LectureNotesin
EarthSciences
Editedby Somdev Bhattacharji,GeraldM. Friedman,
HorstJ. Neugebauerand AdolfSeilacher
29
FritzK. Brunner ChrisRizos(Eds.)
in
Developments
Geodesy
mensional
Four-Di
Selectedpapersof the
Geodesy
RonS. MatherSymposiumon Four-Dimensional
Australia,March28-31, 1989
Sydney,
@
Springer-Verlag
HongKong
LondonParisTokyo
NewYork
BerlinHeidelberg
Lambeck, K., 1990. The fourth dimension in geodesy: observing the deformation of the Earth. In: Developments in Four-Dimensional
Geodesy, (F.K. Brunner and C. Rizos, Eds), Springer-Verlag, 1-14.
The Fourth Dimensionin Geodesy:
Observingthe Deformationof the Barth
K. Lambeck
ResearchSchool of Earth Sciences
Australian National University
Canberra, Australia
ABSTRACT:
The earth is a complex body that deforms over a wide range of length and times scales.
Observationof thesedeformationsconstrainmodelsof the unknolin forces (e.g.,plate
tectonicsdriving forces)and modelsof the planet'sresponseto known forces(e¿.Jtidal or
rotationalforces). Geodeticmeasuremens,in particilar thosebasedon the irira trigtr
preciSionspace-age
technologies,
a¡e centralto ttrelniOyof thesedeformations.The geodeãc
measurements
cover time scalesof hours to decadesand occasionallyto a centuryoilonger.
This is.only a-smallpart of the whole deformationspectrum.Otherþartsare auãilablefrãm
geologicaland geomorphological
observations(at the low frequencyenO¡and from seismic
instrumentation
(at thehigh frequencyend). The geodeticdataprovidesan importantbridging
of these-otherdata_types. They will elucidateknown phenornenathat preiently only"risË
marginallyabovethe noisefevels of exisringmethodologies
and new sìgnals*iU ufp"*"
When combinedwith new developmentsoccurringin other areasof ttreãartn sciencästhe
geodeticmethodologieswill contributesignificantly to our understandingof the working of
theearth.
l.INTRODUCTION
The titie of four dimensionalgeodesyfor this conferencerecognisesthat the time
element is an integral part of understandinggeodetic measurements. In the past
geodesistshave tendedto think of the Earth as a staticbody, occasionallydistortedby
earthquakesor its surface punctured by volcanic eruptions. This view is largely
understandablebecausethe time scaleof the more global and obvious deformationshave
been much longer than our own life spans. But when the Earth is viewed on geoiogical
time scaleswe see a yery different story. Far from being static, we see a planet that is
rent asunderat ocean ridges. We see the buckiing of continents in collision and crust
'We
seeislandsánd mountains rising out of the sea
being recycledback into the mantle.
and large segmentsof crust subsiding. Once the time scale is collapsed we see a very
dynamic Earth indeed. But even on the human time scale the planet is indeed an acrive
entity once it is put under the microscopeof modern geodeticmeasurements.Tidai and
rotational deformations occur with periods of hou¡s to years. Global deformationsof
the planet occur on a variety of time scalesin responseto changing surface loads in the
atmosphere,oceansand hydrosphere.
V/ith the methodsof spacegeodesynow alaiiable a largepart of the spectrumof these
deformations has risen above the measurementnoise level but another large part still
remains inaccessiblebecauseof the very long time scales involved. This part of the
record remainslocked up in geologicalobservationsand one of the challengesof modem
geodesyis to integrate this part of the spectrumof the Earth's deformation with that part
estabüshedby geologicai observationsand, at evenhigher frequencies,with that part of
the spectnrmexplored by seismologists.(Geodesycan be seenmerely as high frequency
geology or as low frequency seismology.) The challengeis to estabiish the links with
records.containedin rocks such as the one illustratedin Figure 1a with the observations
derived from the radio telescopeillustrated in Figure lb. h this case the two span the
extreme ends of the spectrum of the Earth's deformations. This particular rock from
Western Australia contains 4.2 biilion year old minerals, the oldest known terrestrial
material. It indicates that crust was already being created and destroyed at that time.
