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Produced by the NASA Center for Aerospace Information (CASI)
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-.AS

Technical Memorandum 85078

Y

Geodynam ics Branch 

x Research Report - 1982

r (JlAl-°TH-8507$1 GBODXN,bICS BRANCH BESEAECH N84^-11527 

REPORT, 1582 (SA A) 105 p HC A05/MF A01

CSCI 08G

Unclas

G5/42 42435 

Edited by W D. Kahn and S. C. Cohen

C 20

SEPTEMBER 1993 Nov 38^ ON

RECEIV ED

,;;

NASA STI FAClUTY

C.r ACCESS DEPT= 419q

National Aeronautics and

ar,;e Administration

Goddard Space Flight Center

Greenbelt, Maryland 20771

-. ^-
GEODYNAMICS BRANCH RESEARCH REPORT — 1982

Edited by

W. D. Kahn

S. C. Cohen

September 1983

• 

GODDARD SPACE FLIGHT CENTER

Greenbelt, Maryland 20771

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GEODYNAMICS BRANCH

CODE 921

LIST OF RESEARCHERS

David E. Smith, Branch Head

Ph.D., 1966, University of London, Satellite Geodesy

Beatrice S. Boccucei, Secretary

Demosthenes C. ChristodouZidis, Ph.D. 1976, Ohio State University,

Satellite Geodesy

Steven C. Cohen, Ph.D. 1973, University of Maryland, Physics

Theodore L. Felsentreger, M.A., 1961, University of Maryland, Mathematics

Werner D. Kahn, M.S., 1955, University of Illinois, Mathematics

Ronald Kolenkiewicz, M.S., 1965, Catholic University , Space Science and

Applied Physics

William B. KrabiZZ, B.S., 1968, Salisbury State College, Mathematics

Francis J. Lerch, M.S., 1950, University of Delaware, Mathematics

Han-Shou Liu. Ph.D.. 1963, Cornell University, Physics

James G. Marsh, M.S., 1963, West Virginia University, Physics

David C. McAdoo, Ph.D., 1976, Cornell University, Geophysics

Patrick H. McClain, M.S., 1959, Howard University, Mathematics

Barbara H. Putney, B.S., 1960, Brooklyn College, Mathematics

David P. Rubincam, Ph.D., 1973, University of Maryland, Physics

Braulio V. Sanchez, Ph.D., 1975, University of Texas, Aerospace Engineering

Frederick G. Schamann, B.S., 1967, City College of New York, Mathematics

Jean E. Welker, M.A., 1980, University of Maryland, Physical Geography/

p History

George H. Wyatt, B.S., 1962, North Carolina S: ate College, Mathematics

Resident Research Associates

Benjamin F. Chao, A.D., 1981, University of California (San Diego), Earth

.Sciences

Richard S. Gross, Zn-D., 1982, University of Colorado, Geophysics
CONTENTS

Page

LIST OF RESEARCHERS- - w - - - - - - - - - - - - - ii

INTRODUCTION - - _ - - - - - - - - - - - - - _ - _ - - - - - - - v

CHAPTER 1. CRUSTAL MOVEMENTS - - - - - - - - - - - - - - - - 1-1

;(Overview)

A. GLOBAL GEOTECTONICS FROM SATELLITE RANGING

by D.C. Christodoulidis and D.E. Smith - - - - - - 1-2

B. CRUSTAL DEFORMATION DURING THE EARTHQUAKE CYCLE

by S.C. Cohere - - - - - - - - - - - - - - - - -- 1-6

C. GRAVITY SLIDING: CRUSTAL DEFORMATION AND SEISMOTECTONIC

BLOCK MOVEMENTS IN SIBERIA by H.S. Liu - - - -- - 1-10

D. THE VERIFICATION OF THE LURE SYSTEM AS A SATELLITE LASER

RANGING STATION by R. Kolenkiewic? - - - - - - - - - - 1-13

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CHAPTER 2. GLOBAL EARTH DYNAMICS - - - - - - - - - - - 2-1

(Overview)

A. POST GLACIAL REBOUND OBSERVED BY LAGEOS AND THE EFFECTIVE

VISCOSITY OF THE LOWER MANTLE by D.P. Rubincam 2-2

B. DYNAMICS OF THE EARTH'S POLAR MOTION

by B.F. Chao _ - -_ - - - - - - - - - - - - - 2-5

C. POLAR MOTION by R.S. Gross--------------- -2-9

D. INFORMATION THEORY LATERAL DENSITY DISTRIBUTION

by D.P. Rubincam - - - - - - - - - - ------- -2-14

E. ATMOSPHERICALLY INDUCED VARIATIONS IN THE LENGTH-OF-DAY

DERIVED FROM LAGEOS by D.E. Smith, et ai. - - - - - - - - 2-18

CHAPTER 3. GRAVITY FIELD MODEL DErr-LOPMENT- - - - - - - - - 3-1

(Overview)

A. GRAVITY MODEL REFINEMENT FROM LAGEOS by F.J. Lerch - - - -3-2 

B. LAGEOS ORBIT EVOLUTION by D.C. Christodoulidis and

D.E. Smith - - - - - - - - - - ------- --3-5 

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ORIGINAL. PAGE iS

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CONTENTS (Continued)

Page

C. GEODYNAMICS AND GEODETIC PARAMETER ESTIMATION

FROM STARLETTE LASER TRACKING DATA

by J.G. Marsh - - - - - - - - -----------3-10

D. GEODYN PROGRAM SYSTEMS DEVELOPMENT

by B.H. Putney- - - - - - - - - - - - - 3-16

CHAPTER 4. SEA SURFACE TOPOGRAPHY - - - 4-1

(Overview)

A. REGIONAL MEAN SEA SURFACES BASED UPON GEOS-3

AND SEASAT ALTIMETER DATA

by J.G. Marsh - - - - - - - - - - - - -- --4-2

-B= SEASAT OBSER.'ATIONS= OF LITHI OSPHERIC" `FLEXURE

by D.C. McAdoo -------------------- 4-8

C.AN OBJECTIVE ANALYSIS TECHNIQUE FOR EXTRAPOLATING

TIDAL FIELDS

by B.V. Sanchez - - - ----------------4-12

CHAPTER 5. ADVANCED STUDIES - - - `- - - - -' - - - - - 5-1

(Overview)

A. GRAVITY FIELD SIGNAL ANALYSIS STUDY FOR A GEOPOTENTIAL``

RESEARCH MISSION by T.L. Felsentreger- - - - - - -5-2

B. GRAVSAT SIMULATIONS FOR GEOPOTENTIAL ANALYSIS'

by F.J. Lerch - - -. - - - - - - 5-7

C. THE AIRBORNE LASER"RANGING SYSTEM 'by W.D Kahn - 5-10

D. SOIL MOISTURE FROM TEMPERATURE MEASUREMF'4T9 AT THE

EARTHS SURFACE by'J.E. Welker - ,. - - - - - 5-16

PUBLICATIONS AND PRESENTATIONS - 1982- -.- - - A-1'

ACKNOWLEDGMENTS - - - - - - - - - - - - - - - - - - A-5
ORIGINAL PAGE M

OF POOR QUALITY

INTRODUCTION

This report is the first annual summary of the research program of the

Geodynamics Branch. The branch is located within the Earth Survey Applications Division of the Applications Directorate of the Goddard Space

Flight Center. The resear^:h activities of the branch staff cover a broad

spectrum of geoscience disciplines including space geodesy, geopotentialf

field modeling, tectonophysics, and dynamic oceanography. The NASA programs which are supported by the work described in this document include

the Geodynamics and Ocean Programs, the Crustal Dynamics Project, the

proposed Ocean Topography Experiment (TOPEX), and Geopotential Research

Mission (GRM). The reports highlight the investigations conducted by the

Geodynamios Branch Staff during calendar ,ear 1962. The individual papars

are grouped into chapters on Crustal Movements, Global Earth Dynamics,

Gravity Field Model Development, Sea Surface Topography, and Advanced

Studies. Further information on the activities of the branch or the particular research effort described here can be obtained through the Branch

Office or from the individual staff members.

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CHAPTER l

CRUSTAL MOVEMENTS

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OVERVIEW

Studies of crustal movements are devoted to the interrelated goals of

determining tectonic plate motions, understanding their driving forces

and the nature of plate interactions, and predicting the occurrence of

earthquakes. The analysis of global and regional scale crustal

movements provide information on seafloor spreading and continental

drift, the creation and destruction of crustal material, find the

structure, rheology, and dynamics of the earth's interior. Crustal

deformation in seismically active zones provide information on strain

accumulation and release, the state of stress in the earth's crust, and

the mechanisms responsible for earthquakes. The work of the Geodynamics

Branch includes activities in both the Crustal dynamics Project which

involves space geodetic observations and in the Geodynamics Research

Program which involves basic studies into the dynamic processes of the

earth.

This .section of the Geodynamics Branch report includes papers on the

measurement of crustal movements, modeling of earthquake related crustal

deformations, mudeling of sublithospheric stress fields, and the

development of satellite tracking faclliti'es for space geodetic

measurements. The four reports are summarized as follows: 1) The

first report is devoted to observations of crustal movements using

satellite laser ranging measurements to the Lageos satellite. Repeated

determination of the distances between observing sites on the North

American, Australian, Pacific and South American Plates are being used

to determine both relative plate motion and intraplate rigidity. 2) The

second report focuses on the modeling of crustal deformation subsequent

to an earthquake. The analyses is based on the physics of stress

redistribution with time and distaince from the seismic event and yields

information on the rheology and structure of the earth's interior. 3)

In the third report, the sublithospheric stress field in the Baikal

Stanovoy region of Siberia is derived from an analysis of the satellite

determined gravity field. The computed stress field is interpreted in

terms of the regional seismicity, and geologic structure and the

phenomenon of gravity sliding of seismotectonic blocks. 4) The fourth

report describes data confirming the successful conversion of the lunar

laser ranging system of the University of Hawaii at Maui into a system

capable of tracking near-earth satellites, The site is being used in

measurements of tectonic plate motion involving the Pacific Plate.

Contributors to this section are: O.C. Christodoulidis, S.C. Cohen,

R. Kolenkiewicz, H.S. Liu and n.E. Smith.

1-1
ORIGINAL PAU— tS

OF POOR (UAL

GLOBAL GEOTCCTONICS FROM SATELLITE LASER RANGING

Demosthenes C. Christodoulidis

and

David E. Smith

OBJECTIVE

The detection of global geodynamics and tectonic, processes through the use

of satellite laser ranging data.

BACKGROUND

The accuracy with which' tectonic plate- velocity vectors can be computed

increases with the,. repetition rate of the measurements and accuracy in-the

measurement of interplate distances and heights. As a result, a fai..r.amount

of GSFC activity has been -devoted to.increasing the temporal_ resolution and

precision .of baseline and height determinations for laser instruments

deployed surrounding tectonic plate boundaries.

RECENT ACCOMPLISHMENTS

Dynamic reduction .of. Satellite Laser Ranging (SLR) provides a unique tool

for the precise positioning'of a . point on the.Earth's.surface in three _dimensions. 

I

The sensitivity of the SLRdata re,quires ,that, for a well conditioned

sol uti on, ` the 1 ongi tude of one of the tracking stations be constrained to an

a priori value,. The vertical -components -.of. the st;ation5, however, through

the tracking . geometry .provided by the global network and the accurate knowledge of_orbitaT dynamics, are uniquely ,related to the center,-of-mass. of the

earth.

The Lageos ' 1 aser data for .the period May 1976 to -April, 1962 ha ve. been ana -

lyzed, for., the determination of ,sets of ,annual sta.ti on. l.vcati ons and earth

orientation and force model parameters. The results of this analysis,;referred.to as SL5 are approaching the .useful accuracies required by geophysics.

The annual height: variations for eight base stations, spread over, four tectonic plates.are shown in Fig. 1 Station positions determined from data

collected prior to 19,7.9 are of inferior accuracy.,due to the.poorer quality,

quantity:, and..di.stribution of the data. The three sigma formal errors, of

these heights, are . between 2 and.,.5 cm. Inspection .of the, heights versus

their sigmas shows .that, for-most, of the cases, ' the variations are i.nsignificant, with the, ,exceptions being, Maui, Hawaii and Yarragadee, Australia.

The`horizontai,,positions of the.statio'nt,'have an accuracy of better than 2

cm which has permitted preliminary comparisons of.SLR tectonic plate motions

with those estimated by .Minster and Jordan (1974, 1978). These. .comparisons

are discussed below.

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SIGNIFICAKE

The change in the SLR chord lengths, free :.-am height variations give

the horizontal component of the 'velocity vectors between the tectonic

plates. These ellipsoidal chords interconnect. the projections of the

tracking station positions onto the reference ellipsoid. As such, they

may be compared directly with the horizontal changes suggested by (Minster

and Jordan. The Lageos data anclyzed was collected from 1979 through 1981.

In 'Order to increase the sample size, the chords were averaed per tectonic

plate. The computed inter-plate are shown in Figure 2. The

heavy lines connect the geographic barycenter of the sites where more than

one site was available per plate. For the purpose of comparisons the same

pri r plate averaging was applied to the Minster and Jordan rates which are

t;hown i n Fi gu The agreement between the two independent sets is , re _ 2 also,

within one sigma of the laser data (approximately + 2 cm!yr) the exception

bei ng the Aust ral i a to S. Ameri can rate. It has to be kept i n mi nd, however,

that this chord crosses two plates (the Nazca plate and the Pacific plate)

and therefore what we see is the result of the combination of movements

from four plates. Furthermore, the Minster and Jordan rates reflect

average movements over millions-of-years whereas the SLR rates are 2 year

averages. Although these results seem to be very encouraging indeed, much

attention will be given to future higher quality laser results. These

results will increase the length of the movement records for- the laser

sites and will thus enable the verification of the observed deformation

- rates.

FUTURE °EMPHASIS_

The results discused above are viewed as preliminary. Studies are now

underway to better understand and evaluate the ,variation of the .heights

and chord lengths and to further ;improve their temporal resolution and

accuracy over the entire history of the Lageos mission. Improvements in

the current data reduction approach include the incorporation of the

Water Mutation series, the development and use of a Lageos tidal model and

Lageos' tidal di spl acemerit Love numbers, and the description of the site

displacement due to ocean loading via -an available model. Studies are

also underway to better model and .understand the along track acceleration

of the spacecraft, as well as forces due to the earth's albedo. Preliminary error analyses, indicate that the _incorporation . ,of ,_improvements

along with better, control of the overall systems performance could decrease

the average positional uncertainty by about 25 percent.

REFEREi10ES

Minster, J.B., T.H. Jordan, P. Molnar, and E. Haines, "Numerical Modeling

of Instantaneous Plate Tectonics, Geophys. J. of the Royal Astron. Soc:,

36, 541-576,,1974.

Minster, J.B. and T.H. Jordan, "Present''-Day Prate Motions, J. Geophys.

Res., 83 (811), 5331-535.4, 1978.
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ORIGINAL PfrGa

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CRUSTAL DEFORMATION DURING THE EARTHQUAKE CYCLE

Steven C. Cohen

OBJECTIVES 

The purpose of this work is to develop\ an understanding of how the earth's

surface deforms during the cycle of stress accumulation and release along

major faults. The major research thrusts are the development of numerical

models of the spatial and temporal patterns of crustal displacements and

strains and the determination of numerical values of the geophysical parameters that describe the earth's rheology and structure.

BACKGROUND

Vertical -tnd horizontal crustal deformations are common characteri sti cs of

the earth in zones of active seismicity, Certain temporal and spatial patterns of crustal ,deformation evolve as the earth passes through successive

t stages of the earthquake cycle strain accumulation, preseismic movement,

_ earthquake rupture, and postseismic rebound. The patterns that develop

depend on the interacti on of the various forces responsible for driving

earthquakes and tectonic plate movements, the rheology and structure of

the earth, and the fault geometry. The research reported herein involves

the development of numerical models that replicate the patterns of deformation of surface near- and far-field features. The computer simulations of an earthquake cycle are fit to observed geodetic data to deter

mine key physical parameters of the earth. The specific models that are

discussed in this report involve postseismic deformation due to vi sco

elastic flow in subcrustal layers of the earth. The flow is activated by

the coseismic stress field established by an earthquake. As the viscoelastic creep advances in the subcrustal layers coupling to the crust

K results in surface deformation. 

RECENT ACCOMPLISHMENTS AND SIGNIFICANCE

A finite element computer code has been used to study postseismic rebound on

strike-slip and dip-slip faults. A multilayered viscoelastic Theological

structure for the ea, th has been used. In this model the earth's lithosphere

is divided into two layers. The upper layer is elastic and contains within

it a fault that pentrates through all or only a part of the layer. Below

this layer is a viscoelastic lower lithosphere represented by a standard 

linear 'soTid rheol ogy. This representation of the lower lithosphere permits modeling the following "deviatoric behavior: elastic deformation

coseismic to the earthquake fault slip, viscoelastic rebound subsequent to

the earthquake, and permanent elastic support of stress with a shear

modulus reduced from the instantaneous coseismic value. Below the lithosphere lies an asthenospheric layer represented by a Maxwell viscoelastic

1-6

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ORiG4filAL FACE 'S

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fluid. The relaxation time of the Maxwell fluid is significantly less

than that of the overlying linear soli!a due to the expected thermal

enhancement of creep processes at depth.

