THE ESTIMATION OF550 km X 550 km MEANGRAVITY ANOMALIES

M. R. WILLIAMSON and E. M. GAPOSCHKIN

(NASA-CR-142297) THE ESTIMATION OF 550 km X N75-1909-550 km MEAN GRAVITY ANOMALIES (SmithsonianAstrophysical Observatory) 26 p HC $3.75

CSCL 08N UnclasG3/89 13601

Smithsonian Astrophysical ObservatorySPECIAL REPORT 363

https://ntrs.nasa.gov/search.jsp?R=19750011023 2020-04-30T17:53:08+00:00Z

Research in Space ScienceSAO Special Report No. 363

THE ESTIMATION OF 550 km X 550 km

MEAN GRAVITY ANOMALIES

M. R. Williamson and E. M. Gaposchkin

February 20, 1975

Smithsonian InstitutionAstrophysical Observatory

Cambridge, Massachusetts 02138

408-085

TABLE OF CONTENTS

Page

ABSTRACT................................... ... v

1 THE BLOCK COVARIANCE METHOD .................... 1

2 THE 10 X1 0 DATA ......... .......................... 3

3 THE BLOCK GRAVITY ANOMALY ESTIMATES ................ 5

4 REFERENCES... ......................... .. . . 19

FIGURES

1 Distribution of 10 X 10 mean surface-gravity data .............. 4

2 The block covariance function of unit gravity anomalies ........ 7

TABLES

1 Comparison of 10 X 1° mean gravity anomalies withDMAAC (1973) ........... .... .................... 3

2 The block covariance function of unit gravity anomalies ........ 8

3 The block covariance matrix ....................... * 9

4 Estimated block gravity anomalies referred to the 1967 system... 10

iii

ABSTRACT

The calculation of 550 km X 550 km mean gravity anomalies from 1° X 1" mean

free-air gravimetry data is discussed. The block estimate procedure developed by

Kaula is used. Estimates for 1452 of the 1654 blocks are obtained.

RESUME

Dans cet article on discute du calcul des anomalies de la gravite

moyenne sur 550 km x 550 km a partir de donnges de gravim6trie moyenne

sans air sur 1o x 10. On utilise le proced6 d'estimation de blocs d6ve-

lopp' par Kaula. On obtien des estimations pour 1452 des 1654 blocs.

KOHCHIEKT

06cyHaeT F BbuIYFtLeHMe cpe ,HMx rPpaBTaOHHbx aHOMa.EnH

550KM X 550KM, 1CXOZF X3 cpezHiX zaHHblX rpaBMToMeTpM CBB60HC

aTMoc epb 10 X 10. YnoTpe6nFreTc npouegypa oueHK 6 no.a pa3pa-

6OTaHHaH Kayna. HoinyMeHbl OeHKM nAJI 1452 x3 1654 6jOKOB.

THE ESTIMATION OF 550 km X 550 km

MEAN GRAVITY ANOMALIES

M. R. Williamson and E. M. Gaposchkin

1. THE BLOCK COVARIANCE METHOD

The objective is to obtain estimates of mean gravity anomalies for 550 km X 550 km

regions from an incomplete set of 10 X 10 mean free-air gravity anomalies. The esti-

mate procedure is based on the covariance analysis developed by Wiener (1966),

Kolmogoroff, and Kaula (1967). A description and evaluation of the procedure are

given in Gaposchkin (1973).

To obtain the mean gravity anomaly for a 550 km X 550 km block, estimates of all

110 km X 110 km unit mean gravity anomalies in the block are needed. For units

where measurements of 1 X 10 mean gravity anomalies are available, the unit mean

anomalies are taken to be the average of the 10 X 10 mean anomalies within the unit.

The other unit mean anomalies g are calculated from the measured unit anomalies f

in the same block by the equation

N

gi Kik fjk

Kjk= K(f, Tjk)

K is the intra-block covariance function of the unit anomalies f, and Tjk is the distance

between the jth and kth units. The covariance function is estimated from

This work was supported in part by Grant NGR 09-015-002 from the NationalAeronautics and Space Administration.