Between 2.67 and 3.1 billion years ago the sedimentshosting these minerals were
depositedand buried to a depth of more than 15 km and subjected to temperaturesin
excessof 500'C. Later it found its way back to the surface where it has remained for
perhapsthe past billion years. In comparison,the deformations recordedby the radio
telescope(Figure lb) at the other side of the world representonly a miniscule f¡action
of the Earth's history.
(b)
Figure 1:
Two recordersof Earth Deformation.
(a) A conglomeratefrom the Jack Hills area of Westem Asutralia which
contains a record of Earth deformationspanning4.2 billion years.
(b) A radio telescopeused for long baselineinterferometric observationsof
Earttr deformation on time scalesof-hours to years.
4
2. GEODESY AND THE PLATE TECTONICS HYPOTHESIS
The plate tectonicshypothesishas provideda marvellous synthesisof much of the
dynamic behaviour of the Earrh for the past lÙVoof the pianet's history. ln the present
climate when questions of relevance are constantly being raised it should not be
overlooked that the hypothesis has been more than simply an exciting scientific
development. It has also led to an understandingof mineralization processesand
hydrocarbon accumulation that are leading to new resourcediscoveriesin a number of
different tectonic settings. Also important,at leastfor a small segmentof society,is that
the hypothesis has given a new lease of life to the subject of geodesy. With the high
accuracy instrumentation that is now availablethere is simply no place for static Earth
concepts. The planet must be seen as a deformablebody over a wide range of time
scales. This is well recognizedby this conferencewith its emphasison the fourth
dimension.
The hypothesis is essentiallya kinematic one in which averagemotions of large
tectonic units occur, one relative to another. What permits the motion to occu¡ is
largely a matter of describingwhat happensat the boundariesbetweenadjacentplates.
Cartoons of subduction tectonics and of oceanridge spreading (Figure 2) are familiar
parts of the Earth scienceliteraturebut what is less well understoodis the quantifTcation
'We
need to know tlte forcesoperating and we need to know the
of the processinvolved.
rheology of the Earth; how it respondsto these forces. Here geodesypiays an
important role.
o
Continental plate
!
o
q
Occanic platc
h
Fisure2: Cartoon of some of the tectonic processesoccurring at plate margins. New
crust forms at the ocean ridge to be subductedback into the mantle at a later
date. The various forces F operating are understood largely in quaiitative
terms only.
t
One axiom of the plate tectonicshypothesisis that the plate motions are uniform on
time scalesof a million yearsor longer but this may be an artifact of the resolutionof
the geological observations. What is requiredis high temporal resolution of the plate
motions and this is an obvious role for geodesy. A number of recent geodetic
experiments are showing that the present-daymotions are very similar to average
motions for the past few million years,(e.g. Smith et al. 1989; Stolz et al. 1989). The
implications of this are important for it suggestsa sufficiently tight coupling between
lithosphere and asthenospherefor the plates not to respond episodically and abruptly to
changesin stressat the plate margins.
The inter-plate motions can be expressedin a number of ways, as baseline expansion
rates, for example, or as relative rotation rates of the plates. The latter are particularly
useful becausethey are independentof estimatesof the height component of the stations,
generally the least well determined coordinate. Furthermore, they permit straightforward comparisonsto be made with the geologicalestimatesfor the rotation vectors of
the plates. Table 1, from Lambeck (1989), illustrates results based on the baseline
expansionratesbetweenthe Australian, Pacific and Eurasianplates of Smith et al. (1989)
and the results are essentially in agreementwith the geological estimatesof Minster and
Jordan(1978).
Another axiom is that the plate boundaries,usually drawn as simple lines on maps,are
sharply defined and that all inter-plate motion occurs on these boundaries. Closer
inspectionof the geology or seismicevidenceindicatesthat more often than not these
deformationsoccur over a wide zone and the line on the map turns into a complex zone
of up to 500 km or more wide. Here ttre geodeticobservationsagain play a role, in this
casein defining how the motions betweenadjacentplates are absorbed; in defining the
strain field across the boundarv from which the stress field can be deduced if the
rheologyis known.