For strike-slip faults the model predicts that postseismic deformations

increase as the, ratio of fault depth to elastic lithosphere thickness

increases. The effects of partial relaxation of the lower lithosphere

are to increase the magnitude of the postseismic displacements and

strains and to extend the duration of postseismic straining. In addition, the graded decreasing viscosity profile with depth retards the

lateral growth of the zone of significant postseismic restressing. In

general the effects of asthenosphere flow are significant if the

asthenosphere depth is less than about 3 fault depths from -its surface

and the viscosity is on the order of 10 20 poise. The partial

relaxation of the lower lithosphere is significant if the relaxation

time is not much more than an order of magnitude greater than that of

the asthenosphere and if the fractional change in the effective

shear modulus with time. is greater than about: 1/4.

The dominant effect in the postseismic rebound from dip-slip event is

subsidence centered ovev the fault and uplift in the intermediate or

far-field region. Over a. wide range of dip angles _ the magnitude of

the sp^ t,h _ i dence iS _ores--test when the fault extends through one-half the

11fluc_:0ere. For greater or lesser fault depths the subsidence is

r 1-i.ed; it becomes uplift when nearly all the lithosphere is 'pene

'rated. The width of the subsidence ,zone is controlled primarily by

the depth of the top of the asthenosphere and secondarily by the depth

of the lower lithosphere. The influence of relaxation of the lower

lithosphere on the surface deformation is much less than that for the

strike-slip case. Rather the deformation due to asthenosphere relaxation dominates the early postseismic vertical displacement pattern

and continues to develop over times long compared to the Maxwell time.

This viscoelastic model has been compared to geodetic data obtain in

1900, 1934, "a nd 1974 following the 1896 Riku-u, Japan earthquake (see

Figure 1) . The deduced value of total lithosphere thickness of about

40 km and asthenosphere viscosity of 5 x 10 19 poise are moderately

constrained. The thickness and viscosity of the lower lithosphere of

20 km and -1 x 1021 poise respectively fit the data but are poorly

constrained.
E

t?RIMAL PAS

OF POOR QUALITY

FUTURE EMPHASIS

The modeling effort will be extended in the future to include strain

accumulation during the interseismic phase of the earthquake cycle.

It will be possible to model both the deformation due to a single

earthquake cycle or to a sequence of recurring events. The finite

element computer code will provide a general purpose modeling capability that will permit undertaking numerical experiments using different physical assumptions. The deformations that are due to lateral

and vertical variations in rheological structure will be deduced.

Numerical experiments will be performed to test the resolvability of 

different models of crustal deformation. The analysis will focus on

how the surface deformations are influenced by: 1, a thin channel

asthenosphere; 2. a subsurface low viscosity inclusion; 3. lithospheric thinning in a fault zone, and 4, elastic creep.

REFERENCES

Cohen; S=C., '"A Multiiayer Model of Time dependent Deformation Following an Earthquake on a Strike-Slip Fault," J. Geophys. Res., 87,

5404-5421, 1982.

Cohen, S.C., "Postseismic Deformation Due to Subcrustal Viscoelastic

Relaxation Following Dip-Slip Earthquakes." GSF(; TM 84005, Sep,e;,bar

1982, submitted for publication.

Cohen, S.C., "Discussion of Models of Postseismic Rebound," E®S, 63,

429, 1982.
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GRAVITY SLIDING: CRUSTAL DEFORMATION AND SEISMOTECTONIC

BLOCK MOVEMENTS IN SIBERIA

Han-Shoo Liu

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OBJECTIVE

Geodynamics seeks to ascertain the causes of crustal deformation and its

fundamental connection with geophysical and seismological features. The

objective of this study is to develop a genetic model which may account

for the Baikal rift system and the associated seismotectonic block:

movements of Stanovoy Range in Siberia.

BACKGROUND

The knowledge of the seismic activity and tectonic structure of the

Baikal-Stanevoy region in Siberia obtained by the Russian geoscientists

is profound. It provides geological and geophysical facts to test

.Whether the ,volutions of the focal mechanisms for earthquakes, the

distribution of orogenic activity, recent crustal block movements and

upper mantle structure in this region can be integrated within a single

Space Geodynanics Program.

The program for satellite measurement; of 'the earth's gravity offers a

variety of models to interpret the interior of the earth. Among the

various interpretations, the sub-lithospheric stress field serves as

an intraplate character which corresponds to the state of gravity

sliding. In this study, the analysis of the Goddard Gravity Field

Model is used in determining the horizontal projections of lithospheric

sliding under the Baikal-Stanovoy region. This study involves a search

for mutual agreement over large areas of the geopotential field with

respect to seismic stresses

RECENT ACCOMPLISHMENTS

The gravity sliding forces can be inferred from satellite gravity data.

We have obtained stresses at 1,000 grid points in Siberia caused by

gravity sliding. The results have determined a seismic gap and recognized two types of stress conditions in the structure of the RaikalStanovoy seismic belt. The method developed for identifying stress

zones from satellite gravity data makes it possible to direct the

search for the mechanisms of earthquakes and rifts toward these stress

structures. An interdisciplinary investigation of the stress pattern

reveals an anomalous mantle beneath the Baikal Rift System.
SIGNIFICANCE

The stresses as shown in Figure 1 are comprised of several consistent stress

patterns including the remarkable t^!nsional stress field under the Baikal rift

zone and the North-South compression in the Stanovoy Range region. By analyzing

the satellite stress fields in conjunction with tectonic and seismological

structures in Siberia, we have obtained the following significant results:

1. Seismicity and seismic gap All the strong earthquakes in Siberia are

concentrated within the Baikal-Stanovoy Seismic Belt (Figure 2) which includes

the Baikal rift zone and extends eastward as far as the sea of Okhotsk. Around

118°-120°E there is a seismic gap where earthquake foci are absent. The western

segment coincides with the Baikal rift zone in which strucures are under extension. The eastern segment of the belt is located between 120°E and the Okhotsk

Sea coast. Within its limites, Baikal-type grabens disappear completely and

the uplifted topography here points to compression rather than extension. The

stress pattern, as inferred from satellite gravity data, is in good agreement

with these seismological features. The most likely point of no strain along the

Baikal-Stanovoy seismic belt is calculated to lie at 56 0 N 116 0E (figure 1),

which lies at the position of the aforementioned seismic "gap."

2. The ,computed point of no strain (56 0 N 116 0 E), or seismic gap, coincides

almost exactly with the position of the pole- of rotation between the Eurasian

and Amurian plates. This result suggests that gravity sliding may be the main

cause for seismotectonic block movements.

3. Figure 1 shows an anomalous lens of upwelling mantle rocks under the rift

zone which may be verified by seismic or magnetotelluric probing.

4. Mechanism for Baikal rift system - Gravity sliding in this region, as inferred from satellie gravity data, has provided a mechanism for continental rifting.

It has been shown that rift evolution in continents is driven by the inexorable

dissipation of thermal energy from Vie mantle and the concomitant upward transport of the asthenosphere. It may be probable to state that the crustal

tension causing the Baikal rifting was originated by either the suction force

acting on overriding plates at trenches or the collision force between the Indian

and Eurasian plate along the Himalayan frontal thrust.

FUTURE EMPHASIS

Satellite capabilites for gravity measurements have been extended so rapidly in

the past few years that these has'not -been time to bring them fully to bear on

the interesting fundamental problems for which they seem so well suited. By

applying the same method, the author plans to investigate gravity sliding in

Europe. The gravity sliding stresses in the European crust will be obtained

form satellite gravity data. The stress calcualtions will provide a real challenge to the best geophysical theories, and seismological observations.

REFERENCES

Liu, H.S., 1982. Geodynamics of the Baikal-Stanovoy Seismic Belt, Physics of the

Earth and Planetary Interiors, Uol. 31, 1 -82.

_1-11

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LONGITUDE

Figure 1. Subcrustal stresses beneath the Baikal- Stanovoy region as inferred from satellite gravity data. The stress

pattern is consistent with the anomalous lens of upwelling mantle rocks under the Baikal rift region and the

associated crustal compression of the Stanovoy Range.

60

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1-12

V
THE VERIFICATION OF THE LURE SYSTEM AS A SATELLITE LASER RANGING STATION

Ronald Kolenkiewicz

OBJECTIVE

The objective is to qualify the LURE (Lunar Ranging Experiment) laseJ' ra.ngir!g

system of the University of Hawaii located on Maui, Hawaii to verify that it

is suitable to be used as a near-earth satellite system. This enables -it to

join the NASA laser ranging network and thus contribute to the Crustal

Dynamics Project.

BACKGROUNI)

In the past the LURE system was designed exclusively for laser ranging to the

moon. NASA was in need of a Satellite Laser Ranging (SLR) system on the

Pacific Plate in order to perform Global Studies for the Crustal dynamics

Project. These studies include monitoring of tectonic plate motion as well

as polar motion and earth rotation. The LURE system was modified to enable

it to track near-earth satellites. in order to verify the ability of the

LURE system to accomplish this goal, a SLR system, MOBLAS I was collocated

in the vicinity of the LURE laser.

These collocated systems tracked the BE-C, Starlette, and LAGEOS satei tes

to demonstrate that the LURE system gave the same ranging information as

MOBLAS 1. These tests were conducted during September through November 1981.

RESULTS

The laser ranging data from the two collocated laser systems (LURE and MORLAS

I) was analyzed by selecting simultaneous passes of data to the same satellite. The residuals to an orbit calculated to these data based, upon the

x known survey position of the sites, were analyzed for relative range and

timing biases. Figure 1 shows the laser range residuals i-om collocated

Lasers, about an orbit. The average residual for each station is determined. These averages are then differenced to give the mean residual

difference for that pass.. Figure ?_ shows these mean residual differences

plotted for the 36 satellite passes analyzed. Initial results indicated

there was a relative bias of 5 cm between the stations. Allowing for one

station to move to a new position relative to the other removed this bias.

A survey confirmed these analyses by showing the original position of

MOBLAS I was in error by 6.8 cm in latitude and 3.8 cm in longitude and

the calibration board distance was in error by 1.1 cm.

When the corrected position was used in the anlaysis the measurments made by

both systems were in agreement with each other by less than 1 millimeter.
Figure 2 presents the results of this experiment. The mean residual difference

for the 36 passes analyzed are seen to be spread between plus and minus 4 cm

with an average of zero and a sigma of 2.4 cm.

CONCLUSIONS

The LURE system is capable of satellite laser ranging at the centimeter level,

and SLR systems can detect survey errors at the centimeter level. This

implies that relative site positions can be measured at the centimeter level

providing tectonic and earth orientation measurements of value to the Crustal

Dynamics Project investigators.

REFERENCES

"Collocation Test Plan for M06LAS I and LURE Observatory Laser Ranging Systems

at Mt. Haleakala," STDN Report No. 410.2, Goddard Space Flight Center, December 

1980.

Kolenkiewicz, R., M. Torrence, and D. Edge, "Orbital Analysis for Several

Collocated Satellite Ranging Systems," presented at Fourth Annual Conference

on the NASA Geodynamics Program, Goddard Space Flight Center, January 26-29,

1982,

Torrence, M. and R. Kolenkiewicz, "Collocations of Satellite Laser Ranging 

Stations," EOS, Vol. 62, No. 45, November 10, 1981, p. 480.
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CHAPTER 2

GLOBAL EARTH DYNAMICS

OVERVIEW

Studies of global earth dynamics are devoted to improving the understanding

of the origin of moti ons of the whole Earth and determining the structure and

mechanical properties of the Earth's interior. The techniques employed in

such studies are as varied as the studies themselves. They range from the

determination or changes in satellite orbits, to spectrum analyses of polar

motion data, to the inversion of gravity field representations. The reports

in this chapter summarize as follows five research activities underway in the

Geodynamics Branch during 1982:

1) The first report focuses on the determination of the effective viscosity

of the lower mantle using observed accelerations in the node of Lageos'

orbit. The results are discussed in terms constraints on the allowed

modes for mantle convection.

2) The second report is the first of two papers on polar motion. Data from

both the International Latitude Service and observations of Lageos have

been analyzed to determine both the annual and Chandler Wobble component of polar motion. For both of these terms the frequencies, amplitudes, phases, and Q's of the signal have been determined.

3) Continuing the study of polar motion, the next report discusses the

development of a matched filter to improve the signal recovery from a

noisy time serise This filter is being used to determine the frequency

and Q of the Chandler Wobble.

4) The fourth paper describes the use of gravity data in an information

theory based inference scheme to determine the lateral density distribution of the Earth.

5) Finally, a comparison is presented on length-of-day determinations from

atmospheric wind data and from Lageos observations. The correlation

between the 2-day sets argues that changes i n the zonal winds are a

major contributor to l ength-of-day changes„

Contributors to this chapter are B.F. Chao, D.C. Christodoulidis, R. Gross,

D. Rubincam,-D.E. Smith, and George Wyatt.

it

G

2-1
ORIMNAL PPA 15

OF J%UOR QUALITY

POSTGLACIAL REBOUND OBSERVED AY LAGEOS AND THE EFFECTIVE VISCOSITY

OF THE LOWER MANTLE

David P. Ruhincam

OBJECTIVE

The objective of this work is to infer the effective viscosity of the lower

mantle from observations of the node of Lageos' orbit.

BACKGROUND

The Lageos satellite was launched in May 1976 for the purpose of studying

crustal motion, plate motion, polar motion, and earth rotation (Smith and

Dunn, 1980). Five years worth of laser ranging data reveal an acceleration

in the node of Lageos' orbit which is not currently modeled in the GEOnYN

orbit determination computer program (see Fig. 1). Its value is s = -8.1

1.8) x 10-8 areseconds day- 7 ; hence the rate at which the node is

progressing along the equator (SZ = n.343 degrees day- 1 ) is becoming smaller.

An obvious geophysical interpretation of the data is to assume that the

earth's equatorial bulge is getting smaller. Since the rate a is proportional to the J2 term in the spherical harmonic expansion of the earth's

gravitatiorral potential, the observed S (831{-1.8) x ln-8 aresecondls9dayi2

implies that J 2 is changing at the rate of Jp _ (-8.2 ± 1.8) x 1n" s-1.

RECENT ACCOMPLISHMENTS

A complete description orr the work summarized here may be found in Rubincam

(1983). Briefly, the observed J2 cannot be due to the tidal deceleration of

the earth and the subsequent relaxation of the earth; it is a factor of 411

too small. Also, the 'long , -period 18.6 year ocean tide does not appear to be

the cause, since it woud have to be far from equilibrium.

The acceleration of the node does appear to be due to the postglacial rebound

of the earth. During the Ouaternary i.ce Age the weight of the ice caps in

the polar regions squashed the earth into a more elliptical shape; it is now

relaxing and thus decreasing J2. The magnitude of J2 is controlled in part

by the effective -viscosity of the mantle. Hence the observedJ2 places

constraints on earth structure.

Wu and Peltier's (1982) L1 and L2 earth models plus an assumed ice cap

history were used to compute J2 values to compare with the observed value.

The L1 model has a 120 km-thick lithosphere, a in 21 Pa s mantle, and an

inviscid core. The L2 model is the same as the L1, except that the effecfive viscosity of the lower mantle (b low 671 km depth) is 10 - Pa s.

The resulting J77 values were -9.8 x 10- 1 9 s-1 for the L1 model and -32.n x

10- 19 s-1 for & L'2 model. Clearly the Ll model is closer to the observed

value of (-8.1 ± 1.8) x 10- 19 s-1 and is preferred to the L2 model.
SIGNIFICANCE

The results indicate that the effective viscosity of the mantle must be a

fairly uniform 10 21 Pa s. In other words, there is no great difference

between the effective viscosities of the upper and lower mantle. Hence any

objection to whol mantle convection based on such a difference apparently

cannot be invoked.

FUTURE EMPHASIS

f The behavior of the node of Lageos' orbit will be monitored in the future to

see whether it still conforms to that predicted by postglacial rebound.

Also, other possible causes for the acceleration of the node will be

investigated.

REFERENCES

Rubincam, D.P., Postglacial Rebound Observed by Lageos and the Effective

Viscosity of the Lower Mantle, NASAJGSFC TM 84982, Goddard Space Flight

Center, Greenbelt, MD, February 198 .

Smiths DoE., and P.J. Dunn, Long Term Evolution of the Lageos Orbit,

feophys. Res. Lett., 7, 437-440, 1980.

Wu , P., and W.R. Peltier, Viscous Gravitational Relaxation, Geophys. J.R.

Astr. Soc., 70, 435-485, 1982.
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ORIGINAL PAC2 E i, OF POOR QUALITY,

DYNAMICS OF THE EARTH'S POLAR MOTION

B. Fong Chao

OBJECTIVE

To analyze polar motion data obtained by geodetic techniques including classical

astrometry and satellite laser ranging, and to compare the observations with the

atmf.?spheri c and seismic excitation functions.

BACKGROUND

The Earth's rotational axis does not remain fixed relative to the body of the

Earth. Instead, the interception of the axis with the surface of the Earth

(i.e., the pole) traces out a quasi-periodic path about some mean position on a

scale C10 meters. This motion is known as the polar motion of the Earth. The

polar motion in principle consists of a number of components arising from various

dynamical processes. The two major components are the annual wobble with a

yearly period and the 14-month Chandler Wobble.