1

K(f, T7)= 1 E f fk ,jk jk

where the sum includes Njk pairs of measurements with

AT ATT-- < Tjk < T + -

The block anomalies are obtained by averaging the unit anomalies. The mean anomalies

for blocks that include no measured 10 X 10 mean anomalies cannot be estimated by this

procedure.

2

2. THE 10 X 10 DATA

We obtained four sets of 1l X 1l mean free-air gravity anomalies. A set of 29, 209

measured 10 X 10 means was obtained from the Defense Mapping Agency Aerospace

Center (DMAAC) (1973). A set of 1454 10 X 10 means for Australia was obtained from

Mather (1970). Two sets of 10 X 10 means were obtained from Talwani: 4250 10 X 10

means for North America and the North Atlantic (Talwani, Poppe, and Rabinowitz,

1972), and 3944 10 X 10 means for the Indian Ocean (Kahle and Talwani, 1973). The

sets of data were combined, the Mather and the Talwani data were used for regions

when available. The combined set has measured values for 31, 654 of the 64, 800 10 X 10

areas. Figure 1 is a map showing the distribution of the data.

The DMAAC data were compared with the other sets of data and with a previous

compilation by the Aeronautical Chart and Information Center (ACIC) (1971) at common

points. Table 1 shows the results of these comparisons.

Table 1. Comparison of 1° X 10 mean gravity anomalies with DMAAC (1973).

Number of Mean difference RMSData points compared (mgal) (mgal)

Australia 1364 1. 64 24. 16(Mather, 1970)

North America and 3613 -0.18 15.29the North Atlantic(Talwani et al., .1972)

Indian Ocean 2226 -1. 66 23.09(Kahle and Talwani,1973)

Worldwide 19, 164 -0. 23 16. 99

(ACIC, 1971)

3

z-~ _____ --~-- ---. ----------------- 41 g~P~ - ~----r

F-~~---~- --~--~2~2=-~--~ -- ----

i;F_5=-~ ~ ___-Bp "-'- .I ____ ~ _ g t--- ___~

._-1

_ I~_ I-~_,~ ~rlT~__ I..r~~I __

_-~-~--' ----- _ :_1- _ r-_;~~_-~_~ -"-

IP - _-~:1

Ir-~ I . _L_=:r =, ~~------~1~

_ I_ _ ~___

'----:_ ..- =-~-1~_

_

-_-_f

Figure i. Distribution of 1" X 1" mean surface-gravity data.

3. THE BLOCK GRAVITY ANOMALY ESTIMATES

The estimates were obtained with the procedure described in Section 1 by using

the composite data set described in Section 2.

The reference ellipsoid used in the calculation is the Geodetic Reference System

of 1967 (International Union of Geodesy and Geophysics, 1967). A reference ellipsoid

is determined by the geocentric gravitational constant GM, the rotation rate of the

earth w, the semimajor axis of the earth a, and the dynamical form factor J 2 . The

1967 system is defined by the ellipsoid

20 3 -2GM = 3. 98603 X 10 cm sec ,

-5 -1w = 7. 292 115 1467 X 10- 5 rad sec - 1

a = 6. 378160 X 108 cm ,

J2 = 0.001 0827

From these quantities, the flattening f is determined to be

f= 1/298. 247 167 427

A formula for the reference gravity y as a function of latitude 4 is

1l967 = 978031. 85 (1 + 0.005 278 895 sin2 4 + 0.000 023 462 sin4 ) mgal

This formula has an accuracy of 0. 004 mgal. Another formula, which has an accuracy

of 0. 1 mgal, is

y 67 = 978031. 846 (1 + 0. 005 302 86 sin2 O + 5.82 X 10 - 6 sin2 2 ) .

