- 32
- 26 _+ 3
- 30 ,+ 2
- 30 _+ 2
7839-7090
- 28
- 26 ,+ 3
21 _+ 3
- 22 ,+ 3
7939-7090
-14/-15
7834-7090
- 30
- 22 ,+ 3
7835-7090
-21
-22_+4
-
EURA - A UST
-9+3
- 39 _+ 2 ~- 18-+ 2
-11+_2
- 30 _+ 2
- 30 _+ 3
- 31 _+ 3
-17_+4
-18,+4
-
-10,+2
PCFC - SOA M 7110-7907
38
38 _+ 2
37 _+ 1
40 _+ 2
32 _+ 2
7210-7907
61
80 ,+ 3
82 ,+ l
81 +_ 3
81 + 3
PCFC
A UST
7110-7090
-96
-85+3
7210-7090
- 97
- 89 ,+ 2
-88+1
7110-7838
-55
-34+_3
-28+_2
-39_+4
-34_+4
7210-7838
-89
-68_+3
-68_+2
-84_+3
-73_+3
- 99.2
-98-+2
-98_+2
- 99 ,+ 3
- 99 _+ 3
PCFC- EURA /Japan
SOA M- A UST 7907-7090
SOAM-
58 ,+ 3
70 -/-_2
79 ,+ 3
74 _+ 3
- 20
8 -+ 3
12 _+ 2
8 -+ 2
3 ,+ 2
- 79
- 62 ,+ 3
- 81 ,+ 2
74 ,+ 3
- 79 -+ 3
JAPAN
7907-7838
AUST
64
JAPAN
7090-7838
EURA- JAPAN 7840-7838
0
- 28 _+ 4
- 22 -+ 2
- 32 -+ 4
- 26 ± 4
7839-7838
0
-34-+4
-22+2
- 3 1 -+5
-33-+5
7939-7838
0/-
- 31 -+ 4
- 22 -+ 2
- 36 -+ 4
- 36 -+ 4
7834-7838
0
-28-+3
-16-+2
-15_+5
-12-+5
7835-7838
0
- 36 -+ 5
- 28 -+ 7
- 28 ± 7
NOAM
= North American;
3
PCFC = Pacific; SOAM = South American;
AUST = Australian;
EURA
= Eurasian.
390
dee and McDonald (7086) appears however larger than model predictions. Figure 3 presents the rates of change in spherical distance between couples of stations located on stable portions of plate as a function of the NUVEL-1 predictions. The stations concerned are Greenbelt, McDonald, Maui, Yarragadee, RGO, Wettzel, Grasse and Graz. We have also considered Matera (assumed on the African plate) and Mazatlan whose motion does not differ significantly from that of the North American plate. 5.2.2. Motions at plate boundaries Several laser stations are located close to plate boundaries. It is the case of Quincy (7109), Mt. Peak (7110), Arequipa (7907) and Simosato (7838). The relative motion between Quincy and Mt. Peak, apart from the San Andreas Fault, is studied for m a n y years by geodetic techniques (SLR, VLBI, GPS). The AMO-2 model predicts a rate between Quincy and Mt. Peak of - 5 4 r a m / y r . The recent NUVEL-1 model proposes a slower relative motion of - 4 5 m m / y r . The SL7.1 solution based on 8 years of data (1981-1988) provides a value of - 2 6 + 1 m m / y r , in good agreement with VLBI results over the same period ( - 2 8 m m / y r , [25]). The difference between the geodetic estimates and the geological values, currently called the "San Andreas discrepancy", is not yet completely understood (e.g. [26]). A recent analysis based on L A G E O S data [27] provides a rate of - 3 0 + 3 m m / y r . The results of the present study give a rate somewhat higher than previous studies: all solutions we obtained have provided a remarkably stable result of - 33-34 _+ 1 m m / y r . Intermediate solutions based successively on 3 years and 4 years of data have given the same value as with 5 years of data. If the value of - 3 3 - 3 4 m m / y r is confirmed, it reduces significantly the difference with NUVEL-1 to only 11-12 m m / y r . Note that the present estimate agrees with ground-based geodesy results ( - 34 _ 3 m m / y r ; see [26]). Simosato (7838) has been nominally placed on the Eurasian plate. However, Simosato, close to the subduction of the Philippine plate under Eurasia, is located in a region subject to intense collisional deformation. Its motion is expected to differ from that of the Eurasian plate and this is indeed observed. Relative motion with the European stations is of the order of - - 3 0
R. BIANCALE ET AL. +10 QUINCY(7109)
co
o
(..9
-10
IX -I0
0
+10
NUVEL-1(cm/yr) Fig. 4. LAGEOS solution (solution c) for the relative horizontal velocity (in c m / y r ) between Quincy (7109) and all other stations as a function of the NUVEL-1 predictions.
m m / y r except for Wettzel ( - 1 5 m m / y r ) , in accordance with the SL7.1 and the D G F I 8 9 L 0 3 solutions. Arequipa (7907) is located close to the subduction of the Nazca plate under the South American plate, where complex collision processes take place. Looking at Table 3, we note that relative motion of Arequipa with the stations on the North American plate is of opposite sign of the NUVEL-1 rates, except for Greenbelt. A similar behaviour is observed with the European stations (solution c). In the latter case, our results disagree with the SL7.1 and D G F I 8 9 L 0 3 solutions. In view of the large RMS reported for Arequipa in monthly arcs (Fig. 2), we think that the solution for Arequipa is noisy and unstable. Accurate motion of Arequipa will be obtained with longer data span. Nevertheless, the results reported here support the conclusion that Arequipa is subject to regional deformation and does not move like the South American plate. Figures 4 and 5 show the observed rate of change in spherical distance between Quincy and Mt. Peak and all other stations as a function of NUVEL-1 predictions. Departures from the model are clearly observed. 5.2.3. Intra plate deformations Table 4 presents the relative motion between stations located on the same plate (solution c).
TECTONIC
PLATE MOTIONS
DERIVED
391
FROM LAGEOS
+10 Mt PEAK (7110)
=,.,
o
0
{.9
5
-10 -10
+10
NOVEL-1(em/yr) Fig. 5. LAGEOS solution (solution c) for the relative horizontal velocity (in c m / y r ) between Mt. Peak (7110) and all other stations as a function of the NUVEL-1 predictions.
zel supports the conclusion that Matera is located on the African plate. The anomalous behaviour of Graz mentioned above in discussing interplate motions is no more apparent here and remains to be confirmed. On the North American plate, relative motions between Greenbelt, McDonald and Mazatlan are also slow of - 1-3 m m / y r , i.e. of the same order as associated uncertainties. A larger rate is observed between Quincy and Greenbelt, as expected if Quincy is subject to regional deformation. As for the Eurasian plate, the results indicate that no significant intraplate deformations occur inside the North American plate. However, given the present level of accuracy of the solutions, it is not worthwhile to discuss any further individual rates.
6. Comparison with other solutions Relative motion between European stations are slow, of a few m m / y r at most, in particular between RGO, Grasse and Wettzel. The relative motion between Matera and RGO, Grasse, WettTABLE 4 Relative horizontal velocities (in m m / y r ) determined in the global LAGEOS solution (c) over the 5-year period between pairs of stations belonging to the same plate. Also given the NUVEL-1 values as well as the SL7.1 and DGFI89L03 values (also in m m / y r ) SL7.1
DGFI89L03
(c)
NUVEL-1
E URA 7840-7839 7840-7939 7840-7834 7840-7835 7839-7939 7839-7835 7939-7835
2_+2 -8-+2 -3_+2 --1_+5 --4_+3 -3-+5 -11+4
-2+2 -7_+2 -7_+2 -5+2 -
-5+1 -7+1 4_+1 3_+1 -5+1 0+1 --6-+1
0 0/-8.0 0 0 0 0 0/-8
NOAM 7105-7086 7105-7109 7105-7122 7086-7109 7086-7122 7109-7122
8 5=2 4+-2 0-+2 5_+ 2 -7-+3 5 _+2
3 -+ 2 5-+2 1_+5 - 2-+4 0_+4 - 1 +_2
0 0 0 0 0 0
PCFC 7110-7210
4-+2
8+_1
0
EURA = Eurasian; Pacific.