The annual wobble is a forced motion and the variations in atmospheric mass

distribution have long been identified as the major cause for tho annual wobble.

Other mechanisms, such as ocean circulations, core-mantle coupling, solar winds

and radiations, are believed to have minor effects on Earth's polar motion.

Numerically, lacking any information that indicates otherwise, the annual wobble

has been modeled as a pure sinusoid with a period of 365.25 days.

The Chandler wobble, on the other hand, ; the Earth's free motion corresponding

to the Eulerian nutation of a rigid body. Its excitation sources have remained

unidentified despite an ongoing effort over many decades. Two plausible candidates have been proposed; atmospheric and seismic excitations. However, as to

date, both -seeem to suffer from insufficient energy. Despite this difficulty

(rightfully or not), the period and the Q of the Chandler Wobble have been estimated by means of various numerical techniques; and there has been no agreement

on the structure of Chandler period(s) (whether it is single, multiple, or even

time-variable), nor on the value of the Chandler 0 (estimates range from from

-30 to -1000, depending on data and techniques used).

RECENT ACCOMPLISHMENTS AND SIGNIFICANCE

Naturally,, for our purposes (namely, the numerical modeling of polar motion

.' using atmospheric and seismic excitation functions), the essential first 

step is to separate the annual and the Chandler wobbles into optimum numerical

r:

2-5 
2-6

F

1

!t

ORIWNAL P tCZ 1*

OF POOR QUALITY

representations--in the present case, complex harmonic functions of time.

Thus, we completed a harmonic analysis of the following two sets of polar

motion data: (1) monthly solutions by ILS (the International Latitude

Service) using classical astrometry, spanning HO years (1900-1979), and (2)

5-day solutions of LAGEOS (the Laser Geodynamics Satellite) using satellite

laser ranging, spanning 5.7 years (1976.4-1982.1). Tie method used is the

"Autoregressive (AR) method" (Chao and Gilbert 1980), devised to estimate

the complex frequency (frequency and 0) and the complex amplitude (amplitude

and phase) of each complex harmonic function in a time series. Tables 1 and

2 give the results for ILS data (Chao, 1983a). Major conclusions include

(i) the annual wobble is stationary over the long period of time spanned by

ILS observation, and (ii) the ILS data are consistent with a Chandler wobble

model that consists of four-components. fables 3 and 4 give the LAGEOS

results (%hao, 1983b). The multiple-component behavior of the Chandler

wobble, if it exists, cannot. he resolved due to the short record length.

Note that the estimated annual periods are significantly shorter than the

theoretical value 365.25 days (by 5-1n days) during 1976.4-1982.1. It should

be pointed out that the observations in Table 3, including the anomalous

periods, the decay in amplitudes, and the differences in amplitudes and

phases, simply reflect the yearly behavior of the driving mechanism(s) of

the annual wobble, and can and should he accounted for by the Tatter.

On the theoretical front, the problem of excitation of the Earth's (free)

Chandler wobble by a transient, indigenous source (as exemplified by a seismic

event whose duration is generally much shorter than the Chandler period) has

been revisited (Chao 1983c), with particular emphasis on the compatibility in

coordinate systems used for observations and for computations. :Lt 'is found

that the difference between the two types of coordinate systems i^ far from

trivial. However, for most practical purposes, this discrepancy is small

compared with the amplitude of the polar motion itself.

FUTURE EMPHASIS

The long ILS data set is ideal for statistical studies for the excitation of

'polar motion. One such study is a statistical analysis of the relationship

between the polar motion and the occurrence of major earthquakes. Thus,

correlation between the longitudes of over 1500 earthquakes (over the same

period spanned by the ILS observation) and the phases of the pole position fit

the time of the events will be calculated in order to detect the existence of

any possible cause-and-effect relation.

The high-density, accurate LAGE"S data, whose annual and Chandler wobbles

having been separated and analyzed, can now be compared with the atmospheric
ORIGMAL H&C-11 •L;ol

OF POOR QUALMangular momentum data (also available since 1976, see Rosen & Salstein 1981).

In particular, we can compute the polar motion that is caused by the atmospheric variations and subsequently conduct a wobble-by-wobble comparison.

This presumably will account for the behavior of the annual wobble presented

in Table 3, and determine how much of the Chandler wobble can be accounted

for by the atmosphere and hence give clues to the importance of other excitation agents.

Period (days) Q Amplitude Phase

ILS-X 365.20 -1490 n.0884 108

ILS-Y 365.10 1370 0.0840 10

Table 1. AR estimates for the ILS annual Wobble

Comp. No Period (days) 0 Amplitude Phase

1 406.45 1840 0,0267 216

11 426.00 711 0.1199 273

111 437.46 _18q 0.0573 342

IV 452.73 180 0.0686 150

(a)

Comp. No. Period (days) Q Amplitude Phase (0)

1 406.85 -386 0.0170 132

11 426.15 703 0.1195 185

111 437.43 -184 0.0572 253

IV 452.39 320 0.0569 54
ORI(ijy AtiL E

OF POOR QUALITY

Period (days) 0 Amplitude (") Phase (0)

LAG-X 360.0 13.2 0.153 196

LAG-Y 354.9 8.7 0.182 80

Table 3. AR estimates for the LAGEOS annual wobble.

Period (days) 0 Amplitude (") Phase (0)

LAG-X 434.2 22.5 0.188 319

LAG-Y 436.4 12.8 0.245 238

Table 4. AR estimates for the LAGEOS Chandler wobble

REFERENCES

Chao, B.F. and F Gilbert, 1980. Autoregressive Estimation of Complex

Eigenfrequencies in Low Frequency Seismic Spectra, Geop-hys. J. R. Astron.

Soc., 63, 641-657.

Chao, B.F., 1983x, A Harmonic Analysis fo the Earth's Polar Motion Using ILS

Data, submitted to J. Geophys. Res. 

Chao, B.F., 1983b. Analysis of LAGEOS Polar Motion Uata, in preparation.

Chao, B.F., 1983c. On Excitation of Earth's Free !Nobble and Reference Frames,

in preparation.

Rosen, R.D. and B.A. Salstein, 1981. Variations in Atmospheric Angular

Momentum, ERT Technical Report A345-T1.
ORIGINAL K, E,

OF POOR QUALITY

2--9

OBJECTIVES

The ob,ective of this research effort is to study some of the outstanding

problems in the field of polar motion such as the nature of the excitation

mechanism of the Chandler wobble, the value of the period and 0 of the

Chandler wobble, the Markowitz wobble and the long term stability of the

'A a latitude observation stations.

r BACKGROUND

In 1765 Euler predicted that any rigid body, including the earth, which is

rotating about some axis which is not its principal moment of inertia axis

will experience a wobble as it rotates. In 1891 Chandler was able to observe

this wobble of the earth and since 1899 it has been observed and studied by

the International Latitude Service (1LS) and, more recently, by many other

_ organizations. This motion of the rotation pole about the principal moment

of inertia axis is primarily composed of two components. The first has an

annual period and is a forced .motion of Lite pole commonly believed to he

caused by meteorological _events. The second is IEuler's free nutation at a

period of approximately 434 days and is now known as the Chandler wobble.

However, the motion of the rotation pole also exhibits a long term drift in

its mean position and there is some evidence that a component (called the

Markowitz wobble after the person who proposed its existence) might exist

having a period of roughly 24 years.

RECENT ACCOMPLISHMENTS

As a graduate student I used a damped least squares technique to obtain the

polar motion along with station corrections from the homogeneous I_S latitude

observations in order to obtain a polar motion data set at 19-day time

intervals. This polar motion time series spans the years 1899-1979 and can

be used to study the long term behavior of the motion of the pole. Since

the solution technique took into account the individual station contributions

via the station corrections we are also able to study the long term stability

of the individual ILS latitude stations.
2-10

OF POOR QUALIT' f'

As our first use of this newly derived polar motion time series we will

ascertain when the Chandler wobble is undergoing excitation by a technique

based upon matched filters. A matched filter is the optimal linear filter

that maximizes the signal to noise ratio in the output at some instant. This

is desirable if we are trying to detect the onset time of some signal embedded

in noise. The assumption is that our chances of detecting this signal will

be increased if the signal to noise ratio is a maximuh. For a time series

consisting of a known signal s(t) of amplitude A and arrival time to embedded

in noise n(t);

x(t) = As(t-to) + n(t)

it can be shown (see, e.g., Robinson (1967)) that the desired filter in the

frequency domain is simply S*(w), the complex conjugate of the Fourier

transform of the signal s(t):

Y(w) = X(w)S*(w)

where X(w) is the Fourier transform of the input signal x(t) and Y(w)

is the Fourier transform of the output signal y(t). It can be shown (see

Gross (19£32)) that if the signal s(t) we are trying to detect is damped

harmonic motion then the output signal y(t) will exhibit a peak at the signal

arrival time to and it will decay exponentially from this peak value. In the

r 4.1-. Chandler '

which _t,.,..+ An mow:.. case o l the wobble wh 1 ch has a damping t i me of about 4n years thiss

peak in the output will be rather broad. Of course, we would like the peak

to be as delta like as possible. In fact we can form a narrower peak by using

the filter:

S*(w)

Y(w) = X(w)

(IIN (w) 1j2 + 11S( w ) 1)2)1/2

where N(w) is the Fourier transform of our estimate of the noise in the

input time series. To illustrate the use of the above filter figure l shows

the x-component of a synthetic time series we generated which consists of

three signals embedded in noise. figure 2 shows the amplitude of

the time series resulting from applyi-ng the above filter (with N=0.1) to this

input time series. As can be seen the output is peaked at the signal arrival

times which are indicated by the dashed lines.

W,e are currently applying this noisy matched filter to various polar motion

data sets. As an aid in interpreting the results we are also using it on

many synthetic time series.

FUTURE EMPHASIS

We shall continue our investigations into the properties of the excitation

process of the Chandler wobble as well as study other topics in the field of

polar motion. In particular we will calculate the period and Q of the Chandler
ORIGINAL FACE 15

OF POOR QUALITY

wobble by assuming that it is the result of a white noise process exciting a

resonant system. We gill also study the Markowitz wobble as manifested in

the data set derived by Gross (1982) and we will study the long term stability

of the ILS latitude observation stations as indicated by their station

corrections.

REFERENCES

Gross, R.S., "A Determination and Analysis of Polar Motion," Ph.D. Thesis,

University of Colorado, 1982.

Robinson, E.A., "Statistical Communication and Detection," Griffin, London,

1967.
ORIGINAL PACE IS

OF POOR QUALITY

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INFORMATION THEORY 'LATERAL DENSITY DISTRIBUTION

David P. Rubincam

OBJECTIVE

The objective of this work is to use information theory to infer the lateral

density distribution inside the earth, using the external qravity field,

crustal models, and an assumed radial density distribution as data.

BACKGROUND

The external gravity field gives information about the lateral density iii stribution inside the earth. However, it does not given anough information

to determine the actual density distribution pI(y,6,X). The lateral

density distribution must he inferred, not inverted from the data.

The inference technique used here is information theory better known as the

Maximum Entropy Method (MEM) The rationale for using information theory is

that it provides, in a certain sense the least prejudiced inference from the

available data. In other words, it does not read more into the data than is

actual 1y there.

RECENT ACCOMPLISHMENTS

A complete description of the work summarized here may be found in Rubincam

(1982). Briefly, a density distribution pI(-y,6,X) is inferred from the

the GEM 1OB gravity field coefficients C Qm , Skm (complete to degree and

and order 36) after subtracting off the coefficients of the hydrostatic bulge

and an assumed crustal model. Two different models were used: one an isostatically compensated crust, and the other an uncompensated crust. Also the

radial part of pI(y,e,a) is taken to be the Parametric Earth Model of

Dziewonski et al (1975).

The following results were obtained. The density anomalies generated by

PI(y,6,a) tend to be spread throughout the mantle, but the largest

anomalies occur near the top of the mantle. Typical density variations in

the mantle are +0.004 g cm -3 when the compensated crust is removed and

+0.04 g cm-3 when the uncompensated crust is removed. The lateral density

variations across the equatorial plane are shown in Figs. 1 and 2 for compensated and uncompensated crusts remoived, respectively.

SIGNIFICANCE

The pI(y,6,X) for either compensated or uncompensated crusts shows no

obvious convection pattern in the mantle (such as organized convection cells).

Hence mantle convection cannot be inferred from the gravity field data alone.

Also, the information theory density distributions are quite different from

the minimum elastic energy solution of Kaula (1953) and from the minimum

elastic plus gravitational potential energy solution of Sanchez (1980).

2-14
FUTURE EMPHASIS

The extension of the information theory approach so as to include seismic

data appears quite difficult. Hence no future work -in this area is planned.

REFERENCES

Dziewonski, A.M., A.L. Hales, and E.R. Lapwood, Parametrically simple earth

models consistent with geophysical data, Phys. Earth Planet. Interiors, 10,

12-48, 197.5.

f^ Kaula, W.M., Elastic models of the mantle corresponding to variations in the

external gravity field, J. Geophys. Res., 68, 4967-4978, 1953.

Rubincam, D.P., Information theory lateral density distribution for earth

inferred from global gravity field, J. Geophys. Res., 87, 5541-5552, 1982.

Sanchez, B.V., Lateral Density variations in elastic earth models from an

extended minimum energy approach, NASA/GSFC TM 80742, Goddard Spare Flight

x Center, Greenbelt, MD, June 1980.

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Figure 1. Lateral density variation in the equatorial plane of the earth for the case of 30km of compensated

crust removed. Sea level is displaced from the earth's surface fo. clarity, and the rock-equivalent

topography is greatly exaggerated. Anomalies in the core are not shown

2-16

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crust removed. Sea level is displaced from the eart:i's surface for clarity, and the rock-equivalent

topography is g.eatly exaggerated. Anomalies in the core are riot shown.

2-17
2-18

ORIGINAL PAGE 19

OF POOR QUALITY

ATMOSPHERICALLY INDUCED VARIATIONS IN THE LENGTH-OF-DAY DERIVED FROM LAGEOS

David E. Smith

Demosthenes C. Christodoulidis

George H. Wyatt

OBJECTIVE

A comparison is made of the length-of-day derived from Lageos with the lengthof-day inferred from atmospheric wind data in order to determine the extent of

the correlation, accuracies of the two data secs, and to better understand

the causes of the changes in the earth's rotation rate.

BACKGROUND

Recently, global atmospheric wind data have been used to derive estimates for

the angular momentum of the atmosphere (Rosen & Salstein, 1981) and, under the

assumption of the conservation of angular momentum between the solid-earth and

1 - `~1. itYtisptierc^ " ^"^ ^^ cnc ^ cac.l ^ 1 n c ^ , t • g change i.r! ' rotation _ rate of the solid earth has

been derived. In these computations the atmospheric zonal winds have been

integrated from the surface (1000 mbars) to the 100 mbar level (i.e. 16 km) and

averaged into latitude bands from which the angular momentum of the atmosphere

has been derived every 12 hours since 1976. Considerable seasonal and short

period (tens-of-days) variations are evident in this data set which has been 

compared with the actual changes in the earth's length-of-day derived from

laser tracking of the Lageos spacecraft between May 1976 and July 1981.

RECENT ACCOMPLISHMENTS

The atmospheric angular momentum data was averaged to 5-day values so as to

coincide in time with the Lageos length-of-day (LOD) values. The two data sets

were analyzed using identical methods. A spectral analysis of the atmospherically inferred LOD for the whole 6-year period showed considerable power at a

period of l yea r and a smaller, but significant, amount at 6 months. There

appeared to be no secular trend or very long period evident in the data.

The spectrum of the Lageos LOD showed greatest power at 6 months and almost

the same at l year and significant. power also at about 1166 days and 285

days. These latter periods are periods related to the tidal perturbations

of the orbit by the K1 and S2 tides respectively and are not actual variati ons in the rotation rate of the earth. They were estimated and removed

from the Lageos data set. The Lageos data set also showee a secular trend

that indicated that the length-of-day was decreasing (earth was speeding up)

at a rate of about 0.15 msecs fyr over the 6-year period. This trend is

believed to be a result of changes within the earth's core and probably

tv,,iporary in nature. Historical -records of the earth's rotation rate show

"decade length" changes that have g ;generally been ascribed to core motions.
2-19

ORIGINAL PAG'8 x

OF (POOR QUAD

After removal of the secular trend and the tidal perturbations of the Lageos

orbit (1166 days, 285 days) from the Lageos LOD data, the two data sets were

compared. Figure l shows the atmospheric data superimposed on the Lageos data

after the average value has been removed from each set. The correlation between the two "raw" data sets is 0.82 and the rms difference is 0.19 milliseconds. A major contributor to the rms difference is the very large noise

present in the 1976 and 1977 Lageos LOD values. The best year, in terms of

Lageos tracking, is 1980 when. the correlation between the two LOD data sets

is 0.90 and the rms difference in LOD values is 0.15 milliseconds.

The high degree of correlation between the two data sets is partly clue to the

strong annual and semi-annual periods in both data sets, and the rms difference

between the curves is also greatly affected by the fact that each data set has

different amplitudes for these terms. When the annual and semi-annual tems are

removed from the data for the year 1980 the correlation falls to 0.67 (stil

very good) and the rms difference falls to 0.10 milliseconds. The decrease in

rms can be almost completely explained by the removal of the power at 1 year

and 1/2 year that appears in the single point rms, The true level of agreement

between the atmospheric and Lageos data sets can be hest; seen in the year 1980

when .a comparison of the two data sets is made after they have been weakly

smoothed (so as to remove some of the measurement noise) and the annual and

semi-annual terms removed. This comparison is shown in Fig. 2. The smoothing

is achieved by a Gaussian `ire i ghti ng where the FWHM is about 8 days. The

resulting rms difference is 0.069 milliseconds and the correlation is raised to

0.78.