The ACIC data were compiled using this reference system and the International Gravity

Standardization Network, 1971 (Morelli and Gantar, 1974). The other data, however,

are referred to the 1930 international gravity system and the Potsdam Network. To

5

convert these data to the 1967 system, a correction A must be added to the anomalies.

The 1930 international gravity system is defined by the reference gravity

Y1930 = 978049.0 (1 + 0.005 2884 sin 2 + 5. 9X 10- 6 sin2 2 ) mgal

This reference gravity corresponds to an ellipsoid defined by (Heiskanen and Moritz,1967)

20 3 -2GM = 3. 986 329 X 10 cm sec - 2

W = 0.729 211 510 X 10- 4 rad sec -1

a = 6. 378 388 X 108 cm

f = 1/297 .

With the inclusion of the Potsdam correction of 14 mgal, the correction A is

A= 1 9 3 0 -Y 19 6 7 - 14

To an accuracy of 0. 1 mgal

A= 3. 14 - 13. 58 sin2 + 0.02 sin2 24 mgal

This formula was used to convert the 10 X 10 mean anomalies to the 1967 system. Ifthe anomalies are to be combined with satellite data, the effect of the atmosphere mustbe included. The surface gravity given by the anomalies is increased by 0. 87 mgal toobtain the total gravitational force that influences satellite motion. This correction hasnot been made to the anomalies given in this report.

The covariance function is given in Figure 2 and Table 2. The covariance matrixis given in Table 3. The composite set of 31, 654 10 X 10 mean anomalies provided23, 777 of the 41, 350 unit mean anomalies. From these unit mean anomalies, the esti-mate procedure provided 1452 of the 1654 block anomalies. The block anomalies referredto the 1967 system are given in Table 4. A punched card deck can be provided onrequest.

6

408-085

1000 I I

800

N 600

E

400

200 -

I I I I I II 2 3 4 5 6 7

DEGREES

Figure 2. The block covariance function of unit gravity anomalies.

We compared these block anomalies with 1183 block anomalies calculated previously

(Gaposchkin, 1973). The mean difference is 0. 6 mgal and the RMVIS difference is

10 mgal.

7

Table 2. The block covariance function of unit gravity anomalies.

Average angular Covariance functiondistance (mgal2 )

00 948

0.29 1614

0.94 607

1.21 457

1.79 377

2.18 316

2.81 279

3.16 252

3.69 243

4.20 229

4.77 182

5.22 161

5.67 223

6.20 118

6.69 201

8

Table 3. The block covariance matrix.

1 2 3 4 5 6 7 8 9 10 11 12 13

1 9. 4826E+02 5.7175E+02 3.4442E+02 2.6393E+02 2.3447E+02 5.7175E+02 4.2864E+02 3. 1291E+02 2.5177E+02 2.3121E+02 3.4442E+02 3. 1291E02 2.7692E02

2 5.7175E+02 9.4826E+02 5.7175E+02 3.444E+02 2.639344E+02 4.2863E+02 57175E+02 4.2863E+02 3.1291E+02 2. 5177E+02 3. 1291E+02 3.4442E02 3.1291E+02

3 3.4442E+02 5.7175E+02 9.4826E+02 5.7175E+02 3.4442E+02 3. 1291E+02 4.2863E+02 5. 7175E+02 4.2863E+02 3. 1291E+02 2.7692E+02 3. 1291E+02 3. 4442E+02

4 2.6393E+02 3.4442E+02 5.7175E+02 9.4826E+02 5.7175E+02 2.5177E+02 3.1291E+02 4.2863E+02 5.7175E+02 4.2863E+02 2.4411E+02 2.7692E+02 3. 1291E+02

5 2.3447E+02 2.6393E+02 3.4442E+02 5.7175E+02 9.4826E+02 2.3121E+02 2.5177E+02 3. 1291E+02 4.2863E+02 5.7175E+02 2.0662E+02 2.4411E+02 2.7692E+02