11+1 N O A M = North
American;
PCFC =
A few groups, members of the IERS, are currently analysing L A G E O S data to provide regularly, UT1 and polar motion series. SLR station velocities are also computed but most of these solutions remain unpublished and can hardly be used for comparison. Fortunately this is not the case for two recent solutions available in the literature [5,6]. The DGFI89L03 solution [6] is based on five years of L A G E O S data (1983-1987). The method applied is quite similar to the one we develop here although the force model is somewhat different: monthly orbital arcs are computed and monthly normal equations systems are formed. The cumulated normal matrix over the five-year period is then inverted to provide in addition to orbital parameters, solutions for E P R at five-day intervals, station coordinates at a fixed epoch and horizontal station motions. The D G F I 8 9 L 0 3 solution assumes, as we do, that stations move linearly with time over the time interval of analysis. The advantage of this approach is that the solution is derived in a consistent reference system. The SL7.1 solution [6] is based on a longer time series. The total period considered ranges from 1979 to 1988, with stations like Greenbelt and Arequipa having regularly observed over the 10year interval. For the other stations, the time interval of data range from 5 to 8 years. However,
392
R. B I A N C A L E
before 1984, the number of observing stations is poor while increasing regularly with time [6]. The approach adopted to derive the SL7.1 solution differs somewhat from the one adopted here. Monthly normal equations systems are also first computed, but then combined into groups of three months and inverted to provide quarterly solutions for orbital parameters, Earth rotation parameters and average stations coordinates. These quarterly solutions cannot be used directly to study the time dependence of station coordinates. Indeed discontinuities arise from one solution to another due to the use of inhomogeneous reference frames (the terrestrial reference frame used in each quarterly solution varies with time as a result of the variable participation of sites modifying the network geometry). These discontinuities can be
sollliions
Lageos
•
~
2
=
-
S
L
N~Lvel 7
.
i
.IL
i(l-:
1 r
[
cm/yr
DGFI89L03
Z[I :i
ET AL.
removed by transforming the quarterly solutions in a common reference frame through rigid body transformations. In the SL7.1 solution, the common reference frame is obtained from solutions based on multi-year data intervals. Geodesic rates between couples of stations are then derived from the time evolution of transformed quarterly solutions and used to compute, with a least square procedure, absolute station velocities. Relative velocities between pairs of stations for the DGFI89L03 and SL7.1 solutions have been presented in Table 3. We have computed the differences in relative velocities between the NUVEL-1 model and the three L A G E O S solutions, SL7.1, DGFI89L03 and that of the present study ( G R G S solution). These differences are presented in histogram form in Fig. 6 (only for pairs of stations located on different plates). For the three solutions, most differences range from - 1 0 to + 1 0 m m / y r . The G R G S - N U V E L - 1 differences are slightly more dispersed than the SL7.1-NUVEL-1 differences, probably a result of the shorter time span of data used in our solution. Figure 7 presents histograms of the differences between: (a) SL7.1 and G R G S solutions; (b) DGFI89L03 and G R G S solutions; and (c) SL7.1 and DGFI89L03 solutions. We note again that most differences range between - 1 0 and + 1 0 m m / y r , i.e. like with the geological model. This range likely reflects the present level of precision of satellite solutions.
3
7. Conclusions
i0
F
T --3
--1
1
'~
('[11 / \'Y
:?II
~RGS
: 5
5
C
5
3
I
1
:3
5
/
(,]i11 / VY Fig. 6. Histograms of the differences in relative velocity between: (a) SL7.1 solution and NUVEE-1; (b) DGFI89L03 solution and NUVEE-1; and (c) GRGS solution and NUVEL1. Only pairs of stations located on different plates are considered.
In the present study, we have determined from five years of L A G E O S data, horizontal motions at fourteen laser station sites. These motions are compatible, within a few m m / y r , with those predicted by geological models for stations located far enough from plate boundaries. For stations close to the boundaries, some discrepancies are clearly seen between the L A G E O S solution and model predictions. The main results of this study can be summarized as follows: (1) The motion of Matera (Italy) agrees well with the geological model predictions if the station is assumed to lie on the African plate. (2) Simosato (Japan), nominally assumed on the Eurasian plate, presents a relative motion with the European stations of the order of - 30 m m / y r .
TECTONIC
PLATE
MOTIONS
DERIVED
Differerwes Lageos
FROM
between
solutions
E i.-,--
,=
l
-
=
I a
10~: -5
393
LAGEOS
-3
-1
1
3
cm/yr
5
3(I _ 2.., -
(5) Interplate motions between stations located on stable plate interiors agree with the NUVEL-1 model within a few m m / y r . (6) No significant intraplate motions are evidenced. If these exist, they amount less than 5 mm/yr. (7) The present solution based on five years of data agrees reasonably well with two recently published solutions, SL7.1 and DGFI89L03. Most differences between these three solutions fall within - 1 0 and + 10 m m / y r . The SL7.1 solution presents nevertheless less dispersion, probably a result of the use of a longer time span of data.
..--.
Acknowledgments lOz z
•-,t
[1 -=
-5
-3
-I
1
3
5
('rn/v?" 30 _ z
We thank the D G F I for having kindly provided us LAGEOS normal points. We thank M. Feissel and C. Boucher for helpful discussions and for having prepared the homogeneous time series of Earth Rotation parameters and BTS station coordinates.
z
1
References
5
-3
1
1
3
5
(°tl)/)~i" Fig. 7. Histograms of the differences in relative velocity between: (a) SL7.1 solution and GRGS solution; (h) DGFI89L03 solution and GRGS solution; and (c) SL7.1 solution and DGFI89L03 solution. Only pairs of stations located on different plates are considered.
(3) The absolute motions of Quincy and Mt. Peak (California) depart significantly from model predictions. The rate of change of the Quincy-Mt. Peak baseline is estimated to - 3 3 + 3 m m / y r over the period 1984-1988. This value has been found very stable in the various solutions we obt a i n e d a n d t h u s is b e l i e v e d to b e q u i t e r e l i a b l e . I t reduced the "San Andreas discrepancy" to -12 ram/yr. (4) T h e m o t i o n o f A r e q u i p a ( P e r u ) d e p a r t s significantly from the motion of the South American p l a t e . T h e s o l u t i o n f o r A r e q u i p a is h o w e v e r u n stable due to the low quality of the laser data at t h i s s t a t i o n . T h i s d r a w b a c k will b e o v e r c o m e b y analysing a longer time span of observations.
1 X. Le Pichon, Sea-floor spreading and continental drift, J. Geophys. Res. 73, 3661-3697, 1968. 2 J.B. Minster and T.H. Jordan, Present-day plate motions, J. Geophys. Res. 83, 5331-5354, 1978. 3 D.C. Demets, R.G. Gordon, D.F. Argus and S. Stein, Current plate motions, Geophys. J. 101,425-478, 1990. 4 D.C. Christodoulidis, D.E. Smith, R. Kolenkiewicz, S.M. Klosko, M.H. Torrence and P.J. Dunn, Observing tectonic plate motions and deformations from satellite Laser ranging, J. Geophys. Res. 90, 9249-9263, 1985. 5 Ch. Reigber, W. Ellmer, H. Miiller, E. Geiss, P. Schwintzer and F.H. Massman, Plate motions derived from the DGFI89L03 solution, in: Global and Regional Geodynamics, Vyskocil, Reigber and Cross, eds., Springer, New York, N.Y., 1990. 6 D.E. Smith, R. Kolokienwicz, P.J. Dunn, M.H. Torrence, J.W. Robbins, S.M. Klosko, R.G. Williamson, E.C. Pavlis, N.B. Douglas and S.K. Fricke, Tectonic motion and deformation from satellite Laser ranging to LAGEOS, J. Geophys. Res., in press, 1990. 7 J.B. Minster, W. Prescott and L. Royden, Plate motion and deformation, Coolfont workshop, Coolfont, Vi, 1989. 8 M. Dorrer, Le systrme DORIS, Cours international de Technologie Spatiale, Toulouse, 1989. 9 M. Lefebvre, DORIS system, CSTG Bull. 3, DGFI, Munich, 1989. 10 J.G. Marsh et al., The GEM-T2 gravitational model, NASA Tech. Memo., 100746, 99 pp., 1989. 11 G.L. Stephens, G.C. Campbell and T.H. Vonder Haar,
394
12 13
14
15 16
17 18 19 20
R. BIANCALE ET AL. Earth radiation budgets, J. Geophys. Res. 86, 9739-9760, 1981. L. Jacchia, Thermospheric temperature, density and composition: new models, SAO special report 375, 1977. F. Barlier, C. Berger, J.L. Falin, G. Kocharts and G. Thuillier, A thermospheric model based on satellite drag data, Ann. Geophys. 34, 9-24, 1978. G. Afonso, F. Barlier, C. Berger, F. Mignard and J.J. Walch, Reassessment of the charge and neutral drag of LAGEOS and its geophysical interpretation, J. Geophys. Res. 90, 9381-9398, 1985. D.P. Rubincam, On the secular decrease in the semimajor axis of LAGEOS's orbit, Celest. Mech. 26, 361-382, 1982. D.P. Rubincam, LAGEOS orbit decay due to infrared radiation from Earth, J. Geophys. Res. 92, 1287-1294, 1987. D.P. Rubincam, Yarkovsky thermal drag on LAGEOS, J. Geophys. Res. 93, 13805-13810, 1988. M E R I T S T A N D A R D S , U.S. Naval Observatory, Washington, D.C., 1985. E.W. Schwiderski, Ocean tides, Part 1: Global ocean tidal equations, Mar. Geod. 3, 161-207, 1980. C. Destrigneville, Effets de charge de la marre oc~anique, Mrmorie de diplrme d'ingrnieur g6ophysicien, Universit6 de Strasbourg, 1987.