CONCLUSIONS AND FUTURE EMPHASIS

Comparisons of the atmospheric and Lageos data sets strongly support the concept that most changes in the earth's length-of-.day can he ascribed to

changes in the earth's zonal winds. Good correlation appears to exist between the data sets for periods oi' about 10 days to more than a year. The

disparity that appears in the amplitudes (0.17 msecs) at 1/2 year period is

probably caused by winds not included in the atmospheric data, i.e., those

above 100 mbars (Lambeck, 1980). At 1 year, the disparity (0,12 msecs) in

amplitudes is probably associated with the lack of atmospheric data above

100 mbar but. is also affected by the lack of consideration of variations in

the angular momentum of the oceans (Eubanks, 1983).

Future work will try to explain the present differences and investigate other

causes of change in the earth's length-of-day.

REFERENCES AND BIBLIOGRAPHY

Barnes, R.T. H., R. Hide, A.A. White and C.A. Wilson, "Atmospheric Angular

Momentum Fluctuations, Length -of-Day Changes and Polar Motion," Proc. R. Sco.

Lond. A387, 31-73, 1983.

is
ORIS`1.i^ "j

OF POOR QUALITv

EUbanks., T.M., J.A4 .:eppe, J.O. Dickey and P.S. Callahan, "A Spectral Analysis

of tre Earth's ; !lar Momentum Budget," J. Geophys. Res. (in press).

Hide, R., N.T. Birch, L.V. Morrison, D.J. Shea and A.A. White, "Atmospheric

Angular Momentum Fluctuations and Changes in the Length of flay," Nature, Vol.

286, 10, July 1980.

Lambeck, K., The Earth's Variable Rotation: Geophysical Causes and

Consequences, Cambridge University Press, 1-9-8-F.

Lambeck, K., "Changes in Length-of-Day and Atmospheric Circulation," Nature,

Vol. 286, 10 July 1980,

Langley, R.R., R.W. King, I.I. Shapiro, R.D. Rosen and D.A. Salstein,

"Atmospheric Angular Momentum and the Length of flay: A Common Fluctuation

with a Period Near 50 Days," Nature, Vol. 294, 24 December 1981.

Rosen, R.D. and D.A. Salstein, "Variations in Atmosperic Angular Momentum

1 January 1976 - 31 December 1980," ERT Technical Report A345-T1, June 1981.

Rosen, R.D. and D.A. Salstein, "Variations in Atmospheric Angular Momentum

and the Length of Day," ERT Technical Report A345-T2, October 1982.

Rosen, R.n., and O.A. Salstein, "Variations in Atmospheric Angular Momentum

on Global and Regional scales and the Length of Day," J. Geophys. Res. (in

press), 1983.

2-20
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CHAPTER 3

GRAVITY FIELD MODEL DEVELOPMENT

OVERVIEW

Knowledge of the earth's Gravity field is fundamental to understanding

the dynamics of the earth. For solid earth physics, knowledge of the

variations in the gravity field provides information on the earth's

physical properties and geodynamic processes and places constraints on

the internal structure of the earth. In oceanography, knowledge of

departure of the actual sea surface from a unique equipotential surface

of the earth's gravity field (the geoid) can reveal information on oceanic

circulation. In addition, other areas which benefit from knowledge of

the earth's gravity field are satellite orbit determination and classical

geodesy.

This chapter describes: (1) the development of a refined gravity field

model for_AGEOS in order to obtain more accurate orbits that will

provide better baseline measurements for the analysis of tectonic plate

motion; (2) the study of the evolution of the orbit of LAGEOS for the

purpose of improving our knowledge of the force model for the satellite's

motion; (3) the development of specialized earth gravity field model of

the STARLETTE satellite to improve the precision of that satellite's

orbit, and (4) current and future geodynamic computational systems

development.

I"untributors to this chaper include D.C. Christodoulidis, F.J. Lerch,

J.G. Marsh, B.H. Putney and D.E. Smith
OF POOR QUALITY

GRAVITY MODEL REFINEMENT FROM LAGEOS

Francis J. Lerch

OBJECTIVE

The objective is to improve the gravity field model for Lageos in order

to obtain more accurate orbits that will provide better baselines for

plate tectonics, improved polar motion and earth rotation. Also the

purpose is to improve the low degree and order geopotential which will

provide for refinement of our knowledge of the broad features of ocean

circulation.

BACKGROUND

The development of the gravity field for Lageos is a principal investigation in the Crustal Dynamics Project. Based upon the previous Goddard

Earth Model, GEM 9, baselines from Lageos orbits gave an rms of approximately ±5 cm from a global set of laser tracking sites. Statistical

error analysis based upon the GEM 9 accuracy of the coefficients confirms

that the baseline error (±5 cm) from Lageos can be attributed significantly to the gravity field model. From the accuracy of the Lageos

laser data (down to ±10 cm) error analysis shows that the gravity

model can be improved on Lageos to the extent that baseline errors should

reduce by at least 50 perceGt of previous values when considering errors

t

only due to the gravity field.

f

RECENT ACCOMPLISHMENTS

A refined gravity field model, Goddard Earth Model GEM-L2 (Lerch, et

al.), has been derived using the Lageos orbital data yielding better

baseline measurements for the analysis of tectonic plate motion. This

field also contributes to a better understanding of the broad features

of ocean circulation through its improvement of the long wavelength geoid

(terms through degree and order 4) with an accuracy estimated at ±8 cm.

In GEM-L2 two and a half years of Lageos laser data acquired from over

2V well-distributed stations were combined with the existing data from

the best satellite-derived model, GEM-9 (Lerch, et al.). Testing shows

that the Lageos gravity field error at long wavelengths is less than half

that for GEM 9.- A comparison of global laser "base" stations from independent data sets of alternating 15-day data segments over the 2 1/2

years of Lageos show total interstation position to x-1.8 cm (Table 1)

when using this new model. The same comparison using the 1979 versus the 

1980 Lageos data yields ±5.2 cm; this difference in agreement re h,

flects the change in data distrbituion and other systematc errors along

r with the tectonic motion which has occurred between these chronolo

cally distinct data sets. Polar motion values were adjusted in GEM-1_2 

to a precision of 10 cm, which *s shown to be necessary to achieve the 

accurate baseline and geopotential results. 

3-2 

LZ
3-3

SIGNIFICANCE

The accuracy of the GEM-L2 long wavelength geoid of ±8 cm should

provide improved accuracy in the broad features of ocean circulation from

application of Seasat altimetry.

Results based upon the gravity model GEM-L2 including adjustments of BIH

polar motion and earth rotation from Lageos laser data have shown that

laser tracking systems yield an intrinsic accuracy of 1.8 cm for a global

set of baselines (Table 1). Tests in this table clearly show that it is

equally important to adjust the polar motion and earth rotation as well

as the gravity field with the Lageos data in order to achieve the 1.8 cm

baseline agreement.

FUTURE EMPHASIS

Future work is continuing with use of more recent and accurate laser data

from Lageos.

REFERENCES

Lerch, F.J'., S.M. Klosko, R.E. Laubscher, C.A. Wagner, "Gravity Model

Improvement Using rEOS-3 (GEM 9 and 10)," GSFC X=9?1-77-246, September

1977; also, J. Geophys. Res., Vol. 84, 3897-3916, July 31, 1979.

Lerch, F.J., S.M. Klosko, R.E. Laubscher, C.A. Wagner, "Gravity Model

Improvement Using GEOS-3 Altimetry (GEM 10A and 10B)," EMS, Vol. 59,

No. 4, 260, April 1978.

Lerch, F.J., B.H. Putney, C.A. Wagner and S.M. Klosko, "Goddard Earth

Models for Oceanographic Applications (GEM 10B and IOC)," Marine Geodesy,

Vol.. 6, No. 2, 1981.
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OF POOR QU L. ` `r

LAGEOS ORBIT EVOLUTION

Demosthenes C. Christodoulidis

and

David E. Smith

OBJECTIVE

Analysis of the evolution of the orbit of the Lageos satellite can improve

our knowledge of the force model for the satellite ' s motion. More accurate

representations of the earth, ocean and atmospheric tides and of the

gravity model are of general geophysical interest. Improvements in the

perturbation model for drag or radiation pressure will allow better

determination of the geodynamic -easurements which are the main goals of

the Lageos analysis.

BACKGROUND

Rubincam (1980) has suggested charged particle drag as the cause of an

observed downward trend in the satellite's semimajor axis. Anselmo, et

al. (1983) have proposed a model for the variations about this trend based

on the effect of reflected radiation from an earth whose albedo exhibits

hemispherical assymetry.

The procedure employed to determine a set of locations for the network

of stations over the total time period for which laser servations of

the Lageos satellite are available has been described by _ pith, et al.

(1978). It includes the adjustment of Lageos ' elements at the epoch of

each 30-day time span over which a dynamically consistent orbit is determined, and which is the subject of the orbit evolution studies.

RECENT ACCOMPLISHMENTS

The estimated values of along-track acceleration at 30-day intervals

obtained in a recent solution are shown in Figure 1. Their average effect

of -3.3 x 10- 1 2 m/sect corresponds to a semimajor axis decrement of

approxiamtely 1.1 mm/day. The semimajor axis time history due to this

unmodeled force is shown in Figure 2 as two time spans during which the

semimajor axis decrement was about 1.1 mm/day separated by a period in

1979 when it was somewhat larger in magnitude.
az

OF POOR QUALITY

The inclincation and node residual signatures shown in Figures 3a and 3b

include the effects of errors in the adopted tidal model on the estimated

orbit parameters. The variations can be reduced by correcting the

inclination and node values with sinusoidal functions at the three tidal

frequencies of 1051, 521, and 280 days corresponding respectively to the

K1, K2 and S2 tides. If we assume that the earth tidal model (Wahr, 1979)

is correct, these functions can be used to correct the second and fourth

degree terms of the ocean tidal model (due to Schwiderski). The values

derived in the Lageos analysis are shown in Figure 4 together with those

corresponding to the Schwiderski ocean tidal model and that due to Yoder

(JPL E.M. 335-30).

SIGNIFICANCE

The relatively low amplitude in the second degree S2 tide observed by

Lageos could be caused by the atmospheric tide to be expected at this

frequency. The only other serious disagreement with the ocean tidal models

is in the phase of the fourth degree term at the K1 frequency. This is a

manifestation of the long period variation observed in the nodal signature

of Figure 3b. An error in our model of the 18.6 year tide could provide

an alternative reason for this error. Although the effect of the neglected'

ocean tide at this frequency is too small by a factor of 10, an increase

in the effective Earth tidal Live number kp from 0.299 to 0.6 could

produce a nodal variation similar, to that observed.

The amplitude of a quadratic function of time which can be usedto describe

an observed curvature in the nodal signature corresponds t(c a variation in

the second zonal harmonic J 2 amounting to -.35 x 10 /yr. Rubincam

(1983) has proposed post-glacial rebound as the cause of this variation,

which when removed leaves us with a signature dominated by errors in the

adopted time reference system of the BIH Circular D.

FUTURE EMPHASIS

Numerical models of the earth's albedo will be calibrated and employed to

help explain the observed variati ons in the semimajor axis and eccentricity of Lageos. As the time history of the inclination and node signature extends, better separation of the tidal frequencies will be possible.

Improved definition of the quadratic nodal signature which can be described

by a variation in the earth's second zonal harmonic can also be expected.
OF POOR UALP-I

REFERENCES

Rubincam, D.P., "Atmospheric Drag as the Cause of the Secular Decrease in

the Semi-Major Axis of LAGEOS' Orbit," Geophys. Res. Lett. 7, No. 6, 1980.

Anselmo, L., P. Farinella, A. Milani, A.M. Nobili, "Effects of Ear•thReflected Sunlight on the Orbit of the LAGEOS Satellite," Astronomy and

Astro hysics, in press, 1983.

Smith, D.E., R. Kolenkiewicz, P.J. Diann and M. Torrence, ""Determination of

Polar Motion and Earth Rotation from Laser Tracking of Satellites," Proc.

IAU Symp., No. 82, 1978.

Wahr, J.M., "The Tidf Motions of a Rotating, Elliptical, Elastic and

Oceanless Earth," Ph.D. Thesis, University of Colorado, 1,979.

Yoder, C.F., "Spherical Harmonic Decomposition of M.E. Parke's Ocean Tidal

Models," J.P.L. Eng. Memorandum 335-30.

Rubincam, D.P., "Postglacial Rebound Observed by LAGEOS and the Effective

Viscosity of the Lower Mantle," NASA Technical Memorandum 84982, 1983.

3-7 
OF POOR QUALITY

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YEAR

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1976 1977 1978 1979 1980 1981 71

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D 200 40 600 800 1000 1200 1400 1600 1800 2000 2200

DAYS' FROM LAUNCH IN MAY 1976

Figum2. Evolution uf the LAGEO8 Semi-Major Axis

3-8
SECOND DEGREE FOURTH DEGREE

AMP PHASE AMP PHASE

(cm) (deg) (cm) (deg)

K1 LAGEOS 3.03 ±.12 322 ± 2 1.93 +.36 150 ±11

SCHWIDERSKI 2.82 315 1.92 254

PARKE/YODER 2.46 312 1.72 241

K2 LAGEOS 0.10 ±.02 340 ±12 0.23 ±.07 245 ±19

SCHWIDERSKI 0.27 316 0.11 105

PARKE/YO D E R -------- ------- ----- ------

S2 LAGEOS 0.74 ±.04 309 ± 3 1.01 x-.16 85± 9

SCHWIDERSKI 0.93 314 0.37 103

PARKE/YODER 0.88 301 0.39 85

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3-10

R

GEODYNAMICS AND GEODETIC PARAMETER ESTIMATION

FROM STARLETTE LASER TRACKING DATA

James G. Marsh

OBJECTIVES

Laser tracking data covering a 4-year period (1975-1978) have been analyzed for the development of a specialized earth gravity model for

STARLETTE precision orbit computations. Subsequent to this development,

a detailed analysis of the STARLETTE laser data recorded during 1980 has

been performed for the estimation of tracking station coordinates, polar

motion, GM, and ocean tidal constituents. This solution is a simultaneous least squares solution based upon normal equations for 65 5-day

arcs of laser tracking data.

BACKGROUND

satell ite lau 4 February a '75 (CNES. The Starle'Gte ..n..hr `d in 19,E ^ ► , ►vw/ GRGS, 1975) by

the French Centre National d`Etudes Spatiales (CNES) was designed to

minimize the effects of non-gravitational forces and to obtain the highest

possible accuracy for laser range measurements. The satellite is a sphere

with a radius of 12 cm. It is a passive satellite constructed of a core

which is largely Uranium 238 covered by an aluminum alloy shell which

contains 60 laser corner reflectors. The mass of the satellite is 47.295

kg. The orbit has perigee and apogee heights of 810 km and 1105 km

respectively and an inclination of 49.8 degrees. 

Laser tracking data recorded during the time span from 1975 to 1981 have

been used in these analyses. The data analyzed have been contributed by

the CNES, Smithsonian Astrophysical Observatory (SAO), Goddard Space

Flight Center (GSFC) and the Technische Hogeschool Delft in the

Netherlands.

Initial orbit computations using 5-day arc lengths of the laser data

produced rm fits for a typical set of orbits in 1979 which ranged from

1.5 to 3 meters. In these reductions the GEM 10B gravity model was used.

Analyses of these solutions indicated that the primary error source was

the earth gravity model, and thus a comprehensive effort was undertaken

to adjust all gravity model coefficients which would have an effect of 1

cm or larger on the STARLETTE orbit. The final set of coefficients

adjusted consisted of a complete (36,36) model plus selected higher order 

coefficients to degree (48)
The high level of orbital accuracy provided by this gravity model solution

has provided a basis for the adj;.,tment of a global set of tracking

station coordinates, polar motion, GM, and ocean tidal coefficients,

Laser tracking data recorded during 1980 have been used in these analyses.

RECENT ACCOMPLISHMENTS

The nruw STARLETTE -gravity model designated PGS-1331 reduced the rms

orbital fits for the laser data (5-day arcs) from several meters to a few

decimeters.

The analyses of the more precise globally distributed laser tracking data

recorded during 1980 have provided a highly accurate set of tracking

station coordinates. This independently derived solution has provided a

means of independently verifying the Lageos derived values and has thus

placed bounds on the overall precision relative to the center-of-mass cf

the coordinate system.

Comparisons of the STARLETTE derived tracking station coordinates with

those derived from LAGEOS at GSFC (GSFC SL5) and at the University of

Texas (UT8081 A-M) are presented in Table 1. In these comparisons,

translation and rotation parameters have been adjusted in order to removed

any systematic differences in the coordinate system definitions. The

AX and by translation parameters were small (<10 cm) however an

unexplained aZ shift of about 70 cm is noted between the LAGEOS

solutions. The rms agreement of the Starlette"derived values with the

LAGEOS solutions is generally better than 20 cm.