6 5.7175E+02 4.2863E+02 3. 1291E+02 2. 5177E+02 2.3121E+02 9.4826E+02 5.7175E+02 3.4442E+02 2.6393E+02 2. 3447E+02 5.7175E+02 4.2863E+02 3. 1291E+02

7 4.2863E+02 5.7175E+02 4.286.3E+02 3. 1291E+02 2.5177E+02 5.7175E+02 9.4826E+02 5.7175E+02 3.4442E+02 2.6393E+02 4.2863E+02 5.7175E+02 4.2863E+02

8 3.1291E+02 4.2863E+02 5.7175E+02 4.2863E+02 3.1291E+02 3.4442E+02 5.7175E+02 9.4826E+02 5.7175E+02 3.4442E+02 3. 1291E+02 4.2863E+02 5.7175E+02

9 2.5177E+02 3.1291E+02 4.2863E+02 5.7175E+02 4.2863E+02 2.6393E+02 3.4442E+02 5.7175E+02 9.4826E+02 5.7175E+02 2.5177E+02 3.1291E+02 4.2863E+02

10 2.3121E+02 2.5177E+02 3. 1291E+02 4.2863E+02 5.7175E+02 2.3447E+02 2.6393E+02 3.4442E+02 5.7175E+02 9.4826E+02 2.3121E+02 2. 5177E+02 3. 1291E+02

11 3.4442E+02 3.1291E+02 2.7692E+02 2.4411E+02 2.0662E+02 5.7175E+02 4.2863E+02 3. 1291E+02 2.5177E+02 2.3121E+02 9.4826E+02 5.7175E+02 3.4442E+02

12 3.1291E+02 3.4442E+02 3. 1291E+02 2.7692E+02 2.4411E+02 4.2863E+02 5.7175E+02 4.2863E+02 3. 1291E+02 2.5177E+02 5.7175E+02 9.4826E+02 5.7175E+02

13 2.7692E+02 3. 1291E+02 3.4442E+02 3. 1291E+02 2.7692E+02 3. 1291E+02 4.2863E+02 5.7175E+02 4.2863E+02 3. 1291E+02 3.4442E+02 5.7175E+02 9.4826E+02

14 2.4411E+02 2.7692E+02 3. 1291E+02 3.4442E+02 3.1291E+02 2.5177E+02 3. 1291E+02 4.2863E+02 5.7175E+02 4.2863E+02 2.6393E+02 3.4442E+02 5.7175E+02

15 2.0662E+02 2.4411E+02 2.7692E+02 3.1291E+02 3.4442E+02 2.3121E+02 2.5177E+02 3. 1291E+02 4.2863E+02 5.7175E+02 2. 447E+02 2.6393E+02 3.4442E+02

16 2.6393E+02 2.5177E+02 2.4411E+02 2.2541E+02 1.7123E+02 3.4442E+02 3. 1291E+02 2.7692E+02 2.4411E+02 2.0662E+02 5.7175E+02 4.2863E+02 3.1291E+02

17 2.5177E+02 2.6393E+02 2.5177E+02 2.4411E+02 2.2541E+02 3.1291E+02 3.4442E+02 3.1291E+02 2.7692E+02 2.4411E+02 4.2863E+02 5.7175E+02 4.2863E+02

18 2.4411E+02 2.5177E+02 2.6393E+02 2.5177E+02 2.4411E+02 2.7692E+02 3.1291E+02 3.4442E+02 3.1291E+02 2.7692E+02 3. 1291E+02 4.2863E+02 5.7175E+02

19 2.2541E+02 2.4411E+02 2. 5177E+02 2.6393E+02 2.5177E+02 2.4411E+02 2.7692E+02 3. 1291E+02 3.4442E+02 3. 1291E+02 2.5177E+02 3. 1291E+02 4.2863E+02

20 1.7123E+02 2.2541E+02 2.4411E+02 2.5177E+02 2.6393E+02 2.0662E+02 2.4411E+02 2.7692E+02 3.1291E+02 3.4442E+02 2.3121E+02 2.5177E+02 3.1291E+02