Conventionalgeodeticmeasurementshave been important here. Much of what we
know about the stress-straincycle at plate boundaries of the transform type was, for
example,already elucidatedearly this century thanks to geodetic measurementsmade on
the San Andreas Fault of Califomia (NOAA, 1973). Considerableinsight into the stressstrain cycle at subductiontype convergentmarginshas been derived from early geodetic
observationsin Japan (Tsuboi, 1933). Particularlyillustrative have been the geodetic
observationsof the past cenrury for New 7*aland becauseof the way in which the
geodeticdisplacementshave been transformedinto strain and relative velocities that can
be compared directly with the palaeomagneticevidencefor plate motions (Walcott,
1984).
6
Table 1: Baselineexpansionratesds/dt(from Smith et al. i989) and relativeraresof
rotations estimatedfrom individuai baselines,and relative rotation rates from Minster &
Jordan(1978)
Baseline
Australian-Pacificplate
Orroral-Hawaii
Orroral-Huahine
Yaragadee-Hawaii
Yaragadee-Huahine
ds/dt
(mm/a)
11!À
-T
I!+
-8614
-89!2
-78!4
Mean
Minster & Jordan(i978)
Pacific-Eurasianplate
Hawaii-Simosato
Huahine-Simosato
-68r4
-78!7
Mean
Minste¡ & Jordan(1978)
Eurasian-Australianplate
Simosato-Orroral
Simosato-Yaragadee
Mean
Minster & Jordan (1978)
-5515
-6%3
Q("/Ma)
oo("/Ma)
1.407
1.638
r.077
1,.397
0.073
0.076
0.024
0.072
r.r73
t.25
0.065
0.02
-0.662
-0.720
0.039
0.065
-0.677
-0.98
0.045
0.03
-0.573
-0.555
0.052
0.0n
-0.558
-0.70
0.041
0 02
7
'What
thesestudieshaveemphasizedand what is equallyimportantfor thenew classof
spacetechnologybasedinstrumentation,
is:
(i)
The strain fields acrosspiate boundariesare considerablymore significant
than displacementsbetweenisolatedpoints on adjacentplates. A high density of points is
required acrossthe margin in order to establishttre strain field.
(ii)
Short seriesof high-precisionobservationsare no substitutefor long series
of observationsrepeatedfrequently. In some instancesa high frequency of repeat
observationsmay actually be more important than very high precision, although the
latter is of course always desirable. New surveys,particularly with GPS, will therefore
be much enhancedif they are built on older geodeticnetworks.
(iii)
Integrationwith geologicaland geophysicaldatais essential.
A further axiom is that the plates,away from their boundaries,behaveessentiallyas
rigid bodies,moving over the globe relativeto eachother without undergoingdistortion.
It would be truly remarkableif the ïrregular shapedplates, acted on by a variety of
forces along its boundaries,can move relativeto eachother over an ellipsoidallyshaped
surface without undergoing some intemal deformation. What this axiom implies,
therefore, is that either these deformations are small compared wittr the motions at the
plate boundaries or that these internal distortions are very small when averaged over
intervals of millions of years. That the plates undergo some intemal deformations can
be seen in the seismicity that occurs within plates well away from known plate
boundaries. The Australian continent,generallybelievedto be tectonically stable,has
been subject to significant seismicactivity ever sincemonitoring began (Figure 3). What
is required is high temporalresolutionof the plate motions. Clearly this is a role for
geodesy. A number of recent studiesare showing that the internal deformations,if
occurring, are smaller than the intraplate motions but it remains important that this
axiom is continually tested in any experiment for measuring inter-plate motions, if for
no other reason that is provides a test of the validity of the geodetic experiment. The
Smith et al. (1989) solution, for example,gives non-zero baseline expansionrates for a
number of intraplate baselines but it would be premature to conclude that plate
deformation occurs.
Important in the geodetic studies of plate tectonics is the measurementof vertical
movement. With the emphasisplaced on the horizontal displacementsthere has been a
tendency to neglect the vertical component. This is understandablefor not only is this
latter component much smaller, it also does not exhibit the simple global pattems
exhibited by the horizontal displacements.Nevertheless,they are an essentialingredient
in the study of the Earth's deformation. In particular, vertical movements are often
manifestations of horizontal forces at work and major uplifts are possible. Spectacular
examplesinclude the Huon Peninsulaof Papu.aNew Guinea where uplifts of 400 m in as
3
little as 100000 years have occurred in responseto the compressionalinteractions
betweenthe Australian and Pacific plates.