The recovered value for GM is 398600.43 ± .01 km 3/sec 2 which is in good

accord with the value of 398600.436 recovered by Smith, et al. (1983)

from 1980 LAGEOS data. This indicates the overall scale control in the

solution is good and that the potential model is reasonably complete.

From our previous work on STARLETTE presented in Marsh and Williamson

(1078) and in Felsentreger, et al. (1979), we were aware of the fact that

STARLETTE is significantly perturbed by tides. The earth and ocean

tidal effects on satellite position in a typical 5-day arc of STARLETTE

are substantially over a meter. Given a sparse data set, there is little

hope of attaining 10 cm station positions or baseline determinations

without -appropriately modeling this effect. At the time we designed this

current solution, our software system at GSFC, GEODYN, had recently been

enhanced with the capability to model the tides as individual

constituents. This modeling, developed by O. Christodoulidis, provides for linear responses at each specific frequency in the tide generating potential and is expressed in terms of the osculating ecliptic

elements of the disturbing body and the equatorial position of the

desired point on the earth's surface.

j
The approach we were able to use in this study is to recover tidal

parameters directly in the simultaneous least squares data reduction

along with the other geodetic parameters--tracking station locations,

geopotential coefficients, and the like. This technique is possible only

because or the improvement in the quality of the laser tracking data, in

our knowledge of the geopotential, and in our othe'r improved modeling

related to centimeter satellite geodesy and geodynamics.

Table 2 presents the STARLETTE recovered tides. These tides are the full

tidal effect relative to the Wahr free space potential, and the Woolard

nutati<on series coordinate system. Where significant sideband terms

existed (typically those differing by the period of the lunar node from

the dominant central term), the analytic theory of Cartwright and Taylor

(1971) and the later Cartwright and Edden (1973) have been used to

determine the appropriate value at the central frequency. The basic

assumption in this projection is that the earth's response function

(admittance) should be approximately the same at nearby frequencies.

Otherwise, the values are as recovered. Note that the diurnal tides are

appropriate to the coordinate system definitions described which incorporate the Woolard series nutations. The uncertainties in these values

range from about 0.5 cm in C20 to about 0.2 cm in C22.

SIGNIFICANCE

Analyses of the 1980 Starlette tracking data have:

o independently confirmed the relative positioning of the LAGEOS

recovered tricking station locations to an accuracy in each

coordinate of 20 cm.

o illustrated a sub-meter bias in the AZ network center of

origin in the satellite laser systems.

o demonstrated that the tidal response of the earth has been mapped

to better than .01 in effective k2 for the entire tidal frequency

range from the direct analyses of the laser tracking data.

This includes the determination of long period tides which are

fundamental to UT1 variations. This mapping substantially

agrees with a combination of the Schwiderski ocean tides and

the Wahr body tide.

o demonstrated that the precision laser tracked satellites are -

quite sensitive to nutation error and in fact may be a good way

to measure it.

o demonstrated that STARLETTE can be used to recover reasonable

polar motion -values after suitable corrections are made for

-nutation errors.
FUTURE EMPHASIS

Additional analyses using more recent laser tracking data recorded during

1.981 to 1983 are in progress. Techniques to better account for the effect

of using the Woolard notation series as versus using the modem Wahr

series are also in progress. These analyses are expected to provide. a

further refinement of the present parameters and further insight into

precision orbit determination at the decimeter level.

ACKNOWLEDGEMENT

This work has been accomplished as a result of the combined efforts of

myself, F.J. Lerch of the Geodynamics Branch and R.G. Williamson of the

Washington Analytical Services Center, EG&G.

the full details of this work are presented in a paper by Marsh, Lerch

and Williamson (1983).

REFERENCES

Cartwright, D.E. and A.C. Edden, 1973, "Corrected Tables of Tidal

Harmonics," Geophys. J.R. Astr. Soc., 33, 253-264.

Cartwright, D.E., and R.J. Taylor, 19;x':, "New Cm^ap4tations of the Tide

Generating Potential," Geophys. J.R {_ ^_Soct I -,,, . . c3 't5-s`t.

Centre National d'Etudes Spatiales, Groupe de Recherches de Geodesie

Spatiale, STARLETTE, Toulouse, France, February 1975.

Felsentreger, T.L., V.G. Marsh and R.G. Williamson, 1979, "M2 Ocean Tide

Parameters and the Deceleration of the Moon's Mean Longitude from Satellite Orbit Data," J. Geophys. Res, 84, No. b9 4675-4679.

Marsh. J.G., R.G. Williamson, "Precision Orbit Computations for

STARLETTE," Bulletin Geodesique, Vol. 52, No. 1, 1978.

Marsh, J.G., F.J. Lerch, and R.G. Williamson, "Geodynamics and Geodetic

Parameter Estimation from STARLETTE Laser Tracking Data," Bulletin

Geodesique, submitted, 1983.

Smith, D.E., D.C. Christodoulidis, P.J. Dunn, and M.H. Torrence, 1983,

"Geodetic Parameters Estimated from LAGEOS Laser Data, SL-5," presented

at the Fifth Annual NASA. Geodynamics Program Conference and Crustal

Dynamics Project Review, Washington, D.C.

3-13
?i

OF POOR QUALITY

Table 1. Tracking Station Coordinate Comparison

8 Stations

Starlette vs.

UT8081 A-M

Starlette vs.

GSFC SL5

GSFC SL5 vs.

UT8081 A-M

Translation Parameters Rms of Fit

AX eY AZ X Y Z

-9 cm. -4 cm. -43 cm. 19 cm. 25 cm. 19 cm.

8 4 29 17 2n 14

2 -8 -72 6 10 14 

7063 Greenbelt, Maryland

7086 McDonald Observatory, Texas

7090 Ya rragadee, Australia

7091 Haystack Massachusetts

7114 Owens Valley, California

7115 Goldstone, California

7907 Arequipa, Peru 

7943 Arrorai Walley, Australia
Table 2

Tidal Coefficients from 1980 Starlette Data Analyses

Relative to Wahr Earth Potential and Woolard Nutation

Second Degree Fourth Degree

Amplitude - C+ Phase* - e2m Amplitude- C4m Phase* - e4m

(cm) (deg) (cm) (deg)

Mm 065.455 1.99 42.7

M f 075.555 1.70 175.4

085.455 1.47 149.6

01 135.655 2.14 282.1 1..63 227.6

01 145.555 3.32 255.5 1.44 214.5

M 1

155.655 .37 284.6 .66 41.7

162.556 1.14 35.7 1.03 33.0

P1

163.555 .92 106.1 .74 174.9

K 1

165.555 3.28 32.2 3.40 3;'4.4

J 1175.455 1.34 75.9 1.00 292.5

001 185.555 4.56 109.9 .19 252.9

2N2 235.755 .05 159.9 .06 103.5

N 2245.655 .76 232.9 .24 102.7

M2 255.555 2.57 229.2 1.70 28.5-

T2 272.556 .27 13.4 .15 34.4

S2273.555 .78 302.4 .42 4.8

K2 275.555 .83 293.4 .53 6.0

*Doodson (1921) convention-used for Phase Definition

3-15
GEODYN PROGRAM SYSTEMS DEVELOPMENT

B.H. Putney

OBJECTIVES

The purpose of the Geodyn Orbit Determination and Parameter Estimation,

the SOLVE and ERODYN Programs is to recover geodetic and geophysical

parameters from satellite and other data in a state-of-the- art manner.

BACKGROUND

In 1971 the NONAME and GEOSTAR programs were combined to create the GEODYN

program. The SOLVE program was created at the same time. A few years later

the ERODYN, error analysis program was written. The philosophy of the

development of the software system has been maintenace of computer efficient, well-structured software, with appropriate orbit, earth and

numerical models, using precise satellite measurement modeling and efficient,numerical models, and performing careful benchmark procedures.

This care has paid off in the production of several GEM's (Goddard Earth

Models), precision station locations, improved tidal, GM, and polar

motion and earth rotation values and consistent baselines. Careful

usage, analysis, and modeling using laser, altimeter and other

satellite data from LAGEGS, SEASAT, STARLETTE, GEOS and BE-C satellites

as well as many others has made these accomplishments possible.

RECENT ACCOMPLISHMENTS AND SIGNIFICANCE

As part of the Crustal Dynamics Project a significantly improved gravity

field, pole positions, earth rotation, GM and baselines have been determined. The new solid earth and ocean tidal model and observation normal

point technique are being used and evaluated.

In support of GRM, several mission successful simulations were performed

using spherical harmonics, geoid heights and gravity anomalies. Numerical

experiments with block interpolation,= more accurate block integra -

tion, Fourier analysis of geopotential parameters and Householder transformation techniques for least squares estimation, have been studied.

In preparing for the MERIT Campaign the DE 118 JPL sun, moon and planetary ephemerides are available in GEODYN 8210 version. This provides us 

with improved planetary positions and the Wahr nutation series. In

addition, the ocean loading displacement is modeled in that same program.

Conversion of GEODYN and SOLVE to the Control Data Corporation Cyber 205

has been accomplished this year. Both programs are being optimized for

G that fomputer. GEODYN II is a rewrite of the GEODYN program. When

completed it will execute on the Cyber 205 and on IBM compatible 

computers. Initial timings on the sequential GEODYN program show a 20

percent improvement over the IBM 360/95 computer. Solve is running

3-10
i

i

I

i

} 3-17

three times faster on the Cyber than on the IBM 3081. We are pleased

with the progress on the new computer. Modifications to make this a

flexible tool, by allowing multiple satellites (GPS) to be handled in a

single arc, processing a pass of observations simultaneously, allowing

variation in numerical stepsize for high and low degree and order spherical harmonic coefficients, making easier additions of new adjusted parameters, restructuring of observation and input files to allow for more

information and precision, are designed into the new program. The SOLVE

program is currently being vectorized but its basic structure appears to

be appropriate for the Cyber. However, modifications of Input /Output

techniques are required for optimal use of the Cyber and these modifications are underway. Several new versions of GRODYN, SOLVE and ERODYN

were released this year. Versions of the program were requested and

delivered to England, Germany, Japan, the Netherlands, Australia, JPL

and Ohio State University.

FUTURE EMPHASIS

The conversion and optimization of the GEODYN and SOLVE programs on the

Cyber 205 will be completed. It is hoped to begin the conversion of the

ERODYN program as well. At this time it is very important to thoroughly

check out the GEODYN program models, i.e., albedo, relativity, plate

motion, tidal model, coordinate system. Reexamining of approximating

assumptions for correctness and for now required accuracies, of formulation and implement at ion i s now n

e

cessar

y

. Additional changes for the

MERIT campaign such as changing the reference year from 1950 to 2000

need to be implemented. It is desirable to model and solve for a set of

spherical harmonic coefficients for the sea surface topography and to

incorporate a ranc,Ie difference data type to be used with laser data.

The software will be modified to meet the needs of the Topex mission as

they are defined and required. Additional GRM modifications will be

made as defined and funded.

Every effort will be made to continue to mold the software in a timely

manner to support the needs of the scientific community determining

earth models.
CHAPTER 4

SEA SURFACE TOPOGRAPHY

OVERVIEW

The overall goal of this area of research is to apply remote sensing

data to studies of dynamic ocean and earth processes. The primary data

types are satellite altimetry data, orbit perturbation data and gravity

data. These data are analyzed in conjunction with surface observations,

for example, ocean temperature and density measurements.

Global sets of satellite altimeter data have been collected during two

satellite missions: The GEOS-3 mission (1975 to 1978) and the Seasat

mission (197$).

Research programs are underway in the following areas to analyze and

interpret the altimeter data: (1) the computation of highly precise

regional mean sea surfaces which can be used for studying the oceanic

mesoscale variability and to perform detailed analyses of the earth's

crustal structure; (2) the study of lithospheric flexure seaward of

subduction zones to obtain a better mechanical model of oceanic

lithosphere; (3) to develop and test an interpolation technique which

allows accurate extrapolation of tidal height fields in the ocean basins

by making use of selected satellite altimetry and conventional tidal

gauge measurements.

Contributors to this chapter include JeG. Marsh, n.C. McAdoc °^^'

B.V. Sanchez.
REGIONAL MEAN SEA SURFACES BASED UPON

GEOS-3 AND SEASAT ALTIMETER DATA

James G. Marsh

OBJECTIVE

The objective of this work has been the computation of highly precise

regional mean sea surfaces based upon crossing arc adjustments of the

combined GEOS-3 and SEASAT altimeter data sets. These surfaces have

provided a basis for studying the oceanic mesoscale variability and for

detailed analyses of the earth's crustal structure.

BACKGROUND

The GEOS-3 (1975-1978) and SEASAT (1978) altimeter experiments provided

very dense coverage in the N.W. Atlantic, the Gulf of Mexico- and the

Bering Sea. The number of available passes ranged from 558 in the Gulf

of Mexico to 1284 in the N.W. Atlantic. The GEOS-3 data were smotethed

over a frame to prVb 0 de data at a rate of 1 point second_ Only intensive

mode data were used, and gross data outliers were eliminated in the

smoothing process. The SEASAT data used were the JPL distributed

Geophysical Data Records (GDR) also at the rate of 1 point/second.

The precision of the GEOS-3 altimeter measurements is about 25 cm and

that of the SEASAT altimeter measurements is about 3-10 cm. However,

in orderto achieve precision of this order in the computed sea surfaces,

other sources of error, chiefly the radial orbit error of the spacecraft,

which may be on the order of a few meters, must be removed. This is

done in the crossing arcs least squares adjustment process.

The satellite radial orbit error is primarily due to the errors in the

gravity field model. Several studies have shown that most of the radial

orbit error has frequencies close to once per rev. Thus, over distances

of thousands of kilometers, the radial orbit error can be well represented by a linear function of time, and can therefore be removed by

the least squares adjustment process if the parameters of a linear

trend are solved for. Any other long wavelength sources of error, for

example errors caused by mis-modeling of the ocean tides, will also be

removed in the adjustment process. The adjustment process has been

extensively described elsewhere (Marsh, et al., 1980).

The large amount of data in these areas coupled with the increased

constraints provided by the combination of data from two orbital

inclinations has provided the basis for a detailed precision adjustment

of the data. The precision of these surfaces is estimated to be on the

order of 15 cm with a horizontal resolution of 25 km.

F

{

4-Z
4-3

F

f

RECENT ACCOMPLISHMENTS

Figure 1 shows the sea surface contour map of the Northwest Atlantic

derived from the SEASAT and GEOS-3 altimeter data. Sev!aral features of

the ocean floor topography are clearly reflected in the sea surface

topography. Bermuda is clearly visible, and the lbng minimum in the

center corresponds to the Hatteras abyssal plain. To the west, the

Blake Bahama Outer Ridge and the Blake Escarpment are visible.

Figure 2 shows the sea surface computed in the Bering Sea using SEASAT

and GEOS--3 altimeter data. The surface clearly shows where the shallow

ocean over the continental shelf (in the northeastern portion of the

map) is divided from the deeper ocean over the Bering Abyssal Plain in

the southwest of the sea. Also clearly visible are the !ocean bottom

ridge at about 170 1 longitude, and the feature known as Bowers Bank

(the circular feature below latitude 55° and between 175° and 180°

longitude).

The details of this work are presented in a report by Marsh et al.

(1983).

SIGNIFICANCE

Except for mean dynamic topography, the altimetric surfaces presented

in this paper are equivalent to the geoid. It should thus be possible

to use these surfaces to remove the geoid signal from synoptic altimeter

data in ort,`er to detect transient mesoscale features. Of course, one

must proceed with caution for a quasi-permanent current such as the

Gulf Stream, since both synoptic and time-averaged altimeter data

contain a Gulf Stream signal. In contrast, gravimetric reference

surfaces can be used to detect permanent circulation features. This is

demonstrated in Figure 3 where we have differenced the Atlantic 3-year

mean surface with the detailed 5' geoid model of Marsh and Chang (1978).

The Gulf Stream can be clearly seen as a 1-m step running eastward from

Cape Hatteras. South of the Gulf Stream is a broad area in which the

two reference surfaces show agreement to within approximately 20 cm.

Even though this area is populated by cold rings with sea height

signatures of 50-100 cm, the transient nature of these features causes

them to be considerably smoothed in the 3-year mean surface. Large

differences occur in the northeast due , to the New England seamounts and

in the southwest due to the Bahamas. These differences are attributable

principally to errors in the detailed geoid model.

FUTURE EMPHASIS

Future work in this area will be oriented toward further definition of

mesoscale variability from crossover difference statistics, the detection and monitoring of individual cold and warm core rings using the

mean sea surfaces as a reference and toward the orientation of these
highly precise mean sea surfaces into an absolute center-of-mass coordinate reference system.

ACKNOWLEDGEMENTS

This work is the result of the combined efforts of myself, Robert Cheney

of the National Geodetic Survey, and Tom Martin, and John McCart, hy at

the Washington Analytical Services Center, EG&G.

REFERENCES

Marsh, J.G., R.E. Cheney, J. McCarthy, T.V. Martin, "Regional Mean Sea

Surfaces Based Upon GEOS-3 and SEASAT Altiemter Data," submitted to

Marine Geodesy, 1983.

Marsh, J.G., T.V. Martin, J.J. McCarthy, "Mean Sea Surface Computation

Using GEOS-3 Altimeter Data," J. Marine Geodesy, Vol. 3, No. 1-4,, 359-

379, 1980.

