The seasonal deformation normal to the Earth's surface was calculated at stations involved or interested in very long baseline interferometry (VLBI) geodesy and at hypothetical sites in Australia and Brazil using global atmospheric pressure data, values for groundwater storage, and load Love numbers deduced from current Earth models. It was found that the annual range of deformation approached the centimeter level measuring potential of the VLBI technqiue at Greenbank, Haystack, and the Brazil site

Larden, D. R.

Stolz, A.

English

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CRUSTAL DEFORMATION AT VERY LONG BASELINE INTERFEROMETRY 
SITES DUE TO SEASONAL AIR-MASS AND GROUND WATER VARIATIONS 
A. Stolz’ and D. R. Larden 
School of Surveying, University of South New Wales 
ABSTRACT 
Rearrangements of the geographic distribution of air-mass and groundwater load and deform the 
earth’s crust. The seasonal deformation normal to the earth’s surface is calculated at stations in- 
volved or interested in VLBI geodesy and at hypothetical sites in Australia and Brazil using global 
atmospheric pressure data, values for groundwater storage, and load Love numbers deduced from 
current earth models. The annual range of deformation approaches the centimeter-level measuring 
potential of the very long baseline interferometry (VLBI) technique at Greenbank, Haystack, and 
the Brazil site. Baselines between stations of the European network and the northeastern part of 
the United States and between Brazil and Australia could be affected at this level of accuracy. 
IPresent address: University FAF at Munich, Astronomical and Physical Geodesy, Werner-Heisenberg-Weg 39, D8014 Neubiberg, 
West Germany. 
2Joint Institute for Laboratory Astrophysics, University of Colorado and National Bureau of Standards, Boulder, CO 80309, U.S.A. 
145 
https://ntrs.nasa.gov/search.jsp?R=19800020308 2020-03-21T17:49:44+00:00Z
146 RADIO INTERFEROMETRY 
INTRODUCTION 
The new space techniques of laser ranging to artificial satellites and the moon and VLBI have the 
potential of centimeter-level measurement accuracy. With these systems, the accuracy of determin- 
ing dynamic earth motions can be comparable to .the basic measurement accuracies obtainable 
(National Academy of Sciences, 1978). It is quite obvious that models for these motions will play 
an important role in the analysis of the data for positioning to centimeter-level accuracies. In this 
paper, we make a first attempt at one of the many modelling studies which need to be done. We 
estimate the crustal “breathing” that occurs when seasonal atmospheric pressure systems move 
across the globe and when there are seasonal variations in groundwater storage. Results are pre- 
sented for existing VLBI stations in Europe and the United States and hypothetical sites in Australia 
and Brazil. 
Baseline variations between groups of observatories are determined. The mathematical formulation 
of the problem, the data used, and the principal assumptions made are briefly reviewed. 
METHOD 
The problem of crustal deformation caused by the redistribution of surface masses is conveniently 
solved by means of the load Love numbers h: and 2; and the change in potential at the surface aris- 
ing from the variable load (Munk and MacDonald, 1960). The change in potential may be written as 
AU = ZAU, = 4nGr Z - 
n 2n+l 
where 
2n + 1 
9, = - 47r s 
q(4,kt) P,,(cos$> ds 
S 
(2) 
is the nth degree surface spherical harmonic representation of the variable surface load q (0,h;t) at 
a particular point on the globe, G is the gravitational constant, r is the earth’s radius, Pn (cos$) is 
the Legendre polynomial, and $ is the angle between radius vector at the computation point and 
the radius vector at the disturbing load. The corresponding crustal motions are 
where 0 is colatitude, X is east longitude, and g is local gravity. 
We applied equations (l), (2), and (3) to air-mass and groundwater data. The term groundwater re- 