Figure 3:
Map of Australian seismicity of events of magnitude 4 or greater recorded
from 1873-1980. The seismicity to the north defines the northern boundary
of the Australian plate. AG refers to the Late Proterozoic-Cambrian
Adelaide Geosynciineand LFB refers to the PalaeozoicLachlan Fold Belt.
Two zones of innaplate deformationsuggestedby CIeary and Simpson
(1971) are indicatedby the dashedlines.
3. GEODESY AND TT{E HIGH FREQUENCY DEFORMATIONS OF TFIE EARTH
Plate tectonics does not provide the sole rationale for developing the geodetic
discipline. In particular, the planet undergoesa number of defomrations at periods
shorterthan the geological time scalewhose closerinvestigation is of intrinsic interestas
well as of relevanceto underståndingttre workings of the planet on the longer time scale.
To understand the workings of the Earth requires a knowledge of the forces acting on
the Earth and of the responseof the planet to theseforces. In some instancesthe forces
are well known, such as the tide raising gravitationalpotential or the centrifugal force.
Here the observations of the responseof the planet establishesa stress-stminrelation
whose proportionality constantsdefine the rheology of the pianet appropriate for this
I
particular problem. In a secondclass of problemsdeformationsare observedbut the
forces are largely unknown. One example of ttris is the nature of coupling of core
motions to the mantle and vice-versa. Here a rotational response is observedand
attributed to such a generalmechanismbut whether this coupling is electromagnetic,
viscous, or topographic remains largely a matter of choice (Lambeck, 19g0). The
former class of problems, of srudying the stress-strainrelation, is of considerable
importance. In the caseof the tidal deformations,for example, the rheological constants
are usually expressedas Love numbersand phaselags or attenuationfactors, and the
central problem is to obtain representativeobservationsof small deformations over the
tidal spectrum' Becauseof attenuationof stresscycles both the Love number magnitude
and the phaselag are expectedto be frequencydependentand the objective is to measure
their dependencyover ttre tidal band from 12 hoursto 18.6years. This task is not easy.
Ocean tides contaminatethe results and over the longer periods tectonic deformation
may mask the tidal signals. Models for the fluid tides need to be improved but this in
itself requiresthat the Earth'sresponseto surfaceloading be known. The two types of
tidal deformation- solid and fluid - are inextricablylinked. Yet progressin this areais
desirablefor it will improve both solid Earth and ocean understanding. The longer
period tidal deformationsare also contaminatedby meteorologicalsignals,including
the
loading of the Earttr'ssurface,ocean and land, and this needsto be taken into accountas
weIl.
The waxing and waning of the ice sheetsprovidesanotherexample of quasi-periodic
forcing of the Earth. The Late Pleistocenecollapseof the ice sheetsand the addition
of
water into the oceansresults in a redistribution of the surface loads on the Earth.
The
result is crustal subsidencewhere the water load is increasedand crustal rebound where
the ice sheethas vanished. Globally, the flow induced in the mantle changesthe inertia
tensor and gravity field of the planet with the concomitantchangesin rotation. The
glacial rebound problem differs from the tidal problem in several ways.
First, the
characteristicperiod of the former is of the order of 10000 years and only the tail-end
of the last cycle of deformationcan be observedby geodetictechniques. Second,
the
load has a much greater spatial variation than the tidal force and the Earth's response
contains, in consequence,a correspondinglygreater amount of information
of the
Earth's rheology' Third, the load is only partly known and the further back
one goes in
time the more poorly it is known and the more uncertain become the estimates
of the
response. Geodetic observations alone do not suffice to resolve this problern:
geomorphologicalevidenceof past vertical movementsof the crust
relative to sea-level
provide an essentialdata set and glaciological evidenceand arguments
are an important
input into the reconstructionof the load function.
At longer periods anotherexample of surfaceloading problems is provided
by the
loading of the crust by large volcanic structures,particularly in oceanic environments.