Marsh, J,,G., E.S. Chang, "5' Detailed Gravimetric Geoid in the North

Western Atlantic Ocean," J. Marine Geodesy, Vol. 1, No. 3, 253-261,

June 1978.

4-4

w
ORIGINAL PACE iS

OF POOR QUALITY

48 — —

-.r

45

112 SEASAT PASSES

1272 GEOS-3 PASSES

421,993 ALTIMETER OBSERVATIONS

^5

461 0

25

^ ° 1-M CONTOUR

20 = ^^J l^`-^

r 70,532 CROSSOVER POINTS

15 27 cm RMS CROSSOVER DIFFERENCE

10 "' ° ' HI!i I I11lI HIlHlplli!i!!llillULl LI I II II III11 IILI VIII III VIII

275 280 285 290 295 300 305 310 315

Figure 1. Mean Sea Surface Based Upon SEASAT and GEOS-3 Altimeter Data, 1975 - 1978

4-5

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4-7
SEASAT OBSERVATIONS OF LITHOSPHERIC FLEXURE

David C. McAdoo

OBJECTIVE

The individual lithospheric plates move about the Earth's surface as units

which remain relatively rigid on geological time scales. it is of consicierable importance for geophysicists to know as much as possible about

the actual strength of the lithosphere including the dependence of

strength on age. This study of lithospheric flexure seaward of subduction zones seeks a better mechanical model of oceanic lithosphere. The

study is based primarily on SEASAT altimeter observations. An improved

understanding of forces acting at subduction zones is also sought.

BACKGROUND

The Outer Rise seaward of deep ocean trenches is generally attributed to

flexure of the oceanic lithosphere prior to subduction. Various models have

been proposed to describe this flexure. They all include a mechanically

strong lithosphere--loaded from the arcward side of the trench axis--overlying

a fluid-like asthenosphere. Simplest among them is the uniform elastic plate

model which was first applied to Outer Rises by Hanks (1971), and subsequently

by a number of others.

More complex models which include a variable rheology with depth have also

been developed. These complex models produce more realistic estimates of

stress but, aside from this, the elastic model hs been shown (Bodine, et al.,

1981) to be adequate for describing flexure of the oceanic lithosphere.

Quite naturally these lithospheric models have been tested almost exclusively

on bathymetric profiles. However, the Outer Rise also has _a clear gravitational expression. Watts and Talwani (1974) showed that gr-avity anomalies

over the Outer Rise tend to mimic--in form--the bathymetry. It should,

therefore, not be sjrprising that a geoidal counterpart of the Outer Rise

ests and is evidnt in the SEASAT altimeter observations of the marine

geoid. This study extends the popular elastic plate model to include a

predicted geoid signal and then tests this model directly on SEASAT observations of the marine geoid. One anticipated result from this study is a

clea r-or understanding of the dependence of the lithosphere's effective elastic

thickh ss (EET) on age.
Using bathymetric data Bodine, et al. (1981) concluded that- -in the absence

of horizontal loading--M effective thickness, Te, increases with age according to T = C • age Their results suggest the thickness (EET) is,

in severaf regions, significantly less than the value predicted by this

thickness-age relation; they attributed this discrepancy to horizontal compressive loads acting across these trenches.

RECENT ACCOMPLISHMENTS

A paper, McAdoo and Martin (1983) has been completed. In this paper, segments

of 102 SEASAT altimeter passes over six trench/Outer Rise complexes have been

analyzed. For each trench the number of passes analyzed is a follows: 11iddle

America, 14; Philippine, 12; Aleutian, 23; Mariana, 12; Izu-Bonin, 10; Kuril,

30. Thes sea surface height profiles obtained from these passes will be

treated as geoid height profiles.

After long-wavelength component of the geoid is removed, these observed geoid

height profiles--i.e., the SEASAT passes are then compared to geoid profiles

predicted by the elastic model. As an example, one pass over Mariana Trench

is shown in Figure 1.

Using the method of least squares, model parameters are adjusted and estimated

for each SEASAT pass. For each pass an estimate of flexural wavelength is

obtained. A mean flexural wavelength is then obtained from the er emble of

SEASAT passes over each trench. From this mean flexural wavelength, an

effective elastic thickness can be derived. The six crosses in Figure 2

represent the effective elastic thickness versus age of the subducting oceanic

lithosphere for each ol the six trenches studied. The solid curves represent

the thickness age law predicted by Bodine, et al. (1981) from thermal and

experimental constraints. The agreement between this law and effective

elastic thicknesses derived from SEASAT data is good; in fact it is better

than the agreement obtained in previous studies (see Bodine, et al., 1981)

which use bathymetric data--not SEASAT data--to estimate thicknesses (EETY.

The lack of agreement obtained in these previous studies was generally attributed to unmodeled horizontal compressive forces acting 2tcross certain

trenches. This work is described in McAdoo and Martin (1983); see also

MCA(oo, et al (1982).
SIGNIFICANCE

SEASAT altimeter data provide important new information on the deformation

of the lithosphere seaward of deep ocean trenches. These data, when compared with a mechanical model, produce estimates of the effective elastic

thickness of the lithosphere which are more consistent from profile to

profile in a given region than those derived from bathymetry. For the six

trenches which we studied, the effective elastic thickness derived from

altimetry increases with the square root of lithospheric age as predicted

by Bodine, et al. (1981). Significant horizontal compression across

these trenches is not indicated.

FUTURE EMPHASIS

The potential utility of SEASAT and other satellite altimeter data for

studying dynamics of the lithosphere and sub-lithosphere is only beginning

to be exploited. This particular study of outer rises will be extended to

include all the deep ocean trenches. Mechanical structure of the lithosphere can be similarly studied in mid-plate regions. These types of

studies which refine our models of the lithosphere are necessary if we are

to isolate, with confidence, dynamical effects arising beneath the lithosphere such as smallscale convection in the mantle.

REFERENCES

Bodine, J.H., M.S. Steckler and A.B. Watts, "Observations of Flexure and of

the Oceanic Lithosphere," J. Geophys. Res., 86, 3695-3707, 1981.

Hanks, T.C., The Kuril Trench-Hokkaido Rise System Large Shallow Earthquakes and Simple Models of Deformation," Geophys. J.R. abstr. Soc. 23,

173-189, 1971.

McAdoo, D.C. and C.F. Martin, "SEASAT Observations of Lithospheric Flexure

Seaward of Trenches," submitted for publication, 1983.

McAdoo, D.C., R. Kolenkiewicz, C.F. Martin, and S. Poulose, "The Correlation

of Bathymetry with Geoid Heights Near Trenches of the North Pacific," E®S

63, No. 5, 907, 1982.

Watts, A.S. and M. Talwani, "Gravity Anomalies Seaward of Deep-Sea Trenches

and Their Tectonic Implications," Geophys. J.R. Astron. Soc., 38, 119-141,

1974.
-10

I— I I I I I I

n 10 20 30 40 50 60

MARIANA

REV 379

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ORIGINAL PAGNE [S

OF POOR QUALITY,

SEAS' RESIDUAL

10

2

up

Ex

0 0

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TIME (SEC)

Figure 1. A residual SEASAT height profile compared with best fitting

result from the elastic plate model,

AGE (M.Y.)

40 80 120 160 200

F z

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`. R

4 Figure 2. Effective elastic thickness (EET) derived from SEASAT data (crosses)

over six trenches (Middle America. (MD), Aleutian (A), Philippine (P), Kuril (K),

Mariana (M) and Bonin (B). EET's are plotted versus age. Bodine, et al.'s (1981)

age-thickness relation is shown as curves.

4-11

` 4;
f^

AN OBJECTIVE ANALYSIS TECHNIQUE FOR EXTRAPOLATING TIDAL FIELDS

Braulio V. Sanchez

OBJECTIVES

1. ' To develop and test an interpolation technique which allows

accurate extrapolation of tidal height fields in the ocean

basins by making use of selected satellite altimetry measurements and/or conventional gauge measurements.

2. To develop a dynamical model of the ocean tides.

3. To test the technique initially for the M2 tide in a small

water body such as Lake Superior by theoretically computing

the tide and to compare the results with available tidal

data.

4. To test the interpolation technique in Lake Superior in

order to ascertain its capabilities for further application

in the ocean basins.

BACKGROUND

The theoretical foundation of the method used in the calculations is

based on Proudman's theory (1918) as reformulated by D.B. Rao (1966).

The theory provides a formulation for calculation of gravitational

normal modes and rotational normal modes of irregularly shaped basins

with realistic bathymetry. The method has been extended to compute

the forced solution (M2 tide) in Lake Superior to serve as a test to

evaluate the objective analysis procedure. The objective analysis

uses orthogonal functions that formed the basis to represent the water

level fluctuation field in the free and forced calculations. The

available tidal amplitudes and phases are expressed as a linear

combination of these functions. Since data points are usually available only at irregularly spaced points, instead of using the orthogonality property of these functions to determine the expansion coefficients, they are determined through a leas %;: squares procedure.

In the computation of the forced solution we include the effects of

the yielding of the solid earth to tide generating forces.

s

4-12
RECENT ACCOMPLISHMENTS

a. The M2 tide solution

Figure 1 shows the amplitude and phase fields for the M2 aide in

Lake Superior. The maximum amplitudes, which are close to 20 mm,

occur at the western end of the basin. The phase values obtained

by Mortimer and Fee (1976) from analysis of records of water levels

are given in parentheses. The amplitudes values were provided

by C.H. Mortimer (personal communication) from the original

calculations on the water level data. Also given are the phase

and amplitude values obtained in this investigation. The latter

are the values obtained at the grid points closest to the stations

in Mortimer and Fee's analysis. The contours of equal amplitude

and phase are given by the solid and dotted lines respectively.

The solution was obtained by including the first 80 eigenfunctions

from the velocity potential and stream function solutions. The

forced solution then contains 8n coefficients, the magnitudes of

the coefficients indicate the relative importance of the different

characteristic functions in accounting for the variance of the

total solution. Most of the power is contained in the first coefficient. The results for the first 12 coefficients are given in

Table 1. An examination of Figure 1 shows excellent agreement

B between the theoretically- computed tidal response and observed

amplitudes and phases. The theoretical simulation also serves as

a guide in choosing the most energetic modes to be used in the

objective analysis at any order of truncation of the representation.

b. Interpolation Technique Evaluation

c

The data locations selected for the analysis are the ten water

ti level stations analyzed by Mortimer and Fee. The tidal ampli-

*

tudes and phases at these ten locations were extracted from the

theoretical simulation. An objective extrapolation of the tidal

field is carried out with these 10 data points using 2,4,5,8,

and 10 most energetic modes listed in Table 1. A comparison of

the objectively analyzed amplitudes and phases with the "true"

values at all grid points is shown in Table 2. The table lists

the percentage of total grid points where the analyzed and true

values of amplitude and phase agree with each other within the

E limits indicated and for the number modes chosen in the objective

analysis. There are a total of 227 points within the basin.

Also given in the table are the rms errors of the amplitude over

E' the entire basin and only t the data points, as well as the

ratio of the potential energy of the analyzed and true fields.

It is seen from Table 2 that the method of analysis yields a

k, tidal height field that is within 3% of the "true" potential

energy with just 2 basis functions. As the number of functions

are increased to a, the energy difference is within 5%. For the

ten selected data points, the fit with 5 functions appears to be

the best. The tidal pattern using 5 coefficients is shown in

t

4-13

' 666

..,_. . 
4-14

Fig. 2.' Comparison with Fig. 1, the theoretical solution obtained with 80

coefficients, shows excellent agreement between the two fields. As the

expansion coefficients are increased to 10, which represents an exact determination of the values of the coefficients, the overall fit at the tidal

pattern deteriorates. Obviously, the maximum number of coefficients that

would result in a best fit over the entire basin depends on the number and

distribution (in space) of the available data points. The combination of

theoretical simulation and objective analysis also helps in choosing locations for additional observations that would contribute most to the resolution of the tidal field in an ocean basin.

SIGNIFICANCE AND FUTURE EMPHASIS

A method has been described to objectively analyze available tidal amplitudes and phases to map the tidal constituent over an entire basin. The

method consists of constructing a set of orthogonal functions that are

determined by the geometry and topography of the basin. These functions

are linearly combined and the expansion coefficients are determined from

available data in such a way as to minimize the mean-squared error by a

simple matrix inversion. Since the orthogonal functions used are characteristic of the given basin, they would reflect the basin properties in a

sense and hence would be capable of giving the best fit for the overall

tidal field in the basin. Using Lake Superior as a test case, a theoretical simulation was done for the M2 tidal ampitudes and phases in the

basin. This theoretically simulated field has been used as a "true" solution to evaluate the recovery of the total tidal field in the basin from

application of the analysis procedure to data taken at selected points.

The agreement between the analyzed and the "true" fields is found to be

excellent. The theoretically calculated M2 tidal heights and phases also

agree very well with those obtained from analysis of water level data by

Mortimer and Fee. The method is now being extended to ocean basins. The

results of the Lake Superior investigation have been submitted for publication by Sanchez, Rao and Wolfson.

REFERENCES

Mortimer, C.H., and E.J. Fee, 1976. Free surface oscillations and tides of

Lakes Michigan and Superior. Phil. Trans. R. Soc. of Lon. Ser. A, 281,

1-61.

Proudman, J., 1918. On the dynamical equations of the tides. Proc. of the

Lon. Math. Soc. 18, 1-68.

Rao, D.B., 1966. Free gravitational oscillations in rotating rectangular

basins. J. Fluid Mechanics, 25, 523-555.

Sanchez, B.V., D.B. Rao and P.G. Wolfson, 1983. An objective analysis

technique for extrapolating tidal fields in a closed basin. Submitted

to Marine Geodesy.

3
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ORIG#NAL PACE 6S

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8 .221'18) 9—IM

Figure 1. Theoretical solution for the M2 tide in Lake Superior (80 coefficients). Contours of equal

amplitude (mm} and equal phase (degrees) are given by the solid and dotted lines respectively.

The values from Mor—di er and Fee'S data reduction are given in parentheses.

A=22512.0

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A=12.78113.001 d-166(1(A) A=4.GM3.9% A-13.58112.281 0=1101 

0=16(22) 8°011)

Figure 2. Solution for the M2 tide based on objective analysis usilig 5 coefficients corresponding to the

five most powerful modes. Contours of equal amplitude (mm) and equal phase (degrees) are given by

the solid and dotted lines respectively. The values from the theoretical solutioe (80 coefficients)

used as data are g ,z;- in oarentheses.
Coefficients

Amplitude

--1

Phase

PA RMS RMS

<5% <10%0 <20% <50 <100 <200 - Error (Data

PT (mm) PTS)

2 23.8% 43.6% 64.8% 46,7% ^?,7% 83.3% 1.0295 1.2006 1.18

4 26.9% 51.5% 76.7% 64.8% 85.0% 96.0% 1.0749 1.2059 1.11

5 42.3% 67.8% 87.2% 61.2% 86.8% 93.4% 0.9521 0..8838 0.54

8 25.1 % 41.0°% 56.5% 59.9% 87.2% 96.5% 1.0872 3.1046 0.31

10 14.1% 22.9% 36.1% 24.7% 39.6% 58.6% 3.9678 12.185 0

ORIGINAL PAQ^e-' Iii

OF POOR QUALITY

Table 1

Power Spectrum for the M2 Tide

Mode Power (%) Period ( hours)

1 94.62 7.83

2 1.74 4.42

3 0.74 3.75

4 0.95 3.16

5 0.96 2.96

6 0.05 2.57

7 0.03 2.40

8 0.35 2.32

9 0.05 2.20

10 0.15 1.91

11 0.09 1-.82

12 0.10 1.65

Table 2

Comparison between Objectively Analyzed and Theoretical Fields
a

r.

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r

CHAPTER 5

ADVANCED STUDIES

OVERVIEW

The advanced studies activities considered by the Geodynamics Branch provide

a sound basis for the planning, design, and develop-- nt of sensor and space

mission concepts. Studies have been conducted basea on extensive current

research experience and simulations. The utility of the data expected from

these systems is evaluated in terms of predicted contributions to program

objectives and user applications.

Currently, the horizontal resolution of satellite-determined gravity field

models is of the order of 500 km. This level of resolution must be increased

to meet requirements for solid-earth and ocean studies. A gravity field

mapping mission, namely The Geopotential Research Mission (GRM) is planned

for the l atter part of t his decade to map the earth's gravity and magnetic

fields. GRM consists of two spcecraft in the same circular/polar orbit

with a separation distance varying from 1 0 to 6 0 and a nominal orbit altitude

of 160 km. From Doppler measurements made between the two satellites with

a precision of 1 micrometer per second it is the goal for GRM to map the

earth's gravity field to an accuracy of 1 miiligal and the geoid to an

accuracy of 5 cm with a horizontal resolution of 100 km.

Two GRM simulation studies are presen ed in this chapter. The studies

describe (1) the gravity field signal characteristics of the GRM Doppler

sensor and (2) the computer simulations which were performed to assess the

capability of GRM to map the gravity field of the earth for geophysical and

oceanographic applictions. Another new sensor is discussed in this chapter

which provides a method of precise )sitioning of a large number of points

on the earth's surface in a short period of time. That is, a measure of

the relative location of geodetic markers from an aircraft. Such a system,

"The Airborne Laser Ranging System (ALRS) is a potential sensor for performing rapid (few days) mapping of local crustal motion in 'seimsically

active areas.