21 2.3447E+02 2.3121E+02 2.0662E+02 1.7123E+02 2.2093E+02 2.6393E+02 2.5177E+02 2.4411E+02 2.2541E+02 1.7123E+02 3.4442E+02 3. 1291E+02 2.7692E+02

22 2.3121E+02 2.3447E+02 2.3121E+02 2.0662E+02 1.7123E+02 2.5177E+02 2.6393E+02 2.5177E+02 2.4411E+02 2.2541E+02 3. 1291E+02 3.4442E+02 3.1291E+02

23 2.0662E+02 2.3121E+02 2.3447E+02 2.3121E+02 2.0662E+02 2.4411E+02 2.5177E+02 2.6393E+02 2.5177E+02 2.4411E+02 2.7692E+02 3. 1291E+02 3.4442E+02

en 24 1.7123E+02 2.0662E+02 2.3121E+02 2.3447E+02 2.3121E+02 2.2541E+02 2.4411E+02 2.5177E+02 2.6393E+02 2.5177E+02 2.4411E+02 2.7692E+02 3.1291E+02

25 2.2093E+02 1.7123E+02 2.0662E+02 2.3121E+02 2.3447E+02 1.7123E+02 2.2541E+02 2.4411E+02 2.5177E+02 2.6393E+02 2.0662E+02 2.4411E+02 2.7692E+02

14 15 16 17 18 19 20 21 22 23 24 25

1 2.4411E+02 2.0662E+02 2.6393E+02 2.5177E+02 2.4411E+02 2.2541E+02 1.7123E+02 2.3447E+02 2.3121E+02 2.0662E+02 1.7123E+02 2.2093E+02

2 2.7692E+02 2.4411E+02 2.5177E+02 2.6393E+02 2.5177E+02 2.4411E+02 2.2541E+02 2.3121E+02 2.3447E+02 2.3121E+02 2.0662E+02 1.7123E+02

3 3.1291E+02 2.7692E+02 2.4411E+02 2.5177E+02 2.6393E+02 2.5177E+02 2.4411E+02 2.0662E+02 2.3121E+02 2.3447E+02 2.3121E+02 2.0662E+02

4 3.4442E+02 3.1291E+02 2.2541E+02 2.4411E+02 2.5177E+02 2.6393E+02 2.5177E+02 1.7123E+02 2.0662E+02 2.3121E+02 2.3447E+02 2.3121E+02

5 3. 1291E+02 3.4442E+02 1.7123E+02 2.2541E+02 2.4411E+02 2.5177$+02 2.6393E+02 2.2093E+02 1.7123E+02 2.0662E+02 2.3121E+02 2.3447E+02

6 2.5177E+02 2.3121E+02 3.4442E+02 3.1291E+02 2.7692E+02 2.4411E+02 2.0662E+02 2.6393E+02 2. 5177E+02 2.4411E+02 2.2541E+02 1.7123E+02

7 3.1291E+02 2.5177E+02 3.1291E+02 3.4442E+02 3.1291E+02 2.7692E+02 2.4411E+02 2.5177E+02 2.6393E+02 2.5177E+02 2.4411E+02 2.2541E+02

8 4.2863E+02 3.1291E+02 2.7692E+02 3.1291E+02 3.4442E+02 3.1291E+02 2.7692E+02 2.4411E+02 2.5177E+02 2.6393E+02 2.5177E+02 2.4411E+02

9 5.7175E+02 4.2863E+02 2.4411E+02 2.7692E+02 3.1291E+02 3.4442E+02 3.1291E+02 2.2541E+02 2.4411E+02 2.5177E+02 2.6393E+02 2.5177E+02

10 4.2863E+02 5.7175E+02 2.0662E+02 2.4411E+02 2.7692E+02 3.1291E+02 3.4442E+02 1.7123E+02 2.2541E+02 2.4411E+02 2.5177E+02 2.6393E+02