fers to moisture stored on the earth’s land surface, and includes snow, variable water storage in the 
MOVEMENTS TERRESTRIAL AND CELESTIAL 147 
form of plant material, and water between the surface and the shallowest positioii of the watertable. 
The complete calculations are rather lengthy. Since the load Love numbers !Zk required for the 
problem are about two orders of the magnitude smaller than their hi counterparts and the radial 
crustal distortions are already small, we calculated only dr. 
DATA 
We used the January, April, July, and October averages of sea-level pressure compiled by Schutz and 
Gates (1971, 1972, 1973, 1974) which are given at gridpoints spaced every 4” of latitude and 5” of 
longitude over the entire earth. These data need to be adjusted back to station elevation before 
evaluation of AU,. Laplace’s formula was used to make the necessary adjustment. The ground- 
water calculations are based on van Hylckama’s (1956) monthly compilations for 10” X 10” areas. 
We have taken his January, April, July, and October volumes and divided these by the area of the 
corresponding compartment to yield surface loads. Data beyond 70”s does not appear and have 
been ignored. Dahlens’s (1976) load Love numbers for earth model 1066 A were preferred for no 
special reason. 
RESULTS 
The calculation for the radial deformations due to atmospheric loading and groundwater have been 
published separately by Stolz and Larden (1979) and Larden (1980),* respectively, and are depicted 
in contour form on maps for January, April, July, and October. The crustal motion attributable to 
the atmosphere approaches significance over parts of Asia, in Greenland, and in Antarctica. It is 
well below 1 cm in other parts of the globe. The deformations due to groundwater variations are 
also small and reach 1 cm only over the Himalayas and the northern United States. For this study, 
we have combined the results of Stolz and Larden (1979) and Larden (1980) to produce the ampli- 
tude and phase of the annual radial deformation (the annual term of deformation at a particular 
location is A cos (o-phase), where A is the amplitude and @ is the sun’s longitude measured from 
the beginning of the year) at sites which are actively involved or are interested in VLBI experiments. 
The horizontal gradients of the deformations over Europe and parts of the United States are small. 
We have averaged the distortions for these regions (table 1). Thus, Owens Valley and Goldstone be- 
come SW U.S. (37”N, 246”E), Ft. Davis and Richmond become SE U.S. (30”N, 270”E), Haystack 
and Greenbank become NE U.S. (45”N, 280”E), and stations in Spain, England, Holland, Germany, 
Italy, Sweden, Poland, Finland, and Crimea (U.S.S.R.) become Europe (50”N, 1O”E). The results 
are plotted in figure 1. The vertical motions at Greenbank, Haystack, and Brazil have an annual 
range of roughly 1 cm. Since the VLBI technique measures baselines and it is possible that the mo- 
tions at two sites compound to produce bigger motions, we studied the baselines listed in table 2. 
Only the baselines Europe-NE U.S. (a) and Brazil-Australia (c) (an unlikely possibility because the 
sites are separated by nearly 180” in longitude) vary by approximately 1 cm (figure 2). 
*Larden, D. R., Ph.D. Thesis, University of New South Wales, Sydney, N.S.W., Australia, 1980. 
148 RADIO LNTERFEROMETRY 
Table 1 
Radial Deformation 
I Amplitude, Phase, mm deg. 
Europe 
Australia 
SW U.S. 
SE U.S. 
NE U.S. 
Brazil 
3.1 233 (a) 
1.7 19 (b) 
2.4 266 (c) 
1.9 260 (d) 
5.8 243 (e) 
4.5 282 (0 
J F MAMJJASONDJ 
Figure 1. Radial deformations for sites located in: (a) Europe; 
(b) Australia; (c) SW U.S.; (d) SE U.S.; (e) NE U.S.; and (f) Brazil. 
MOVEMENTS TERRESTRIAL AND CELESTIAL 149 
Table 2 
Baseline Variations 
Amplitude, 
mm 
(a) Europe, NE U.S. 4.2 
NE U.S., SE U.S. 0.9 
SE U.S., SW U.S. 0.8 
(b) SE U.S., Brazil 3.0 
(c) Brazil, Australia 4.2 
4 
2 
0 
-2 
E 
E -4 
j 
JFMAMJJASONDJ 