Here the loading occurs on the time scaleso¡ 166-yearsand the responseis measured
in
10
terms of the net displacemens of the crust, either directly by measuringthe shapeof the
sea-floor topography or by geomorphologicalevidence of the uplift of surrounding
islands, or inferentially by measuringgravity or geoid height. Here the load is aknostas
great an unknown as the responseand the supplementaryobservationsare from
andgeology.
seismology,geomorphology,geochronology
What these various observationspermit us to establish,at least in principle, is a
spectrum of Earttr deformations from which the rheology function can be established.
The range of relevant processesare illustrated in Figure 4. The rheoiogy function will
nor be simple. Firstly, it will exhibit some depth dependencewith high strengthfor the
lithosphere and low viscosity for the asthenosphere.Secondly,the fiurction wiil exhibit
frequency dependence. At the seismic end of the spectrum the mantle responds
primarily as if elastic and anelastic effects are secondarY,but at very long periods,
corresponding to seamount lóading for example, the mantle behaves essentially as a
fluid. How the function varies at the intermediatefrequencies remains unclear and a
worthy objective for geodetic studies. Thirdly, the function may also exhibit stress
magnitude dependence,with the planet respondingfaster to large loads than to smal^
loads. Fourthly, the function will certainly exhibit lateral variations for there is
abundantgeophysicaievidencefor lateralvariationsin a vaúety of physical propertiesof
the Earth. Once this function, or parts of it, is mapped it becomes possible to make
predictions about the mechanical forces responsible for the other deformations. It
becomespossible, for example, to draw conclusionsabout mantle convection and the
driving forces of plate tectonics. If, for example, the mantle viscosity increases
significantly with depth then convection may be largely restricted to the upper mantle.
Little mixing with the lower mantle may result and lead to different chemical and
isotopic signatures of the volcanism at ocean islands and mid-plate hotspots. If the
mantle viscosity is more uniform then a greaterdegreeof mixing of the upper and lower
regions of the mantle may occur and the chemical composition is likely to be more
homogeneous. Clearly any geodeticobservationsttrat lead to improved mantle viscosity
estirnates make an important contribution in constraining models of the Earth's
evolution.
IVhat geodetic observationsare important here? Global graviry field or geoid height
measurementsare one obvious answer. The "secular" part of the field constitutesa
measureof the responseof the Earth to the very long period forces associatedwith plate
tectonics and mantle convection. There would be little dispute these days with the
argumentthat this field reflects the dynamicsof the Earttr'smantle on time scaiesof 106168 years and that it constrains,in principle at least, models of mantle convectionand
plate driving forces. After all, convection in its simplest definition is the motion
resulting from the gravitational forces acting on laterai and radial density variations.
But just how to use theseobservationsmost effectively remains a difficult matterbecause
of the fundamental non-uniquenessof interpreting gravity fields. Complementary
t l
geophysicaldataarerequiredandthemostexactingonescomefromthemethodsof
structure of the mantle is being
seismic tomography Uy it ictr the three dimensional
1984)' But much progressneedsto
rnapped(e.g. Dziewonrki, 1984;Woodhouseet al''
resolution that begins to approachthe
be made in this discipline before we have a spatial
Nevertheless'the combination
resolution attainable with gravity or geoid oúservations.
provide important new insights into the
of the gravity and seismic data is begirLningto
mantleviscosity (Richardset a1.,1984)'
Measure of non'elastic behaviour
hlgh attenuatlon
low attenuatlon
GlobalgravítY,i7o^o,,tt
I s o s t a s Y r!'t ,
I
year líilet
/
'U
Chandler
Þ
Seasonal íiles
I
zo
x
t
I
' Free
I
l
I
r
oa
Figure 4:
t
I
wobble
I
oscillatíons (seísmíc)
r
lBody wøves
l
t
;
!
Lob,irrotory exPerímeÅ¡s
I
I
function is not
-Several 'nìt:r:"-'-'--T:.*r"togvspectrum of Earth-deforming
may
î.ñÀruti. examples of how this function
(cannor *iilin;å.
vary with frequencYare snoliln'
in understandingthe long term
The gravity observationsplay another important role
structure' The altimeter
dynamics of the mantle thiough the study of lithospheric
image of the gravity field over
satelliteshave provided an unprecedentedhigh resolution
images over the continents
the oceans(e.g. Haxby et al., 1983)but comparableresolution
up of national borders to
await a new generationof satellitesor the rapid opening
combined with seismic and other
terrestrial gravity surveys. The altimetry data, when
of the evolution of
geophysicaland geological observations,has led to the understanding
and provides constraintson the
the mechanical prope-niesof the ocean iithosphere
convection' The altimeter
boundary conditions that this layer imposeì on mantle
12
satellites have also led to the identification of numerousnew features
in the oceanfloor
and have provided one of the best ways to provide an approximate
but quick surveyof
the oceanfloor topography.