In a somewhat different vein, an analysis of soil moisture based on measurements of the earth surface temperature has also been under study. Although

this study is most applicable to problems in non-renewable resources, the

coupling of soil moisture and atmospheric conditions to geodynamic processes

is also under investigati on,

Contributors to this section are: T.L. Felsentreger, F.J. Lerch,'W.D. Kahn,

and J.E. Welker_

i

f^A.

r,
ORIGINAL. PACE 19

OF POOR QUALITY

GRAVITY FIELD SIGNAL ANALYSIS STUDY FOR A GEOPOTENTIAL RESEARCH MISSION

(GRM)

Theodore L. Felsentreger

OBJECTIVE

The objective of this report is to discuss the gravity field signal

characteristics of the SST Doppler sensor to be flown on GRM.

BACKGROLND AND RECENT ACCOMPLISHMENTS.

The Geopotential Research Mission (GRM), formerly known as GRAVSAT/MAGSAT,

has been proposed for the mapping of the Earth's gravity field. It is a

candidate for a NASA new start in the near future. GRM is to be composed

of a pair of surface-force compensated satellites in identical polar

orbits, spaced approximately B° apart at a nominal altitude of 160 km

with a system precision of 1 um`sec.

The perturbation by the gravity field induced on the intersatellite

Doppler si gnal is given by the following relati onshi p:

t

i

 + st tl

E 07_

t 

LT dt —

1 aT dt

(1) r 8^ r `a^

where

ft to

T disturbing potential

a = Earth's mean equatorial radius

h satellite orbit altitude

r = a+h

V true anomaly

8t= time separation of two satellites in identical orbits.

The form of the disturbing potential most useful for formulating (1) is

F given by the formula

a

r Xg S(r ^) drs 1' (r) 47r f J (2 )

a

where 2a a 30 a2 r— a cos 0+ Q 

S (r, 'G) + r — T2— — ^ cos ^i S + 3 lin ( ) 

2r 

Q = [r2 + a2 — 2r a cos i,] %

og = mean gravity anomaly

da = element of area.
5-3

1'

4

OF POOR QUALITY

Using (1) and (2), velocity profiles resulting from the perturbation

produced by a (1° x1°) 1 mgal gravity anomaly as sensed by the two

satellites are shown in Figure 1-•-results are shown for 160 km and 200 km

satellite altitudes. The amplitude of the gravity signal drops off by a

factor of 1.5 when the altitude increases from 160 km to 200 km By

extrapolation the amplitude is further decreased by,about a factor of 3

when the orbital altitude is increased to 250 km. Thus, the amplitude of

the measurement drops off as the altitude increases, to the point where

the measurement amplitude is insignificant at the 1 mgal level for altitudes above 200 km. By way of contrast, Figure 2 shows the SST signal

generated by GRM for one full orbit, under the influence of a full

(36,36) spherical harmonic gravity field (GEM 10B).

The ability to resolve the signal from a (Y° x 1°) 1 mgal gravity anomaly

for two spacecraft whose orbits are displaced from the anomaly by l° and

5 0 is shown in Figure 3. For a 1 0 displacement, better than 50% of the

gravity signal is sensed; however, for a 5° displacement, only 10% of the

gravity signal is sensed. This implies that the gravity anomaly signals

from adjacent blocks drop off drastically with increased distance from

the satellite ground track. Nevertheless, it is significant that remote

gravity anomalies do contribute appreciably to the overall gravity signal.

FUTURE EMPHASIS

Studies of this type will be continued, along with rapid error analysis

and full-scale simulation studies.

REFERENCES

Kahn, W.D. and T.L. Felsentreger, "Signal Analysis and Error Analysis

Studies for a Geopotential Research Mission (GRM)," NASA TM 83970, July

1982.

Jekeli, C., and R.N. Rapp, "Accuracy of the Determination of Mean Anomalies

and Mean Geoid Undulations from a Satellite Gravity Field Mapping

Mission," The Ohio State University Department of Geodetic Science Report

307, August 1980.

Heiskanen, W. and H. Moritz, 1967, "Physical Geodesy," W.H. Freeman.

Lambeck, K., "Methods and Geophysical Applications of Satellite Geodesy,"

Reports on Progress in Physics 1972, Vol. 42, 547-628.

Kaula, W,.M., "The Appropriate Representation of the Gravity Field for

Satellite Geodesy," Proceedings of the IV Symposium of Mathematical

Geodesy; Trieste, 196.

Lerch, F.J., et al., "Gravity Model Improvement Using GEOS-3 (GEM-9 and

GEM-10),'" GSFC X-921-77-246, 1978.
ORIGINAL FAG. 'S OF POOR

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30 60 80 120 150 'ISO 210 240 270 300

TIME (SEC)

RANGE RATE SIGNAL PRODUCED, AT TWO ORBIT ALTITUDES

BY A SINGLE 1 DEG. X 1 DEG., 1 MGAL GRAVITY ANOMALY

Figure 1. GRM Anomaly Se'osing at Two Altitudes.

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ORIGINAL PAGE 10

OF POOR QUALITY
GRAVSAT SIMULATIONS FOR GEOPOTENTIAL ANALYSIS

Francis J. Lerch

OBJECTIVES

The objective of this work is to assess through computer simulations the capability of the Geopotential Research Mission (formerly Gra ysat for improving

the gravity field of the earth for geophysical and oceanographic applications.

Objectives of the mission are 3 mgal for gravity anomaly for geophysical analysis

and 10 cm for the geoid for ocean circulation with resolution down to 1 0 halfwavelength.

BACKGROUND

The Geoptential Research Mission (GRM) through use of a dedicated satellite

will map the gravity field fine structure over the earth and thus provide

knowledge and understanding of (1) the origin and structure of geological

features on the earth's sufface; (2) the mechanical properties of the earth's

lithospheric plates and the forces which drive their motion; and (3) the largescale circulation of the oceans and major current systems by the determination

of an improved ocean geoid.

The mission configuration for the GRM spacecraft consisted of two low-altitude

satellites at 160 km in a drag free system separated by 300 km (used for

simulations) with satellite-to-satellite doppler tracking (±1 micron/sec)

surveying the globe in polar orbits. Error analysis studies have been made for

GRM (see references). However, the main benefit of the present technique is

that a simulation is performed from numerical integration of the force equations

where a set of exact GRM observations are computed from an assumed gravity

model (ground truth) which is to be recovered from the study. This method is

free of a number of different approximations made in other studies but is

generally costly in computer time and hence must be limited to scope.

4

RECENT ACCOMPLISHMENTS

Computer simulation results for the Geopotential Research Mission (formerly

Gra y sat) have been obtained which support accuracy objectives of the mission,

namely 3 mgals for gravity anomaly and 10 cm for geoid height with a half-wavelength resolution of 1 degree. The computer <imulations were performed with

satellite =to-satellite doppler tracking (+ 1 micron/sec) between two low alti- tude satellites at 160 km in polar orbits and separated by 300 km in a dragfree environment for a 6-month mission lifetime. Results from studies have

been obtained as follows: (1) the recovery of sphrurical harmonics with potential coefficients complete through degree and order 36 gave an accuracy of 2

to 3 orders of magnitude better than current knowledge; (2) recovery of geoid

height and gravity anomaly in a local region (50 0 LAT x 20 0 LONG) in the presence of unmodeled errors external to the region gave an accuracyof 7 cm for

f geoid height and 4 mgal for the gravity anomaly for 1 0 x 1 0 blocks within the

interior of the region; (3) the recovery of 1/2 0 x 1/2 0 blocks of geoid height

and gravity anomaly in a local area containing a trench region gave, with use

of eigenvalue analysis, commission errors of 5 cm for geoid height and 3 mgal
for gravity anomaly for 1° x 1° block sizes; and (4) a Fourier analysis over the

trench region in (3) confirmed the results of this study which satisfy accuracy

goals of GRM. Table 1 gives a further summary of these results.

SIGNIFICAME AND FUTURE EMPHASIS

Results obtained so far are encouraging in that they satisfy mission goals but

they are not complete and need to be extended. Future analysis should be

conducted "Co s=,-xtend the spherical harmonics to high degree (10 to 100) to reduce

the aliasing eFfect on the solution due to the truncation of the harmonics.

Because of computer time limitations it is necessary to truncate the spherical

harmonic series. The residual potential including the smaller wavelengths of

the truncated harmonics will then be recovered from localized functions by

combining steps (2) and (3) above to cover a considerably broader region than

the 50° x 20° area used in the present analysis. Also, because of computer time

efficiency, the technique of deriving the potential first at satellite altitude

and then downward continuing the result to the surface of the earth is being

investigated.

TABLE 1. SUMMARY OF GRAVSAT SST SIMULATIONS

1. Recovery of Spherical Harmonics to 36 x 36

0 20 days of SST data only employed

0 2 to 3 orders of magnitude improvement over GEM 9

o Iteration will give another order of magnitude improvement

o Aliasing error is significant so a high degree solution is required

o Orbit parameters modeled with a priori constraints of 30 m in position

3 cm/sec in velocity

o Combined SST+NWL dopper tracking gave similar solution as above,

2. Geoid Solution in a Local Region

o Local solution of 1 0 x 1 0 geoid heights in a 20 0 x 500 region gave

7 cm accuracy for the interior region

0 Error mostly due to aliasing effects of unmodeled residual potential

exterior to the region

o A buffer zone of a priori constraints between the interior and exterior

regions was necessary to control the aliasing error

3. Short-Wavelength Resolution in Trench Aiki4a (Tonga Tr.)

0 1/20 x 1/20 geoid heights and gravity anomalies simulated over a

5 0 x 51 trench area

a The recovery gave errors for 1 0 x 1 0 blocks of 5.0 cm for geoid

height and 3.0 mgal for gravity anomaly by eigenvalue analysis.

Y 
5-9

REFERENCES

Bender, P.L., "Spherical Harmonic Fitting to GRAVSAT Rata," paper presented at

Fall Meeting of the AGU, 1982.

Breakwell, J.V., "Satellite Determinations of Snort Wavelength Gravity

Variations," J. Astronaut. Sci., 2.7 (4), 1979.

Colombo, O.L., "Global Geopotential Modeling from Satellite-to-Satellite

Tracking," Ohio State University Department Geological Science, Columbus, Rep.

317, 1981.

Douglas, B.C., C.G. Goad, and F.F. Morrison, "Determination of Geopotential from

Satellite-to-Satellite Tracking Data," J. Geophys. Res. 85, 5471-5480, 1980.

Jekeli, C. and R.H. Rapp, "Accuracy of the Determination of Mean Anomalies and

Mean Geoid Undulations from a Satellite Gravity Field Mapping Mission," Ohio

State Univesity Department of Geodetic Science, Columbus, Rep. 307, 22 pp, 1980.

Kahn, W.D. and T.L. Felsentreger, "Signal Analysis and Error Analysis Studies

for a Geopotential Research Mission (GRM)," NASA TM 83970, GSFC, Greenbelt, MD,

July 1982.

Kaula, W.M., "Inference of Variations in the Gravity Field from Satellite -toSatellite Range-Rate," J. Geophys. Res., in press, 1983.

Kaula, W.M., "The Next Development in Satellite Determintion of the Earth's

Gravity Field," Proc. USA-Hungarian 1981 Workshop on Dynamics, E6tv8s

University, Budapest, 127-134, 1982.

NAS (National Academy of Sciences) Committee on Geodesy of the National Research

Council, "Applications of a Dedicated Gravitational Satellite Mission,"

Washington, DC, 1979.

Pisacane, V.L. and S.M. Yionoul s, "Recovery of Gravity Variations from

Satellite-to-Satellite Tracking," Johns Hopkins University, Applied Physicsl

Lab, Baltimore, Rep. SDO-5583, 1980.

Pisacane, V.L., J.L. MacArthur, J.C. Ray, and S.E. Bergson-Willis, "Description

of the Dedicated Gravitational Satellite Mission (GRAVSAT)," Proc. Symp. Inst.

Geosci. and Remote Sensing, Washington, in press, 1981.

Rummel R., "Geoid Heights, Geoid Height Differences, and Mean Gravity Anomalies

from 'low-low' Satellite -to-Satellite Tracking--an Error Analysis," Ohio State

University Dept. Geod. Sci,, Columbus, Rep. 306, 44 pp, 1980.

Wagner, C.A. and C.C. Goad "Direct Determination of Gravitational Harmonics

fror- Low-Low GRAVSAT Data," J. Geophys. Res., submitted, 1983.
THE AIRBORNE LASER RANGING SYSTEM

Werner D. Kahn

OBJECTIVES

The Airborne Laser Ranging System (ALRS) is a potential sensor for performing

rapid (few days) mapping of local crustal motion in seismically active areas.

Through the use of covariance error analysis techniques, studies are performed

to determine measurement precision, measurement rate accuracy, and geometry

requirements for the ALRS to detect and monitor small earth surface motions.

BACKGROUND

The Airborne Laser Ranging Sytem is a proposed multibeam short pulse laser

ranging system on board an aircraft. It simultaneously measures the distances

betweeen the aircraft and six laser retroreflectors (targets) deployed c ► n the

earth's surface. Depending on the host aircraft and terrain characteristics,

the system can interrogate hundreds of targets distributed over an area as

large as 5 x 10 4 sq. kilometers in a matter of hours. Potentially, a total of

1.3 million individual range measurements can be made in a six hour flight.

The precision of these range measurements is approximately ±1 cm. These

! measurements are then used in a 'procedure which is basically an extension of

trilateration techniques to derive the intersite vector between the laser ground

targets. By repeating the estimation of the intersite vector, strain and strain

rate errors can he estimated. These quantities are essential for crustal

dynamics studies which include determination and monitoring of regional strain

in the vicinity of active fault zones, land subsidence, and edifice building

preceding volcanic eruptions.

G RECENT ACCOMPLISHMENTS

Simulations have shown that range measurements must be taken at two widely

separated altitudes in order to strengthen the geometry sufficiently to recover

baselines at the centimeter level in agreement with earlier results (1). Thus,

in a typical mission, the aircraft (i.e., NASA's NP3A Orion) approaches the

target grid at an altitude of 3.9 km as in Figure to After acquiring the first

few targets, the instrument shifts to the tracking mode for the remainder of

the mission. After overflying the rows of targets at 3.9 km, the aircraft

climbs to its maximum cruise altitude (say 6 km) for a second set of passes

over the target grid.

The spacing between targets will depend on several factors including the

scientific objectives of the mission, the aircaft altitude and the terrain

limitations. For the NP3A aircraft, the spacing is nominally taken to be 7 km.

At typical cruise velocities (i.e., 200 knots), laser range data to a given

target is taken for approximately • 130 seconds- before the pointing system is

commanded to acquire a new target. Fora laser repetition rate of 10 pps, this

corresponds to 1300 range measurements per target. Since a given target is

common to a number of six target sets, and data are collected at two altitudes, 

approximately 7800 measurements are typically made to each target.

5=10
Figure 2 shows the important of refraction errors and also illustrates that an

extensive network of meteorological sensors is not required. Atmospheric

measurements made at a single site collocated with a laser target within the

ALRS grid, will significantly reduce the effects of atmospheric refraction upon

ALBS baseline precision. In the estimation process, if the information from

that single "met sensor" is used and the atmospheric parameters for the other

ALRS targets are made part of the set of estimated parameters, a factor of about

7 improvement in baseline precision is achieved. The figure also shows that

the inclusion of additional meteorological sensors within the ALRS target area

does not signficantly improve baseline precision. In the simulation it was

assumed that the surface measurements of pressure and temperature were accurate

to 1 mbar and 1.4°C respectively. The vertical variation in pressure was

assumed to be determined by the hydrostatic equation.

In Figure 3 the evolution of baseline precision is given fora series of randomly

deployed laser targets. These targets are distributed (as shown in the inset)

in a potential ALRS flight test region in the vicinity of Shenandoah, VA. The

targets were located at approximately 17 first order survey monuments currently

maintained by the U.S. Geological Survey. The simulation indicates that the

random pattern does not significantly affect baseline precision as can be seen

by comparing the results with those in Figure 2. The baseline error typically

grows at the rate of 0.05 cm/km. for the simulation one meteorological sensor

was located in the middle of the gap and the meteorological parameter at other

sites were determined in the estimation process.

The ALRS System has the potential capability to measure the relative horizontal

and vertical locations of targets spaced tens to hundreds of kilometers apart

to precisions of a few centimeters, it is thus an attractive candidate for use

i,n a number of fundamental and applied crustal geodynamics measurements. Among

these measurements are relative motions of tectonic plates across the plate

boundaries and crustal determinations prior to and after major earthquakes.

Baseline rate accuracies can be obtained from the baseline precision by using

the covariance matrix from a least squares fit to a linear regression line.

S.C. Cohen in (2) analyzed the level of precision with which crustal strain

rates can be determined. The method used for the results given here follow his

analysis. By assuming that the baselines are surveyed during a one-day period

every 90 days, then as shown in Figure 4, baseline rate accuracies at the end

of°a ten-year observation period under the assumption of constant baseline

motion can be determined for 5 km baselines to better than 0.02 cm/yr and for

100 km baselines to about 0.1 cm/yr. By repeated measurements of the grid area

within the seismically active region to the baseline rate accuracy level

indicated, the ALRS could observe the deformation of plates at their boundaries,

as well as general plate motion and attempt to "capture" a moderate sized

earthquake, i.e., one of approximately magnitude 7 through repeated and densified monitoring of the grid area once changes in the baseline rate are

observed.
FUTURE EMPHASIS

Rigorous covariance error analysis studies for ALRS have been completed.