11 2.6393E+02 2.3447E+02 5.7175E+02 4.2863E+02 3.1291E+02 2.5177E+02 2.3121E+02 3.4442E+02 3.1291E+02 2.7692E+02 2.4411E+02 2.0662E+02

12 3.4442E+02 2.6393E+02 4.2863E+02 5.7175E+02 4.2863E+02 3. 1291E+02 2.5177E+02 3.1291E+02 3.4442E+02 3.1291E+02 2.7692E+02 2.4411E+02

13 5.7175E+02 3.4442E+02 3.1291E+02 4.2863E+02 5.7175E+02 4.2863E+02 3.1291E+02 2.7692E+02 3.1291E+02 3.4442E+02 3.1291E+02 2.7692E+02

14 9. 4826E+02 5.7175E+02 2.5177E+02 3. 1291,+02 4.2863E+02 5.7175E+02 4.2863E+02 2.4411E+02 2.7692E+02 3.1291E+02 3.4442E+02 3.1291E+02

15 5.7175E+02 9.4826E+02 2.3121E+02 2.5177E+02 3.1291E+02 4.2863E+02 5.7175E+02 2.0662E+02 2.4411E+02 2.7692E+02 3.1291E+02 3.4442E+02

16 2.5177E+02 2.3121E+02 9.4826E+02 5.7175E+02 3.4442E+02 2.6393E+02 2.3447E+02 5.7175E+02 4.2863E+02 3.1291E+02 2.5177E+02 2.3121E+02

17 3.1291E+02 2.5177E+02 5.7175E+02 9.4826E+02 5.7175E+02 3.4442E+02 2.6393E+02 4.2863E+02 5.7175E+02 4.2863E+02 3.1291E+02 2.5177E+02

18 4.2863E+02 3.1291E+02 3.4442E+02 5.7175E+02 9.4826E+02 5.7175E+02 3.4442E+02 3.1291E+02 4.2863E+02 5.7175E+02 4.2863E+02 3.1291E+02

19 5.7175E+02 4.2863E+02 2.6393E+02 3.4442E+02 5.7175E+02 9.4826E+02 5.7175E+02 2. 5177E+02 3.1291E+02 4.2863E+02 5.7175E+02 4.2863E+02

20 4.2863E+02 5.7175E+02 2.3447E+02 2.6393E+02 3.4442E+02 5.7175E+02 9.4826E+02 2.3121E+02 2.5177E+02 3.1291E+02 4.2863E+02 5.7175E+02

21 2.4411E+02 2.0662E+02 5.7175E+02 4.2863E+02 3.1291E+02 2.5177E+02 2.3121E+02 9.4826E+02 5.7175E+02 3.4442E+02 2.6393E+02 2.3447E+02

22 2.7692E+02 2.4411E+02 4.2863E+02 5.7175E+02 4.2863E+02 3.1291E+02 2.5177E+02 5.7175E+02 9.4826E+02 5.7175E+02 3.4442E+02 2.6393E+02

23 3.1291E+02 2.7692E+02 3.1291E+02 4.2863E+02 5.7175E+02 4.2863E+02 3.1291E+02 3.4442E+02 5.7175E+02 9.4826E+02 5.7175E+02 3.4442E+02

24 3.4442E+02 3.1291E+02 2.5177E+02 3.1291E+02 4.2863E+02 5.7175E+02 4.2863E+02 2.6393E+02 3.4442E+02 5.7175E+02 9.4826E+02 5.7175E+02

25 3.1291E+02 3.4442E+02 2.3121E+02 2.5177E+02 3.1291E+02 4.2863E+02 5.7175E+02 2.3447E+02 2.6393E+02 3.4442E+02 5.7175E+02 9.4826E+02

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4. REFERENCES

AERONAUTICAL CHART AND INFORMATION CENTER

1971. 10 X 10 Mean Free-Air Gravity Anomalies. ACIC Reference Publ. No. 29,

August, 324 pp.

DEFENSE MAPPING AGENCY AEROSPACE CENTER

1973. 10 X 10 Mean Free-Air Gravity Anomalies. DMAAC Reference Publ. No.