Figure 2. Baseline variations between: (a) Europe and NE U.S., 
(b) SE U.S. and Brazil; and (c) Brazil and Australia. 
150 RADIO INTERFEROMETRY 
DISCUSSIONS 
When performing the deformation calculations, we need to allow for changes in sea level produced 
by the response of the oceans to the atmospheric pressure variations and the interchange of water 
between land and oceans, and atmosphere and oceans. The inverted barometer rule states that for 
every millibar of atmospheric pressure at a particular place over and above the mean pressure over 
the entire ocean surface the sea surface is locally depressed by 1 cm. This rule is normally invoked 
to account for the response of the oceans. This introduces a number of problems. The two main 
ones are: (1) oceanic mass conservation is implied, which is impossible if we also wish to consider 
the interchange of water between the constituent parts of the earth; and (2) we end up with a sea 
surface which is not quite an equipotential. Fortunately, their effect on our results is small (Stolz 
and Larden, 1979). Data for sea-level variations caused by the exchange of water between land and 
oceans and atmosphere and oceans are too inaccurate at present to make a reliable estimate of the 
effect on our results. Larden (1980), op. cit.) has estimated the contribution by assuming that the 
moisture which is not in the atmosphere or on land during any season is in the oceans. Our results 
change at most by 1 mm. 
Another difficulty, concerning the zero degree load Love numbers, arises from the manner in which 
we have produced the results presented here. The zero degree load Love numbers vanish if mass is 
conserved (Rochester and Smylie, 1974) but not if the effect of air mass and groundwater is calcu- 
lated separately as we have done. Thus, our results contain a zero degree contribution which should 
not be there. Larden (1980) has considered this problem and finds the results to be in error by 
roughly 10 percent. This clearly does not affect the conclusion we may draw from the calculations; 
that is, the general seasonal variations in the continental and intercontinental baselines are small. 
Accordingly, until considerable improvement is achieved in instrument stabilities and corrections 
for ionospheric and tropospheric effects, it does not seem necessary to adjust baseline determina- 
tions for seasonal variations, and even then, these variations will only be marginally significant. 
ACKNOWLEDGMENT 
This paper was written while the first author was the holder of an Alexander von Humboldt Re- 
search Fellowship. The second author is supported by a Fulbright Travel Award. 
REFERENCES 
Dahlen, F. A., The Passive Influence of the Oceans upon the Rotation of the Earth, Geophys. J. R. 
Astr. Sot., 46,363406, 1976. - 
Munk, W. H., and G. J. F. MacDonald, The Rotation of the Earth, Cambridge University Press, 
London, 1960. 
National Academy of Sciences, Geodesy: Trends and Prospects, Washington, D.C., 1978. 
MOVEMENTS TERRESTRIAL ANJI CELESTIAL 151 
Rochester, M. G., and D. E. Smylie, On Changes in the Trace of the Earth’s Inertia Tensor, J- 
Geophys. Res., 2,4948-4951, 1974. 
Schutz, C., and W. Gates, Global Climatic Data for Surface, 800 mb, 400 mb: January, ARPA 
Rept. R-915-ARPA, Rand Corporation, Santa Monica, 197 1. 
Schutz, C. and W. Gates, Global Climatic Data for Surface, 800 mb, 400 mb: July, ARPA Rept. 
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Rept. R-1425-ARPA, Rand Corporation, Santa Monica 1974. 
Stolz, A., and D. R. Larden, Seasonal Displacement and Deformation of the Earth by the Atmos- 
phere, J. Geophys. Res., in press, 1979. 
van Hylckama, T. E. A., The Water Balance of the Earth, Drexel Inst. of Technol., Publ. in Clima- 
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Crustal deformation at very long baseline interferometry sites due to seasonal air-mass and ground water variations

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