21 J.M. Wahr, The forced nutations of an elliptical, rotating, elastic and oceanless earth, Geophys. J. 64, 705-727, 1981. 22 J.H. Lieske, T. Lederle, W. Fricke and B. Morando, Expressions for the Precession quantities based upon the IAU (1976) system of astronomical constants, Astron. Astrophys. 58, 1-16, 1977. 23 M. Feissel and B. Guinot, A homogeneous series of the Earth Rotation Parameters based on all observing techniques, 1962-1987. Annual Report of the BIH for 1987, D-79-84, Paris Observatory, 1988. 24 M. Feissel, Annual Report of the IERS for 1990, Paris Observatory, 1990. 25 R. Kolenkiewicz, M.H. Torrence, C. Ma and J.W. Ryan, Comparison of SLR and VLBI Geodesic rates, Proceedings of the 4th International Conference of the W E G E N E R M E D L A S project, University of Technology, Delft, 1990. 26 J.B. Minster and T.H. Jordan, Vector constraints on Western U.S. deformation from Space Geodesy, neotectonics and plate motions, J. Geophys, Res. 92, 4798-4804, 1987. 27 A. Stolz, M.A. Vincent, P.L. Bender, R.J. Earnes, M.M. Watkins and B.D. Tapley, Rate of change of the Quincy. Mt. Peak baseline from a translocation analysis of L A G E O S Laser Range data, Geophys. Res. Lett. 16, 539-543, 1989.
379
[XLeP]
Tectonic plate motions derived from LAGEOS R. Biancale, A. C a z e n a v e a n d K. D o m i n h CNES-GRGS, 18 Avenue E. Belin, 31055 Toulouse Cedex, France Received February 21, 1990; revision accepted October 29, 1990
ABSTRACT Five years of laser data (1984-1988) between the LAGEOS satellite and the ground station network have been analysed to recover tectonic motions affecting the stations. Precise orbit computations of the LAGEOS satellite have been carried out on a monthly basis. Then a global inversion over the five-year period has been performed to obtain solutions for absolute velocities in latitude and longitude of a selected subset of fourteen stations. Relative horizontal velocities have been derived between couples of stations located on different tectonic plates and compared to predictions of the NUVEL-1 geological model. For stations located far enough from plate boundaries, the agreement between the LAGEOS solution and the model is quite satisfactory. For some stations close to plate boundaries, the satellite solution shows discrepancies with the model as expected. This is the case in particular for Quincy (California), Simosato (Japan) and Arequipa (Peru). The relative motion between Quincy and Mt. Peak across the San Andreas Fault is found to be - 33 + 3 m m / y r , reducing the discrepancy with NUVEL-1 to only 12 ram/yr. The motion of Matera (Italy) agrees well with NUVEL-1 if the station is assumed on the African plate. Finally, no significant intraplate motions have been found over the five-year period.
1. Introduction
During the last decade, space geodesy has demonstrated its capability in measuring, at the cmlevel accuracy, station coordinates and baseline length between couples of stations. Secular changes in station coordinates have been also detected. Among the various potential applications of such measurements, tectonic plate kinematics is recognized as a goal of major importance. Global plate motions are determined by kinematic models based on geological data [1,2,3]. These models provide relative velocity between approx, twelve plates moving rigidly at the surface of a spherical earth. Three basic types of data are utilized: (1) spreading rates at mid-ocean ridges; (2) directions of relative motions from transformfault azimuths; and (3) earthquake slip vectors. Because spreading rates are based on magnetic anomalies averaged over the last 1-3 million years, geological models give plate motions averaged over this time-scale. The latest model by DeMets et al. [3] is the NUVEL-1 model. It gives the rotation vectors of ten plates relative to the Pacific plate assumed fixed. 0012-821X/91/$03.50
© 1991 - Elsevier Science Publishers B.V.
Space geodesy gives instantaneous plate motions since the current time scale over which geodetic data are analysed is a few years. Two space geodetic techniques are presently applied to monitor large-scale motions of the major tectonic plates as well as deformations at plate boundaries: (1) Very Long Baseline Interferometry (VLBI), and (2) Satellite Laser Ranging (SLR). VLBI utilizes couples of radio telescopes observing extragalactic radio sources. Time delays in receiving the signal at the two antennas depend, among others, on the Earth orientation in space and on the vector baseline between the two antennas. SLR comprises two components: a ground-based laser system sending a laser pulse to a satellite which is reflected back down to the l a s e r station, and a satellite equipped with an array of laser retroflectors. Laser data (i.e. station-satellite vector) are used to compute precise orbital elements of the satellite and station coordinates. If the station is slowly moving as a result of plate motions, the station velocity vector is also determined together with the above parameters. The best adapted laser satellite for global plate motion studies is LAGEOS. Launched in 1976 by
380
NASA into a circular orbit at 6000 km altitude, it is less perturbed by gravitational forces, in particular the Earth potential, and by atmospheric drag than low orbiting satellites like Starlette. Hence, its orbit and station position vectors can be accurately determined. Observed from more than a decade now by the international laser tracking network, LAGEOS has already been used to determine global plate motions over a few years time scale [4,5,6]. The remarkable agreement obtained statistically between SLR results and geological model predictions (e.g. [6]) constitutes a success for space geodetic methods. It confirms moreover the basic assumption of plate tectonic theory, i.e. plates move rigidly and accelerations in relative motion are negligible. The objectives in measuring instantaneous plate motion by space geodesy have been clearly defined [7]. They are as follows: (1) refine the instantaneous inter-plate motions by multiplying baselines crossing a variety of plate boundaries; (2) measure vector motions between plates with poorly determined relative velocities; (3) determine the kinematics of deformation along plate margins; and (4) measure the non-rigid large scale behaviour of plates. For such a diversity of objectives, the various techniques of precise positioning developed by space geodesy have to be used. The SLR and VLB1 techniques are quite accurate but cost effective and limited to networks covering only portions of the global tectonic plate system. Doppler based techniques such as the Global Positioning System (GPS) and the DORIS system [8,9] allow more flexibility owing to easily deployable networks. They are most useful to study the objectives (2) and (3). DORIS should also deserve the objectives (1) and (4) via the dense large-scale network of - 5 0 fixed beacons in place for at least a decade. Involvement of space geodesy in measuring plate motion is still at its beginning. The first SLR solution was published by Christodoulis et al. [4]. It was based on 2-3 years of data on LAGEOS collected between 1979 and 1981, an epoch where the stations coverage was very poor. The recent solution by Smith et al. [6], the SL7.1 solution, uses a longer time span of data (up to 1988). The agreement observed between the SL7.1 solution and geologic models suggests that the numerous sources of errors affecting the SLR data
R. BIANCALE ET AL.
analyses have been handled correctly. We cannot be yet sure, however, that the remaining (although small) differences, of a few m m / y r , reveal real discrepancy between present day plate motions and million-year averaged motions. These differences may still result from errors affecting the geodetic solutions. Hence, independent analyses should be conducted by groups having the capabilities of precise orbit determination. Because the problem is important and challenging, because also new SLR data from the L A G E O S 2 (to be launched in 1991) will be available in the near future, we have initiated recently such an effort. We have analysed five years of LAGEOS data from 1984,0. Before this date, the coverage of observations collected by the global SLR network is too poor to obtain reliable solutions. Precise monthly orbital arcs of LAGEOS have been computed and horizontal absolute and relative station velocities have been determined over a five-year period. 2. The precise orbit computation software: the GIN and D Y N A M O systems The LAGEOS data have been analysed using the G I N - D Y N A M O software package developed at the Groupe de Recherche de Grod6sie Spatiale (GRGS) for precise orbit computation and geopotential models (GRIM) computation. G I N D Y N A M O performs a numerical integration of the satellite's equations of motion, using Cowell's method. It is based on a predictor-corrector type scheme with a fixed time step. The forces model includes: (a) the earth gravity field; (b) luni-solar and planetary gravitational perturbations; (c) direct and earth-reflected radiation pressure; (d) atmospheric drag and charged particules drag; and (e) solid and ocean tides. 2.1. Gravitational potential A spherical harmonic representation is used for the earth gravitational potential UGp: UG p _
GM r
1+
-{- Snm s i n m
(~m
cosm ),
n=2 m=0
)~)Pnm(Sin th)}
(1)
381
TECTONIC PLATE MOTIONS DERIVED FROM LAGEOS
where r, ~, 2~, are the spherical coordinates of the satellite in a terrestrial reference frame, a e and M are equatorial radius and mass of the earth. G is the gravitational constant. Cnm, Snm are normalised spherical harmonic coefficients. We used the C,m, Snm coefficients of the G E M - T 2 model, recently computed by the Geodynamics Branch of G o d d a r d Space Flight Center [10].