73-0002, December, 100 pp.

GAPOSCHKIN, E. M., Editor

1973. 1973 Smithsonian Standard Earth (III). Smithsonian Astrophys. Obs. Spec.

Rep. No. 353, 388 pp.

HEISKANEN, W. A., and MORITZ, H.

1967. Physical Geodesy. W. H. Freeman and Company, San Francisco, pp. 79-

80.

INTERNATIONAL UNION OF GEODESY AND GEOPHYSICS

1967. Geodetic Reference System 1967. International Association of Geodesy

Spec. Publ. No. 3, Bureau Central de l'Association Internationale de

Geodesie, 116 pp.

KAHLE, H. G., and TALWANI, M.

1973. Gravimetric Indian Ocean geoid. Zs. f. Geophys., vol. 39, pp. 167-187.

KAULA, W. M.

1967. Theory of statistical analysis of data distributed over a sphere. Rev.

Geophys., vol. 5, pp. 38-107.

MATHER, R.

1970. The Australian geodetic datum in earth space. UNISURV Rep. No. 19,

Univ. New South Wales, p. 80.

MORELLI, C., and GANTAR, C.

1974. The International Gravity Standardization Net 1971. International Union

of Geodesy and Geophysics, 200 pp.

TALWANI, M., POPPE, H. R., and RABINOWITZ, P. D.

1972. Gravimetrically determined geoid in the western North Atlantic. In Sea

Surface Topography from Space, vol. II, ed. by J. Apel, NOAA Tech.

Rep. ERL 228 - AOML 7-2, pp. 23-1 to 23-33.

19

WIENER, N.

1966. Extrapolation, Interpolation, and Smoothing of Stationary Time Serieswith Engineering Applications. The MIT Press, Cambridge, Mass.,160 pp.

20

BIOGRAPHICAL NOTES

M. R. WILLIAMSON graduated in applied mathematics from Brown University in

1963. She received an M. S. in 1965 and a Ph.D. in 1970 in physics from Tufts

University.

She has been with the Smithsonian Astrophysical Observatory since 1971 as a

mathematician in the Analytical Satellite Geophysics Group. She has developed pro-

grams for analyzing surface-gravity data and for studying the effects of solar radiation

pressure on satellite motion.

E. M. GAPOSCHKIN graduated in electrical engineering from Tufts University in

1957. He received a Degree of Numerical Analysis in 1959 from Cambridge University

in England and a Ph. D. in geophysics from Harvard University in 1969.

Dr. Gaposchkin joined the staff at Smithsonian Astrophysical Observatory in 1959,

where he has been programer and Division Chief of the Computations Division and

mathematician in the Research and Analysis Department. He has helped develop the

basic computer program used in all analyses of satellite motion.

Since 1968, Dr. Gaposchkin has been principal scientist of the Analytical Satellite

Geophysics Group. His main interests include satellite geodesy and geophysics and

applied mathematics. Dr. Gaposchkin spent the last year at Groupe de Recherches de

Geodesie Spatiale at the Observatoire de Meudon, Universite' de Paris.

NO TICE

This series of Special Reports was instituted under the supervisionof Dr. F. L. Whipple, Director of the Astrophysical Observatory of theSmithsonian Institution, shortly after the launching of the first artificialearth satellite on October 4, 1957. Contributions come from the Staffof the Observatory.

First issued to ensure the immediate dissemination of data for satel-lite tracking, the reports have continued to provide a rapid distributionof catalogs of satellite observations, orbital information, and prelimi-nary results of data analyses prior to formal publication in the appro-priate journals. The Reports are also used extensively for the rapidpublication of preliminary or special results in other fields of astro-physics.

The Reports are regularly distributed to all institutions partici-pating in the U. S. space research program and to individual scientistswho request them from the Publications Division, Distribution Section,Smithsonian Astrophysical Observatory, Cambridge, Massachusetts02138.