The time dependenceof the gravity field has been an important
subject of study for
many decades through the measurementsof the tidai
deformations. Important
developmentshave been the high precision absolutegravity merers
and the higiriy stable
cryogenic gravimeters for measuring the terrestrial deformations
out of the seismic
frequency band- of considerablesignificance are the measurements
of the long period
tides and the rotational tide, or pole tide. one parameterof interest
is the lag in the
responseof the Earth to the tide raising potential aithough very
few, if any, sigìriRcarrt
measurements yet exist, in part because of unknown instrumental
lags *d in purt
becauseof the oceanographicpernrrbationsof the solid tide signai.
The ocean-solidtide
inte¡action remains a problem and a close inte¡action with physica.L
oceanographyis
essential' The other parameterof importanceis rhe amplitude
of the tidai iesponse,
particularly the frequency dependenceof the amplitude
urros the diurnal band of the
spectrum becauseof the core resonancephenomenon(wahr,
l9g1). The amplitude
variation over the longer periods resulting from the planet's
deparnrrefrom elasticity
have the potential of measuringthe non-elasticresponseover
a frequencyrangefrom
hours to years but here also the resultsare perturbedby ocean
tides and, at the seasonal
frequencies,by meteorologicalfactors.
The terrestrial measurementsof the tidal responseis contained
in Love number
combinationsof the form (l+,tn-k) or (1+2hn/n-kiØ+I)ln with
mosr observationsbeing
limited to n=2. These functions are less sensitiveto the frequency
dependentprocesses
than the individual Love numbersthemselvesand an important
developmentof the past
decade has been the ability to measurethe potential Love
number kn alonefrom the
analysesof satellite orbits. Othe¡ than this response,the
displacementLove numbers
hn,ln ate worth investigating more closely becausethey reflecì
more regional and even
local responsesand becausethey provide independentmeasures
of the pianet'selasticand
aneiasticparameters.
Also important are the high precision analysesof the LAGEOS
satellite orbit for
time-dependenceof the gravity field through the measurement
of the time dependenceof
the zonal stokescoefficients-/¿. Recentresultsby Cheng
et al. (19g9) are particulariy
interesting.
4. CONCLUSION
From the few examplesraisedhere it is clear that the Earth
is a very dynamic planet
in whose study the geodeticmeasurementsare playing
an ever increasingrole. The
essentialcharacteristicof the geodeticmeasurements
is that it fills a gap in the time
spectrumbetweengeological observationson the one end
and seismic observationsat the
13
other end. Geologicalmodel predictionscan be testedwith geodeticmeasurements
and
missing elements of the geological models can be filled in, thereby expanding the
usefulnessof the model conceptsfor extrapolationto present-dayor future tectonic
settingsas in subductionzonesor in sea-levelchange.
The very nature of many of the deformation phenomenarequires observational
records that extend over many years. ln consequence,the new measurementprocedures
basedon the space-agetechnologieshavenot yet madea major impact. yet new signals
are already rising beyond the noise levels and the promises that proponents of the new
measurementmethodshave been making for two decadesare now being delivered. It
would be hazardousto predict where the new resultswill lead: new responsesto known
driving forces will be discovered and new mechanismswill be postulated as
developmentsoccur in other areasof the Earth sciences; in seismic tomographyor in
core dynamics,for example. One reasonwhy this prediction is hazardousis that the
levels of observation are now such that thêy are much contaminatedby environmental
factors and what is required in order to exploit the new results fully is a parallel
program of measuringregional and global atmospheric-oceanic-hydrologic
parameters;
winds, wind-stress,atmosphericpressure,sea-leveland oceancirculation, ground water
storageand snow and ice coverage. Much of this would be tedious if it were not for the
fact that such data compilationswill also advancetheseenvironmentalsciences,but the
rewardsare potentially great. The exciting work is only beginning.
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