2.2. Luni-solar and planetary perturbations The gravitational attraction of the sun, moon and planets on the satellite derives from the potential Up:
0] m ' and r ' are mass and geocentric distance of the attracting body. d and 0 are distance and geocentric angle between satellite and attracting body. Gravitational perturbations of all planets except Uranus, Neptune, and Pluto are taken into account.
atmospheric density. O varies with season, altitude, local hour, solar and geomagnetic activity. Numerical tables have been proposed by several authors (e.g. [12,13]). ka is a free parameter adjusted to account for model errors. Charged particule drag is due to the relative displacement of electrons in the magnetosphere and the satellite. This perturbation has been considered by a number of authors as mainly responsible for the observed average decay of the semi-major axis of L A G E O S [14,15]. Recently, Rubincam [16,17] has proposed that Yarkovsky thermal drag is the major source of orbital decay of L A G E O S and accounts for at least 50% of the observed drag. Thermal drag depends on the L A G E O S spin axis position which evolution with time is not known. For this reason, we have not taken into account Yarkovsky thermal drag. Charged particule drag is modeled through a constant perturbing acceleration of - 3 × 10 -a2 ms -2. A constant term plus a linear drift are adjusted over monthly periods to absorb errors of the drag model.
2.5. Solid and ocean tides 2.3. Direct and earth-reflected radiation pressure Direct radiation pressure acting on the satellite is given by:
siS
ffp=kpm c S
(3)
s / m is the area to mass ratio of the satellite, I is energy of incident photons, c is light velocity. S is the sun-satellite vector, kp is a parameter adjusted by the differential correction process to account for variations of the satellite reflective properties. Indirect radiation pressure due to Earth albedo and emitted I R flux are modeled according to the Stephens et al. model [11]. Crossing of the satellite into the earth and moon shadow is modeled through a regularizing function. 2.4. Atmospheric drag and charged particle drag Atmospheric drag on the satellite induces a force given by: 1
S
fro = - ~k o-~ CoPV~
(4)
Cd is the aerodynamic coefficient, ~ is the satellite velocity vector relative to the atmosphere, p is
The gravitational potential due to elastic deformation of the earth caused by the sun and moon is given by:
u, =
7k217
Pn(COS O)
(5)
0 is the geocentric angle between the perturbing body and the satellite, m ' and r ' are mass and geocentric distance of the perturbing body. We have assumed k 2 = 0 . 3 , except for five tidal components for which we applied Wahr's corrections according to the M E R I T standards [18]. Ocean tides potential is based on a spherical harmonic representation of the tidal model of Schwiderski [19]. Eleven ocean tides developed in spherical harmonics up to 20 are taken into account. Stations position are corrected for the solid earth tide and loading effect [20].
2.6. References system Numerical integration of the equations of motion is performed in the instantaneous celestial reference frame which is related to the J2000
382 reference frame by using the nutation model of Wahr [21] and precession model of Lieske et al. [22]. 2.7. Station coordinates and Earth rotation parameters
Earth rotation parameters (polar motion and UT1) are derived from a homogeneous series computed at the International Earth Rotation Service (IERS) for the period 1962-1987. This series utilizes, with an increasing weight through time, SLR and VLBI determinations of polar motion and UT1 [23]. This series has been completed for the years 1988 to 1990 by the series EOP (IERS)90-C-04 [24]. Necessary corrections have been applied to insure continuity between the two series. Coordinates of a selected station network have been computed by IERS to provide the BIH Terrestrial system (BTS) homogeneous with the earth rotation parameters series. Coordinates of the SLR stations provided by the BTS have been used. These are given at a fixed epoch. Position at any epoch t is derived using the absolute velocities of the global plate motion AMO-2 [2] in agreement with the M E R I T standards (1985).
3. SLR tracking data Five years of laser data on L A G E O S have been analysed. The period of analysis starts in January 1984 up to December 1988. Before 1984, the coverage of SLR observations is quite poor so that accurate L A G E O S orbit cannot be computed. Hence, we have not considered the data prior to 1984. About 50 laser stations have observed L A G E O S during the five-year period. Some stations however have observed over very short time spans (a few months) so that secular plate motions cannot be accurately determined at these stations. Although data of all stations have participated in the analysis, a subset of sixteen stations has been first selected for the purpose of plate velocities study. Figure 1 shows the geographical location of the sixteen laser stations, while Table 1 gives their geographical coordinates. Because of the large number of raw data within a satellite pass above a station (several thousands), it is usual to apply data compression techniques
R. B I A N C A L E E T A L .
and compute normal points. This procedure provides a reduced number of representative observations and eliminates aberrant data. We used L A G E O S normal points c o m p u t e d by the Deutsches Geodatisches Forschungsinstitut ( D G F I ) and kindly provided to us. L A G E O S normal points have been corrected for tropospheric refraction and spacecraft center of mass offset.
4. Analysis A three-step analysis process has been applied. The time span of data has been divided into 30-day intervals forming the basic arcs of orbital analysis. The successive monthly arcs have been processed using the G I N software. Individual monthly solutions consist in initial orbital parameters (at the starting epoch of each arc), a constant parameter kp for the radiation pressure, a constant parameter k~ plus a linear drift for the drag acceleration. The intrinsic quality of each monthly arc is given by the RMS of the residuals between observations (tracking data) and theoretical stationsatellite vector. RMS of monthly arcs are typically around 10 cm. RMS for individual station observations are also estimated. The latter are useful indicators of the quality of the data and of the precision of the station itself. We will see in section 5 that the quality of the solution for the station velocity is directly related to the RMS of the station observations. If the RMS is high ( > 15 cm, on the average over the five-year period), the solution is unstable. If the RMS is low (~< 10 cm), the solution is quite stable whatever the boundary conditions. Figure 2 presents the temporal variations of the RMS for each of the sixteen stations of the selected network. The lowest RMS (~< 10 cm) are observed at Matera, Quincy, M o n u m e n t Peak, Wettzel, Graz, R G O and Greenbelt. Quite high RMS are reported for Potsdam, in particular beyond March 1985. In view of the poor quality of the laser data collected at Potsdam, we have eliminated the data of this station in the final solution. Other stations (see Fig. 2) have RMS oscillating between 10 and 20 cm. Arequipa has particularly high RMS. Some caution will be necessary when interpreting the results obtained at this station. Huahine presents also rather high RMS. Moreover, the data at Huahine cover a
9O
.
qS0
0 ~
~
j
-
7907
71og~ 7 ss -"Gos 711tZ~,.+ 0
"L
I
/ '," .
.... -
L
L"
[
-)
-L\/,
:ig. 1. Geographical location of the permanent stations of the global laser tracking network. Boundaries of major tectonic plates are shown.
-
7121
+
T210
%
r~
11 0
) )
)
q
384
R. BIANCALE ET AL.
TABLE 1 G e o g r a p h i c a l c o o r d i n a t e s of the laser stations Station
Potsdam McDonald Yarragadee Greenbelt Quincy M o n u m e n t Peak Huahine Mazatlan Maui Wet tzel Grasse Simosato Graz RGO Arequipa Matera
Number
1181 7086 7090 7105 7109 7110 7121 7122 7210 7834 7835 7838 7839 7840 7907 7939
Latitude
Longitude
(°)
(°)
52.19 30.51 - 28.88 38.83 39.79 32.72 - 16.63 23.20 20.58 48.95 43.56 33.40 46.88 50.68 - 16.36 40.46
13.07 255.98 115.35 283.17 239.06 243.58 208.96 253.54 203.74 12.88 6.92 135.94 15.49 0.34 288.51 16.70
short time interval (less than 3 years) with many gaps in 1985. Tests have shown that the velocity solution at Huahine is in error (quite large departures from model predictions). Such a result may be due to the too short time span of data used and low quality of SLR data over the period considered. We have thus decided to not solve for the Huahine velocity which has been fixed at its value of the initial model (AMO-2 model). In the second step of analysis, monthly normal equations are generated using the D Y N A M O software from the last iteration of the monthly-arc solutions. Computed partial derivatives concern: (1) orbital parameters; (2) station coordinates at origin epoch; (3) absolute velocities 0, ~ for each station; (4) corrections to the J2, J3 and J 4 earth potential zonal coefficients; (5) their time derivative J2, J.'~, J4; and (6) polar motion and UT1. In the final step, a global solution for the station coordinates and horizontal velocities over the five-year period are computed by cumulation of monthly normal equations, using a least square procedure and the inversion module of the DYN A M O software. Internal parameters (orbit parameters, drag and radiation pressure coefficient, etc.) are expressed as a function of external parameters. Zonal coefficients and their time derivatives are not solved. Earth rotation parameters (polar motion and UT1) can either be adjusted or fixed at their model values. The solution is stabi-
Plate
Eurasian North American Australian North American North American Pacific Pacific North American Pacific Eurasian Eurasian Eurasian Eurasian Eurasian South A m e r i c a n Eurasian
lized by fixing coordinates and horizontal velocity of one or two stations at their model values (BTS values for coordinates, AMO-2 model for velocity). Possible local displacements of the laser station over a given site are accounted for by entering constraints before inversion.