Approval is sought for an ALRS demonstration experiment. Upon approval, computer software must be developed in order to perform simulations which are to

verify the covariance analysis performed to date, also to test the closed

loop data processing capability and to develop the experiment plan encompassing

the operational aspects of the ALRS remonstration test.

REFERENCES

Mueller, I.I., B.H.W. Van Gelder and M. Kumar, "Error Analysis for the Proposed

Closed Grid Geodynamics Satellite Measurement System (CLOGEOS)," Department of

Geodetic Science Report No. 230, The Ohio State Univesity, September 1975.

Cohen, S.C. and G.R. Cook, "Determining Crustal `.,train Rates with a Spaceborne

Geodynamics Ranging System Data," Manuscripta Geodetica, Vol. 4 (1979), 245-260.

Kahn, W.D., J.J. Degnan and T.S. Englar, "The Airborne Laser Ranging System,

Its Capabilities and Applications," NASA TM 83984, September 1982.
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5-16
SOIL MOISTURE FROM TEMPERATURE MEASUREMENTS AT THE EARTH'S SURFACE

Jean E. Welker

OBJECTIVE

To determine soil moisture budgets at the earth's surface from soil and

atmospheric, temperature variations.

BACKGROUND

The soil surface and atmospheric interface can be considered a boundary

between two dynamic systems. On the one hand, the atmospheric strata.

immediately above the earth's surface can be viewed as a number of layers,

each responding individually and collectively to air flows and currents,

to irradiation both from incoming solar radiation as well as reflected

and emitted radiations from the ground surface below, and to rapid changes

of moisture content in its various states and accompanying heat transfers.

The soil immediately below the earth's surface can also be treated as layers

undergoing heat transfers, temperature changes, and moisture flows. Both

sides of the earth's interface, the 1 to 2 meter layer at either atmosphere

above or soil 'below, are coupled in a complex manner to this surface interface

by a variety of effects.

From a one-dimensional view of temperature alone, variations at the earth's

surface manifest themselves in two cyclic patterns of diurnal and annual

periods, due principally to the effects of diurnal and seasonal changes in

solar heating as well as gains and losses of available moisture. Beside

these two well known cyclic patterns, a third cycle has been identified which

occurs over a mesoscale period of roughly 3 to 10 days. This cycle, which

occurs in diurnal maxima and minima extrema, is the subject of this current

research.

RECENT ACCOMPLiSHMENTS

A number of data sets were plotted and statistically analyzed in order to

accentuate the existence and the characteristics of this mesoscale soil

temperature extrema variations and its relations to other parameters. The

cycle is initiated by a preciptation event, which bathes the soil and causes 

an immediate drop in the temperature extrema. This is followed by a tempera.

ture recovery period of roughly a week in the absence of any more precipitation. In a 5-month, March through July period in northern mid-latitudes

with no elongated periods of drought, the cycle can be expected to occur

approximately one to three times a month. This temperature less and recovery can be seen in Figure 1, in which drops in maximum soil temperatures

at depths of 5, 10 and 20 cm for the Tifton Meteorological Station in the

State of Georgia for the period of March through July of 1979 are plotted.

Other data plotted with maximum diurnal soil temperatures are maximum air

and evaporation pan (4' in diameter) temperatures, recorded precipitation

and pan evaporation°
5-18

This study was initiated using data from the State of Georgia, because of

the contrasting severe drought and non-drought years which occurred in the

late seventies-early eighties in that region. In contrast to the nondrought data in Figure 1, Figure 2 contains 1980 data which is characterized

by a severe 27-day drought period in May and June with only a trace of rainfall

on 1 day in this period. ' To eliminate soils as a critical factor in this

study, Iowa station data with completely different soil characteristics were

used in comparison with Georgian data. In order to broaden the contrast

further, Soviet data was used in a good year/bad year comparison for the years

1971 and :972, respectively. Other earlier data sets form Eastern Europe were

also included.

All data sets are being analyzed in order to determine regional characterization of drought conditions. A number of broad drought: descriptions were

considered additionally in conjunction with the station temperature extrema

data described above.

Analyses of the data sets have been directed toward the behavior of temperature extrema before and immediately after a precipitation event. With or

without a drought condition, the diurnal minimum soil temperatures at 10 cm

depth are highly correlated for 153 values, March through July diurnal values,

with both the diurnal minimum air and evaporation pan temperatures. This is

not to say that the 10 -cm minimum soil temperatures and minimum air and eva p oration pan temperatures have the same values without some offset, but only

that they are highly correlated statistically,. with a value greater than 0.85,

for those cases tested for both drought and non-drought conditions. The

presence of drought is manifested in a high correlation of diurnal maximum

values rather than diurnal minimum values, for the data sets of the 10 cm soil

temperatures, air temperatures, and evaporation pan temperaturES. The 10 cm

maximum soil_ temperatures and air temperatures move together under drought

conditions because solar radiation at the ground during the hottest part of

the day heats the soil and air together, with no energy loss to the evaporation of soil moisture. After a precipitation event, in the period when

the soil is hindered in regaining its original temperature because of heat

absorption by the evaporation process, it is again the diurnal maximum rather

than minimum soil temperatures that appear most sensitive. For all maximum

and minimum temperature data sets tested so far, the temperature recovery law

is:

T 8tx

where

T - extremum temperature minimum after a precipitation event

t - recovery time in days

x - exponent ranging between 0.52 < x < 0.92
SIGNIFICANCE

The correlations between diurnal temperature extrema for air and soil in

drought and non-drought periods appear to follow different characteristic

patterns, allowing an inference of soil moisture content from temperature

data. The recovery of temperature extrema after a precipitation event also

follows a characteristic exponential rise between two' limiting values which

is an indicator of evaporation rates. If these indicators can be applied

universally to regional temperature data, soil moisture content or droughtconditions can be inferred directly from temperature measurements.

FUTURE' EMPHASIS

An adequate statistical correlation testing of the 26 annual station data

sets which have been assembled and plotted will be completed. Ail 26 data

sets have already shown a similar characteristic temperature recovery after

a precipitation event. HCMM data will be used for regional temperature data

comparisons. An attempt will be made to inccrpft.rate this technique in estimates of ground water excesses related to seasonal variations of earth's

rotation/L.A.D. estimates. This work gill continue to be developed in consultation with Professor Helmut Landsberg of t;ne University of Maryland

REFERENCES

Brooks, F.A. and D.G. Rhoades, "Daytime Partition of Irradiation and the

Evaporation Chilling of the Ground," Trans. Amer. Geophys. Un., 35, No. 1,

February 1954, 145-152.

—

Landsberg, Helmut E., "Drought, A Recurring Element of Climate," World Meteorological Organization Special Environmental Report No. 5 Drought WMD No. 403

Geneva, Switzerland, Secretariat of the World Meteoro ogT i'ca1- Organization

1975, 40-61.

Lettau, Heinz, "Improved Models of Thermal Diffusion in the Soil,"" Trans.

Amer. Geophys. Un., 35, No. 1, February 1954, 121-132.

Palmer, W.C., "Meteorological Drought," Washington, DC, U.S. Department of

Commerce, Weather Bureau Research Paper No. 45, February 1965, 55pp.

Schmugge, T.J ., T.J. Jackson and H.L. Kim, "Survey of In-Situ and Remote

Sensing Methods for Soil Mosture Determinations," in Deutsch, M., Wiesnet,

D.R., and'Rango, A. eds. Satellite Hydrology American Water Resources Association, June 1979.

Vehrencamp John E., "Experimental Investigations of Heat Transfer at an

Air-Earth Interface," T rans. Amer. Geophys. Un., 34, No. 1, February 1953,

22-30.

Welker, J.F., "Thermal Infrared Remote Sensing of Surface Features for Renewable Reso:zrce Applications," NASA TM 82106, Greenbelt, MD, Goddard Space flight

Center, Jag-luary 1981, 26 pp.

5-19

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5-,21
PUBLICATIONS ANP PRESENTATIONS - 1982

1. Chao, B.F., "Excitation of Normal Modes on Non-Rotating and Rotating

Earth Models," Geophys. J. Royal Astr. Soc., 68, 295-315.

2. Chao, B.F., "A Fine Structure Analysis of the Earth's Polar Motion

Using ILS Data," EOS, 63, 903. (Presented at the Fall 1982 AGU

Meeting). r

3. Cheney, R.E., J.G. Marsh, and B.D. Beckley, "Global Mesoscale Variability from Repeat Tracks of Seasat Altimeter Data," J. Geophys. Res.,

' in press.

4. Cheney, R.E. and J.G. Marsh, "Ocean Current Detection by Satellite {._

ffi.

Altimetry," Proceedings of the Marne Technology Society, Oceans.

K.

5. Christodoulidis, D.C., D.E. Smith, P.J. Dunn, M.H..Tor " ence, S. Knode,

and S. Anders, "The SL5 Geodetic Parameter Solution," Proceedings of

Third International Symposium on the Use of Artificial el l i tos for Sat

.r Geodesy and Geodynamics, National Technical University, Athens, Greece.

6. Cohen, S.C., "A Multilayer Model of Time Dependent Deformation Following

an Earthquake on a Strike-Slip Fault," J. Geophys. Res., BY, 5409-5421.

7. Cohen, S.C., "Postseismic Deformation Due to Subcrustal Viscoelastic

Relaxation Follwing Dip Slip Earthquakes," NASA TM 84005.

5421.

8. Cohen, S.C., "Discussion of Models of Postseismic Rebounds," EOS Trans.

Am. Geophy. Un. (abstract), 63, 429.

9. Cohen, S.C., "Crustal Deformation During the Earthquake Cycle Temporal

and Spatial Dependence, "Fifth Annual NASA Geodynamics Program

Conference (abstract), p. 59.

10. Dunn, P.J., M.H. Torrence, D.C. Christodoulidis and D.E. Smith,

"Earth Scale and Orientation from Lageos," EOS Trans. Amer. Geophys.

Union, 63, 45.

11. Gross, R.S., 1982, "A Matched Filter for the Chandler Wobble," EOS

Trans. Amer. Geophys. Union, 63, p. 903.

-- 

12. Kahn, W.D., et al., "Mean Gravity Anomalies from a Combination of

Apollo/ATS and GEOS-3/ATS-6 SST Tracking Campaigns.," J. Geophys. Res.,

Vol. 37, No. B4, pp 2904-2918, April 10.

} 

s

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i
PUBLICATIONS AND PRESENTATIONS - 1982 - (Continued)

13. Kahn, W.D., and T.L. Felsentreger, "Signal Analysis and Error Analysis

Studies for a Geopotential Research Mission (GRM)," NASA TM 83970,

July.

14. Kahn, W..D., et al., "The Airborne Laser Ranging System, Its Capabilities

and Applications," NASA TM 83984, September.

15. Kahn, W.D., "ALRS Simulation Studies," Fourth Annual Conference on the

NASA Oeodynamics Program, Greenbelt, MD 1982.

16. Kolenkiewicz, R., D.E. Smith, M.H. Torrence, P.J. Dunn and D.C.

Christodoulidis, "Satellite Laser Ranging Techniques in Geophysical

Research," European Geophysical Society and European Seismological

Commission, the University of Leeds, England.

17. Krabill W., C.F. Martin and F.E. Hoge, "Baseline Monitoring Using

Aircraft Laser Ranging--Spaceborne Laser Simulation and Aircraft

Laser Tracking," NASA TM 73298, June.

18. Krabill, W., L.E. Link and R.N. Swift, "A Prospectus on Airborne Laser

Mapping Systems," 1982 COSPAR, May.

19. Krabill, W. and R.N. Swift, "Preliminary Results of Shoreline Mapping

Investigations Conducted at Wrightsville Beach, North Carolina,"

Proceedings of Corps of Engineers Hydrographic Survey Meeting,

Jacksonville, Florida, February 1982.

20. Lerch, F.J., J.G. Marsh, S.M. Klosko and R.G. Williamson, "Gravity

Model Improvement for Seasat," J. Geophys. Res., Vol. 87, 3281-3296,

April 30, 1982.

21. Lerch, F.J., S.M. Klosko and G.B. Patel, "A Refined Gravity Model from

Lageos (GEM-L2)," Geophys. Res. Lett., Vol. 9, 1236-1266, November

1982.

22. Lerch, F.J., "Gravity Model Errors in SLR," Crustal Dynamics Conference, Greenbelt, MD,. 1982 (presentation).

23. Lerch, F.J., "A Refined Gravity Model for Lageos (GEM L2)," Fall 1982

AGU Meeting, San Francisco, 1982 (presentation).

24. Lerch, F.J., "Gra y sat Simulations at GSFC," Fourth Annual Conference

on the NASA Geodynamics Program, Greenbelt, MD 1982.

v

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11-
PUBLICATIONS AND PRESENTATIONS - 1982 (Continued)

25. Liu, Han-Shou, "Geodynamics of the Baikal-Stanovoy Seismic Belt,"

Physics of the Earth and Planetary Interiors, Vol. 31, 77-82, 1982.

26. Liu, Han-Shou, "A Dynamical Basis for Crustal Deformation and Seismotectonic Block Movements in Central Europe," NASA TM 84933, 1982.

27. Marsh, J.G. and T.V. Martin, "The Seasat Altimeter Mean Sea Surface

Model," J. Geophys. Res., Vol. 87, No. C5, 3269-3280.

28. Marsh, J.G. and R.G. Williamson, "Seasat Altimeter Timing Bias Estimation," J. Geophys. Res., Vol. 87, No. C5, 3232-3238.

29. Marsh, J.G., R.E. Cheney, T.V. Martin and J. McCarthy, "Computation of

a Precise Mean Sea Surface in the Eastern North Pacific Using Seasat

Altimetry," EGOS Trans. Amer. Geophys. U., Vol. 63, No. 9, 178-179.

30. Marsh, J.G., R.E. Cheney, T.V. Martin and J.J. McCarthy, "Mean Sea

Surface Computations in the Northwest Pacific Based Upon Satellite

Altimeter Data," Proceedings of the General Meeting of the IAG, Tokyo,

May 7-15, 1982; J. of the Geodetic Society of Japan, 454-465.

_ 31. Marsh, J.G., T.V. Martin, and J.J. McCarthy, "Global Mean Sea Surface

` Computation Using GEOS-3 Altimeter Data," J. Geophys. Res., Vol. 87,

No. B13, 10955-10964.

32. McAdoo, D.C., R. Kolenkiewicz, C.F. Martin and S. Poulose, "The

` Correlation of Bathymetry with Geoid Heights Near Trenches of the

s North Pacific," EOS 63, No. 5,907, (abstract).

ik

33. McAdoo, D.C., "Ithaca Chasma: A Product of Tidal Stress on Tethys," EOS

63, No. 18, 365, 1982 (abstract).

34. Mognard, N.M., W. Campbell, R.E. Cheney, J.G. Marsh and S. Ross, "South

Ocean Waves and Winds Derived from Seasat Altimeter Measurements,"

Wave Dynamics and Radio Probing of the Ocean Surface, in press.

35. Mognard, N.M., W.J. Campbell, R.E. Cheney and J.G. Marsh, "Southern

x Ocean ,Mean Monthly Waves and Surface Winds for Winter 1978 by Seasat 

w Radar Altimeter," J. Geophys. Res., in press. 

36. Rubincam, D.P., "On the Secular Decrease in the Semimajor Axis of

La eos's Orbit," Celestial Mechanics, 26, 361-382 (1982).

°. 37. Rubincam, D.P., "Information Theory Lateral Density Distribution for

Earth Inferred from Global Gravity Field," J. Geophys. Res., 87, 5541-

5552 (1982).

A-3
PUBLICATIONS AND PRESENTATIONS - 1982 (Continued)

38. Smith, D.E., P.J. Dunn, D.C. Christodoulidis and M.H. Torrence, "Global

Baselines from Laser Ranging," Fourth Annual Conference on NASA

Geodynamics Program, Greenbelt, MD 1982.

39.

Torrence, M.H., D.C. Christodoulidis, P.J. Dunn, S. Knode, S. Anders,

R. Kolenkiewicz, G. Wyatt and D.E. Smith, "Geodetic Parameters from

Laser Tracking of the Lageos Spacecraft," EOS Trans. Amer. Geophys.

Union, 63, 18.

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ACKNOWLEDGMENTS

We would like to acknowledge the support provided by the following:

Business and Technological Systems, Inc.

T. S. Englar, Jr.

R.H. Estes

Computer Sciences Corporation

G.B. Patel

EG&G/Washington Analytical Services Center, Inc,

W.T. Wells J.J. McCarthy

C.F. Martin A. Brenner

P.J. Dunn H.J. Rhee

T.V. Martin R.G. Williamson

M:H. Torrence B. Beckley

W.F. Eddy N.L. Boulware

S.M. Klosko D.D. Rowlands

Pacer Systems, Inc.

C. Boss

Republic Management Systems

R.A. LeDoa:;,,

M.A. Abresch

S. Blackwell

S.M. Fricke

S.G. Poulose

N.R. Weiss

i