5. Results: global solution over the five-year period 5.1. Absolute motions
A global inversion has been carried over the 5-year period. Solutions for coordinates and absolute horizontal velocities d), ~ of the fourteen remaining stations have been computed. Several different solutions have been derived to evaluate the influence of boundary conditions: (1) Earth rotation parameters EPR (polar motion and UT1) fixed or adjusted at a 5-day interval; (2) one or two SLR station fixed (coordinates and horizontal velocity) at their model values. Table 2 displays the g; and ~ cos q5 values obtained in four different solutions: (a) EPR adjusted, coordinates and velocity of Greenbelt (7105) and R G O (7840) fixed at their model values; (b) EPR adjusted, coordinates and velocity of Greenbelt and Maui (7210) fixed at their model values; (c) EPR adjusted, coordinates and velocity of Maui fixed at their model values; and (d) same as (c) but EPR fixed.
TECTONIC PLATE MOTIONS DERIVED FROM LAGEOS
385
Also given in Table 2 are the values predicted by the geological models A M O - 2 and N U V E L - 1 ( N U V E L - 1 gives relative velocities with respect to the Pacific plate. To obtain absolute plate motions, we have assumed that the Pacific plate moves as in the A M O - 2 model. This is of course a simplification; but constructing an "absolute" N U V E L - 1 model using the " n o net rotation" cono
--
J oOeoooOoeoO
•
o°
--
•
cept as in A M O - 2 is b e y o n d the scope of this study). The reason for fixing either Greenbelt or Maui and R G O results from internal tests made in the course of the data analysis which have shown that the velocity estimated at these stations is stable and comparable to the model predictions. Results presented in Table 2 for cases (a) to (d)
•
1181 POTSOAM
°°°o
•o
--
°o°°e°°°°e°o°°°
e°oO°e°°°°°°°°Oo°°O
7086 MCDONALD
DoOOeooooeoOo
~ -- o Do eo eeooo • eloOOoOoooeO ° ° ° o ° ° o eOQO ooeoQeOo°oOOoOOOoO°OOoOo
7090 YARAGADEE
~oeOooeoooOeooOOooooooeoOeooO°oooe o oeoO°oeeoOoOOOOOooeOeoOO
7105 GREENBELT 7109 QUINCY
~ooO°O°eoO°°oOoooo°OooeoOOOoeOoeoeooeoO°°°oo°o°eOooOOooooeO
~°o°°°OoooOoooeOOooooOooO°Oo°OoooQoeooo°OOOoO°oOoOOOoooooe -o _
E
Oo°OoOoo°°oo o
°°o •
•
7110 Mt PEAK
7121 HUAHINE
oo o ° ° ° ° °
°°°eooeoOOOeO°OooeOOOOooeoeo ° o °ooOeoo oo°e oo Ooo
7122 MAZATLAN 7210
10 4oo°OOeooo oOooe°oOoOooOeeoOoOOOOoeo
e O o e ° ° o O o e o ° o ° ° ° ° ° o o°o
30 20 10 loOeOOoooOOo °ooOooooOOoOOoooO ° oOOoo • oooOoooooOOoooOoooOo 30 20 10 -
°oOe°oOOO°°ooOOOoo o o
30 20 10 ~ ° e ° ° 30 20 10
e°°°°
~ ° ° ° o ° o ° o °°
eo • Oo
e°°e°°°°°°°°e°lo°°oe°e°
oo ° ° e Oo°
go oo°o
• oo
•
MAUl 7834 WET[ZELL
oo°ooeoooooOo o
7835 GRASSE
eo°°°oo°°°°o °
7838 S~OSATO
eOlo°Oo • oo o°o°°oee°OooOooOoooOoOo
7839 GRAZ
30
784O
I°o°OOeooe°°Oooo°oooOoOOoOlOOoooooooooooooooooeeoooe°l°ooeoo
RGO
30
°°oeOo~oo°e°eoe°eooo°°
-
OooOO°OOoOOOo°oeoeoooo°oo° °oOOOOOoo
7939 MATERA
Jo°eOeeOeOe°eeeeoeeeeeeeeooe°°Oeeeeeoe°e°e°oeeeeeeeeOeoeeoeo I IllllllllllllllIlllIIIlll
1984
lllllllllllllllllllllllllllll
1985
1986
1987
~07 AREQUI~
llllll
1988
Fig. 2. RMS per station of monthly orbital arcs as a function of time.
386
R. B1ANCALE ET AL.
show a good general consistency: differences in and X cos 4' from one solution to another for a given station can be larger than associated standard errors but of the same order of magnitude as the differences between the AMO-2 and NUVEL-1 models. Results for McDonald (7086), Greenbelt (7105), Yarragadee (7090) and Maui (7210) are rather stable and in good agreement with the geological models. For the European stations (7840, 7835, 7839 and 7939) solutions (a), (b), and (c) indicate an absolute motion in latitude significantly larger than both the AMO-2 and NUVEL-1 models, while solution (d) (earth rotation parameters fixed) gives a better agreement with the model predictions. For Wettzel, the L A G E O S solution gives a slower motion in latitude than models. For stations located close to plate boundaries, the four solutions depart significantly from model values. This is particularly clear for Arequipa (7907) for which the AMO-2 and NUVEL-1 models predict a negative value for X cos 4' whereas L A G E O S results give a value of the order of - 30 m m / y r . We think however that the results for Arequipa lack reliability in view of the large RMS reported during the five years of analysis (see Fig. 2).
An important discrepancy in latitude between observed and predicted motion is noticed at Mt. Peak (7110) and Simosato (7838). The results for Simosato are nevertheless rather unstable from one solution to another, which is again probably linked to the low quality of the data. A smaller discrepancy is observed for Quincy (7109) although departure from global plate motions is expected at this station. Among the four solutions presented in Table 2, we believe that solutions (c) and (d) are the most reliable since they show globally less deviation from the geological models than the others. It is also reasonable to assume that the motion of Maul is well described by the geological models. The differences observed in absolute motions between solution (c) and (d) which differ only by adjusting the earth rotation parameters, result from systematic effects associated with the different reference frame used.
5.2. Relative motions
Relative velocities between couples of stations have been computed by estimating the temporal
TABLE 2 Absolute velocities ,~ and X cos ~ in m m / y r derived from the LAGEOS solution over the five-year period for the fourteen SLR stations selected
7086 7090 7105 7109 7110 7122 7210 7834 7835 7838 7840 7907 7839 7939
AMO-2
NUVEL-1
(a)
(b)
(c)
(d)
~, x cos ,~
~, Xcos ,t,
~, ~ cos,
~, ~ cos ,¢,
~, x cos ~,
~, ~ cos ,t,
10, 13 61, 43 2, 17 -16, -14 28, - 4 8 -11, -11 37, 68 16,20 17, 20 15,24 18, 17 10, - 7 16,21 16,21
3, 17 60, 37 2, 19 -10. -18 28, 48 -4, -15 37, 68 11,19 12, 19 -17,13 14, 17 12, - 1 1 10,20 10,20
- 4 +1, 16+2 62 _+1, 46 _+1 8 _+1, 16+1 - 2 1 _+1, -18_+1 9 -+1, - 3 6 + 1 6.5-+1, -6_+1 5 +2,23+2 24 _+1,23-+1 2 +2,7-+2 30 -+1,20_+1 20 +1,34-+1 30 _+2,22+2 35 _+1,25-+1
-2_+1, -19_+2 67 ± 1, 48 _+1 3_+1, - 1 2 + 1 -14+1, -16+1 15-+1, - 3 4 - + 1 -3+l, 7_+1 -8_+1,19_+1 13-+1, 21_+1 1-+1, - 4 + 2 17+1, 18_+1 10_+1,27_+2 22_+1,20+2 26+1,20-+1
10+1, - 2 2 + 2 59 _+1, 42 + 1 -25_+1, -23_+1 6+1, 39+1 -10_+1, -11_+1 26+1, 67+1 3-+1,20_+2 24+1, 15_+1 -6_+1,4_+2 15+1,35+1 28_+1,17_+2 34_+1,20_+1
- 7 + 1 , -13_+2 69 + 1, 48 _+1 20+1, 16+1 9_+1, 33_+1 -7+1, -4+1 6_+2,21-+2 26-+1, 18-+1 6-+2,9-+2 30-+1, 16+1 18+1,39_+1 31_+1,18_+2 36+1,22+_1
Solution (a) corresponds to EPR adjusted, 7805 and 7840 fixed (coordinates and velocities). Solution (b) is similar to solution (a) but with 7805 and 7210 fixed. Solution (c) is similar to solution (a) but with only 7210 fixed. Solution (d) corresponds to EPR fixed and 7210 fixed. Also given the values (in m m / y r ) predicted by the AMO-2 and NUVEL-I models (see text for explanations).
TECTONIC PLATE MOTIONS DERIVED FROM LAGEOS
387
change in the spherical distance r between two stations 1 and 2: 1 = sin r { [sin 4', cos <
+10
cos( ,l -
- c o s 4', sin 4'2]4, + [sin 4'2 cos 4'/'1 cos(X, - X2) - cos 4'2 sin 4', ] 42
+ c o s < cos4'2
(6)
with: COS
r =
COS 4'1 COS 4'2 C O S ( ~ I - - ~ 2 ) -10
+ sin 4'1 sin 4'2
+10
(7) NUVEL-1(cm/yr)
Table 3 presents relative velocities in m m / y r between couples of stations located on different plates as well as associated uncertainty. Only results for solutions (c) and (d) are given in Table 3. Standard errors have been computed using the covariance matrix of the global solution. Also given in Table 3 relative velocities from the NUVEL-1 model as well as from the SL7.1 solution [6] and DGFI89L03 solution [5].
5.2.1. Interplate motions North American-Eurasian plates. Relative motion between Greenbelt (7105) and McDonald (7086), on one hand, and European stations, on the other hand, appear systematically lower than NUVEL-1 predictions, except for Wettzel. A mean relative motion of - 13 m m / y r is reported for solution (c) and of 16-17 m m / y r for solution (d). The lowest relative motion concerns Graz (7839) and Matera (7939). Although Matera is located close to the boundary between Eurasian and African plates, we have nominally assumed this station on the Eurasian plate. It is clear from the L A G E O S solutions that its relative motion with the North American plate would be in much better agreement with the NUVEL-1 model if this station belongs to the African plate (14 m m / y r ) . Such a conclusion has also been drawn by Smith et al. [5]. We notice also from Table 3 that relative motion between Graz (7839) and all other stations is always very similar to that of Matera (7939). Graz which is classically affected to the Eurasian plate
Fig. 3. LAGEOS solution over the five-year period (solution c) for the relative horizontal velocity (in c m / y r ) between couples of stations located in stable tectonic regions as a function of the NUVEL-1 model predictions. The straight line corresponds to a perfect agreement between LAGEOS solution and model.
seems to move very much like Matera. Results for Wettzel (7834) appear in closer agreement with NUVEL-1 than all other European stations. Then if we exclude Matera and Graz the average relative motion between N O A M and E U R A raises to - 2 0 23 m m / y r , now in perfect agreement with NUVEL-1.
Pacific plate to North American and Eurasian plates. Mr. Peak (7110) is located close to the San Andreas Fault System so that its motion is not representative of the Pacific plate. Thus relative motion between North American and Pacific plates is only given by the relative velocity between Maui (7210) and Greenbelt (7105) and McDonald (7086). Results of both solutions (c) and (d) are very comparable to the NUVEL-1 predictions (but recall that the motion of Maui is constrained). A similar conclusion can be drawn for the motion of Maui relative to RGO, Wettzel and Grasse (solution c). Australian plate to Eurasian, Pacific and North American plates. Relative motion between Yarragadee (7090) and stations located on the North American, Pacific and Eurasian plates (7105, 7210, 7840, 7834, 7835, 7839) are globally in good agreement with NUVEL-1. The rate between Yarraga-
388
R. BIANCALE ET AL.
TABLE 3 Relative horizontal velocities (in m m / y r ) determined in the global LAGEOS solutions (c) and (d) over the 5-yr period for all couples of laser stations except those belonging to the same plate. Also given the values predicted by the NUVEL-1 model, as well as the values of the SL7.1 and DGFI89L03 solutions. The two model values for Matera correspond to the Eurasian and African plates respectively NUVEL-1 N O A M - EUR A 7105-7840 7105-7839 7105-7939 7105-7834 7105-7835 7086-7840 7086-7839 7086-7939 7086-7834 7086-7835 7109-7840 7109-7839 7109-7939 7109-7834 7109-7835 7122-7840 7122-7839 7122-7939 7122-7834 7122-7835
22 22 23/16 21 23 22 22 22/14 21 22 20 19 20/11 19 20 22 21 22/15 21 22
SL7.1 18±2 19±2 11±2 14±4 21±4 23±3 23±3 16±3 19±3 26±5 12±3 9±2 3±2 8±2 12±5 16±2 16±3 9±2 12±3 19±4
NOAM- PCFC 7105-7110 7105-7210 7086-7110 7086-7210 7109-7110 7109-7210 7122-7110 7122-7210
15 14 35 3l - 45 7 47 43
25±2 26±2 -26±1 6±2 34±2 ~±2
NOAM-SOAM 7105-7907 7086-7907 7109-7907 7122-7907
-5 - 8 - 8 - 9
-5±2 2±2 10±2 5±2
NOAM- A UST 7105-7090 7086-7090 7109-7090 7122-7090
16±2 -
87 67 80 54
-75±3 -65±3 -74±3 -48±3
NOAM- EURA(Japan) 7105-7838 -5 7086-7838 - 9 7109-7838 - 9 7122-7838 -10
-7±3 -3±3 -7±3 0±3
-
DGF189L03 14±2 6±2 9±2 10±2 6±2 7±2 21±2 14±2 17±2 -
23±2 3±2 28±2 49±2
33±1 50±2
-3±2 --2±2 3±1
-79±2 -50±2 -48±2
2±2 10±2 -
(c)
(d)
17±6 11±6 11±6 23±6 17±7 16±4 10±5 9±4 27±5 18+6 19±3 13±4 10±4 35±4 21±6 13±3 8±4 7±3 24±4 15±6
19±6 14±6 10±6 25±6 21±7 21±4 14±5 11±4 28±5 24±6 21±3 13±4 9±4 37±4 24±6 15±3 9±4 6±3 26±4 18±6
15±5 18±5 22±1 32±3 -33±1 3±2 33±2 52±2
13±5 21±5 18±1 29±2 -34±1 7±2 33±2 51±2
-7±5 9±3 6±2 7±2
-8±5 5±3 -2±2 0±2
-94±2 -75±2 -90±2 -55±2
--92±2 -81±2 -92±2 --57±2
-15±7 --12+5 -8±4 -5±4
-7±6 -10±5 -3±4 0±4
TECTONIC PLATE MOTIONS DERIVED FROM LAGEOS
TABLE
389
3 (continued) NUVEL-I
SL7.1
DGFI89L03
(c)
(d)
E URA - P C F C 7840-7110
9
10_+2
7839-7110
5
6 _+ 2
15_+2
9+3
- 1 _+ 4
1 +4
-3-+4
7939-7110
8
1 +2
7834-7110
1
4,+ 2
7835-7110
0
7840-7210
- 24
- 30 ± 3
7839-7210
- 37
- 4 6 ,+ 3
- 46 _+ 5
- 48 + 5
7939-7210
-37/-46
-51_+3
-39+2
-53_+6
-53+6
7834-7210
-41
-43+3
-3l_+2
-28_+5
-17_+5
7835-7210
- 27
- 35 _+ 5
EURA
7+ 1
9_+3
1 _+ 4 10 -+ 2
22 _+ 4
13+5 - 22 + 2
21 _+ 4
13_+6
13_+6
28 _+ 4
- 26 ,+ 4
27 _+ 7
- 27 + 6
SOAM
7840-7907
18
6 _+ 3
7839-7907
21
11 ,+ 4
7939-7907
24/22
7834-7907 7835-7907
10 ,+ 2
- 5+ 3
6 ,+ 3
-
- 9+ 6
7 _+ 6
5 ,+ 3
4 ,+ 2
- 8 _+ 6
6 ,+ 6
20
4 _+ 3
1 _+ 2
- 14 ,+ 4
2 _+ 4
22
14 ,+ 4
- 8 _+ 6
8 _+ 6
7840-7090
- 32
- 26 _+ 3
- 30 ,+ 2
- 30 _+ 2
7839-7090
- 28
- 26 ,+ 3
21 _+ 3
- 22 ,+ 3
7939-7090
-14/-15
7834-7090
- 30
- 22 ,+ 3
7835-7090
-21
-22_+4
-
EURA - A UST
-9+3
- 39 _+ 2 ~- 18-+ 2
-11+_2
- 30 _+ 2
- 30 _+ 3
- 31 _+ 3
-17_+4
-18,+4
-
-10,+2
PCFC - SOA M 7110-7907
38
38 _+ 2
37 _+ 1
40 _+ 2
32 _+ 2
7210-7907
61
80 ,+ 3
82 ,+ l
81 +_ 3
81 + 3
PCFC
A UST
7110-7090
-96
-85+3
7210-7090
- 97
- 89 ,+ 2
-88+1
7110-7838
-55
-34+_3
-28+_2
-39_+4
-34_+4
7210-7838
-89
-68_+3
-68_+2
-84_+3
-73_+3
- 99.2
-98-+2
-98_+2
- 99 ,+ 3
- 99 _+ 3
PCFC- EURA /Japan
SOA M- A UST 7907-7090
SOAM-
58 ,+ 3
70 -/-_2
79 ,+ 3
74 _+ 3
- 20
8 -+ 3
12 _+ 2
8 -+ 2
3 ,+ 2
- 79
- 62 ,+ 3
- 81 ,+ 2
74 ,+ 3
- 79 -+ 3
JAPAN
7907-7838
AUST
64
JAPAN
7090-7838
EURA- JAPAN 7840-7838
0
- 28 _+ 4
- 22 -+ 2
- 32 -+ 4
- 26 ± 4
7839-7838
0
-34-+4
-22+2
- 3 1 -+5
-33-+5
7939-7838
0/-
- 31 -+ 4
- 22 -+ 2
- 36 -+ 4
- 36 -+ 4
7834-7838
0
-28-+3
-16-+2
-15_+5
-12-+5
7835-7838
0
- 36 -+ 5
- 28 -+ 7
- 28 ± 7
NOAM
= North American;
3
PCFC = Pacific; SOAM = South American;
AUST = Australian;
EURA
= Eurasian.
390
dee and McDonald (7086) appears however larger than model predictions. Figure 3 presents the rates of change in spherical distance between couples of stations located on stable portions of plate as a function of the NUVEL-1 predictions. The stations concerned are Greenbelt, McDonald, Maui, Yarragadee, RGO, Wettzel, Grasse and Graz. We have also considered Matera (assumed on the African plate) and Mazatlan whose motion does not differ significantly from that of the North American plate. 5.2.2. Motions at plate boundaries Several laser stations are located close to plate boundaries. It is the case of Quincy (7109), Mt. Peak (7110), Arequipa (7907) and Simosato (7838). The relative motion between Quincy and Mt. Peak, apart from the San Andreas Fault, is studied for m a n y years by geodetic techniques (SLR, VLBI, GPS). The AMO-2 model predicts a rate between Quincy and Mt. Peak of - 5 4 r a m / y r . The recent NUVEL-1 model proposes a slower relative motion of - 4 5 m m / y r . The SL7.1 solution based on 8 years of data (1981-1988) provides a value of - 2 6 + 1 m m / y r , in good agreement with VLBI results over the same period ( - 2 8 m m / y r , [25]). The difference between the geodetic estimates and the geological values, currently called the "San Andreas discrepancy", is not yet completely understood (e.g. [26]). A recent analysis based on L A G E O S data [27] provides a rate of - 3 0 + 3 m m / y r . The results of the present study give a rate somewhat higher than previous studies: all solutions we obtained have provided a remarkably stable result of - 33-34 _+ 1 m m / y r . Intermediate solutions based successively on 3 years and 4 years of data have given the same value as with 5 years of data. If the value of - 3 3 - 3 4 m m / y r is confirmed, it reduces significantly the difference with NUVEL-1 to only 11-12 m m / y r . Note that the present estimate agrees with ground-based geodesy results ( - 34 _ 3 m m / y r ; see [26]). Simosato (7838) has been nominally placed on the Eurasian plate. However, Simosato, close to the subduction of the Philippine plate under Eurasia, is located in a region subject to intense collisional deformation. Its motion is expected to differ from that of the Eurasian plate and this is indeed observed. Relative motion with the European stations is of the order of - - 3 0
R. BIANCALE ET AL. +10 QUINCY(7109)
co
o
(..9
-10
IX -I0
0
+10
NUVEL-1(cm/yr) Fig. 4. LAGEOS solution (solution c) for the relative horizontal velocity (in c m / y r ) between Quincy (7109) and all other stations as a function of the NUVEL-1 predictions.
m m / y r except for Wettzel ( - 1 5 m m / y r ) , in accordance with the SL7.1 and the D G F I 8 9 L 0 3 solutions. Arequipa (7907) is located close to the subduction of the Nazca plate under the South American plate, where complex collision processes take place. Looking at Table 3, we note that relative motion of Arequipa with the stations on the North American plate is of opposite sign of the NUVEL-1 rates, except for Greenbelt. A similar behaviour is observed with the European stations (solution c). In the latter case, our results disagree with the SL7.1 and D G F I 8 9 L 0 3 solutions. In view of the large RMS reported for Arequipa in monthly arcs (Fig. 2), we think that the solution for Arequipa is noisy and unstable. Accurate motion of Arequipa will be obtained with longer data span. Nevertheless, the results reported here support the conclusion that Arequipa is subject to regional deformation and does not move like the South American plate. Figures 4 and 5 show the observed rate of change in spherical distance between Quincy and Mt. Peak and all other stations as a function of NUVEL-1 predictions. Departures from the model are clearly observed. 5.2.3. Intra plate deformations Table 4 presents the relative motion between stations located on the same plate (solution c).
TECTONIC
PLATE MOTIONS
DERIVED
391
FROM LAGEOS
+10 Mt PEAK (7110)
=,.,
o
0
{.9
5
-10 -10
+10
NOVEL-1(em/yr) Fig. 5. LAGEOS solution (solution c) for the relative horizontal velocity (in c m / y r ) between Mt. Peak (7110) and all other stations as a function of the NUVEL-1 predictions.
zel supports the conclusion that Matera is located on the African plate. The anomalous behaviour of Graz mentioned above in discussing interplate motions is no more apparent here and remains to be confirmed. On the North American plate, relative motions between Greenbelt, McDonald and Mazatlan are also slow of - 1-3 m m / y r , i.e. of the same order as associated uncertainties. A larger rate is observed between Quincy and Greenbelt, as expected if Quincy is subject to regional deformation. As for the Eurasian plate, the results indicate that no significant intraplate deformations occur inside the North American plate. However, given the present level of accuracy of the solutions, it is not worthwhile to discuss any further individual rates.
6. Comparison with other solutions Relative motion between European stations are slow, of a few m m / y r at most, in particular between RGO, Grasse and Wettzel. The relative motion between Matera and RGO, Grasse, WettTABLE 4 Relative horizontal velocities (in m m / y r ) determined in the global LAGEOS solution (c) over the 5-year period between pairs of stations belonging to the same plate. Also given the NUVEL-1 values as well as the SL7.1 and DGFI89L03 values (also in m m / y r ) SL7.1
DGFI89L03
(c)
NUVEL-1
E URA 7840-7839 7840-7939 7840-7834 7840-7835 7839-7939 7839-7835 7939-7835
2_+2 -8-+2 -3_+2 --1_+5 --4_+3 -3-+5 -11+4
-2+2 -7_+2 -7_+2 -5+2 -
-5+1 -7+1 4_+1 3_+1 -5+1 0+1 --6-+1
0 0/-8.0 0 0 0 0 0/-8
NOAM 7105-7086 7105-7109 7105-7122 7086-7109 7086-7122 7109-7122
8 5=2 4+-2 0-+2 5_+ 2 -7-+3 5 _+2
3 -+ 2 5-+2 1_+5 - 2-+4 0_+4 - 1 +_2
0 0 0 0 0 0
PCFC 7110-7210
4-+2
8+_1
0
EURA = Eurasian; Pacific.
11+1 N O A M = North
American;
PCFC =
A few groups, members of the IERS, are currently analysing L A G E O S data to provide regularly, UT1 and polar motion series. SLR station velocities are also computed but most of these solutions remain unpublished and can hardly be used for comparison. Fortunately this is not the case for two recent solutions available in the literature [5,6]. The DGFI89L03 solution [6] is based on five years of L A G E O S data (1983-1987). The method applied is quite similar to the one we develop here although the force model is somewhat different: monthly orbital arcs are computed and monthly normal equations systems are formed. The cumulated normal matrix over the five-year period is then inverted to provide in addition to orbital parameters, solutions for E P R at five-day intervals, station coordinates at a fixed epoch and horizontal station motions. The D G F I 8 9 L 0 3 solution assumes, as we do, that stations move linearly with time over the time interval of analysis. The advantage of this approach is that the solution is derived in a consistent reference system. The SL7.1 solution [6] is based on a longer time series. The total period considered ranges from 1979 to 1988, with stations like Greenbelt and Arequipa having regularly observed over the 10year interval. For the other stations, the time interval of data range from 5 to 8 years. However,
392
R. B I A N C A L E
before 1984, the number of observing stations is poor while increasing regularly with time [6]. The approach adopted to derive the SL7.1 solution differs somewhat from the one adopted here. Monthly normal equations systems are also first computed, but then combined into groups of three months and inverted to provide quarterly solutions for orbital parameters, Earth rotation parameters and average stations coordinates. These quarterly solutions cannot be used directly to study the time dependence of station coordinates. Indeed discontinuities arise from one solution to another due to the use of inhomogeneous reference frames (the terrestrial reference frame used in each quarterly solution varies with time as a result of the variable participation of sites modifying the network geometry). These discontinuities can be
sollliions
Lageos
•
~
2
=
-
S
L
N~Lvel 7
.
i
.IL
i(l-:
1 r
[
cm/yr
DGFI89L03
Z[I :i
ET AL.
removed by transforming the quarterly solutions in a common reference frame through rigid body transformations. In the SL7.1 solution, the common reference frame is obtained from solutions based on multi-year data intervals. Geodesic rates between couples of stations are then derived from the time evolution of transformed quarterly solutions and used to compute, with a least square procedure, absolute station velocities. Relative velocities between pairs of stations for the DGFI89L03 and SL7.1 solutions have been presented in Table 3. We have computed the differences in relative velocities between the NUVEL-1 model and the three L A G E O S solutions, SL7.1, DGFI89L03 and that of the present study ( G R G S solution). These differences are presented in histogram form in Fig. 6 (only for pairs of stations located on different plates). For the three solutions, most differences range from - 1 0 to + 1 0 m m / y r . The G R G S - N U V E L - 1 differences are slightly more dispersed than the SL7.1-NUVEL-1 differences, probably a result of the shorter time span of data used in our solution. Figure 7 presents histograms of the differences between: (a) SL7.1 and G R G S solutions; (b) DGFI89L03 and G R G S solutions; and (c) SL7.1 and DGFI89L03 solutions. We note again that most differences range between - 1 0 and + 1 0 m m / y r , i.e. like with the geological model. This range likely reflects the present level of precision of satellite solutions.
3
7. Conclusions
i0
F
T --3
--1
1
'~
('[11 / \'Y
:?II
~RGS
: 5
5
C
5
3
I
1
:3
5
/
(,]i11 / VY Fig. 6. Histograms of the differences in relative velocity between: (a) SL7.1 solution and NUVEE-1; (b) DGFI89L03 solution and NUVEE-1; and (c) GRGS solution and NUVEL1. Only pairs of stations located on different plates are considered.
In the present study, we have determined from five years of L A G E O S data, horizontal motions at fourteen laser station sites. These motions are compatible, within a few m m / y r , with those predicted by geological models for stations located far enough from plate boundaries. For stations close to the boundaries, some discrepancies are clearly seen between the L A G E O S solution and model predictions. The main results of this study can be summarized as follows: (1) The motion of Matera (Italy) agrees well with the geological model predictions if the station is assumed to lie on the African plate. (2) Simosato (Japan), nominally assumed on the Eurasian plate, presents a relative motion with the European stations of the order of - 30 m m / y r .
TECTONIC
PLATE
MOTIONS
DERIVED
Differerwes Lageos
FROM
between
solutions
E i.-,--
,=
l
-
=
I a
10~: -5
393
LAGEOS
-3
-1
1
3
cm/yr
5
3(I _ 2.., -
(5) Interplate motions between stations located on stable plate interiors agree with the NUVEL-1 model within a few m m / y r . (6) No significant intraplate motions are evidenced. If these exist, they amount less than 5 mm/yr. (7) The present solution based on five years of data agrees reasonably well with two recently published solutions, SL7.1 and DGFI89L03. Most differences between these three solutions fall within - 1 0 and + 10 m m / y r . The SL7.1 solution presents nevertheless less dispersion, probably a result of the use of a longer time span of data.
..--.
Acknowledgments lOz z
•-,t
[1 -=
-5
-3
-I
1
3
5
('rn/v?" 30 _ z
We thank the D G F I for having kindly provided us LAGEOS normal points. We thank M. Feissel and C. Boucher for helpful discussions and for having prepared the homogeneous time series of Earth Rotation parameters and BTS station coordinates.
z
1
References
5
-3
1
1
3
5
(°tl)/)~i" Fig. 7. Histograms of the differences in relative velocity between: (a) SL7.1 solution and GRGS solution; (h) DGFI89L03 solution and GRGS solution; and (c) SL7.1 solution and DGFI89L03 solution. Only pairs of stations located on different plates are considered.
(3) The absolute motions of Quincy and Mt. Peak (California) depart significantly from model predictions. The rate of change of the Quincy-Mt. Peak baseline is estimated to - 3 3 + 3 m m / y r over the period 1984-1988. This value has been found very stable in the various solutions we obt a i n e d a n d t h u s is b e l i e v e d to b e q u i t e r e l i a b l e . I t reduced the "San Andreas discrepancy" to -12 ram/yr. (4) T h e m o t i o n o f A r e q u i p a ( P e r u ) d e p a r t s significantly from the motion of the South American p l a t e . T h e s o l u t i o n f o r A r e q u i p a is h o w e v e r u n stable due to the low quality of the laser data at t h i s s t a t i o n . T h i s d r a w b a c k will b e o v e r c o m e b y analysing a longer time span of observations.
1 X. Le Pichon, Sea-floor spreading and continental drift, J. Geophys. Res. 73, 3661-3697, 1968. 2 J.B. Minster and T.H. Jordan, Present-day plate motions, J. Geophys. Res. 83, 5331-5354, 1978. 3 D.C. Demets, R.G. Gordon, D.F. Argus and S. Stein, Current plate motions, Geophys. J. 101,425-478, 1990. 4 D.C. Christodoulidis, D.E. Smith, R. Kolenkiewicz, S.M. Klosko, M.H. Torrence and P.J. Dunn, Observing tectonic plate motions and deformations from satellite Laser ranging, J. Geophys. Res. 90, 9249-9263, 1985. 5 Ch. Reigber, W. Ellmer, H. Miiller, E. Geiss, P. Schwintzer and F.H. Massman, Plate motions derived from the DGFI89L03 solution, in: Global and Regional Geodynamics, Vyskocil, Reigber and Cross, eds., Springer, New York, N.Y., 1990. 6 D.E. Smith, R. Kolokienwicz, P.J. Dunn, M.H. Torrence, J.W. Robbins, S.M. Klosko, R.G. Williamson, E.C. Pavlis, N.B. Douglas and S.K. Fricke, Tectonic motion and deformation from satellite Laser ranging to LAGEOS, J. Geophys. Res., in press, 1990. 7 J.B. Minster, W. Prescott and L. Royden, Plate motion and deformation, Coolfont workshop, Coolfont, Vi, 1989. 8 M. Dorrer, Le systrme DORIS, Cours international de Technologie Spatiale, Toulouse, 1989. 9 M. Lefebvre, DORIS system, CSTG Bull. 3, DGFI, Munich, 1989. 10 J.G. Marsh et al., The GEM-T2 gravitational model, NASA Tech. Memo., 100746, 99 pp., 1989. 11 G.L. Stephens, G.C. Campbell and T.H. Vonder Haar,
394
12 13
14
15 16
17 18 19 20
R. BIANCALE ET AL. Earth radiation budgets, J. Geophys. Res. 86, 9739-9760, 1981. L. Jacchia, Thermospheric temperature, density and composition: new models, SAO special report 375, 1977. F. Barlier, C. Berger, J.L. Falin, G. Kocharts and G. Thuillier, A thermospheric model based on satellite drag data, Ann. Geophys. 34, 9-24, 1978. G. Afonso, F. Barlier, C. Berger, F. Mignard and J.J. Walch, Reassessment of the charge and neutral drag of LAGEOS and its geophysical interpretation, J. Geophys. Res. 90, 9381-9398, 1985. D.P. Rubincam, On the secular decrease in the semimajor axis of LAGEOS's orbit, Celest. Mech. 26, 361-382, 1982. D.P. Rubincam, LAGEOS orbit decay due to infrared radiation from Earth, J. Geophys. Res. 92, 1287-1294, 1987. D.P. Rubincam, Yarkovsky thermal drag on LAGEOS, J. Geophys. Res. 93, 13805-13810, 1988. M E R I T S T A N D A R D S , U.S. Naval Observatory, Washington, D.C., 1985. E.W. Schwiderski, Ocean tides, Part 1: Global ocean tidal equations, Mar. Geod. 3, 161-207, 1980. C. Destrigneville, Effets de charge de la marre oc~anique, Mrmorie de diplrme d'ingrnieur g6ophysicien, Universit6 de Strasbourg, 1987.
21 J.M. Wahr, The forced nutations of an elliptical, rotating, elastic and oceanless earth, Geophys. J. 64, 705-727, 1981. 22 J.H. Lieske, T. Lederle, W. Fricke and B. Morando, Expressions for the Precession quantities based upon the IAU (1976) system of astronomical constants, Astron. Astrophys. 58, 1-16, 1977. 23 M. Feissel and B. Guinot, A homogeneous series of the Earth Rotation Parameters based on all observing techniques, 1962-1987. Annual Report of the BIH for 1987, D-79-84, Paris Observatory, 1988. 24 M. Feissel, Annual Report of the IERS for 1990, Paris Observatory, 1990. 25 R. Kolenkiewicz, M.H. Torrence, C. Ma and J.W. Ryan, Comparison of SLR and VLBI Geodesic rates, Proceedings of the 4th International Conference of the W E G E N E R M E D L A S project, University of Technology, Delft, 1990. 26 J.B. Minster and T.H. Jordan, Vector constraints on Western U.S. deformation from Space Geodesy, neotectonics and plate motions, J. Geophys, Res. 92, 4798-4804, 1987. 27 A. Stolz, M.A. Vincent, P.L. Bender, R.J. Earnes, M.M. Watkins and B.D. Tapley, Rate of change of the Quincy. Mt. Peak baseline from a translocation analysis of L A G E O S Laser Range data, Geophys. Res. Lett. 16, 539-543, 1989.